A wide angle and high Mach number parabolic equation.

PubMed

Lingevitch, Joseph F; Collins, Michael D; Dacol, Dalcio K; Drob, Douglas P; Rogers, Joel C W; Siegmann, William L

2002-02-01

Various parabolic equations for advected acoustic waves have been derived based on the assumptions of small Mach number and narrow propagation angles, which are of limited validity in atmospheric acoustics. A parabolic equation solution that does not require these assumptions is derived in the weak shear limit, which is appropriate for frequencies of about 0.1 Hz and above for atmospheric acoustics. When the variables are scaled appropriately in this limit, terms involving derivatives of the sound speed, density, and wind speed are small but can have significant cumulative effects. To obtain a solution that is valid at large distances from the source, it is necessary to account for linear terms in the first derivatives of these quantities [A. D. Pierce, J. Acoust. Soc. Am. 87, 2292-2299 (1990)]. This approach is used to obtain a scalar wave equation for advected waves. Since this equation contains two depth operators that do not commute with each other, it does not readily factor into outgoing and incoming solutions. An approximate factorization is obtained that is correct to first order in the commutator of the depth operators.

Effect of current on spectrum of breaking waves in water of finite depth

NASA Technical Reports Server (NTRS)

Tung, C. C.; Huang, N. E.

1987-01-01

This paper presents an approximate method to compute the mean value, the mean square value and the spectrum of waves in water of finite depth taking into account the effect of wave breaking with or without the presence of current. It is assumed that there exists a linear and Gaussian ideal wave train whose spectrum is first obtained using the wave energy flux balance equation without considering wave breaking. The Miche wave breaking criterion for waves in finite water depth is used to limit the wave elevation and establish an expression for the breaking wave elevation in terms of the elevation and its second time derivative of the ideal waves. Simple expressions for the mean value, the mean square value and the spectrum are obtained. These results are applied to the case in which a deep water unidirectional wave train, propagating normally towards a straight shoreline over gently varying sea bottom of parallel and straight contours, encounters an adverse steady current whose velocity is assumed to be uniformly distributed with depth. Numerical results are obtained and presented in graphical form.

Three-dimensional wave-induced current model equations and radiation stresses

NASA Astrophysics Data System (ADS)

Xia, Hua-yong

2017-08-01

After the approach by Mellor (2003, 2008), the present paper reports on a repeated effort to derive the equations for three-dimensional wave-induced current. Via the vertical momentum equation and a proper coordinate transformation, the phase-averaged wave dynamic pressure is well treated, and a continuous and depth-dependent radiation stress tensor, rather than the controversial delta Dirac function at the surface shown in Mellor (2008), is provided. Besides, a phase-averaged vertical momentum flux over a sloping bottom is introduced. All the inconsistencies in Mellor (2003, 2008), pointed out by Ardhuin et al. (2008) and Bennis and Ardhuin (2011), are overcome in the presently revised equations. In a test case with a sloping sea bed, as shown in Ardhuin et al. (2008), the wave-driving forces derived in the present equations are in good balance, and no spurious vertical circulation occurs outside the surf zone, indicating that Airy's wave theory and the approach of Mellor (2003, 2008) are applicable for the derivation of the wave-induced current model.

Propagation and attenuation of Rayleigh waves in generalized thermoelastic media

NASA Astrophysics Data System (ADS)

Sharma, M. D.

2014-01-01

This study considers the propagation of Rayleigh waves in a generalized thermoelastic half-space with stress-free plane boundary. The boundary has the option of being either isothermal or thermally insulated. In either case, the dispersion equation is obtained in the form of a complex irrational expression due to the presence of radicals. This dispersion equation is rationalized into a polynomial equation, which is solvable, numerically, for exact complex roots. The roots of the dispersion equation are obtained after removing the extraneous zeros of this polynomial equation. Then, these roots are filtered out for the inhomogeneous propagation of waves decaying with depth. Numerical examples are solved to analyze the effects of thermal properties of elastic materials on the dispersion of existing surface waves. For these thermoelastic Rayleigh waves, the behavior of elliptical particle motion is studied inside and at the surface of the medium. Insulation of boundary does play a significant role in changing the speed, amplitude, and polarization of Rayleigh waves in thermoelastic media.

A depth-averaged 2-D shallow water model for breaking and non-breaking long waves affected by rigid vegetation

USDA-ARS?s Scientific Manuscript database

This paper presents a depth-averaged two-dimensional shallow water model for simulating long waves in vegetated water bodies under breaking and non-breaking conditions. The effects of rigid vegetation are modelled in the form of drag and inertia forces as sink terms in the momentum equations. The dr...

Development of an Integrated Modeling Framework for Simulations of Coastal Processes in Deltaic Environments Using High-Performance Computing

DTIC Science & Technology

2008-01-01

exceeds the local water depth. The approximation eliminates the vertical dimension of the elliptic equation that is normally required for the fully non...used for vertical resolution. The shallow water equations (SWE) are a set of non-linear hyperbolic equations. As the equations are derived under...linear standing wave with a wavelength of 10 m in a square 10 m by 10 m basin. The still water depth is 0.5 m. In order to compare with the analytical

Approximation of wave action flux velocity in strongly sheared mean flows

NASA Astrophysics Data System (ADS)

Banihashemi, Saeideh; Kirby, James T.; Dong, Zhifei

2017-08-01

Spectral wave models based on the wave action equation typically use a theoretical framework based on depth uniform current to account for current effects on waves. In the real world, however, currents often have variations over depth. Several recent studies have made use of a depth-weighted current U˜ due to [Skop, R. A., 1987. Approximate dispersion relation for wave-current interactions. J. Waterway, Port, Coastal, and Ocean Eng. 113, 187-195.] or [Kirby, J. T., Chen, T., 1989. Surface waves on vertically sheared flows: approximate dispersion relations. J. Geophys. Res. 94, 1013-1027.] in order to account for the effect of vertical current shear. Use of the depth-weighted velocity, which is a function of wavenumber (or frequency and direction) has been further simplified in recent applications by only utilizing a weighted current based on the spectral peak wavenumber. These applications do not typically take into account the dependence of U˜ on wave number k, as well as erroneously identifying U˜ as the proper choice for current velocity in the wave action equation. Here, we derive a corrected expression for the current component of the group velocity. We demonstrate its consistency using analytic results for a current with constant vorticity, and numerical results for a measured, strongly-sheared current profile obtained in the Columbia River. The effect of choosing a single value for current velocity based on the peak wave frequency is examined, and we suggest an alternate strategy, involving a Taylor series expansion about the peak frequency, which should significantly extend the range of accuracy of current estimates available to the wave model with minimal additional programming and data transfer.

Forcing a three-dimensional, hydrostatic, primitive-equation model for application in the surf zone: 2. Application to DUCK94

NASA Astrophysics Data System (ADS)

Newberger, P. A.; Allen, J. S.

2007-08-01

A three-dimensional primitive-equation model for application to the nearshore surf zone has been developed. This model, an extension of the Princeton Ocean Model (POM), predicts the wave-averaged circulation forced by breaking waves. All of the features of the original POM are retained in the extended model so that applications can be made to regions where breaking waves, stratification, rotation, and wind stress make significant contributions to the flow behavior. In this study we examine the effects of breaking waves and wind stress. The nearshore POM circulation model is embedded within the NearCom community model and is coupled with a wave model. This combined modeling system is applied to the nearshore surf zone off Duck, North Carolina, during the DUCK94 field experiment of October 1994. Model results are compared to observations from this experiment, and the effects of parameter choices are examined. A process study examining the effects of tidal depth variation on depth-dependent wave-averaged currents is carried out. With identical offshore wave conditions and model parameters, the strength and spatial structure of the undertow and of the alongshore current vary systematically with water depth. Some three-dimensional solutions show the development of shear instabilities of the alongshore current. Inclusion of wave-current interactions makes an appreciable difference in the characteristics of the instability.

Small data global solutions for the Camassa–Choi equations

NASA Astrophysics Data System (ADS)

Harrop-Griffiths, Benjamin; Marzuola, Jeremy L.

2018-05-01

We consider solutions to the Cauchy problem for an internal-wave model derived by Camassa–Choi (1996 J. Fluid Mech. 313 83–103). This model is a natural generalization of the Benjamin–Ono and intermediate long wave equations for weak transverse effects as in the case of the Kadomtsev–Petviashvili equations for the Korteweg-de Vries equation. For that reason they are often referred to as the KP-ILW or the KP–Benjamin–Ono equations regarding finite or infinite depth respectively. We prove the existence and long-time dynamics of global solutions from small, smooth, spatially localized initial data on . The techniques applied here involve testing by wave packet techniques developed by Ifrim and Tataru in (2015 Nonlinearity 28 2661–75 2016 Bull. Soc. Math. France 144 369–94).

Large-wave simulation of spilling breaking and undertow current over constant slope beach

NASA Astrophysics Data System (ADS)

Dimas, Athanassios; Kolokythas, Gerasimos; Dimakopoulos, Aggelos

2011-11-01

The three-dimensional, free-surface flow, developing by the propagation of nonlinear breaking waves over a constant slope bed, is numerically simulated. The main objective is to investigate the effect of spilling breaking on the characteristics of the induced undertow current by performing large-wave simulations (LWS) based on the numerical solution of the Navier-Stokes equations subject to the fully nonlinear free-surface boundary conditions and the appropriate bottom, inflow and outflow boundary conditions. The equations are properly transformed so that the computational domain becomes time-independent. In the present study, the case of incoming waves with wavelength to inflow depth ratio λ/ d ~ 6.6 and wave steepness H/ λ ~0.025, over bed of slope tan β = 1/35, is investigated. The LWS predicts satisfactorily breaking parameters - height and depth - and wave dissipation in the surf zone, in comparison to experimental data. In the corresponding LES, breaking height and depth are smaller and wave dissipation in the surf zone is weaker. For the undertow current, it is found that it is induced by the breaking process at the free surface, while its strength is controlled by the bed shear stress. Finally, the amplitude of the bed shear stress increases substantially in the breaking zone, becoming up to six times larger than the respective amplitude at the outer region.

On the stability of lumps and wave collapse in water waves.

PubMed

Akylas, T R; Cho, Yeunwoo

2008-08-13

In the classical water-wave problem, fully localized nonlinear waves of permanent form, commonly referred to as lumps, are possible only if both gravity and surface tension are present. While much attention has been paid to shallow-water lumps, which are generalizations of Korteweg-de Vries solitary waves, the present study is concerned with a distinct class of gravity-capillary lumps recently found on water of finite or infinite depth. In the near linear limit, these lumps resemble locally confined wave packets with envelope and wave crests moving at the same speed, and they can be approximated in terms of a particular steady solution (ground state) of an elliptic equation system of the Benney-Roskes-Davey-Stewartson (BRDS) type, which governs the coupled evolution of the envelope along with the induced mean flow. According to the BRDS equations, however, initial conditions above a certain threshold develop a singularity in finite time, known as wave collapse, due to nonlinear focusing; the ground state, in fact, being exactly at the threshold for collapse suggests that the newly discovered lumps are unstable. In an effort to understand the role of this singularity in the dynamics of lumps, here we consider the fifth-order Kadomtsev-Petviashvili equation, a model for weakly nonlinear gravity-capillary waves on water of finite depth when the Bond number is close to one-third, which also admits lumps of the wave packet type. It is found that an exchange of stability occurs at a certain finite wave steepness, lumps being unstable below but stable above this critical value. As a result, a small-amplitude lump, which is linearly unstable and according to the BRDS equations would be prone to wave collapse, depending on the perturbation, either decays into dispersive waves or evolves into an oscillatory state near a finite-amplitude stable lump.

Versatile rogue waves in scalar, vector, and multidimensional nonlinear systems

NASA Astrophysics Data System (ADS)

Chen, Shihua; Baronio, Fabio; Soto-Crespo, Jose M.; Grelu, Philippe; Mihalache, Dumitru

2017-11-01

This review is dedicated to recent progress in the active field of rogue waves, with an emphasis on the analytical prediction of versatile rogue wave structures in scalar, vector, and multidimensional integrable nonlinear systems. We first give a brief outline of the historical background of the rogue wave research, including referring to relevant up-to-date experimental results. Then we present an in-depth discussion of the scalar rogue waves within two different integrable frameworks—the infinite nonlinear Schrödinger (NLS) hierarchy and the general cubic-quintic NLS equation, considering both the self-focusing and self-defocusing Kerr nonlinearities. We highlight the concept of chirped Peregrine solitons, the baseband modulation instability as an origin of rogue waves, and the relation between integrable turbulence and rogue waves, each with illuminating examples confirmed by numerical simulations. Later, we recur to the vector rogue waves in diverse coupled multicomponent systems such as the long-wave short-wave equations, the three-wave resonant interaction equations, and the vector NLS equations (alias Manakov system). In addition to their intriguing bright-dark dynamics, a series of other peculiar structures, such as coexisting rogue waves, watch-hand-like rogue waves, complementary rogue waves, and vector dark three sisters, are reviewed. Finally, for practical considerations, we also remark on higher-dimensional rogue waves occurring in three closely-related (2  +  1)D nonlinear systems, namely, the Davey-Stewartson equation, the composite (2  +  1)D NLS equation, and the Kadomtsev-Petviashvili I equation. As an interesting contrast to the peculiar X-shaped light bullets, a concept of rogue wave bullets intended for high-dimensional systems is particularly put forward by combining contexts in nonlinear optics.

Generation of long subharmonic internal waves by surface waves

NASA Astrophysics Data System (ADS)

Tahvildari, Navid; Kaihatu, James M.; Saric, William S.

2016-10-01

A new set of Boussinesq equations is derived to study the nonlinear interactions between long waves in a two-layer fluid. The fluid layers are assumed to be homogeneous, inviscid, incompressible, and immiscible. Based on the Boussinesq equations, an analytical model is developed using a second-order perturbation theory and applied to examine the transient evolution of a resonant triad composed of a surface wave and two oblique subharmonic internal waves. Wave damping due to weak viscosity in both layers is considered. The Boussinesq equations and the analytical model are verified. In contrast to previous studies which focus on short internal waves, we examine long waves and investigate some previously unexplored characteristics of this class of triad interaction. In viscous fluids, surface wave amplitudes must be larger than a threshold to overcome viscous damping and trigger internal waves. The dependency of this critical amplitude as well as the growth and damping rates of internal waves on important parameters in a two-fluid system, namely the directional angle of the internal waves, depth, density, and viscosity ratio of the fluid layers, and surface wave amplitude and frequency is investigated.

2D instabilities of surface gravity waves on a linear shear current

NASA Astrophysics Data System (ADS)

Francius, Marc; Kharif, Christian

2016-04-01

Periodic 2D surface water waves propagating steadily on a rotational current have been studied by many authors (see [1] and references therein). Although the recent important theoretical developments have confirmed that periodic waves can exist over flows with arbitrary vorticity, their stability and their nonlinear evolution have not been much studied extensively so far. In fact, even in the rather simple case of uniform vorticity (linear shear), few papers have been published on the effect of a vertical shear current on the side-band instability of a uniform wave train over finite depth. In most of these studies [2-5], asymptotic expansions and multiple scales method have been used to obtain envelope evolution equations, which allow eventually to formulate a condition of (linear) instability to long modulational perturbations. It is noted here that this instability is often referred in the literature as the Benjamin-Feir or modulational instability. In the present study, we consider the linear stability of finite amplitude two-dimensional, periodic water waves propagating steadily on the free surface of a fluid with constant vorticity and finite depth. First, the steadily propagating surface waves are computed with steepness up to very close to the highest, using a Fourier series expansions and a collocation method, which constitutes a simple extension of Fenton's method [6] to the cases with a linear shear current. Then, the linear stability of these permanent waves to infinitesimal 2D perturbations is developed from the fully nonlinear equations in the framework of normal modes analysis. This linear stability analysis is an extension of [7] to the case of waves in the presence of a linear shear current and permits the determination of the dominant instability as a function of depth and vorticity for a given steepness. The numerical results are used to assess the accuracy of the vor-NLS equation derived in [5] for the characteristics of modulational instabilities due to resonant four-wave interactions, as well as to study the influence of vorticity and nonlinearity on the characteristics of linear instabilities due to resonant five-wave and six-wave interactions. Depending on the dimensionless depth, superharmonic instabilities due to five-wave interactions can become dominant with increasing positive vorticiy. Acknowledgments: This work was supported by the Direction Générale de l'Armement and funded by the ANR project n°. ANR-13-ASTR-0007. References [1] A. Constantin, Two-dimensionality of gravity water flows of constant non-zero vorticity beneath a surface wave train, Eur. J. Mech. B/Fluids, 2011, 30, 12-16. [2] R. S. Johnson, On the modulation of water waves on shear flows, Proc. Royal Soc. Lond. A., 1976, 347, 537-546. [3] M. Oikawa, K. Chow, D. J. Benney, The propagation of nonlinear wave packets in a shear flow with a free surface, Stud. Appl. Math., 1987, 76, 69-92. [4] A. I Baumstein, Modulation of gravity waves with shear in water, Stud. Appl. Math., 1998, 100, 365-90. [5] R. Thomas, C. Kharif, M. Manna, A nonlinear Schrödinger equation for water waves on finite depth with constant vorticity, Phys. Fluids, 2012, 24, 127102. [6] M. M Rienecker, J. D Fenton, A Fourier approximation method for steady water waves , J. Fluid Mech., 1981, 104, 119-137 [7] M. Francius, C. Kharif, Three-dimensional instabilities of periodic gravity waves in shallow water, J. Fluid Mech., 2006, 561, 417-437

Prestack reverse time migration for tilted transversely isotropic media

NASA Astrophysics Data System (ADS)

Jang, Seonghyung; Hien, Doan Huy

2013-04-01

According to having interest in unconventional resource plays, anisotropy problem is naturally considered as an important step for improving the seismic image quality. Although it is well known prestack depth migration for the seismic reflection data is currently one of the powerful tools for imaging complex geological structures, it may lead to migration error without considering anisotropy. Asymptotic analysis of wave propagation in transversely isotropic (TI) media yields a dispersion relation of couple P- and SV wave modes that can be converted to a fourth order scalar partial differential equation (PDE). By setting the shear wave velocity equal zero, the fourth order PDE, called an acoustic wave equation for TI media, can be reduced to couple of second order PDE systems and we try to solve the second order PDE by the finite difference method (FDM). The result of this P wavefield simulation is kinematically similar to elastic and anisotropic wavefield simulation. We develop prestack depth migration algorithm for tilted transversely isotropic media using reverse time migration method (RTM). RTM is a method for imaging the subsurface using inner product of source wavefield extrapolation in forward and receiver wavefield extrapolation in backward. We show the subsurface image in TTI media using the inner product of partial derivative wavefield with respect to physical parameters and observation data. Since the partial derivative wavefields with respect to the physical parameters require extremely huge computing time, so we implemented the imaging condition by zero lag crosscorrelation of virtual source and back propagating wavefield instead of partial derivative wavefields. The virtual source is calculated directly by solving anisotropic acoustic wave equation, the back propagating wavefield on the other hand is calculated by the shot gather used as the source function in the anisotropic acoustic wave equation. According to the numerical model test for a simple geological model including syncline and anticline, the prestack depth migration using TTI-RTM in weak anisotropic media shows the subsurface image is similar to the true geological model used to generate the shot gathers.

Validation and Comparison of 2D and 3D Codes for Nearshore Motion of Long Waves Using Benchmark Problems

NASA Astrophysics Data System (ADS)

Velioǧlu, Deniz; Cevdet Yalçıner, Ahmet; Zaytsev, Andrey

2016-04-01

Tsunamis are huge waves with long wave periods and wave lengths that can cause great devastation and loss of life when they strike a coast. The interest in experimental and numerical modeling of tsunami propagation and inundation increased considerably after the 2011 Great East Japan earthquake. In this study, two numerical codes, FLOW 3D and NAMI DANCE, that analyze tsunami propagation and inundation patterns are considered. Flow 3D simulates linear and nonlinear propagating surface waves as well as long waves by solving three-dimensional Navier-Stokes (3D-NS) equations. NAMI DANCE uses finite difference computational method to solve 2D depth-averaged linear and nonlinear forms of shallow water equations (NSWE) in long wave problems, specifically tsunamis. In order to validate these two codes and analyze the differences between 3D-NS and 2D depth-averaged NSWE equations, two benchmark problems are applied. One benchmark problem investigates the runup of long waves over a complex 3D beach. The experimental setup is a 1:400 scale model of Monai Valley located on the west coast of Okushiri Island, Japan. Other benchmark problem is discussed in 2015 National Tsunami Hazard Mitigation Program (NTHMP) Annual meeting in Portland, USA. It is a field dataset, recording the Japan 2011 tsunami in Hilo Harbor, Hawaii. The computed water surface elevation and velocity data are compared with the measured data. The comparisons showed that both codes are in fairly good agreement with each other and benchmark data. The differences between 3D-NS and 2D depth-averaged NSWE equations are highlighted. All results are presented with discussions and comparisons. Acknowledgements: Partial support by Japan-Turkey Joint Research Project by JICA on earthquakes and tsunamis in Marmara Region (JICA SATREPS - MarDiM Project), 603839 ASTARTE Project of EU, UDAP-C-12-14 project of AFAD Turkey, 108Y227, 113M556 and 213M534 projects of TUBITAK Turkey, RAPSODI (CONCERT_Dis-021) of CONCERT-Japan Joint Call and Istanbul Metropolitan Municipality are all acknowledged.

Conservation laws and conserved quantities for (1+1)D linearized Boussinesq equations

NASA Astrophysics Data System (ADS)

Carvalho, Cindy; Harley, Charis

2017-05-01

Conservation laws and physical conserved quantities for the (1+1)D linearized Boussinesq equations at a constant water depth are presented. These equations describe incompressible, inviscid, irrotational fluid flow in the form of a non steady solitary wave. A systematic multiplier approach is used to obtain the conservation laws of the system of third order partial differential equations (PDEs) in dimensional form. Physical conserved quantities are derived by integrating the conservation laws in the direction of wave propagation and imposing decaying boundary conditions in the horizontal direction. One of these is a newly discovered conserved quantity which relates to an energy flux density.

Simple equations guide high-frequency surface-wave investigation techniques

USGS Publications Warehouse

Xia, J.; Xu, Y.; Chen, C.; Kaufmann, R.D.; Luo, Y.

2006-01-01

We discuss five useful equations related to high-frequency surface-wave techniques and their implications in practice. These equations are theoretical results from published literature regarding source selection, data-acquisition parameters, resolution of a dispersion curve image in the frequency-velocity domain, and the cut-off frequency of high modes. The first equation suggests Rayleigh waves appear in the shortest offset when a source is located on the ground surface, which supports our observations that surface impact sources are the best source for surface-wave techniques. The second and third equations, based on the layered earth model, reveal a relationship between the optimal nearest offset in Rayleigh-wave data acquisition and seismic setting - the observed maximum and minimum phase velocities, and the maximum wavelength. Comparison among data acquired with different offsets at one test site confirms the better data were acquired with the suggested optimal nearest offset. The fourth equation illustrates that resolution of a dispersion curve image at a given frequency is directly proportional to the product of a length of a geophone array and the frequency. We used real-world data to verify the fourth equation. The last equation shows that the cut-off frequency of high modes of Love waves for a two-layer model is determined by shear-wave velocities and the thickness of the top layer. We applied this equation to Rayleigh waves and multi-layer models with the average velocity and obtained encouraging results. This equation not only endows with a criterion to distinguish high modes from numerical artifacts but also provides a straightforward means to resolve the depth to the half space of a layered earth model. ?? 2005 Elsevier Ltd. All rights reserved.

PHYSICS OF OUR DAYS: Nonlinear long waves on water and solitons

NASA Astrophysics Data System (ADS)

Zeytounian, R. Kh

1995-12-01

The water wave problem has been pivotal in the history of nonlinear wave theory. This problem is one of the most interesting and successful applications of nonlinear hydrodynamics. Waves on the free surface of a body of water (perfect liquid) have always been a fascinating subject, for they represent a familiar yet complex phenomenon, easy to observe but very difficult to describe! The archetypical model equations of Kordeweg and de Vries and of Boussinesq, for example, were originally derived as approximations for water waves, and research into the problem has been sustained vigorously up to the present day. In the present paper, the derivation of the model equations is given in depth and rational use is made of asymptotic methods. Indeed, it is important to understand that in some cases the derivation of these approximate equations is intuitive and heuristic. In fact, it is not clear how to insert the model equation under consideration into a hierarchy of rational approximations, which in turn result from the exact formulation of the selected water wave problem.

Non-perturbational surface-wave inversion: A Dix-type relation for surface waves

USGS Publications Warehouse

Haney, Matt; Tsai, Victor C.

2015-01-01

We extend the approach underlying the well-known Dix equation in reflection seismology to surface waves. Within the context of surface wave inversion, the Dix-type relation we derive for surface waves allows accurate depth profiles of shear-wave velocity to be constructed directly from phase velocity data, in contrast to perturbational methods. The depth profiles can subsequently be used as an initial model for nonlinear inversion. We provide examples of the Dix-type relation for under-parameterized and over-parameterized cases. In the under-parameterized case, we use the theory to estimate crustal thickness, crustal shear-wave velocity, and mantle shear-wave velocity across the Western U.S. from phase velocity maps measured at 8-, 20-, and 40-s periods. By adopting a thin-layer formalism and an over-parameterized model, we show how a regularized inversion based on the Dix-type relation yields smooth depth profiles of shear-wave velocity. In the process, we quantitatively demonstrate the depth sensitivity of surface-wave phase velocity as a function of frequency and the accuracy of the Dix-type relation. We apply the over-parameterized approach to a near-surface data set within the frequency band from 5 to 40 Hz and find overall agreement between the inverted model and the result of full nonlinear inversion.

Mathematical Modeling of Torsional Surface Wave Propagation in a Non-Homogeneous Transverse Isotropic Elastic Solid Semi-Infinite Medium Under a Layer

NASA Astrophysics Data System (ADS)

Sethi, M.; Sharma, A.; Vasishth, A.

2017-05-01

The present paper deals with the mathematical modeling of the propagation of torsional surface waves in a non-homogeneous transverse isotropic elastic half-space under a rigid layer. Both rigidities and density of the half-space are assumed to vary inversely linearly with depth. Separation of variable method has been used to get the analytical solutions for the dispersion equation of the torsional surface waves. Also, the effects of nonhomogeneities on the phase velocity of torsional surface waves have been shown graphically. Also, dispersion equations have been derived for some particular cases, which are in complete agreement with some classical results.

Effect of higher order nonlinearity, directionality and finite water depth on wave statistics: Comparison of field data and numerical simulations

NASA Astrophysics Data System (ADS)

Fernández, Leandro; Monbaliu, Jaak; Onorato, Miguel; Toffoli, Alessandro

2014-05-01

This research is focused on the study of nonlinear evolution of irregular wave fields in water of arbitrary depth by comparing field measurements and numerical simulations.It is now well accepted that modulational instability, known as one of the main mechanisms for the formation of rogue waves, induces strong departures from Gaussian statistics. However, whereas non-Gaussian properties are remarkable when wave fields follow one direction of propagation over an infinite water depth, wave statistics only weakly deviate from Gaussianity when waves spread over a range of different directions. Over finite water depth, furthermore, wave instability attenuates overall and eventually vanishes for relative water depths as low as kh=1.36 (where k is the wavenumber of the dominant waves and h the water depth). Recent experimental results, nonetheless, seem to indicate that oblique perturbations are capable of triggering and sustaining modulational instability even if kh<1.36. In this regard, the aim of this research is to understand whether the combined effect of directionality and finite water depth has a significant effect on wave statistics and particularly on the occurrence of extremes. For this purpose, numerical experiments have been performed solving the Euler equation of motion with the Higher Order Spectral Method (HOSM) and compared with data of short crested wave fields for different sea states observed at the Lake George (Australia). A comparative analysis of the statistical properties (i.e. density function of the surface elevation and its statistical moments skewness and kurtosis) between simulations and in-situ data provides a confrontation between the numerical developments and real observations in field conditions.

First-arrival traveltime computation for quasi-P waves in 2D transversely isotropic media using Fermat’s principle-based fast marching

NASA Astrophysics Data System (ADS)

Hu, Jiangtao; Cao, Junxing; Wang, Huazhong; Wang, Xingjian; Jiang, Xudong

2017-12-01

First-arrival traveltime computation for quasi-P waves in transversely isotropic (TI) media is the key component of tomography and depth migration. It is appealing to use the fast marching method in isotropic media as it efficiently computes traveltime along an expanding wavefront. It uses the finite difference method to solve the eikonal equation. However, applying the fast marching method in anisotropic media faces challenges because the anisotropy introduces additional nonlinearity in the eikonal equation and solving this nonlinear eikonal equation with the finite difference method is challenging. To address this problem, we present a Fermat’s principle-based fast marching method to compute traveltime in two-dimensional TI media. This method is applicable in both vertical and tilted TI (VTI and TTI) media. It computes traveltime along an expanding wavefront using Fermat’s principle instead of the eikonal equation. Thus, it does not suffer from the nonlinearity of the eikonal equation in TI media. To compute traveltime using Fermat’s principle, the explicit expression of group velocity in TI media is required to describe the ray propagation. The moveout approximation is adopted to obtain the explicit expression of group velocity. Numerical examples on both VTI and TTI models show that the traveltime contour obtained by the proposed method matches well with the wavefront from the wave equation. This shows that the proposed method could be used in depth migration and tomography.

Wave friction factor rediscovered

NASA Astrophysics Data System (ADS)

Le Roux, J. P.

2012-02-01

The wave friction factor is commonly expressed as a function of the horizontal water particle semi-excursion ( A wb) at the top of the boundary layer. A wb, in turn, is normally derived from linear wave theory by {{U_{{wb}}/T_{{w}}}}{{2π }} , where U wb is the maximum water particle velocity measured at the top of the boundary layer and T w is the wave period. However, it is shown here that A wb determined in this way deviates drastically from its real value under both linear and non-linear waves. Three equations for smooth, transitional and rough boundary conditions, respectively, are proposed to solve this problem, all three being a function of U wb, T w, and δ, the thickness of the boundary layer. Because these variables can be determined theoretically for any bottom slope and water depth using the deepwater wave conditions, there is no need to physically measure them. Although differing substantially from many modern attempts to define the wave friction factor, the results coincide with equations proposed in the 1960s for either smooth or rough boundary conditions. The findings also confirm that the long-held notion of circular water particle motion down to the bottom in deepwater conditions is erroneous, the motion in fact being circular at the surface and elliptical at depth in both deep and shallow water conditions, with only horizontal motion at the top of the boundary layer. The new equations are incorporated in an updated version (WAVECALC II) of the Excel program published earlier in this journal by Le Roux et al. Geo-Mar Lett 30(5): 549-560, (2010).

An Experiment on Two-Dimensional Interaction of Solitary Waves in Shallow Water System

NASA Astrophysics Data System (ADS)

Tsuji, Hidekazu; Yufu, Kei; Marubayashi, Kenji

2012-11-01

The dynamics of solitary waves in horizontally two-dimensional region is not yet well understood. Recently two-dimensional soliton interaction of Kadmotsetv-Petviashvili (KP) equation which describes the weakly nonlinear long wave in shallow water system has been theoretically studied (e.g. Kodama (2010)). It is clarified that the ``resonant'' interaction which forms Y-shaped triad can be described by exact solution. Li et al. (2011) experimentally studied the reflection of solitary wave at the wall and verified the theory of KP equation. To investigate more general interaction process, an experiment in wave tank using two wave makers which are controlled independently is carried out. The wave tank is 4 m in length and 3.6 m in width. The depth of the water is about 8cm. The wavemakers, which are piston-type and have board about 1.5 m in length, can produce orderly solitary wave which amplitude is 1.0-3.5 cm. We observe newly generated solitary wave due to interaction of original solitary waves which have different amplitude and/or propagation direction. The results are compared with the aforementioned theory of KP equation.

Analysis of pulse thermography using similarities between wave and diffusion propagation

NASA Astrophysics Data System (ADS)

Gershenson, M.

2017-05-01

Pulse thermography or thermal wave imaging are commonly used as nondestructive evaluation (NDE) method. While the technical aspect has evolve with time, theoretical interpretation is lagging. Interpretation is still using curved fitting on a log log scale. A new approach based directly on the governing differential equation is introduced. By using relationships between wave propagation and the diffusive propagation of thermal excitation, it is shown that one can transform from solutions in one type of propagation to the other. The method is based on the similarities between the Laplace transforms of the diffusion equation and the wave equation. For diffusive propagation we have the Laplace variable s to the first power, while for the wave propagation similar equations occur with s2. For discrete time the transformation between the domains is performed by multiplying the temperature data vector by a matrix. The transform is local. The performance of the techniques is tested on synthetic data. The application of common back projection techniques used in the processing of wave data is also demonstrated. The combined use of the transform and back projection makes it possible to improve both depth and lateral resolution of transient thermography.

Topographical scattering of gravity waves

NASA Astrophysics Data System (ADS)

Miles, J. W.; Chamberlain, P. G.

1998-04-01

A systematic hierarchy of partial differential equations for linear gravity waves in water of variable depth is developed through the expansion of the average Lagrangian in powers of [mid R:][nabla del, Hamilton operator][mid R:] (h=depth, [nabla del, Hamilton operator]h=slope). The first and second members of this hierarchy, the Helmholtz and conventional mild-slope equations, are second order. The third member is fourth order but may be approximated by Chamberlain & Porter's (1995) ‘modified mild-slope’ equation, which is second order and comprises terms in [nabla del, Hamilton operator]2h and ([nabla del, Hamilton operator]h)2 that are absent from the mild-slope equation. Approximate solutions of the mild-slope and modified mild-slope equations for topographical scattering are determined through an iterative sequence, starting from a geometrical-optics approximation (which neglects reflection), then a quasi-geometrical-optics approximation, and on to higher-order results. The resulting reflection coefficient for a ramp of uniform slope is compared with the results of numerical integrations of each of the mild-slope equation (Booij 1983), the modified mild-slope equation (Porter & Staziker 1995), and the full linear equations (Booij 1983). Also considered is a sequence of sinusoidal sandbars, for which Bragg resonance may yield rather strong reflection and for which the modified mild-slope approximation is in close agreement with Mei's (1985) asymptotic approximation.

Spatial nonlinear absorption of Alfven waves by dissipative plasma taking account bremsstrahlung

NASA Astrophysics Data System (ADS)

Taiurskii, A. A.; Gavrikov, M. B.

2016-10-01

We study numerically the nonlinear absorption of a plane Alfven wave falling on the stationary boundary of dissipative plasma. This absorption is caused by such factors as the magnetic viscosity, hydrodynamic viscosity, and thermal conductivity of electrons and ions, bremsstrahlung and energy exchange between plasma components. The relevance of this investigation is due to some works, published in 2011, with regard to the heating mechanism of the solar corona and solar wind generation as a result of the absorption of plasma Alfven waves generated in the lower significantly colder layers of the Sun. Numerical analysis shows that the absorption of Alfven waves occurs at wavelengths of the order of skin depth, in which case the classical MHD equations are inapplicable. Therefore, our research is based on equations of two-fluid magnetohydrodynamics that take into account the inertia of the electrons. The implicit difference scheme proposed here for calculating plane-parallel flows of two-fluid plasma reveals a number of important patterns of absorption and thus allows us to study the dependence of the absorption on the Alfven wave frequency and the electron thermal conductivity and viscosity, as well as to evaluate the depth and the velocity of plasma heating during the penetration of Alfven waves interacting with dissipative plasma.

Tsunamis generated by subaerial mass flows

USGS Publications Warehouse

Walder, S.J.; Watts, P.; Sorensen, O.E.; Janssen, K.

2003-01-01

Tsunamis generated in lakes and reservoirs by subaerial mass flows pose distinctive problems for hazards assessment because the domain of interest is commonly the "near field," beyond the zone of complex splashing but close enough to the source that wave propagation effects are not predominant. Scaling analysis of the equations governing water wave propagation shows that near-field wave amplitude and wavelength should depend on certain measures of mass flow dynamics and volume. The scaling analysis motivates a successful collapse (in dimensionless space) of data from two distinct sets of experiments with solid block "wave makers." To first order, wave amplitude/water depth is a simple function of the ratio of dimensionless wave maker travel time to dimensionless wave maker volume per unit width. Wave amplitude data from previous laboratory investigations with both rigid and deformable wave makers follow the same trend in dimensionless parameter space as our own data. The characteristic wavelength/water depth for all our experiments is simply proportional to dimensionless wave maker travel time, which is itself given approximately by a simple function of wave maker length/water depth. Wave maker shape and rigidity do not otherwise influence wave features. Application of the amplitude scaling relation to several historical events yields "predicted" near-field wave amplitudes in reasonable agreement with measurements and observations. Together, the scaling relations for near-field amplitude, wavelength, and submerged travel time provide key inputs necessary for computational wave propagation and hazards assessment.

Experimental wave attenuation study over flexible plants on a submerged slope

NASA Astrophysics Data System (ADS)

Yin, Zegao; Yang, Xiaoyu; Xu, Yuanzhao; Ding, Meiling; Lu, Haixiang

2017-12-01

Using plants is a kind of environmentally-friendly coastal protection to attenuate wave energy. In this paper, a set of experiments were conducted to investigate the wave attenuation performance using flexible grasses on a submerged slope, and the wave attenuation coefficient for these experiments was calculated for different still water depths, slope and grass configurations. It was found that the slope plays a significant role in wave attenuation. The wave attenuation coefficient increases with increasing relative row number and relative density. For a small relative row number, the two configurations from the slope top to its toe and from the slope toe to its top performed equally to a large extent. For a medium relative row number, the configuration from the slope toe to its top performed more poorly than that from the slope top to its toe; however, it performed better than that from the slope top to its toe for a high relative row number. With a single row of grasses close to the slope top from the slope toe, the wave attenuation coefficient shows double peaks. With increasing grass rows or still water depth, the grass location corresponding to the maximum wave attenuation coefficient is close to the slope top. The dimensional analysis and the least square method were used to derive an empirical equation of the wave attenuation coefficient considering the effect of relative density, the slope, the relative row number and the relative location of the middle row, and the equation was validated to experimental data.

Evolution of initial discontinuities in the Riemann problem for the Kaup-Boussinesq equation with positive dispersion

NASA Astrophysics Data System (ADS)

Congy, T.; Ivanov, S. K.; Kamchatnov, A. M.; Pavloff, N.

2017-08-01

We consider the space-time evolution of initial discontinuities of depth and flow velocity for an integrable version of the shallow water Boussinesq system introduced by Kaup. We focus on a specific version of this "Kaup-Boussinesq model" for which a flat water surface is modulationally stable, we speak below of "positive dispersion" model. This model also appears as an approximation to the equations governing the dynamics of polarisation waves in two-component Bose-Einstein condensates. We describe its periodic solutions and the corresponding Whitham modulation equations. The self-similar, one-phase wave structures are composed of different building blocks, which are studied in detail. This makes it possible to establish a classification of all the possible wave configurations evolving from initial discontinuities. The analytic results are confirmed by numerical simulations.

Evolution of initial discontinuities in the Riemann problem for the Kaup-Boussinesq equation with positive dispersion.

PubMed

Congy, T; Ivanov, S K; Kamchatnov, A M; Pavloff, N

2017-08-01

We consider the space-time evolution of initial discontinuities of depth and flow velocity for an integrable version of the shallow water Boussinesq system introduced by Kaup. We focus on a specific version of this "Kaup-Boussinesq model" for which a flat water surface is modulationally stable, we speak below of "positive dispersion" model. This model also appears as an approximation to the equations governing the dynamics of polarisation waves in two-component Bose-Einstein condensates. We describe its periodic solutions and the corresponding Whitham modulation equations. The self-similar, one-phase wave structures are composed of different building blocks, which are studied in detail. This makes it possible to establish a classification of all the possible wave configurations evolving from initial discontinuities. The analytic results are confirmed by numerical simulations.

Hamiltonian models for the propagation of irrotational surface gravity waves over a variable bottom

NASA Astrophysics Data System (ADS)

Compelli, A.; Ivanov, R.; Todorov, M.

2017-12-01

A single incompressible, inviscid, irrotational fluid medium bounded by a free surface and varying bottom is considered. The Hamiltonian of the system is expressed in terms of the so-called Dirichlet-Neumann operators. The equations for the surface waves are presented in Hamiltonian form. Specific scaling of the variables is selected which leads to approximations of Boussinesq and Korteweg-de Vries (KdV) types, taking into account the effect of the slowly varying bottom. The arising KdV equation with variable coefficients is studied numerically when the initial condition is in the form of the one-soliton solution for the initial depth. This article is part of the theme issue 'Nonlinear water waves'.

Numerical modeling of surface wave development under the action of wind

NASA Astrophysics Data System (ADS)

Chalikov, Dmitry

2018-06-01

The numerical modeling of two-dimensional surface wave development under the action of wind is performed. The model is based on three-dimensional equations of potential motion with a free surface written in a surface-following nonorthogonal curvilinear coordinate system in which depth is counted from a moving surface. A three-dimensional Poisson equation for the velocity potential is solved iteratively. A Fourier transform method, a second-order accuracy approximation of vertical derivatives on a stretched vertical grid and fourth-order Runge-Kutta time stepping are used. Both the input energy to waves and dissipation of wave energy are calculated on the basis of earlier developed and validated algorithms. A one-processor version of the model for PC allows us to simulate an evolution of the wave field with thousands of degrees of freedom over thousands of wave periods. A long-time evolution of a two-dimensional wave structure is illustrated by the spectra of wave surface and the input and output of energy.

Three-dimensional seismic depth migration

NASA Astrophysics Data System (ADS)

Zhou, Hongbo

1998-12-01

One-pass 3-D modeling and migration for poststack seismic data may be implemented by replacing the traditional 45sp° one-way wave equation (a third-order partial differential equation) with a pair of second and first order partial differential equations. Except for an extra correction term, the resulting second order equation has a form similar to Claerbout's 15sp° one-way wave equation, which is known to have a nearly circular horizontal impulse response. In this approach, there is no need to compensate for splitting errors. Numerical tests on synthetic data show that this algorithm has the desirable attributes of being second-order in accuracy and economical to solve. A modification of the Crank-Nicholson implementation maintains stability. Absorbing boundary conditions play an important role in one-way wave extrapolations by reducing reflections at grid edges. Clayton and Engquist's 2-D absorbing boundary conditions for one-way wave extrapolation by depth-stepping in the frequency domain are extended to 3-D using paraxial approximations of the scalar wave equation. Internal consistency is retained by incorporating the interior extrapolation equation with the absorbing boundary conditions. Numerical schemes are designed to make the proposed absorbing boundary conditions both mathematically correct and efficient with negligible extra cost. Synthetic examples illustrate the effectiveness of the algorithm for extrapolation with the 3-D 45sp° one-way wave equation. Frequency-space domain Butterworth and Chebyshev dip filters are implemented. By regrouping the product terms in the filter transfer function into summations, a cascaded (serial) Butterworth dip filter can be made parallel. A parallel Chebyshev dip filter can be similarly obtained, and has the same form as the Butterworth filter; but has different coeffcients. One of the advantages of the Chebyshev filter is that it has a sharper transition zone than that of Butterworth filter of the same order. Both filters are incorporated into 3-D one-way frequency-space depth migration for evanescent energy removal and for phase compensation of splitting errors; a single filter achieves both goals. Synthetic examples illustrate the behavior of the parallel filters. For a given order of filter, the cost of the Butterworth and Chebyshev filters is the same. A Chebyshev filter is more effective for phase compensation than the Butterworth filter of the same order, at the expense of some wavenumber-dependent amplitude ripples. An analytical formula for geometrical spreading is derived for a horizontally layered transversely isotropic medium with a vertical symmetry axis. Under this expression, geometrical spreading can be determined only by the anisotropic parameters in the first layer, the traveltime derivatives, and source-receiver offset. An explicit, numerically feasible expression for geometrical spreading can be further obtained by considering some of the special cases of transverse isotropy, such as weak anisotropy or elliptic anisotropy. Therefore, with the techniques of non-hyerbolic moveout for transverse isotropic media, geometrical spreading can be calculated by using picked traveltimes of primary P-wave reflections without having to know the actual parameters in the deeper subsurface; no ray tracing is needed. Synthetic examples verify the algorithm and show that it is numerically feasible for calculation of geometrical spreading.

Observation of the seismic anisotropy effects on free oscillations below 4 mHz

NASA Astrophysics Data System (ADS)

Hu, X.; Liu, L.

2009-12-01

We present observations of significant fundamental spheroidal-toroidal mode coupling at frequencies below 4 mHz in the early part of vertical component records from seismic stations on near-equatorial source-receiver propagation paths and in Antarctica after the 26 December 2004 and 28 March 2005 great Sumatra earthquakes. When seismic surface waves propagate along the equator, the particle motion of Love waves runs parallels to the Earth’s rotation axis, and the particle motion of Rayleigh waves runs perpendicular to it, thus the Coriolis force has no vertical deflection effect on Love waves and no transverse deflection effect on the Rayleigh waves. Coriolis coupling can be naturally minimized at a station on a nearequatorial source-receiver propagation path. In Antarctica, especially near the South Pole, the vertical deflection of toroidial motion is very weak but there are lateral gradients in the anisotropic properties of upper mantle. Therefore, we can find a chance to directly observe seismic anisotropy coupling below 4 mHz without the disturbance of Coriolis coupling at Antarctic station, and at the seismic station locate close to the Earth’s equator when the epicenter also locates close to the equator. Our observations of strong anomalous toroidal-spheroidal coupling at these stations provide direct evidence to confirm the theory that the azimuthal anisotropy has pronounced effects on the quasi-toroidal mode excitations at the frequencies below 4 mHz, which can convince the skeptics that anisotropy really is visible in the low-frequency normal mode data. Strong anisotropic coupling is usually observed at stations having the geometric nodes for the spheroidal fundamentals, giving the association of quasi-toroidal excitation with the geometric effect. The presence of significant anisotropy coupling below 4 mHz depends not only on anisotropic depth, anisotropic identities and orientations but also on radiation nodes for Rayleigh waves and geometry nodes for spheroidal fundamentals. The quasi-toroidal modes below 4 mHz have significant sensitivity throughout most of the mantle, extending into the lower mantle, and therefore, it is likely that the resolution of locating the depth of origin of azimuthal anisotropy in the mantle will be improved by joint inversions that take advantage of the partly complementary depth resolution of anisotropy coupling measurements, quasi-Love surface-wave measurements, body wave splitting measurements and surface-wave dispersion measurements.

Wave Propagation Analysis of Edge Cracked Circular Beams under Impact Force

PubMed Central

Akbaş, Şeref Doğuşcan

2014-01-01

This paper presents responses of an edge circular cantilever beam under the effect of an impact force. The beam is excited by a transverse triangular force impulse modulated by a harmonic motion. The Kelvin–Voigt model for the material of the beam is used. The cracked beam is modelled as an assembly of two sub-beams connected through a massless elastic rotational spring. The considered problem is investigated within the Bernoulli-Euler beam theory by using energy based finite element method. The system of equations of motion is derived by using Lagrange's equations. The obtained system of linear differential equations is reduced to a linear algebraic equation system and solved in the time domain by using Newmark average acceleration method. In the study, the effects of the location of crack, the depth of the crack, on the characteristics of the reflected waves are investigated in detail. Also, the positions of the cracks are calculated by using reflected waves. PMID:24972050

Mechanical Balance Laws for Boussinesq Models of Surface Water Waves

NASA Astrophysics Data System (ADS)

Ali, Alfatih; Kalisch, Henrik

2012-06-01

Depth-integrated long-wave models, such as the shallow-water and Boussinesq equations, are standard fare in the study of small amplitude surface waves in shallow water. While the shallow-water theory features conservation of mass, momentum and energy for smooth solutions, mechanical balance equations are not widely used in Boussinesq scaling, and it appears that the expressions for many of these quantities are not known. This work presents a systematic derivation of mass, momentum and energy densities and fluxes associated with a general family of Boussinesq systems. The derivation is based on a reconstruction of the velocity field and the pressure in the fluid column below the free surface, and the derivation of differential balance equations which are of the same asymptotic validity as the evolution equations. It is shown that all these mechanical quantities can be expressed in terms of the principal dependent variables of the Boussinesq system: the surface excursion η and the horizontal velocity w at a given level in the fluid.

Solitary wave runup and force on a vertical barrier

NASA Astrophysics Data System (ADS)

Liu, Philip L.-F.; Al-Banaa, Khaled

2004-04-01

In this paper we investigate the interaction between a solitary wave and a thin vertical barrier. A set of laboratory experiments was performed with different values of incident wave height to water depth ratio, H/h, and the draught of the barrier to water depth ratio, D/h. While wave gauges were used to measure the reflected and transmitted waves, pressure transducers were installed on both sides of the barrier, enabling the calculation of wave force. The particle image velocimetry (PIV) technique is also employed to measure the velocity field in the vicinity of the barrier. A numerical model, based on the Reynolds-averaged Navier Stokes (RANS) equations and the k - epsilon turbulence closure model, was first checked with experimental data and then employed to obtain additional results for the range of parameters where the laboratory experiments were not performed. Using both experimental data and numerical results, formulae for the maximum runup height, and the maximum wave force are derived in terms of H/h and D/h.

Hamiltonian models for the propagation of irrotational surface gravity waves over a variable bottom.

PubMed

Compelli, A; Ivanov, R; Todorov, M

2018-01-28

A single incompressible, inviscid, irrotational fluid medium bounded by a free surface and varying bottom is considered. The Hamiltonian of the system is expressed in terms of the so-called Dirichlet-Neumann operators. The equations for the surface waves are presented in Hamiltonian form. Specific scaling of the variables is selected which leads to approximations of Boussinesq and Korteweg-de Vries (KdV) types, taking into account the effect of the slowly varying bottom. The arising KdV equation with variable coefficients is studied numerically when the initial condition is in the form of the one-soliton solution for the initial depth.This article is part of the theme issue 'Nonlinear water waves'. © 2017 The Author(s).

Modeling of matter-wave solitons in a nonlinear inductor-capacitor network through a Gross-Pitaevskii equation with time-dependent linear potential

NASA Astrophysics Data System (ADS)

Kengne, E.; Lakhssassi, A.; Liu, W. M.

2017-08-01

A lossless nonlinear L C transmission network is considered. With the use of the reductive perturbation method in the semidiscrete limit, we show that the dynamics of matter-wave solitons in the network can be modeled by a one-dimensional Gross-Pitaevskii (GP) equation with a time-dependent linear potential in the presence of a chemical potential. An explicit expression for the growth rate of a purely growing modulational instability (MI) is presented and analyzed. We find that the potential parameter of the GP equation of the system does not affect the different regions of the MI. Neglecting the chemical potential in the GP equation, we derive exact analytical solutions which describe the propagation of both bright and dark solitary waves on continuous-wave (cw) backgrounds. Using the found exact analytical solutions of the GP equation, we investigate numerically the transmission of both bright and dark solitary voltage signals in the network. Our numerical studies show that the amplitude of a bright solitary voltage signal and the depth of a dark solitary voltage signal as well as their width, their motion, and their behavior depend on (i) the propagation frequencies, (ii) the potential parameter, and (iii) the amplitude of the cw background. The GP equation derived in this paper with a time-dependent linear potential opens up different ideas that may be of considerable theoretical interest for the management of matter-wave solitons in nonlinear L C transmission networks.

Effects of elastic bed on hydrodynamic forces for a submerged sphere in an ocean of finite depth

NASA Astrophysics Data System (ADS)

Mohapatra, Smrutiranjan

2017-08-01

In this paper, we consider a hydroelastic model to examine the radiation of waves by a submerged sphere for both heave and sway motions in a single-layer fluid flowing over an infinitely extended elastic bottom surface in an ocean of finite depth. The elastic bottom is modeled as a thin elastic plate and is based on the Euler-Bernoulli beam equation. The effect of the presence of surface tension at the free-surface is neglected. In such situation, there exist two modes of time-harmonic waves: the one with a lower wavenumber (surface mode) propagates along the free-surface and the other with higher wavenumber (flexural mode) propagates along the elastic bottom surface. Based on the small amplitude wave theory and by using the multipole expansion method, we find the particular solution for the problem of wave radiation by a submerged sphere of finite depth. Furthermore, this method eliminates the need to use large and cumbersome numerical packages for the solution of such problem and leads to an infinite system of linear algebraic equations which are easily solved numerically by any standard technique. The added-mass and damping coefficients for both heave and sway motions are derived and plotted for different submersion depths of the sphere and flexural rigidity of the elastic bottom surface. It is observed that, whenever the sphere nearer to the elastic bed, the added-mass move toward to a constant value of 1, which is approximately twice of the value of added-mass of a moving sphere in a single-layer fluid flowing over a rigid and flat bottom surface.

Wave propagation against current : a study of the effects of vertical shears of the mean current on the geometrical focusing of water waves

NASA Astrophysics Data System (ADS)

Charland, Jenna; Touboul, Julien; Rey, Vincent

2013-04-01

Wave propagation against current : a study of the effects of vertical shears of the mean current on the geometrical focusing of water waves J. Charland * **, J. Touboul **, V. Rey ** jenna.charland@univ-tln.fr * Direction Générale de l'Armement, CNRS Délégation Normandie ** Université de Toulon, 83957 La Garde, France Mediterranean Institute of Oceanography (MIO) Aix Marseille Université, 13288 Marseille, France CNRS/INSU, IRD, MIO, UM 110 In the nearshore area, both wave propagation and currents are influenced by the bathymetry. For a better understanding of wave - current interactions in the presence of a 3D bathymetry, a large scale experiment was carried out in the Ocean Basin FIRST, Toulon, France. The 3D bathymetry consisted of two symmetric underwater mounds on both sides in the mean wave direction. The water depth at the top the mounds was hm=1,5m, the slopes of the mounds were of about 1:3, the water depth was h=3 m elsewhere. For opposite current conditions (U of order 0.30m/s), a huge focusing of the wave up to twice its incident amplitude was observed in the central part of the basin for T=1.4s. Since deep water conditions are verified, the wave amplification is ascribed to the current field. The mean velocity fields at a water depth hC=0.25m was measured by the use of an electromagnetic current meter. The results have been published in Rey et al [4]. The elliptic form of the "mild slope" equation including a uniform current on the water column (Chen et al [1]) was then used for the calculations. The calculated wave amplification of factor 1.2 is significantly smaller than observed experimentally (factor 2). So, the purpose of this study is to understand the physical processes which explain this gap. As demonstrated by Kharif & Pelinovsky [2], geometrical focusing of waves is able to modify significantly the local wave amplitude. We consider this process here. Since vertical velocity profiles measured at some locations have shown significant vertical shears, further theoretical expansions have considered this shearing following the hypothesis proposed by Kirby [3]. A numerical solver for this new equation is being developed. Results obtained with this new equation will be compared to a new set of experiments. This comparison will allow us to quantify the role of a sheared current in the geometrical focusing of the wave. References : [1] W. Chen, V. Panchang, and Z. Demirbilek. On the modeling of wave-current interaction using the elliptic mild-slope wave equation. Ocean Engineering, 32 :2135-2164, 2005. [2] C. Kharif and E. Pelinovsky. Physical mechanisms of the rogue wave phenomenon. European Journal of Mechanics B/Fluids, 22 : 603-634, 2003 [3] J. T. Kirby. A note on linear surface wave-current interaction over slowly varying topography. Journal of Geophysical Research, 89(C1) : 745-747, January 20 1984. [4] V. Rey, F. Guinot, and J. Touboul. Large scale experimental study of wave current interactions in presence of a 3d bathymetry. Genoa : s.n., 2011. International Maritime Association of the Mediterranean.

Rayleigh-wave diffractions due to a void in the layered half space

USGS Publications Warehouse

Xia, J.; Xu, Y.; Miller, R.D.; Nyquist, Jonathan E.

2006-01-01

Void detection is challenging due to the complexity of near-surface materials and the limited resolution of geophysical methods. Although multichannel, high-frequency, surface-wave techniques can provide reliable shear (S)-wave velocities in different geological settings, they are not suitable for detecting voids directly based on anomalies of the S-wave velocity because of limitations on the resolution of S-wave velocity profiles inverted from surface-wave phase velocities. Xia et al. (2006a) derived a Rayleigh-wave diffraction traveltime equation due to a void in the homogeneous half space. Encouraging results of directly detecting a void from Rayleigh-wave diffractions were presented (Xia et al., 2006a). In this paper we used four two-dimensional square voids in the layered half space to demonstrate the feasibility of detecting a void with Rayleigh-wave diffractions. Rayleigh-wave diffractions were recognizable for all these models after removing direct surface waves by F-K filtering. We evaluate the feasibility of applying the Rayleigh-wave diffraction traveltime equation to a void in the layered earth model. The phase velocity of diffracted Rayleigh waves is predominately determined by surrounding materials of a void. The modeling results demonstrate that the Rayleigh-wave diffraction traveltime equation due to a void in the homogeneous half space can be applied to the case of a void in the layered half space. In practice, only two diffraction times are necessary to define the depth to the top of a void and the average velocity of diffracted Rayleigh waves. ?? 2005 Society of Exploration Geophysicists.

Effect of quantum correction on nonlinear thermal wave of electrons driven by laser heating

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nafari, F.; Ghoranneviss, M., E-mail: ghoranneviss@gmail.com

2016-08-15

In thermal interaction of laser pulse with a deuterium-tritium (DT) plane, the thermal waves of electrons are generated instantly. Since the thermal conductivity of electron is a nonlinear function of temperature, a nonlinear heat conduction equation is used to investigate the propagation of waves in solid DT. This paper presents a self-similar analytic solution for the nonlinear heat conduction equation in a planar geometry. The thickness of the target material is finite in numerical computation, and it is assumed that the laser energy is deposited at a finite initial thickness at the initial time which results in a finite temperaturemore » for electrons at initial time. Since the required temperature range for solid DT ignition is higher than the critical temperature which equals 35.9 eV, the effects of quantum correction in thermal conductivity should be considered. This letter investigates the effects of quantum correction on characteristic features of nonlinear thermal wave, including temperature, penetration depth, velocity, heat flux, and heating and cooling domains. Although this effect increases electron temperature and thermal flux, penetration depth and propagation velocity are smaller. This effect is also applied to re-evaluate the side-on laser ignition of uncompressed DT.« less

Nonuniform depth grids in parabolic equation solutions.

PubMed

Sanders, William M; Collins, Michael D

2013-04-01

The parabolic wave equation is solved using a finite-difference solution in depth that involves a nonuniform grid. The depth operator is discretized using Galerkin's method with asymmetric hat functions. Examples are presented to illustrate that this approach can be used to improve efficiency for problems in ocean acoustics and seismo-acoustics. For shallow water problems, accuracy is sensitive to the precise placement of the ocean bottom interface. This issue is often addressed with the inefficient approach of using a fine grid spacing over all depth. Efficiency may be improved by using a relatively coarse grid with nonuniform sampling to precisely position the interface. Efficiency may also be improved by reducing the sampling in the sediment and in an absorbing layer that is used to truncate the computational domain. Nonuniform sampling may also be used to improve the implementation of a single-scattering approximation for sloping fluid-solid interfaces.

Nonlinear Schroedinger Approximations for Partial Differential Equations with Quadratic and Quasilinear Terms

NASA Astrophysics Data System (ADS)

Cummings, Patrick

We consider the approximation of solutions of two complicated, physical systems via the nonlinear Schrodinger equation (NLS). In particular, we discuss the evolution of wave packets and long waves in two physical models. Due to the complicated nature of the equations governing many physical systems and the in-depth knowledge we have for solutions of the nonlinear Schrodinger equation, it is advantageous to use approximation results of this kind to model these physical systems. The approximations are simple enough that we can use them to understand the qualitative and quantitative behavior of the solutions, and by justifying them we can show that the behavior of the approximation captures the behavior of solutions to the original equation, at least for long, but finite time. We first consider a model of the water wave equations which can be approximated by wave packets using the NLS equation. We discuss a new proof that both simplifies and strengthens previous justification results of Schneider and Wayne. Rather than using analytic norms, as was done by Schneider and Wayne, we construct a modified energy functional so that the approximation holds for the full interval of existence of the approximate NLS solution as opposed to a subinterval (as is seen in the analytic case). Furthermore, the proof avoids problems associated with inverting the normal form transform by working with a modified energy functional motivated by Craig and Hunter et al. We then consider the Klein-Gordon-Zakharov system and prove a long wave approximation result. In this case there is a non-trivial resonance that cannot be eliminated via a normal form transform. By combining the normal form transform for small Fourier modes and using analytic norms elsewhere, we can get a justification result on the order 1 over epsilon squared time scale.

Observation of wave celerity evolution in the nearshore using digital video imagery

NASA Astrophysics Data System (ADS)

Yoo, J.; Fritz, H. M.; Haas, K. A.; Work, P. A.; Barnes, C. F.; Cho, Y.

2008-12-01

Celerity of incident waves in the nearshore is observed from oblique video imagery collected at Myrtle Beach, S.C.. The video camera covers the field view of length scales O(100) m. Celerity of waves propagating in shallow water including the surf zone is estimated by applying advanced image processing and analysis methods to the individual video images sampled at 3 Hz. Original image sequences are processed through video image frame differencing, directional low-pass image filtering to reduce the noise arising from foam in the surf zone. The breaking wave celerity is computed along a cross-shore transect from the wave crest tracks extracted by a Radon transform-based line detection method. The observed celerity from the nearshore video imagery is larger than the linear wave celerity computed from the measured water depths over the entire surf zone. Compared to the nonlinear shallow water wave equation (NSWE)-based celerity computed using the measured depths and wave heights, in general, the video-based celerity shows good agreements over the surf zone except the regions across the incipient wave breaking locations. In the regions across the breaker points, the observed wave celerity is even larger than the NSWE-based celerity due to the transition of wave crest shapes. The observed celerity using the video imagery can be used to monitor the nearshore geometry through depth inversion based on the nonlinear wave celerity theories. For this purpose, the exceeding celerity across the breaker points needs to be corrected accordingly compared to a nonlinear wave celerity theory applied.

Acoustic Gravity Waves Generated by an Oscillating Ice Sheet in Arctic Zone

NASA Astrophysics Data System (ADS)

Abdolali, A.; Kadri, U.; Kirby, J. T., Jr.

2016-12-01

We investigate the formation of acoustic-gravity waves due to oscillations of large ice blocks, possibly triggered by atmospheric and ocean currents, ice block shrinkage or storms and ice-quakes.For the idealized case of a homogeneous weakly compressible water bounded at the surface by ice sheet and a rigid bed, the description of the infinite family of acoustic modes is characterized by the water depth h and angular frequency of oscillating ice sheet ω ; The acoustic wave field is governed by the leading mode given by: Nmax=\\floor {(ω h)/(π c)} where c is the sound speed in water and the special brackets represent the floor function (Fig1). Unlike the free-surface setting, the higher acoustic modes might exhibit a larger contribution and therefore all progressive acoustic modes have to be considered.This study focuses on the characteristics of acoustic-gravity waves generated by an oscillating elastic ice sheet in a weakly compressible fluid coupled with a free surface model [Abdolali et al. 2015] representing shrinking ice blocks in realistic sea state, where the randomly oriented ice sheets cause inter modal transition and multidirectional reflections. A theoretical solution and a 3D numerical model have been developed for the study purposes. The model is first validated against the theoretical solution [Kadri, 2016]. To overcome the computational difficulties of 3D models, we derive a depth-integrated equation valid for spatially varying ice sheet thickness and water depth. We show that the generated acoustic-gravity waves contribute significantly to deep ocean currents compared to other mechanisms. In addition, these waves travel at the sound speed in water carrying information on ice sheet motion, providing various implications for ocean monitoring and detection of ice-quakes. Fig1:Snapshots of dynamic pressure given by an oscillating ice sheet; h=4500m, c=1500m/s, semi-length b=10km, ζ =1m, omega=π rad/s. Abdolali, A., Kirby, J. T. and Bellotti, G., 2015, Depth-integrated equation for hydro-acoustic waves with bottom damping, Journal of Fluid Mechanics, 766, R1 doi:10.1017/jfm.2015.37 Kadri, U., 2016, Generation of Hydroacoustic Waves by an Oscillating Ice Block in Arctic Zones, Advances in Acoustics and Vibration. 2016. doi:10.1155/2016/8076108

Numerical Simulations of a Multiscale Model of Stratified Langmuir Circulation

NASA Astrophysics Data System (ADS)

Malecha, Ziemowit; Chini, Gregory; Julien, Keith

2012-11-01

Langmuir circulation (LC), a prominent form of wind and surface-wave driven shear turbulence in the ocean surface boundary layer (BL), is commonly modeled using the Craik-Leibovich (CL) equations, a phase-averaged variant of the Navier-Stokes (NS) equations. Although surface-wave filtering renders the CL equations more amenable to simulation than are the instantaneous NS equations, simulations in wide domains, hundreds of times the BL depth, currently earn the ``grand challenge'' designation. To facilitate simulations of LC in such spatially-extended domains, we have derived multiscale CL equations by exploiting the scale separation between submesoscale and BL flows in the upper ocean. The numerical algorithm for simulating this multiscale model resembles super-parameterization schemes used in meteorology, but retains a firm mathematical basis. We have validated our algorithm and here use it to perform multiscale simulations of the interaction between LC and upper ocean density stratification. ZMM, GPC, KJ gratefully acknowledge funding from NSF CMG Award 0934827.

Fully three-dimensional direct numerical simulation of a plunging breaker

NASA Astrophysics Data System (ADS)

Lubin, Pierre; Vincent, Stéphane; Caltagirone, Jean-Paul; Abadie, Stéphane

2003-07-01

The scope of this paper is to show the results obtained for simulating three-dimensional breaking waves by solving the Navier-Stokes equations in air and water. The interface tracking is achieved by a Lax-Wendroff TVD scheme (Total Variation Diminishing), which is able to handle interface reconnections. We first present the equations and the numerical methods used in this work. We then proceed to the study of a three-dimensional plunging breaking wave, using initial conditions corresponding to unstable periodic sinusoidal waves of large amplitudes. We compare the results obtained for two simulations, a longshore depth perturbation has been introduced in the solution of the flow equations in order to see the transition from a two-dimensional velocity field to a fully three-dimensional one after plunging. Breaking processes including overturning, splash-up and breaking induced vortex-like motion beneath the surface are presented and discussed. To cite this article: P. Lubin et al., C. R. Mecanique 331 (2003).

Coherent reflection from surface gravity water waves during reciprocal acoustic transmissions.

PubMed

Badiey, Mohsen; Song, Aijun; Smith, Kevin B

2012-10-01

During a recent experiment in Kauai, Hawaii, reciprocal transmissions were conducted between two acoustic transceivers mounted on the seafloor at a depth of 100 m. The passage of moving surface wave crests was shown to generate focused and intense coherent acoustic returns, which had increasing or decreasing delay depending on the direction of propagation relative to the direction of surface wave crests. It is shown that a rough surface two-dimensional parabolic equation model with an evolving sea surface can produce qualitative agreement with data for the dynamic surface returns.

Nucleon-anti-nucleon intruder state of Dirac equation for nucleon in deep scalar potential well

NASA Astrophysics Data System (ADS)

Kuo, T. T. S.; Kuo, T. K.; Osnes, E.; Shu, S.

We solve the Dirac radial equation for a nucleon in a scalar Woods-Saxon potential well of depth V0 and radius r0. A sequence of values for the depth and radius are considered. For shallow potentials with -1000MeV ≤ V0 < 0 the wave functions for the positive-energy states ψ+(r) are dominated by their nucleon component f(r). But for deeper potentials with V0 ≤ -1500MeV the ψ+(r) s begin to have dominant anti-nucleon component f(r). In particular, a special intruder state enters with wave function ψ1/2(r) and energy E1/2. We have considered several r0 values between 2 and 8fm. For V0 ≤ -2000 MeV and the above r0 values. ψ1/2(r) is the only bound positive-energy state and has its g(r) closely equal to -f(r), both having a narrow wave packet shape centered around r0. The E1/2 of this state is practically independent of V0 for the above V0 range and obeys closely the relation E1/2 = ℏc/r0.

Wave-current interactions in three dimensions: why 3D radiation stresses are not practical

NASA Astrophysics Data System (ADS)

Ardhuin, Fabrice

2017-04-01

The coupling of ocean circulation and wave models is based on a wave-averaged mass and momentum conservation equations. Whereas several equivalent equations for the evolution of the current momentum have been proposed, implemented, and used, the possibility to formulate practical equations for the total momentum, which is the sum of the current and wave momenta, has been obscured by a series of publications. In a recent update on previous derivations, Mellor (J. Phys. Oceanogr. 2015) proposed a new set of wave-forced total momentum equations. Here we show that this derivation misses a term that integrates to zero over the vertical. This is because he went from his depth-integrated eq. (28) to the 3D equation (30) by simply removing the integral, but any extra zero-integrating term can be added. Corrected for this omission, the equations of motion are equivalent to the earlier equations by Mellor (2003) which are correct when expressed in terms of wave-induced pressure, horizontal velocity and vertical displacement. Namely the total momentum evolution is driven by the horizontal divergence of a horizontal momentum flux, ----- --- ∂^s- Sαβ = ^uα^uβ + δαβ ∂ς (^p- g^s) (1) and the vertical divergence of a vertical flux, Sαz = (p^-g^s)∂^s/∂xα, (2) where p is the wave-induced non-hydrostatic pressure, s is the wave-induced vertical displacement, and u^ α is the horizontal wave-induced velocity in direction α. So far, so good. Problems arise when p and s are evaluated. Indeend, Ardhuin et al. (J. Phys. Oceanogr. 2008) showed that, over a sloping bottom ∂Sαβ/∂xβ is of order of the slope, hence a consistent wave forcing requires an estimation of Sαz that must be estimated to first order in the bottom slope. For this, Airy wave theory, i.e. cosh(kz-+-kh) p ≃ ga cosh (kD ) cosψ, (3) is not enough. Ardhuin et al. (2008) has shown that using an exact solution of the Laplace equations the vertical flux can indeed be computed. The alternative of neglecting completely Sαz, as suggested by Mellor (2011) for small slopes, will always generate spurious currents because of the unbalanced forcing ∂Sαβ/∂xβ. Fortunately, there are many explicit versions of the wave-averaged equations without the wave momentum in them (Suzuki and Fox-Kemper 2016), with or without vortex force which are all consistent with the exact 3D equations of Andrews and McIntyre (1978). There is thus no need to stumble again and again on this fundamental problem of vertical momentum flux, which is a flux of wave momentum. The problem simply goes away by writing the equations for the current momentum only, without the problematic wave momentum. The current and wave momentum are coupled by forcing terms, and the wave momentum can be solved in 2D, the vertical distribution of momentum being maintained by the complex flux Sαz.

Reverse time migration in tilted transversely isotropic media

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhang, Linbing; Rector III, James W.; Hoversten, G. Michael

2004-07-01

This paper presents a reverse time migration (RTM) method for the migration of shot records in tilted transversely isotropic (TTI) media. It is based on the tilted TI acoustic wave equation that was derived from the dispersion relation. The RTM is a full depth migration allowing for velocity to vary laterally as well as vertically and has no dip limitations. The wave equation is solved by a tenth-order finite difference scheme. Using 2D numerical models, we demonstrate that ignoring the tilt angle will introduce both lateral and vertical shifts in imaging. The shifts can be larger than 0.5 wavelength inmore » the vertical direction and 1.5 wavelength in the lateral direction.« less

Charging System Optimization of Triboelectric Nanogenerator for Water Wave Energy Harvesting and Storage.

PubMed

Yao, Yanyan; Jiang, Tao; Zhang, Limin; Chen, Xiangyu; Gao, Zhenliang; Wang, Zhong Lin

2016-08-24

Ocean waves are one of the most promising renewable energy sources for large-scope applications due to the abundant water resources on the earth. Triboelectric nanogenerator (TENG) technology could provide a new strategy for water wave energy harvesting. In this work, we investigated the charging characteristics of utilizing a wavy-structured TENG to charge a capacitor under direct water wave impact and under enclosed ball collision, by combination of theoretical calculations and experimental studies. The analytical equations of the charging characteristics were theoretically derived for the two cases, and they were calculated for various load capacitances, cycle numbers, and structural parameters such as compression deformation depth and ball size or mass. Under the direct water wave impact, the stored energy and maximum energy storage efficiency were found to be controlled by deformation depth, while the stored energy and maximum efficiency can be optimized by the ball size under the enclosed ball collision. Finally, the theoretical results were well verified by the experimental tests. The present work could provide strategies for improving the charging performance of TENGs toward effective water wave energy harvesting and storage.

Nonlinear ultrasonic imaging with X wave

NASA Astrophysics Data System (ADS)

Du, Hongwei; Lu, Wei; Feng, Huanqing

2009-10-01

X wave has a large depth of field and may have important application in ultrasonic imaging to provide high frame rate (HFR). However, the HFR system suffers from lower spatial resolution. In this paper, a study of nonlinear imaging with X wave is presented to improve the resolution. A theoretical description of realizable nonlinear X wave is reported. The nonlinear field is simulated by solving the KZK nonlinear wave equation with a time-domain difference method. The results show that the second harmonic field of X wave has narrower mainlobe and lower sidelobes than the fundamental field. In order to evaluate the imaging effect with X wave, an imaging model involving numerical calculation of the KZK equation, Rayleigh-Sommerfeld integral, band-pass filtering and envelope detection is constructed to obtain 2D fundamental and second harmonic images of scatters in tissue-like medium. The results indicate that if X wave is used, the harmonic image has higher spatial resolution throughout the entire imaging region than the fundamental image, but higher sidelobes occur as compared to conventional focus imaging. A HFR imaging method with higher spatial resolution is thus feasible provided an apodization method is used to suppress sidelobes.

The nature of the sunspot phenomenon. I - Solutions of the heat transport equation

NASA Technical Reports Server (NTRS)

Parker, E. N.

1974-01-01

It is pointed out that sunspots represent a disruption in the uniform flow of heat through the convective zone. The basic sunspot structure is, therefore, determined by the energy transport equation. The solutions of this equation for the case of stochastic heat transport are examined. It is concluded that a sunspot is basically a region of enhanced, rather than inhibited, energy transport and emissivity. The heat flow equations are discussed and attention is given to the shallow depth of the sunspot phenomenon. The sunspot is seen as a heat engine of high efficiency which converts most of the heat flux into hydromagnetic waves.

Experimental Observation of Dark Solitons on Water Surface

DTIC Science & Technology

2016-06-13

Experimental observation of dark solitons on water surface A. Chabchoub1,∗, O. Kimmoun2, H. Branger3, N. Hoffmann1, D. Proment4, M. Onorato4,5, and N...The shape and width of the soliton depend on the water depth, carrier frequency and the amplitude of the background wave. The experimental data...partic- ular, the governing equation describing the dynamics of weakly nonlinear and quasi -monochromatic waves prop- agating on the surface of water with

Fast, purely growing collisionless reconnection as an eigenfunction problem related to but not involving linear whistler waves

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bellan, Paul M.

If either finite electron inertia or finite resistivity is included in 2D magnetic reconnection, the two-fluid equations become a pair of second-order differential equations coupling the out-of-plane magnetic field and vector potential to each other to form a fourth-order system. The coupling at an X-point is such that out-of-plane even-parity electric and odd-parity magnetic fields feed off each other to produce instability if the scale length on which the equilibrium magnetic field changes is less than the ion skin depth. The instability growth rate is given by an eigenvalue of the fourth-order system determined by boundary and symmetry conditions. Themore » instability is a purely growing mode, not a wave, and has growth rate of the order of the whistler frequency. The spatial profile of both the out-of-plane electric and magnetic eigenfunctions consists of an inner concave region having extent of the order of the electron skin depth, an intermediate convex region having extent of the order of the equilibrium magnetic field scale length, and a concave outer exponentially decaying region. If finite electron inertia and resistivity are not included, the inner concave region does not exist and the coupled pair of equations reduces to a second-order differential equation having non-physical solutions at an X-point.« less

Kinematic parameters of internal waves of the second mode in the South China Sea

NASA Astrophysics Data System (ADS)

Kurkina, Oxana; Talipova, Tatyana; Soomere, Tarmo; Giniyatullin, Ayrat; Kurkin, Andrey

2017-10-01

Spatial distributions of the main properties of the mode function and kinematic and non-linear parameters of internal waves of the second mode are derived for the South China Sea for typical summer conditions in July. The calculations are based on the Generalized Digital Environmental Model (GDEM) climatology of hydrological variables, from which the local stratification is evaluated. The focus is on the phase speed of long internal waves and the coefficients at the dispersive, quadratic and cubic terms of the weakly non-linear Gardner model. Spatial distributions of these parameters, except for the coefficient at the cubic term, are qualitatively similar for waves of both modes. The dispersive term of Gardner's equation and phase speed for internal waves of the second mode are about a quarter and half, respectively, of those for waves of the first mode. Similarly to the waves of the first mode, the coefficients at the quadratic and cubic terms of Gardner's equation are practically independent of water depth. In contrast to the waves of the first mode, for waves of the second mode the quadratic term is mostly negative. The results can serve as a basis for expressing estimates of the expected parameters of internal waves for the South China Sea.

Formation of Hydro-acoustic Waves in Dissipative Coupled Weakly Compressible Fluids

NASA Astrophysics Data System (ADS)

Abdolali, A.; Kirby, J. T., Jr.; Bellotti, G.

2014-12-01

Recent advances in deep sea measurement technology provide an increasing opportunity to detect and interpret hydro-acoustic waves as a component in improved Tsunami Early Warning Systems (TEWS). For the idealized case of a homogeneous water column above a moving but otherwise rigid bottom (in terms of assessing acoustic wave interaction), the description of the infinite family of acoustic modes is characterized by local water depth at source area; i.e. the period of the first acoustic mode is given by four times the required time for sound to travel from the seabed to the surface. Spreading off from earthquake zone, the dominant spectrum is filtered and enriched by seamounts and barriers. This study focuses on the characteristics of hydro-acoustic waves generated by sudden sea bottom motion in a weakly compressible fluid coupled with an underlying sedimentary layer, where the added complexity of the sediment layer rheology leads to both the lowering of dominant spectral peaks and wave attenuation across the full spectrum. To overcome the computational difficulties of three-dimensional models, we derive a depth integrated equation valid for varying water depth and sediment thickness. Damping behavior of the two layered system is initially taken into account by introducing the viscosity of fluid-like sedimentary layer. We show that low frequency pressure waves which are precursor components of tsunamis contain information of seafloor motion.

Long-Term Global Morphology of Gravity Wave Activity Using UARS Data

NASA Technical Reports Server (NTRS)

Eckermann, Stephen D.; Jackman, C. (Technical Monitor)

2000-01-01

Gravity waves in satellite data from CRISTA and MLS are studied in depth this quarter. Results this quarter are somewhat limited due to the PI'S heavy involvement throughout this reporting period in on-site forecasting of mountain wave-induced turbulence for the NASA's ER-2 research aircraft at Kiruna, Sweden during the SAGE Ill Ozone Loss and Validation Experiment (SOLVE). Results reported concentrate on further mesoscale modeling studies of mountain waves over the southern Andes, evident in CRISTA and MLS data. Two-dimensional mesoscale model simulations are extended through generalization of model equations to include both rotation and a first-order turbulence closure scheme. Results of three experiments are analyzed in depth and submitted for publication. We also commence simulations with a three-dimensional mesoscale model (MM5) and present preliminary results for the CRISTA 1 period near southern South America. Combination of ground-based temperature data at 87 km from two sites with global HRDl data was continued this quarter, showing stationary planetary wave structures. This work was also submitted for publication.

Determination of Love- and Rayleigh-Wave Magnitudes for Earthquakes and Explosions and Other Studies

DTIC Science & Technology

2012-12-30

the dip- slip or oblique mechanisms . Figure 30. Comparison of Mw (a) and depth (b) computed using srfgrd96 program (Herrmann, 2004...example it follows from Equations A5 and A7 that the Love wave amplitudes for the strike- slip focal mechanism are greater than those for a dip- slip ...These events ranged in size between 3.2 < Mw < 5.1 with the focal mechanisms (Herrmann, pers. comm. 2010) being predominantly strike- slip

Scattering of Lamb waves in a composite plate

NASA Technical Reports Server (NTRS)

Bratton, Robert; Datta, Subhendu; Shah, Arvind

1991-01-01

A combined analytical and finite element technique is developed to gain a better understanding of the scattering of elastic waves by defects. This hybrid method is capable of predicting scattered displacements from arbitrary shaped defects as well as inclusions of different material. The continuity of traction and displacements at the boundaries of the two areas provided the necessary equations to find the nodal displacements and expansion coefficients. Results clearly illustrate the influence of increasing crack depth on the scattered signal.

Nonlinear reflection and refraction of ultrashort light pulses at the surfaces of resonant media and phase memory effects

NASA Astrophysics Data System (ADS)

Vlasov, R. A.; Gadomskii, O. H.; Gadomskaia, I. V.; Samartsev, V. V.

1986-06-01

The method of integrodifferential equations related to the optical Bloch equations is used to study the nonlinear reflection (or refraction) of a scanning laser beam at the surface of a resonant medium excited by traveling and standing surface electromagnetic waves at resonant frequency. The effect of the phase memory of surface atoms on the pulsed action of fields with space-time resolution is taken into account. The reversal of the scanning beam from the excited surface with phase conjugation of the wave front is considered. In addition, the spectrum of the nonlinear surface polaritons is analyzed as a function of the area of the exciting pulse and the penetration depth of polaritons in the resonant optical medium.

Propagation of acoustic-gravity waves in arctic zones with elastic ice-sheets

NASA Astrophysics Data System (ADS)

Kadri, Usama; Abdolali, Ali; Kirby, James T.

2017-04-01

We present an analytical solution of the boundary value problem of propagating acoustic-gravity waves generated in the ocean by earthquakes or ice-quakes in arctic zones. At the surface, we assume elastic ice-sheets of a variable thickness, and show that the propagating acoustic-gravity modes have different mode shape than originally derived by Ref. [1] for a rigid ice-sheet settings. Computationally, we couple the ice-sheet problem with the free surface model by Ref. [2] representing shrinking ice blocks in realistic sea state, where the randomly oriented ice-sheets cause inter modal transition at the edges and multidirectional reflections. We then derive a depth-integrated equation valid for spatially slowly varying thickness of ice-sheet and water depth. Surprisingly, and unlike the free-surface setting, here it is found that the higher acoustic-gravity modes exhibit a larger contribution. These modes travel at the speed of sound in water carrying information on their source, e.g. ice-sheet motion or submarine earthquake, providing various implications for ocean monitoring and detection of quakes. In addition, we found that the propagating acoustic-gravity modes can result in orbital displacements of fluid parcels sufficiently high that may contribute to deep ocean currents and circulation, as postulated by Refs. [1, 3]. References [1] U. Kadri, 2016. Generation of Hydroacoustic Waves by an Oscillating Ice Block in Arctic Zones. Advances in Acoustics and Vibration, 2016, Article ID 8076108, 7 pages http://dx.doi.org/10.1155/2016/8076108 [2] A. Abdolali, J. T. Kirby and G. Bellotti, 2015, Depth-integrated equation for hydro-acoustic waves with bottom damping, J. Fluid Mech., 766, R1 doi:10.1017/jfm.2015.37 [3] U. Kadri, 2014. Deep ocean water transportation by acoustic?gravity waves. J. Geophys. Res. Oceans, 119, doi:10.1002/ 2014JC010234

Acoustic Velocity Log Numerical Simulation and Saturation Estimation of Gas Hydrate Reservoir in Shenhu Area, South China Sea

PubMed Central

Xiao, Kun; Zou, Changchun; Xiang, Biao; Liu, Jieqiong

2013-01-01

Gas hydrate model and free gas model are established, and two-phase theory (TPT) for numerical simulation of elastic wave velocity is adopted to investigate the unconsolidated deep-water sedimentary strata in Shenhu area, South China Sea. The relationships between compression wave (P wave) velocity and gas hydrate saturation, free gas saturation, and sediment porosity at site SH2 are studied, respectively, and gas hydrate saturation of research area is estimated by gas hydrate model. In depth of 50 to 245 m below seafloor (mbsf), as sediment porosity decreases, P wave velocity increases gradually; as gas hydrate saturation increases, P wave velocity increases gradually; as free gas saturation increases, P wave velocity decreases. This rule is almost consistent with the previous research result. In depth of 195 to 220 mbsf, the actual measurement of P wave velocity increases significantly relative to the P wave velocity of saturated water modeling, and this layer is determined to be rich in gas hydrate. The average value of gas hydrate saturation estimated from the TPT model is 23.2%, and the maximum saturation is 31.5%, which is basically in accordance with simplified three-phase equation (STPE), effective medium theory (EMT), resistivity log (Rt), and chloride anomaly method. PMID:23935407

Numerical modeling of porosity waves in the Nankai accretionary wedge décollement, Japan: implications for aseismic slip

NASA Astrophysics Data System (ADS)

Joshi, Ajit; Appold, Martin S.

2017-01-01

Seismic and hydrologic observations of the Nankai accretionary wedge décollement, Japan, show that overpressures at depths greater than ˜2 km beneath the seafloor could have increased to near lithostatic values due to sediment compaction and diagenesis, clay dehydration, and shearing. The resultant high overpressures are hypothesized then to have migrated in rapid surges or pulses called `porosity waves' up the dip of the décollement. Such high velocities—much higher than expected Darcy fluxes—are possible for porosity waves if the porous media through which the waves travel are deformable enough for porosity and permeability to increase strongly with increasing fluid pressure. The present study aimed to test the hypothesis that porosity waves can travel at rates (kilometers per day) fast enough to cause aseismic slip in the Nankai décollement. The hypothesis was tested using a one-dimensional numerical solution to the fluid mass conservation equation for elastic porous media. Results show that porosity waves generated at depths of ˜2 km from overpressures in excess of lithostatic pressure can propagate at rates sufficient to account for aseismic slip along the décollement over a wide range of hydrogeological conditions. Sensitivity analysis showed porosity wave velocity to be strongly dependent on specific storage, fluid viscosity, and the permeability-depth gradient. Overpressure slightly less than lithostatic pressure could also produce porosity waves capable of traveling at velocities sufficient to cause aseismic slip, provided that hydrogeologic properties of the décollement are near the limits of their geologically reasonable ranges.

Gravity–capillary waves in finite depth on flows of constant vorticity

PubMed Central

Hsu, Hung-Chu; Francius, Marc; Kharif, Christian

2016-01-01

This paper considers two-dimensional periodic gravity–capillary waves propagating steadily in finite depth on a linear shear current (constant vorticity). A perturbation series solution for steady periodic waves, accurate up to the third order, is derived using a classical Stokes expansion procedure, which allows us to include surface tension effects in the analysis of wave–current interactions in the presence of constant vorticity. The analytical results are then compared with numerical computations with the full equations. The main results are (i) the phase velocity is strongly dependent on the value of the vorticity; (ii) the singularities (Wilton singularities) in the Stokes expansion in powers of wave amplitude that correspond to a Bond number of 1/2 and 1/3, which are the consequences of the non-uniformity in the ordering of the Fourier coefficients, are found to be influenced by vorticity; (iii) different surface profiles of capillary–gravity waves are computed and the effect of vorticity on those profiles is shown to be important, in particular that the solutions exhibit type-2-like wave features, characterized by a secondary maximum on the surface profile with a trough between the two maxima. PMID:27956873

Characteristics of wind waves in shallow tidal basins and how they affect bed shear stress, bottom erosion, and the morphodynamic evolution of coupled marsh and mudflat landforms

NASA Astrophysics Data System (ADS)

Tommasini, Laura; Carniello, Luca; Goodwin, Guillaume; Mudd, Simon M.; Matticchio, Bruno; D'Alpaos, Andrea

2017-04-01

Wind-wave induced erosion is one of the main processes controlling the morphodynamic evolution of shallow tidal basins, because wind waves promote the erosion of subtidal platforms, tidal flats and salt marshes. Our study considered zero-, one-and two-dimensional wave models. First, we analyzed the relations between wave parameters, depth and bed shear stress with constant and variable wave period considering two zero-dimensional models based on the Young and Verhagen (1996), and Carniello et al. (2005, 2011) approaches. The first one is an empirical method that computes wave height and the variable wave period from wind velocity, fetch and water depth. The second one is based on the solution of wave action conservation equation, we use this second approach for computing the bottom shear stress and wave height, considering variable and constant (t=2s) wave period. Second, we compared the wave spectral model SWAN with a fully coupled Wind-Wave Tidal Model applied to a 1D rectangular domain. These models describe both the growth and propagation of wind waves. Finally, we applied the two-dimensional Wind Wave Tidal Model (WWTM) to six different configurations of the Venice lagoon considering the same boundary conditions and we evaluated the spatial variation of mean wave power density. The analysis with zero-dimensional models show that the effects of the different model assumptions on the wave period and on the wave height computation cannot be neglected. In particular, the relationships between bottom shear stress and water depth have different shapes. Two results emerge: first, the differences are higher for small depths, and then the maximum values reached with the Young and Verhagen (1996) approach are greater than the maximum values obtained with WWTM approach. The results obtained with two-dimensional models suggest that the wave height is different in particular for small fetch, this could be due to the different formulation of the wave period. Finally, the application of WWTM for the entire Lagoon basin underlines an increase of the mean power density in the last four centuries, in particular in the central-southern part of the lagoon between Chioggia and Malamocco inlets.

Velocities of Subducted Sediments and Continents

NASA Astrophysics Data System (ADS)

Hacker, B. R.; van Keken, P. E.; Abers, G. A.; Seward, G.

2009-12-01

The growing capability to measure seismic velocities in subduction zones has led to unusual observations. For example, although most minerals have VP/ VS ratios around 1.77, ratios <1.7 and >1.8 have been observed. Here we explore the velocities of subducted sediments and continental crust from trench to sub-arc depths using two methods. (1) Mineralogy was calculated as a function of P & T for a range of subducted sediment compositions using Perple_X, and rock velocities were calculated using the methodology of Hacker & Abers [2004]. Calculated slab-top temperatures have 3 distinct depth intervals with different dP/dT gradients that are determined by how coupling between the slab and mantle wedge is modeled. These three depth intervals show concomitant changes in VP and VS: velocities initially increase with depth, then decrease beyond the modeled decoupling depth where induced flow in the wedge causes rapid heating, and increase again at depth. Subducted limestones, composed chiefly of aragonite, show monotonic increases in VP/ VS from 1.63 to 1.72. Cherts show large jumps in VP/ VS from 1.55-1.65 to 1.75 associated with the quartz-coesite transition. Terrigenous sediments dominated by quartz and mica show similar, but more-subdued, transitions from ~1.67 to 1.78. Pelagic sediments dominated by mica and clinopyroxene show near-monotonic increases in VP/ VS from 1.74 to 1.80. Subducted continental crust that is too dry to transform to high-pressure minerals has a VP/ VS ratio of 1.68-1.70. (2) Velocity anisotropy calculations were made for the same P-T dependent mineralogies using the Christoffel equation and crystal preferred orientations measured via electron-backscatter diffraction for typical constituent phases. The calculated velocity anisotropies range from 5-30%. For quartz-rich rocks, the calculated velocities show a distinct depth dependence because crystal slip systems and CPOs change with temperature. In such rocks, the fast VP direction varies from slab-normal at shallow depths through trench-parallel at moderate depths to down-dip approaching sub-arc depths. Vertically incident waves have VP/ VS of 1.7-1.3 over the same range of depths, waves propagating up dip have VP/ VS of 1.7-1.3, and waves propagating along the slab at constant depth have VP/ VS of 1.7-1.45. These remarkably low VP/ VS ratios are due to the anomalous elastic behavior of quartz. More aluminous lithologies have elevated VP/ VS ratios: 1.85 for slab-normal waves, 1.75 for trench-parallel waves, and 1.65 for down-dip waves. Subducted continental crust that is too dry to transform to high-pressure minerals has relatively ordinary VP/ VS ratio of 1.71-1.75 for vertically incident waves, 1.6-1.7 for waves propagating up dip, and 1.65-1.75 for waves propagating along the slab. Thus, subducted mica-rich sediments can have high VP/ VS ratios, whereas quartzose lithologies generate low VP/ VS ratios.

Rogue wave variational modelling through the interaction of two solitary waves

NASA Astrophysics Data System (ADS)

Gidel, Floriane; Bokhove, Onno

2016-04-01

The extreme and unexpected characteristics of Rogue waves have made them legendary for centuries. It is only on the 1st of January 1995 that these mariners' tales started to raise scientist's curiosity, when such a wave was recorded in the North Sea; a sudden wall of water hit the Draupner offshore platform, more than twice higher than the other waves, providing evidence of the existence of rogue or freak waves. Since then, studies have shown that these surface gravity waves of high amplitude (at least twice the height of the other sea waves [Dyste et al., 2008]) appear in non-linear dispersive water motion [Drazin and Johnson, 1989], at any depth, and have caused a lot of damage in recent years [Nikolkina and Didenkulova, 2011 ]. So far, most of the studies have tried to determine their probability of occurrence, but no conclusion has been achieved yet, which means that we are currently unenable to predict or avoid these monster waves. An accurate mathematical and numerical water-wave model would enable simulation and observation of this external forcing on boats and offshore structures and hence reduce their threat. In this work, we aim to model rogue waves through a soliton splash generated by the interaction of two solitons coming from different channels at a specific angle. Kodama indeed showed that one way to produce extreme waves is through the intersection of two solitary waves, or one solitary wave and its oblique reflection on a vertical wall [Yeh, Li and Kodama, 2010 ]. While he modelled Mach reflection from Kadomtsev-Petviashvili (KP) theory, we aim to model rogue waves from the three-dimensional potential flow equations and/or their asymptotic equivalent described by Benney and Luke [Benney and Luke, 1964]. These theories have the advantage to allow wave propagation in several directions, which is not the case with KP equations. The initial solitary waves are generated by removing a sluice gate in each channel. The equations are derived through a variational approach, based on Luke's variational principle [Luke, 1967], and its dynamical equivalent from Miles [Miles, 1977], that describe incompressible and inviscid potential flows with free surface, through the variations of the Lagrangian. This Lagrangian, obtained from Bernouilli's equations, can be expressed in a Hamiltonian form, for which robust time integrators have been derived [Gagarina et al., 2015]. A Galerkin finite element method is then used to solve the system numerically, and we aim to compare our simulations to exact solutions of the KP-equation.

Scattering of surface water waves involving semi-infinite floating elastic plates on water of finite depth

NASA Astrophysics Data System (ADS)

Chakrabarti, Aloknath; Mohapatra, Smrutiranjan

2013-09-01

Two problems of scattering of surface water waves involving a semi-infinite elastic plate and a pair of semi-infinite elastic plates, separated by a gap of finite width, floating horizontally on water of finite depth, are investigated in the present work for a two-dimensional time-harmonic case. Within the frame of linear water wave theory, the solutions of the two boundary value problems under consideration have been represented in the forms of eigenfunction expansions. Approximate values of the reflection and transmission coefficients are obtained by solving an over-determined system of linear algebraic equations in each problem. In both the problems, the method of least squares as well as the singular value decomposition have been employed and tables of numerical values of the reflection and transmission coefficients are presented for specific choices of the parameters for modelling the elastic plates. Our main aim is to check the energy balance relation in each problem which plays a very important role in the present approach of solutions of mixed boundary value problems involving Laplace equations. The main advantage of the present approach of solutions is that the results for the values of reflection and transmission coefficients obtained by using both the methods are found to satisfy the energy-balance relations associated with the respective scattering problems under consideration. The absolute values of the reflection and transmission coefficients are presented graphically against different values of the wave numbers.

Overdetermined shooting methods for computing standing water waves with spectral accuracy

NASA Astrophysics Data System (ADS)

Wilkening, Jon; Yu, Jia

2012-01-01

A high-performance shooting algorithm is developed to compute time-periodic solutions of the free-surface Euler equations with spectral accuracy in double and quadruple precision. The method is used to study resonance and its effect on standing water waves. We identify new nucleation mechanisms in which isolated large-amplitude solutions, and closed loops of such solutions, suddenly exist for depths below a critical threshold. We also study degenerate and secondary bifurcations related to Wilton's ripples in the traveling case, and explore the breakdown of self-similarity at the crests of extreme standing waves. In shallow water, we find that standing waves take the form of counter-propagating solitary waves that repeatedly collide quasi-elastically. In deep water with surface tension, we find that standing waves resemble counter-propagating depression waves. We also discuss the existence and non-uniqueness of solutions, and smooth versus erratic dependence of Fourier modes on wave amplitude and fluid depth. In the numerical method, robustness is achieved by posing the problem as an overdetermined nonlinear system and using either adjoint-based minimization techniques or a quadratically convergent trust-region method to minimize the objective function. Efficiency is achieved in the trust-region approach by parallelizing the Jacobian computation, so the setup cost of computing the Dirichlet-to-Neumann operator in the variational equation is not repeated for each column. Updates of the Jacobian are also delayed until the previous Jacobian ceases to be useful. Accuracy is maintained using spectral collocation with optional mesh refinement in space, a high-order Runge-Kutta or spectral deferred correction method in time and quadruple precision for improved navigation of delicate regions of parameter space as well as validation of double-precision results. Implementation issues for transferring much of the computation to a graphic processing units are briefly discussed, and the performance of the algorithm is tested for a number of hardware configurations.

Numerical modelling of wind effects on breaking waves in the surf zone

NASA Astrophysics Data System (ADS)

Xie, Zhihua

2017-10-01

Wind effects on periodic breaking waves in the surf zone have been investigated in this study using a two-phase flow model. The model solves the Reynolds-averaged Navier-Stokes equations with the k - 𝜖 turbulence model simultaneously for the flows both in the air and water. Both spilling and plunging breakers over a 1:35 sloping beach have been studied under the influence of wind, with a focus during wave breaking. Detailed information of the distribution of wave amplitudes and mean water level, wave-height-to-water-depth ratio, the water surface profiles, velocity, vorticity, and turbulence fields have been presented and discussed. The inclusion of wind alters the air flow structure above water waves, increases the generation of vorticity, and affects the wave shoaling, breaking, overturning, and splash-up processes. Wind increases the water particle velocities and causes water waves to break earlier and seaward, which agrees with the previous experiment.

Stability of wave processes in a rotating electrically conducting fluid

NASA Astrophysics Data System (ADS)

Peregudin, S. I.; Peregudina, E. S.; Kholodova, S. E.

2018-05-01

The paper puts forward a mathematical model of dynamics of spatial large-scale motions in a rotating layer of electrically conducting incompressible perfect fluid of variable depth with due account of dissipative effects. The resulting boundary-value problem is reduced to a vector system of partial differential equations for any values of the Reynolds number. Theoretical analysis of the so-obtained analytical solution reveals the effect of the magnetic field diffusion on the stability of the wave mode — namely, with the removed external magnetic field, the diffusion of the magnetic field promotes its damping. Besides, a criterion of stability of a wave mode is obtained.

Building a USGS National Crustal Model: Theoretical foundation, inputs, and calibration for the Western United States

NASA Astrophysics Data System (ADS)

Shah, A. K.; Boyd, O. S.; Sowers, T.; Thompson, E.

2017-12-01

Seismic hazard assessments depend on an accurate prediction of ground motion, which in turn depends on a base knowledge of three-dimensional variations in density, seismic velocity, and attenuation. We are building a National Crustal Model (NCM) using a physical theoretical foundation, 3-D geologic model, and measured data for calibration. An initial version of the NCM for the western U.S. is planned to be available in mid-2018 and for the remainder of the U.S. in 2019. The theoretical foundation of the NCM couples Biot-Gassmann theory for the porous composite with mineral physics calculations for the solid mineral matrix. The 3-D geologic model is defined through integration of results from a range of previous studies including maps of surficial porosity, surface and subsurface lithology, and the depths to bedrock and crystalline basement or seismic equivalent. The depths to bedrock and basement are estimated using well, seismic, and gravity data; in many cases these data are compiled by combining previous studies. Two parameters controlling how porosity changes with depth are assumed to be a function of lithology and calibrated using measured shear- and compressional-wave velocity and density profiles. Uncertainties in parameters derived from the model increase with depth and are dependent on the quantity and quality of input data sets. An interface to the model provides parameters needed for ground motion prediction equations in the Western U.S., including, for example, the time-averaged shear-wave velocity in the upper 30 meters (VS30) and the depths to 1.0 and 2.5 km/s shear-wave speeds (Z1.0 and Z2.5), which have a very rough correlation to the depths to bedrock and basement, as well as interpolated 3D models for use with various Urban Hazard Mapping strategies. We compare parameters needed for ground motion prediction equations including VS30, Z1.0, and Z2.5 between those derived from existing models, for example, 3-D velocity models for southern California available from the Southern California Earthquake Center, and those derived from the NCM and assess their ability to reduce the variance of observed ground motions.

Quantum theory of rotational isomerism and Hill equation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ugulava, A.; Toklikishvili, Z.; Chkhaidze, S.

2012-06-15

The process of rotational isomerism of linear triatomic molecules is described by the potential with two different-depth minima and one barrier between them. The corresponding quantum-mechanical equation is represented in the form that is a special case of the Hill equation. It is shown that the Hill-Schroedinger equation has a Klein's quadratic group symmetry which, in its turn, contains three invariant subgroups. The presence of these subgroups makes it possible to create a picture of energy spectrum which depends on a parameter and has many merging and branch points. The parameter-dependent energy spectrum of the Hill-Schroedinger equation, like Mathieu-characteristics, containsmore » branch points from the left and from the right of the demarcation line. However, compared to the Mathieu-characteristics, in the Hill-Schroedinger equation spectrum the 'right' points are moved away even further for some distance that is the bigger, the bigger is the less deep well. The asymptotic wave functions of the Hill-Schroedinger equation for the energy values near the potential minimum contain two isolated sharp peaks indicating a possibility of the presence of two stable isomers. At high energy values near the potential maximum, the height of two peaks decreases, and between them there appear chaotic oscillations. This form of the wave functions corresponds to the process of isomerization.« less

The GeoClaw software for depth-averaged flows with adaptive refinement

USGS Publications Warehouse

Berger, M.J.; George, D.L.; LeVeque, R.J.; Mandli, Kyle T.

2011-01-01

Many geophysical flow or wave propagation problems can be modeled with two-dimensional depth-averaged equations, of which the shallow water equations are the simplest example. We describe the GeoClaw software that has been designed to solve problems of this nature, consisting of open source Fortran programs together with Python tools for the user interface and flow visualization. This software uses high-resolution shock-capturing finite volume methods on logically rectangular grids, including latitude-longitude grids on the sphere. Dry states are handled automatically to model inundation. The code incorporates adaptive mesh refinement to allow the efficient solution of large-scale geophysical problems. Examples are given illustrating its use for modeling tsunamis and dam-break flooding problems. Documentation and download information is available at www.clawpack.org/geoclaw. ?? 2011.

Simulation of Wave-Current Interaction Using a Three-Dimensional Hydrodynamic Model Coupled With a Phase Averaged Wave Model

NASA Astrophysics Data System (ADS)

Marsooli, R.; Orton, P. M.; Georgas, N.; Blumberg, A. F.

2016-02-01

The Stevens Institute of Technology Estuarine and Coastal Ocean Model (sECOM) has been coupled with a more advanced surface wave model to simulate wave‒current interaction, and results have been validated in estuarine and nearshore waters. sECOM is a three‒dimensional, hydrostatic, free surface, primitive equation model. It solves the Navier‒Stokes equations and the conservation equations for temperature and salinity using a finite‒difference method on an Arakawa C‒grid with a terrain‒following (sigma) vertical coordinate and orthogonal curvilinear horizontal coordinate system. The model is coupled with the surface wave model developed by Mellor et al. (2008), which solves the spectral equation and takes into account depth and current refraction, and deep and shallow water. The wave model parameterizes the energy distribution in frequency space and the wave‒wave interaction process by using a specified spectrum shape. The coupled wave‒hydrodynamic model considers the wave‒current interaction through wave‒induced bottom stress, depth‒dependent radiation stress, and wave effects on wind‒induced surface stress. The model is validated using the data collected at a natural sandy beach at Duck, North Carolina, during the DUCK94 experiment. This test case reveals the capability of the model to simulate the wave‒current interaction in nearshore coastal systems. The model is further validated using the data collected in Jamaica Bay, a semi‒enclosed body of water located in New York City region. This test reveals the applicability of the model to estuarine systems. These validations of the model and comparisons to its prior wave model, the Great Lakes Environmental Research Laboratory (GLERL) wave model (Donelan 1977), are presented and discussed. ReferencesG.L. Mellor, M.A. Donelan, and L‒Y. Oey, 2008, A Surface Wave Model for Coupling with Numerical Ocean Circulation Models. J. Atmos. Oceanic Technol., 25, 1785‒1807.Donelan, M. A 1977. A simple numerical model for wave and wind stress application. Report, National Water Research Institute, Burlington, Ontario, Canada, 28 pp.

Evolution of Nonlinear Internal Waves in China Seas

NASA Technical Reports Server (NTRS)

Liu, Antony K.; Hsu, Ming-K.; Liang, Nai K.

1997-01-01

Synthetic Aperture Radar (SAR) images from ERS-I have been used to study the characteristics of internal waves of Taiwan in the East China Sea, and east of Hainan Island in the South China Sea. Rank-ordered packets of internal solitons propagating shoreward from the edge of the continental shelf were observed in the SAR images. Based on the assumption of a semidiurnal tidal origin, the wave speed can be estimated and is consistent with the internal wave theory. By using the SAR images and hydrographic data, internal waves of elevation have been identified in shallow water due to a thicker mixed layer as compared with the bottom layer on the continental shelf. The generation mechanism includes the influences of the tide and the Kuroshio intrusion across the continental shelf for the formations of elevation internal waves. The effects of water depth on the evolution of solitons and wave packets are modeled by nonlinear Kortweg-deVries (KdV) type equation and linked to satellite image observations. The numerical calculations of internal wave evolution on the continental shelf have been performed and compared with the SAR observations. For a case of depression waves in deep water, the solitons first disintegrate into dispersive wave trains and then evolve to a packet of elevation waves in the shallow water area after they pass through a turning point of approximately equal layer depths has been observed in the SAR image and simulated by numerical model.

Assessing Tsunami Vulnerabilities of Geographies with Shallow Water Equations

NASA Technical Reports Server (NTRS)

Aras, Rifat; Shen, Yuzhong

2012-01-01

Tsunami preparedness is crucial for saving human lives in case of disasters that involve massive water movement. In this work, we develop a framework for visual assessment of tsunami preparedness of geographies. Shallow water equations (also called Saint Venant equations) are a set of hyperbolic partial differential equations that are derived by depth-integrating the Navier-Stokes equations and provide a great abstraction of water masses that have lower depths compared to their free surface area. Our specific contribution in this study is to use Microsoft's XNA Game Studio to import underwater and shore line geographies, create different tsunami scenarios, and visualize the propagation of the waves and their impact on the shore line geography. Most importantly, we utilized the computational power of graphical processing units (GPUs) as HLSL based shader files and delegated all of the heavy computations to the GPU. Finally, we also conducted a validation study, in which we have tested our model against a controlled shallow water experiment. We believe that such a framework with an easy to use interface that is based on readily available software libraries, which are widely available and easily distributable, would encourage not only researchers, but also educators to showcase ideas.

Wave scattering by an axisymmetric ice floe of varying thickness

NASA Astrophysics Data System (ADS)

Bennetts, Luke G.; Biggs, Nicholas R. T.; Porter, David

2009-04-01

The problem of water wave scattering by a circular ice floe, floating in fluid of finite depth, is formulated and solved numerically. Unlike previous investigations of such situations, here we allow the thickness of the floe (and the fluid depth) to vary axisymmetrically and also incorporate a realistic non-zero draught. A numerical approximation to the solution of this problem is obtained to an arbitrary degree of accuracy by combining a Rayleigh-Ritz approximation of the vertical motion with an appropriate variational principle. This numerical solution procedure builds upon the work of Bennets et al. (2007, J. Fluid Mech., 579, 413-443). As part of the numerical formulation, we utilize a Fourier cosine expansion of the azimuthal motion, resulting in a system of ordinary differential equations to solve in the radial coordinate for each azimuthal mode. The displayed results concentrate on the response of the floe rather than the scattered wave field and show that the effects of introducing the new features of varying floe thickness and a realistic draught are significant.

Computation of rapidly varied unsteady, free-surface flow

USGS Publications Warehouse

Basco, D.R.

1987-01-01

Many unsteady flows in hydraulics occur with relatively large gradients in free surface profiles. The assumption of hydrostatic pressure distribution with depth is no longer valid. These are rapidly-varied unsteady flows (RVF) of classical hydraulics and also encompass short wave propagation of coastal hydraulics. The purpose of this report is to present an introductory review of the Boussinnesq-type differential equations that describe these flows and to discuss methods for their numerical integration. On variable slopes and for large scale (finite-amplitude) disturbances, three independent derivational methods all gave differences in the motion equation for higher order terms. The importance of these higher-order terms for riverine applications must be determined by numerical experiments. Care must be taken in selection of the appropriate finite-difference scheme to minimize truncation error effects and the possibility of diverging (double mode) numerical solutions. It is recommended that practical hydraulics cases be established and tested numerically to demonstrate the order of differences in solution with those obtained from the long wave equations of St. Venant. (USGS)

On the modeling of wave-enhanced turbulence nearshore

NASA Astrophysics Data System (ADS)

Moghimi, Saeed; Thomson, Jim; Özkan-Haller, Tuba; Umlauf, Lars; Zippel, Seth

2016-07-01

A high resolution k-ω two-equation turbulence closure model, including surface wave forcing was employed to fully resolve turbulence dissipation rate profiles close to the ocean surface. Model results were compared with observations from Surface Wave Instrument Floats with Tracking (SWIFTs) in the nearshore region at New River Inlet, North Carolina USA, in June 2012. A sensitivity analysis for different physical parameters and wave and turbulence formulations was performed. The flux of turbulent kinetic energy (TKE) prescribed by wave dissipation from a numerical wave model was compared with the conventional prescription using the wind friction velocity. A surface roughness length of 0.6 times the significant wave height was proposed, and the flux of TKE was applied at a distance below the mean sea surface that is half of this roughness length. The wave enhanced layer had a total depth that is almost three times the significant wave height. In this layer the non-dimensionalized Terray scaling with power of - 1.8 (instead of - 2) was applicable.

Contribution of non-resonant wave-wave interactions in the dynamics of long-crested sea wave fields

NASA Astrophysics Data System (ADS)

Benoit, Michel

2017-04-01

Gravity waves fields at the surface of the oceans evolve under the combined effects of several physical mechanisms, of which nonlinear wave-wave interactions play a dominant role. These interactions transfer energy between components within the energy spectrum and allow in particular to explain the shape of the distribution of wave energy according to the frequencies and directions of propagation. In the oceanic domain (deep water conditions), dominant interactions are third-order resonant interactions, between quadruplets (or quartets) of wave components, and the evolution of the wave spectrum is governed by a kinetic equation, established by Hasselmann (1962) and Zakharov (1968). The kinetic equation has a number of interesting properties, including the existence of self-similar solutions and cascades to small and large wavelengths of waves, which can be studied in the framework of the wave (or weak) turbulence theory (e.g. Badulin et al., 2005). With the aim to obtain more complete and precise modelling of sea states dynamics, we investigate here the possibility and consequences of taking into account the non-resonant interactions -quasi-resonant in practice- among 4 waves. A mathematical formalism has recently been proposed to account for these non-resonant interactions in a statistical framework by Annenkov & Shrira (2006) (Generalized Kinetic Equation, GKE) and Gramstad & Stiassnie (2013) (Phase Averaged Equation, PAE). In order to isolate the non-resonant contributions, we limit ourselves here to monodirectional (i.e. long-crested) wave trains, since in this case the 4-wave resonant interactions vanish. The (stochastic) modelling approaches proposed by Annenkov & Shrira (2006) and Gramstad & Stiassnie (2013) are compared to phase-resolving (deterministic) simulations based on a fully nonlinear potential approach (using a high-order spectral method, HOS). We study and compare the evolution dynamics of the wave spectrum at different time scales (i.e. over durations ranging from a few wave periods to 1000 periods), with the aim of highlighting the capabilities and limitations of the GKE-PAE models. Different situations are considered by varying the relative water depth, the initial steepness of the wave field, and the shape of the initial wave spectrum, including arbitrary forms. References: Annenkov S.Y., Shrira V.I. (2006) Role of non-resonant interactions in the evolution of nonlinear random water wave fields. J. Fluid Mech., 561, 181-207. Badulin S.I., Pushkarev A.N., Resio D., Zakharov V.E. (2005) Self-similarity of wind-driven seas. Nonlin. Proc. Geophys., 12, 891-946. Gramstad O., Stiassnie M. (2013) Phase-averaged equation for water waves. J. Fluid Mech., 718, 280- 303. Hasselmann K. (1962) On the non-linear energy transfer in a gravity-wave spectrum. Part 1. General theory. J. Fluid Mech., 12, 481-500. Zakharov V.E. (1968) Stability of periodic waves of finite amplitude on the surface of a deep fluid. J. App. Mech. Tech. Phys., 9(2), 190-194.

Wave trapping by dual porous barriers near a wall in the presence of bottom undulation

NASA Astrophysics Data System (ADS)

Kaligatla, R. B.; Manisha; Sahoo, T.

2017-09-01

Trapping of oblique surface gravity waves by dual porous barriers near a wall is studied in the presence of step type varying bottom bed that is connected on both sides by water of uniform depths. The porous barriers are assumed to be fixed at a certain distance in front of a vertical rigid wall. Using linear water wave theory and Darcy's law for flow past porous structure, the physical problem is converted into a boundary value problem. Using eigenfunction expansion in the uniform bottom bed region and modified mild-slope equation in the varying bottom bed region, the mathematical problem is handled for solution. Moreover, certain jump conditions are used to account for mass conservation at slope discontinuities in the bottom bed profile. To understand the effect of dual porous barriers in creating tranquility zone and minimum load on the sea wall, reflection coefficient, wave forces acting on the barrier and the wall, and surface wave elevation are computed and analyzed for different values of depth ratio, porous-effect parameter, incident wave angle, gap between the barriers and wall and slope length of undulated bottom. The study reveals that with moderate porosity and suitable gap between barriers and sea wall, using dual barriers an effective wave trapping system can be developed which will exert less wave force on the barriers and the rigid wall. The proposed wave trapping system is likely to be of immense help for protecting various facilities/ infrastructures in coastal environment.

Two dimensional modelling of flood flows and suspended sedimenttransport: the case of the Brenta River, Veneto (Italy)

NASA Astrophysics Data System (ADS)

Martini, P.; Carniello, L.; Avanzi, C.

2004-03-01

The paper presents a numerical model for the simulation of flood waves and suspended sediment transport in a lowland river basin of North Eastern Italy. The two dimensional depth integrated momentum and continuity equations are modified to take into account the bottom irregularities that strongly affect the hydrodynamics in partially dry areas, as for example, in the first stages of an inundation process or in tidal flow. The set of equations are solved with a standard Galerkin finite element method using a semi-implicit numerical scheme where the effects of both the small channel network and the regulation devices on the flood wave propagation are accounted for. Transport of suspended sediment and bed evolution are coupled with the hydrodynamics using an appropriate form of the advection-dispersion equation and Exner's equation. Applications to a case study are presented in which the effects of extreme flooding on the Brenta River (Italy) are examined. Urban and rural flood risk areas are identified and the effects of a alleviating action based on a diversion channel flowing into Venice Lagoon are simulated. The results show that this solution strongly reduces the flood risk in the downstream areas and can provide an important source of sediment for the Venice Lagoon. Finally, preliminary results of the sediment dispersion due to currents and waves in the Venice Lagoon are presented.

Explicit wave action conservation for water waves on vertically sheared flows

NASA Astrophysics Data System (ADS)

Quinn, Brenda; Toledo, Yaron; Shrira, Victor

2016-04-01

Water waves almost always propagate on currents with a vertical structure such as currents directed towards the beach accompanied by an under-current directed back toward the deep sea or wind-induced currents which change magnitude with depth due to viscosity effects. On larger scales they also change their direction due to the Coriolis force as described by the Ekman spiral. This implies that the existing wave models, which assume vertically-averaged currents, is an approximation which is far from realistic. In recent years, ocean circulation models have significantly improved with the capability to model vertically-sheared current profiles in contrast with the earlier vertically-averaged current profiles. Further advancements have coupled wave action models to circulation models to relate the mutual effects between the two types of motion. Restricting wave models to vertically-averaged non-turbulent current profiles is obviously problematic in these cases and the primary goal of this work is to derive and examine a general wave action equation which accounts for these shortcoming. The formulation of the wave action conservation equation is made explicit by following the work of Voronovich (1976) and using known asymptotic solutions of the boundary value problem which exploit the smallness of the current magnitude compared to the wave phase velocity and/or its vertical shear and curvature. The adopted approximations are shown to be sufficient for most of the conceivable applications. This provides correction terms to the group velocity and wave action definition accounting for the shear effects, which are fitting for application to operational wave models. In the limit of vanishing current shear, the new formulation reduces to the commonly used Bretherton & Garrett (1968) no-shear wave action equation where the invariant is calculated with the current magnitude taken at the free surface. It is shown that in realistic oceanic conditions, the neglect of the vertical structure of the currents in wave modelling which is currently universal, might lead to significant errors in wave amplitude and the predicted wave ray paths. An extension of the work toward the more complex case of turbulent currents will also be discussed.

On the hyperbolic nature of the equations of alluvial river hydraulics and the equivalence of stable and energy dissipating shocks

NASA Astrophysics Data System (ADS)

Zanraea, D. D. L.; Needham, D. J.

The depth-averaged hydraulic equations augmented with a suitable bed-load sediment transport function form a closed system which governs the one-dimensional flow in an alluvial river or channel. In this paper, it is shown that this system is hyperbolic and yields three families of shock-wave solutions. These are determined to be temporally stable in restricted regions of the (H, F0)-plane, via the Lax shock inequalities. Further, it is demonstrated that this criterion is equivalent to the energy dissipation criterion developed by Needham and Hey (1991).

USSR and Eastern Europe Scientific Abstracts, Geophysics, Astronomy and Space, Number 398

DTIC Science & Technology

1977-05-25

Determining Ship’s Speed 25 Compensation of Cross Coupling Effect in Marine Gravimetry ... 26 Korteweg-De Vries Equation for Internal Waves in...winters and increased precipitation , favorable conditions for vegetation. [287] RADIOACOUSTIC SOUNDING OF THE ATMOSPHERE Moscow IZVESTIYA AKADEMII...complex of geophys- ical and geological methods was used: seismic profiling, gravimetry , mag- netometry, depth sounding and dredging. The director

Study of interfacial behavior in concurrent gas-liquid flows

NASA Astrophysics Data System (ADS)

McCready, Mark J.

1989-02-01

This research is focused on acquiring an understanding of the fundamental processes which occur within the liquid layer of separated (i.e., annular or stratified) gas-liquid flows. Knowledge of this behavior is essential for interpretation of pressure drops, entrainment fraction, transport processes and possibly flow regime transitions in gas-liquid flows. We are examining the qualitative and quantitative nature of the interface, using this information to predict the behavior of the flow field within the film and also studying the effect of the flow field on interface and wall heat and mass transfer rates. Study of waves on sheared liquid layers is best broken into two limiting cases, film depth ratio to wavelength ratio (epsilon) much less than one (typical of annular flows) and epsilon is greater than or equal to 1 (typical of stratified flows). Our study of waves where epsilon = O(1) has shown that wave amplitude spectrum is determined by overtone interactions between various modes which lead to a net flux of energy from low (where it is fed in from gas shear) to high frequency waves (where it is dissipated). Interfacial shear and film depth determine the interaction rates and therefore the spectral shape. Using a balance equation for wave energy, we developed a procedure for quantitatively predicting the wave spectrum. For waves with epsilon is dominated by 1, it is appropriate to examine individual traveling wave shapes (rather than the wave spectrum). We have found that measured wavelengths and speeds of periodic waves exhibit small but significant deviations from predictions of linear stability theory.

There’s plenty of light at the bottom: statistics of photon penetration depth in random media

PubMed Central

Martelli, Fabrizio; Binzoni, Tiziano; Pifferi, Antonio; Spinelli, Lorenzo; Farina, Andrea; Torricelli, Alessandro

2016-01-01

We propose a comprehensive statistical approach describing the penetration depth of light in random media. The presented theory exploits the concept of probability density function f(z|ρ, t) for the maximum depth reached by the photons that are eventually re-emitted from the surface of the medium at distance ρ and time t. Analytical formulas for f, for the mean maximum depth 〈zmax〉 and for the mean average depth reached by the detected photons at the surface of a diffusive slab are derived within the framework of the diffusion approximation to the radiative transfer equation, both in the time domain and the continuous wave domain. Validation of the theory by means of comparisons with Monte Carlo simulations is also presented. The results are of interest for many research fields such as biomedical optics, advanced microscopy and disordered photonics. PMID:27256988

Laboratory tests of short intense envelope solitons

NASA Astrophysics Data System (ADS)

Slunyaev, A.; Clauss, G. F.; Klein, M.; Onorato, M.

2012-04-01

Stability of short intense nonlinear wave groups propagating over deep water is tested in laboratory runs which are performed in the facility of the Technical University of Berlin. The strongly nonlinear simulation of quasi-steady nonlinear wave groups within the framework of the Euler equations is used to generate the surface elevation time series at a border of the water tank. Besides, the exact analytic solution of the nonlinear Schrodinger equation is used for this purpose. The time series is then transformed to a wave maker signal with use of a designed transfer algorithm. Wave group propagation along the tank was recorded by 4 distant gauges and by an array of 6 densely situated gauges. This setup allows to consider the wave evolution from 10 to 85 m from the wave maker, and to obtain the wave envelope shape directly from the instrumental data. In the experiments wave groups were characterized by the steepness values up to kAcr < 0.32 and kAtr < 0.24, where k is the mean wavenumber, Acr is the crest amplitude, and Atr is the trough amplitude; and the maximum local wave slope was up to 0.34. Wave breaking phenomenon was not observed in the experiments. Different mean wave numbers and wave groups of different intensities were considered. In some cases the wave groups exhibit noticeable radiation in the course of propagation, though the groups are not dispersed fully. The effect of finite water depth is found to be significant on the wave group stability. Intense wave groups have shorter time of adjustment, what in some sense may help them to manifest their individuality clearer. The experimental tests confirm recent numerical simulations of fully nonlinear equations, where very steep stable single and interacting nonlinear wave groups were reported [1-3]. The quasi-stationary wave groups observed in numerical and laboratory experiments are strongly nonlinear analogues of the nonlinear Schrodinger envelope solitons. The results emphasize the importance of long-living nonlinear wave groups in dynamics of intense sea waves. [1] V.E. Zakharov, A.I. Dyachenko, A.O. Prokofiev, Eur. J. Mech. B / Fluids 25, 677 (2006). [2] A.I. Dyachenko, V.E. Zakharov, JETP Lett. 88, 307 (2008). [3] A.V. Slunyaev, JETP 109, 676 (2009).

Alfvén wave interactions in the solar wind

NASA Astrophysics Data System (ADS)

Webb, G. M.; McKenzie, J. F.; Hu, Q.; le Roux, J. A.; Zank, G. P.

2012-11-01

Alfvén wave mixing (interaction) equations used in locally incompressible turbulence transport equations in the solar wind are analyzed from the perspective of linear wave theory. The connection between the wave mixing equations and non-WKB Alfven wave driven wind theories are delineated. We discuss the physical wave energy equation and the canonical wave energy equation for non-WKB Alfven waves and the WKB limit. Variational principles and conservation laws for the linear wave mixing equations for the Heinemann and Olbert non-WKB wind model are obtained. The connection with wave mixing equations used in locally incompressible turbulence transport in the solar wind are discussed.

Optimization of one-way wave equations.

USGS Publications Warehouse

Lee, M.W.; Suh, S.Y.

1985-01-01

The theory of wave extrapolation is based on the square-root equation or one-way equation. The full wave equation represents waves which propagate in both directions. On the contrary, the square-root equation represents waves propagating in one direction only. A new optimization method presented here improves the dispersion relation of the one-way wave equation. -from Authors

Tsunamis generated by long and thin granular landslides in a large flume

NASA Astrophysics Data System (ADS)

Miller, Garrett S.; Andy Take, W.; Mulligan, Ryan P.; McDougall, Scott

2017-01-01

In this experimental study, granular material is released down slope to investigate landslide-generated waves. Starting with a known volume and initial position of the landslide source, detailed data are obtained on the velocity and thickness of the granular flow, the shape and location of the submarine landslide deposit, the amplitude and shape of the near-field wave, the far-field wave evolution, and the wave runup elevation on a smooth impermeable slope. The experiments are performed on a 6.7 m long 30° slope on which gravity accelerates the landslides into a 2.1 m wide and 33.0 m long wave flume that terminates with a 27° runup ramp. For a fixed landslide volume of 0.34 m3, tests are conducted in a range of still water depths from 0.05 to 0.50 m. Observations from high-speed cameras and measurements from wave probes indicate that the granular landslide moves as a long and thin train of material, and that only a portion of the landslide (termed the "effective mass") is engaged in activating the leading wave. The wave behavior is highly dependent on the water depth relative to the size of the landslide. In deeper water, the near-field wave behaves as a stable solitary-like wave, while in shallower water, the wave behaves as a breaking dissipative bore. Overall, the physical model observations are in good agreement with the results of existing empirical equations when the effective mass is used to predict the maximum near-field wave amplitude, the far-field amplitude, and the runup of tsunamis generated by granular landslides.

Combination of highly nonlinear fiber, an optical bandpass filter, and a Fabry-Perot filter to improve the signal-to-noise ratio of a supercontinuum continuous-wave optical source.

PubMed

Nan, Yinbo; Huo, Li; Lou, Caiyun

2005-05-20

We present a theoretical study of a supercontinuum (SC) continuous-wave (cw) optical source generation in highly nonlinear fiber and its noise properties through numerical simulations based on the nonlinear Schrödinger equation. Fluctuations of pump pulses generate substructures between the longitudinal modes that result in the generation of white noise and then in degradation of coherence and in a decrease of the modulation depths and the signal-to-noise ratio (SNR). A scheme for improvement of the SNR of a multiwavelength cw optical source based on a SC by use of the combination of a highly nonlinear fiber (HNLF), an optical bandpass filter, and a Fabry-Perot (FP) filter is presented. Numerical simulations show that the improvement in modulation depth is relative to the HNLF's length, the 3-dB bandwidth of the optical bandpass filter, and the reflection ratio of the FP filter and that the average improvement in modulation depth is 13.7 dB under specified conditions.

Sensitivity of storm wave modeling to wind stress evaluation methods

NASA Astrophysics Data System (ADS)

Chen, Yingjian; Yu, Xiping

2017-06-01

The application of the wave boundary layer model (WBLM) for wind stress evaluation to storm wave modeling is studied using Hurricane Katrina (2005) as an example, which is chosen due to its great intensity and good availability of field data. The WBLM is based on the momentum and energy conservation equations and takes into account the physical details of air-sea interaction processes as well as energy dissipation due to the presence of sea spray. Four widely-used bulk-type formulas are also used for comparison. Simulated significant wave heights with WBLM are shown to agree well with the observed data over deep water. The WBLM yields a smaller wind stress coefficient on the left hand side of the hurricane track, which is reasonable considering the effect of the sea state on momentum transfer. Quantitative results show that large differences of the significant wave height are observed in the hurricane core among five wind stress evaluation methods and the differences are up to 12 m, which is in agreement with the general knowlege that the ocean dynamic processes under storm conditions are very sensitive to the amount of momentum exchange at the air-sea interface. However, it is the depth-induced energy dissipation, rather than the wind energy input, that dominates the wave height in the shallow water region. A larger value of depth-induced breaking parameter in the wave model results in better agreement with the measurements over shallow water.

Linear excitation of the trapped waves by an incident wave

NASA Astrophysics Data System (ADS)

Postacioglu, Nazmi; Sinan Özeren, M.

2016-04-01

The excitation of the trapped waves by coastal events such as landslides has been extensively studied. The events in the open sea have in general larger magnitude. However the incident waves produced by these events in the open sea can only excite the the trapped waves through no linearity if the isobaths are straight lines that are in parallel with the coastline. We will show that the imperfections of the coastline can couple the incident and trapped waves using only linear processes. The Coriolis force is neglected in this work . Accordingly the trapped waves are consequence of uneven bathimetry. In the bathimetry we consider, the sea is divided into zones of constant depth and the boundaries between the zones are a family of hyperbolas. The boundary conditions between the zones will lead to an integral equation for the source distribution on the boundaries. The solution will contain both radiating and trapped waves. The trapped waves pose a serious threat for the coastal communities as they can travel long distances along the coastline without losing their energy through geometrical spreading.

High-order rogue waves of the Benjamin-Ono equation and the nonlocal nonlinear Schrödinger equation

NASA Astrophysics Data System (ADS)

Liu, Wei

2017-10-01

High-order rogue wave solutions of the Benjamin-Ono equation and the nonlocal nonlinear Schrödinger equation are derived by employing the bilinear method, which are expressed by simple polynomials. Typical dynamics of these high-order rogue waves are studied by analytical and graphical ways. For the Benjamin-Ono equation, there are two types of rogue waves, namely, bright rogue waves and dark rogue waves. In particular, the fundamental rogue wave pattern is different from the usual fundamental rogue wave patterns in other soliton equations. For the nonlocal nonlinear Schrödinger equation, the exact explicit rogue wave solutions up to the second order are presented. Typical rogue wave patterns such as Peregrine-type, triple and fundamental rogue waves are put forward. These high-order rogue wave patterns have not been shown before in the nonlocal Schrödinger equation.

Propagation Path Effects for Rayleigh and Love Waves

DTIC Science & Technology

1981-05-01

The method finally selected is similar in some respects to the integral equation formulation. It is the Parker- Oldenburg -iuestis method (Parker, 1972...REGIONAL ANOMALIE S BASIN MODEL DEPTH RESIDUALS AND STRIPPING BOREHOLE DATA PROCESS DATA mots" 12 THE PARKER- OLDENBURG -HUESTIS POTENTIAL INVERSION Parker...series convergLnce and other properties are given by Parker (1972), Parker and Huestis (1974), and Oldenburg (1974). A discussion of this theory from

Evolution of wave and tide over vegetation region in nearshore waters

NASA Astrophysics Data System (ADS)

Zhang, Mingliang; Zhang, Hongxing; Zhao, Kaibin; Tang, Jun; Qin, Huifa

2017-08-01

Coastal wetlands are an important ecosystem in nearshore regions, where complex flow characteristics occur because of the interactions among tides, waves, and plants, especially in the discontinuous flow of the intertidal zone. In order to simulate the wave and wave-induced current in coastal waters, in this study, an explicit depth-averaged hydrodynamic (HD) model has been dynamically coupled with a wave spectral model (CMS-Wave) by sharing the tide and wave data. The hydrodynamic model is based on the finite volume method; the intercell flux is computed using the Harten-Lax-van Leer (HLL) approximate Riemann solver for computing the dry-to-wet interface; the drag force of vegetation is modeled as the sink terms in the momentum equations. An empirical wave energy dissipation term with plant effect has been derived from the wave action balance equation to account for the resistance induced by aquatic vegetation in the CMS-Wave model. The results of the coupling model have been verified using the measured data for the case with wave-tide-vegetation interactions. The results show that the wave height decreases significantly along the wave propagation direction in the presence of vegetation. In the rip channel system, the oblique waves drive a meandering longshore current; it moves from left to right past the cusps with oscillations. In the vegetated region, the wave height is greatly attenuated due to the presence of vegetation, and the radiation stresses are noticeably changed as compared to the region without vegetation. Further, vegetation can affect the spatial distribution of mean velocity in a rip channel system. In the co-exiting environment of tides, waves, and vegetation, the locations of wave breaking and wave-induced radiation stress also vary with the water level of flooding or ebb tide in wetland water, which can also affect the development and evolution of wave-induced current.

Evolution of basic equations for nearshore wave field

PubMed Central

ISOBE, Masahiko

2013-01-01

In this paper, a systematic, overall view of theories for periodic waves of permanent form, such as Stokes and cnoidal waves, is described first with their validity ranges. To deal with random waves, a method for estimating directional spectra is given. Then, various wave equations are introduced according to the assumptions included in their derivations. The mild-slope equation is derived for combined refraction and diffraction of linear periodic waves. Various parabolic approximations and time-dependent forms are proposed to include randomness and nonlinearity of waves as well as to simplify numerical calculation. Boussinesq equations are the equations developed for calculating nonlinear wave transformations in shallow water. Nonlinear mild-slope equations are derived as a set of wave equations to predict transformation of nonlinear random waves in the nearshore region. Finally, wave equations are classified systematically for a clear theoretical understanding and appropriate selection for specific applications. PMID:23318680

A numerical investigation of wave-breaking-induced turbulent coherent structure under a solitary wave

NASA Astrophysics Data System (ADS)

Zhou, Zheyu; Sangermano, Jacob; Hsu, Tian-Jian; Ting, Francis C. K.

2014-10-01

To better understand the effect of wave-breaking-induced turbulence on the bed, we report a 3-D large-eddy simulation (LES) study of a breaking solitary wave in spilling condition. Using a turbulence-resolving approach, we study the generation and the fate of wave-breaking-induced turbulent coherent structures, commonly known as obliquely descending eddies (ODEs). Specifically, we focus on how these eddies may impinge onto bed. The numerical model is implemented using an open-source CFD library of solvers, called OpenFOAM, where the incompressible 3-D filtered Navier-Stokes equations for the water and the air phases are solved with a finite volume scheme. The evolution of the water-air interfaces is approximated with a volume of fluid method. Using the dynamic Smagorinsky closure, the numerical model has been validated with wave flume experiments of solitary wave breaking over a 1/50 sloping beach. Simulation results show that during the initial overturning of the breaking wave, 2-D horizontal rollers are generated, accelerated, and further evolve into a couple of 3-D hairpin vortices. Some of these vortices are sufficiently intense to impinge onto the bed. These hairpin vortices possess counter-rotating and downburst features, which are key characteristics of ODEs observed by earlier laboratory studies using Particle Image Velocimetry. Model results also suggest that those ODEs that impinge onto bed can induce strong near-bed turbulence and bottom stress. The intensity and locations of these near-bed turbulent events could not be parameterized by near-surface (or depth integrated) turbulence unless in very shallow depth.

Full Equations (FEQ) model for the solution of the full, dynamic equations of motion for one-dimensional unsteady flow in open channels and through control structures

USGS Publications Warehouse

Franz, Delbert D.; Melching, Charles S.

1997-01-01

The Full EQuations (FEQ) model is a computer program for solution of the full, dynamic equations of motion for one-dimensional unsteady flow in open channels and through control structures. A stream system that is simulated by application of FEQ is subdivided into stream reaches (branches), parts of the stream system for which complete information on flow and depth are not required (dummy branches), and level-pool reservoirs. These components are connected by special features; that is, hydraulic control structures, including junctions, bridges, culverts, dams, waterfalls, spillways, weirs, side weirs, and pumps. The principles of conservation of mass and conservation of momentum are used to calculate the flow and depth throughout the stream system resulting from known initial and boundary conditions by means of an implicit finite-difference approximation at fixed points (computational nodes). The hydraulic characteristics of (1) branches including top width, area, first moment of area with respect to the water surface, conveyance, and flux coefficients and (2) special features (relations between flow and headwater and (or) tail-water elevations, including the operation of variable-geometry structures) are stored in function tables calculated in the companion program, Full EQuations UTiLities (FEQUTL). Function tables containing other information used in unsteady-flow simulation (boundary conditions, tributary inflows or outflows, gate settings, correction factors, characteristics of dummy branches and level-pool reservoirs, and wind speed and direction) are prepared by the user as detailed in this report. In the iterative solution scheme for flow and depth throughout the stream system, an interpolation of the function tables corresponding to the computational nodes throughout the stream system is done in the model. FEQ can be applied in the simulation of a wide range of stream configurations (including loops), lateral-inflow conditions, and special features. The accuracy and convergence of the numerical routines in the model are demonstrated for the case of laboratory measurements of unsteady flow in a sewer pipe. Verification of the routines in the model for field data on the Fox River in northeastern Illinois also is briefly discussed. The basic principles of unsteady-flow modeling and the relation between steady flow and unsteady flow are presented. Assumptions and the limitations of the model also are presented. The schematization of the stream system and the conversion of the physical characteristics of the stream reaches and a wide range of special features into function tables for model applications are described. The modified dynamic-wave equation used in FEQ for unsteady flow in curvilinear channels with drag on minor hydraulic structures and channel constrictions determined from an equivalent energy slope is developed. The matrix equation relating flows and depths at computational nodes throughout the stream system by the continuity (conservation of mass) and modified dynamic-wave equations is illustrated for four sequential examples. The solution of the matrix equation by Newton's method is discussed. Finally, the input for FEQ and the error messages and warnings issued are presented.

Application of a Phase-resolving, Directional Nonlinear Spectral Wave Model

NASA Astrophysics Data System (ADS)

Davis, J. R.; Sheremet, A.; Tian, M.; Hanson, J. L.

2014-12-01

We describe several applications of a phase-resolving, directional nonlinear spectral wave model. The model describes a 2D surface gravity wave field approaching a mildly sloping beach with parallel depth contours at an arbitrary angle accounting for nonlinear, quadratic triad interactions. The model is hyperbolic, with the initial wave spectrum specified in deep water. Complex amplitudes are generated based on the random phase approximation. The numerical implementation includes unidirectional propagation as a special case. In directional mode, it solves the system of equations in the frequency-alongshore wave number space. Recent enhancements of the model include the incorporation of dissipation caused by breaking and propagation over a viscous mud layer and the calculation of wave induced setup. Applications presented include: a JONSWAP spectrum with a cos2s directional distribution, for shore-perpendicular and oblique propagation, a study of the evolution of a single directional triad, and several preliminary comparisons to wave spectra collected at the USACE-FRF in Duck, NC which show encouraging results although further validation with a wider range of beach slopes and wave conditions is needed.

A delayed action oscillator shared by biennial, interannual, and decadal signals in the Pacific Basin

USGS Publications Warehouse

White, Warren B.; Tourre, Y.M.; Barlow, M.; Dettinger, M.

2003-01-01

Biennial, interannual, and decadal signals in the Pacific basin are observed to share patterns and evolution in covarying sea surface temperature (SST), 18??C isotherm depth (Z18), zonal surface wind (ZSW), and wind stress curl (WSC) anomalies from 1955 to 1999. Each signal has warm SST anomalies propagating slowly eastward along the equator, generating westerly ZSW anomalies in their wake. These westerly ZSW anomalies produce cyclonic WSC anomalies off the equator which pump baroclinic Rossby waves in the western/central tropical North Pacific Ocean. These Rossby waves propagate westward, taking ???6, ???12, and ???36 months to reach the western boundary near ???7??N, ???12??N, and ???18??N on biennial, interannual, and decadal period scales, respectively. There, they reflect as equatorial coupled waves, propagating slowly eastward in covarying SST, Z18, and ZSW anomalies, taking ???6, ???12, and ???24 months to reach the central/eastern equatorial ocean. These equatorial coupled waves produce a delayed-negative feedback to the warm SST anomalies there. The decrease in Rossby wave phase speed with latitude, the increase in meridional scale of equatorial SST anomalies with period scale, and the associated increase in latitude of Rossby wave forcing are consistent with the delayed action oscillator (DAO) model used to explain El Nin??o. However, this is not true of the western-boundary reflection of Rossby waves into slow equatorial coupled waves. This requires modification of the extant DAO model. We construct a modified DAO model, demonstrating how the various mechanisms and the size and sources of their delays yield the resulting frequency of each signal.

Run-up parameterization and beach vulnerability assessment on a barrier island: a downscaling approach

NASA Astrophysics Data System (ADS)

Medellín, G.; Brinkkemper, J. A.; Torres-Freyermuth, A.; Appendini, C. M.; Mendoza, E. T.; Salles, P.

2016-01-01

We present a downscaling approach for the study of wave-induced extreme water levels at a location on a barrier island in Yucatán (Mexico). Wave information from a 30-year wave hindcast is validated with in situ measurements at 8 m water depth. The maximum dissimilarity algorithm is employed for the selection of 600 representative cases, encompassing different combinations of wave characteristics and tidal level. The selected cases are propagated from 8 m water depth to the shore using the coupling of a third-generation wave model and a phase-resolving non-hydrostatic nonlinear shallow-water equation model. Extreme wave run-up, R2%, is estimated for the simulated cases and can be further employed to reconstruct the 30-year time series using an interpolation algorithm. Downscaling results show run-up saturation during more energetic wave conditions and modulation owing to tides. The latter suggests that the R2% can be parameterized using a hyperbolic-like formulation with dependency on both wave height and tidal level. The new parametric formulation is in agreement with the downscaling results (r2 = 0.78), allowing a fast calculation of wave-induced extreme water levels at this location. Finally, an assessment of beach vulnerability to wave-induced extreme water levels is conducted at the study area by employing the two approaches (reconstruction/parameterization) and a storm impact scale. The 30-year extreme water level hindcast allows the calculation of beach vulnerability as a function of return periods. It is shown that the downscaling-derived parameterization provides reasonable results as compared with the numerical approach. This methodology can be extended to other locations and can be further improved by incorporating the storm surge contributions to the extreme water level.

The propagation of ion-acoustic waves carrying orbital angular momentum in the electron-positron-ion plasmas

NASA Astrophysics Data System (ADS)

Mehdian, H.; Nobahar, D.; Hajisharifi, K.

2018-02-01

Ion-acoustic (IA) waves carrying orbital angular momentum (OAM) are investigated in an unmagnetized, uniform, and collisionless electron-positron-ion (e-p-i) plasma system. Employing the hydrodynamic theory, the paraxial equation in term of ion perturbed number density is derived and discussed about its Laguerre-Gaussian (LG) beam solutions. Obtaining an approximate solution for the electrostatic potential, the IA wave characteristics including helical electric field structure, energy density, and OAM density are theoretically studied. Based on the numerical analysis, the effects of positron concentration, radial and angular mode number as well as beam waist on the obtained potential profile are investigated. It is shown that the depth (height) and width of the LG potential profile wells (barriers) are considerably modify by the variation of positron concentration.

Effects of initial amplitude and pycnocline thickness on the evolution of mode-2 internal solitary waves

NASA Astrophysics Data System (ADS)

Cheng, Ming-Hung; Hsieh, Chih-Min; Hwang, Robert R.; Hsu, John R.-C.

2018-04-01

Numerical simulations are performed to investigate the effects of the initial amplitude and pycnocline thickness on the evolutions of convex mode-2 internal solitary waves propagating on the flat bottom. A finite volume method based on a Cartesian grid system is adopted to solve the Navier-Stokes equations using the improved delayed detached eddy simulation turbulent closure model. Mode-2 internal solitary waves (ISWs) are found to become stable at t = 15 s after lifting a vertical sluice gate by a gravity collapse mechanism. Numerical results from three cases of pycnocline thickness reveal the following: (1) the occurrence of a smooth mode-2 ISW when the wave amplitude is small; (2) the PacMan phenomenon for large amplitude waves; and (3) pseudo vortex shedding in the case of very large amplitudes. In general, basic wave properties (wave amplitude, wave speed, vorticity, and wave energy) increase as the wave amplitude increases for a specific value of the pycnocline thickness. Moreover, the pycnocline thickness chiefly determines the core size of a convex mode-2 ISW, while the step depth (that generates an initial wave amplitude) and offset in pycnocline govern the waveform type during its propagation on the flat bottom.

A shear-wave velocity model of the European upper mantle from automated inversion of seismic shear and surface waveforms

NASA Astrophysics Data System (ADS)

Legendre, C.; Meier, T.; Lebedev, S.; Friederich, W.; Viereck-Götte, L.

2012-04-01

Broadband waveforms recorded at stations in Europe and surrounding regions were inverted for shear-wave velocity of the European upper mantle. For events between 1995 and 2007 seismograms were collected from all permanent stations for which data are available via the data centers ORFEUS, GEOFON, ReNaSs and IRIS. In addition, we incorporated data from temporary experiments, including SVEKALAPKO, TOR, Eifel Plume, EGELADOS and other projects. Automated Multimode Inversion of surface and S-wave forms was applied to extract structural information from the seismograms, in the form of linear equations with uncorrelated uncertainties. Successful waveform fits for about 70,000 seismograms yielded over 300,000 independent linear equations that were solved together for a three-dimensional tomographic model. Resolution of the imaging is particularly high in the mantle lithosphere and asthenosphere. The highest velocities in the mantle lithosphere of the East European Craton are found at about 150 km depth. There are no indications for a large scale deep cratonic root below about 330 km depth. Lateral variations within the cratonic mantle lithosphere are resolved by our model as well. The locations of diamond bearing kimberlites correlate with reduced S-wave velocities in the cratonic mantle lithosphere. This anomaly is present in regions of both Proterozoic and Archean crust, pointing to an alteration of the mantle lithosphere after the formation of the craton. Strong lateral changes in S-wave velocity are found at the western margin of the East European Craton and hint to erosion of cratonic mantle lithosphere beneath the Scandes by hot asthenosphere. The mantle lithosphere beneath Western Europe and between the Tornquist-Teyissere Zone and the Elbe Line shows moderately high velocities and is of an intermediate character, between cratonic lithosphere and the thin lithosphere of central Europe. In central Europe, Caledonian and Variscian sutures are not associated with strong lateral changes in the lithosphere-asthenosphere system. Cenozoic anorogenic intraplate volcanism in central Europe and the Circum Mediterranean is found in regions of shallow asthenosphere and close to sharp gradients in the depth of the lithosphere-asthenosphere boundary. Low-velocity anomalies extending vertically from shallow upper mantle down to the transition zone are found beneath the Massive Central, Sinai, Canary Islands and Iceland.

On the Pathways of the Return Flow of the Meridional Overturning Circulation in the Tropical Atlantic

NASA Technical Reports Server (NTRS)

Jochum, Markus

2002-01-01

A numerical model of the tropical Atlantic ocean is used to investigate the upper layer pathways of the Meridional Overturning Circulation (MOC) in the tropical Atlantic. The main focus of this thesis is on those parts of the tropical circulation that are thought to be important for the MOC return flow, but whose dynamics have not been understood yet. It is shown how the particular structure of the tropical gyre and the MOO act to inhibit the flow of North Atlantic water into the equatorial thermocline. As a result, the upper layers of the tropical Atlantic are mainly fed by water from the South Atlantic. The processes that carry the South Atlantic water across the tropical Atlantic into the North Atlantic as part of the MOO are described here, and three processes that were hitherto not understood are explained as follows: The North Brazil Current rings are created as the result of the reflection of Rossby waves at the South American coast. These Rossby waves are generated by the barotropically unstable North Equatorial Countercurrent. The deep structure of the rings can be explained by merger of the wave's anticyclones with the deeper intermediate eddies that are generated as the intermediate western boundary current crosses the equator. The bands of strong zonal velocity in intermediate depths along the equator have hitherto been explained as intermediate currents. Here, an alternative interpretation of the observations is offered: The Eulerian mean flow along the equator is negligible and the observations are the signature of strong seasonal Rossby waves. The previous interpretation of the observations can then be explained as aliasing of the tropical wave field. The Tsuchyia Jets are driven by the Eliassen-Palm flux of the tropical instability waves. The equatorial current system with its strong shears is unstable and generates tropical instability waves.

Calculating Depth of Closure Using WIS Hindcast Data

DTIC Science & Technology

2016-03-01

revised the Hallermeier (1978, 1981) equations using data from the Duck , NC, U.S. Army Corps of Engineers (USACE) Field Research Facility. Many studies ... Study (WIS) hindcast stations along the United States coastlines. The results summarized in this CHETN are available in the form of a spreadsheet on...theoretical definition of DOC came from a study by Hallermeier (1978, 1981) using wave tank and field data. Initially, the DOC was related to the critical

Vertical coherence and forward scattering from the sea surface and the relation to the directional wave spectrum.

PubMed

Dahl, Peter H; Plant, William J; Dall'Osto, David R

2013-09-01

Results of an experiment to measure vertical spatial coherence from acoustic paths interacting once with the sea surface but at perpendicular azimuth angles are presented. The measurements were part of the Shallow Water 2006 program that took place off the coast of New Jersey in August 2006. An acoustic source, frequency range 6-20 kHz, was deployed at depth 40 m, and signals were recorded on a 1.4 m long vertical line array centered at depth 25 m and positioned at range 200 m. The vertical array consisted of four omni-directional hydrophones and vertical coherences were computed between pairs of these hydrophones. Measurements were made over four source-receiver bearing angles separated by 90°, during which sea surface conditions remained stable and characterized by a root-mean-square wave height of 0.17 m and a mixture of swell and wind waves. Vertical coherences show a statistically significant difference depending on source-receiver bearing when the acoustic frequency is less than about 12 kHz, with results tending to fade at higher frequencies. This paper presents field observations and comparisons of these observations with two modeling approaches, one based on bistatic forward scattering and the other on a rough surface parabolic wave equation utilizing synthetic sea surfaces.

Modelling Of Anticipated Damage Ratio On Breakwaters Using Fuzzy Logic

NASA Astrophysics Data System (ADS)

Mercan, D. E.; Yagci, O.; Kabdasli, S.

2003-04-01

In breakwater design the determination of armour unit weight is especially important in terms of the structure's life. In a typical experimental breakwater stability study, different wave series composed of different wave heights; wave period and wave steepness characteristics are applied in order to investigate performance the structure. Using a classical approach, a regression equation is generated for damage ratio as a function of characteristic wave height. The parameters wave period and wave steepness are not considered. In this study, differing from the classical approach using a fuzzy logic, a relationship between damage ratio as a function of mean wave period (T_m), wave steepness (H_s/L_m) and significant wave height (H_s) was further generated. The system's inputs were mean wave period (T_m), wave steepness (H_s/L_m) and significant wave height (H_s). For fuzzification all input variables were divided into three fuzzy subsets, their membership functions were defined using method developed by Mandani (Mandani, 1974) and the rules were written. While for defuzzification the centroid method was used. In order to calibrate and test the generated models an experimental study was conducted. The experiments were performed in a wave flume (24 m long, 1.0 m wide and 1.0 m high) using 20 different irregular wave series (P-M spectrum). Throughout the study, the water depth was 0.6 m and the breakwater cross-sectional slope was 1V/2H. In the armour layer, a type of artificial armour unit known as antifer cubes were used. The results of the established fuzzy logic model and regression equation model was compared with experimental data and it was determined that the established fuzzy logic model gave a more accurate prediction of the damage ratio on this type of breakwater. References Mandani, E.H., "Application of Fuzzy Algorithms for Control of Simple Dynamic Plant", Proc. IEE, vol. 121, no. 12, December 1974.

Propagation of 3D internal gravity wave beams in a slowly varying stratification

NASA Astrophysics Data System (ADS)

Fan, Boyu; Akylas, T. R.

2017-11-01

The time-mean flows induced by internal gravity wave beams (IGWB) with 3D variations have been shown to have dramatic implications for long-term IGWB dynamics. While uniform stratifications are convenient both theoretically and in the laboratory, stratifications in the ocean can vary by more than an order of magnitude over the ocean depth. Here, in view of this fact, we study the propagation of a 3D IGWB in a slowly varying stratification. We assume that the stratification varies slowly relative to the local variations in the wave profile. In the 2D case, the IGWB bends in response to the changing stratification, but nonlinear effects are minor even in the finite amplitude regime. For a 3D IGWB, in addition to bending, we find that nonlinearity results in the transfer of energy from waves to a large-scale time-mean flow associated with the mean potential vorticity, similar to IGWB behavior in a uniform stratification. In a weakly nonlinear setting, we derive coupled evolution equations that govern this process. We also use these equations to determine the stability properties of 2D IGWB to 3D perturbations. These findings indicate that 3D effects may be relevant and possibly fundamental to IGWB dynamics in nature. Supported by NSF Grant DMS-1512925.

A conservative scheme for electromagnetic simulation of magnetized plasmas with kinetic electrons

NASA Astrophysics Data System (ADS)

Bao, J.; Lin, Z.; Lu, Z. X.

2018-02-01

A conservative scheme has been formulated and verified for gyrokinetic particle simulations of electromagnetic waves and instabilities in magnetized plasmas. An electron continuity equation derived from the drift kinetic equation is used to time advance the electron density perturbation by using the perturbed mechanical flow calculated from the parallel vector potential, and the parallel vector potential is solved by using the perturbed canonical flow from the perturbed distribution function. In gyrokinetic particle simulations using this new scheme, the shear Alfvén wave dispersion relation in the shearless slab and continuum damping in the sheared cylinder have been recovered. The new scheme overcomes the stringent requirement in the conventional perturbative simulation method that perpendicular grid size needs to be as small as electron collisionless skin depth even for the long wavelength Alfvén waves. The new scheme also avoids the problem in the conventional method that an unphysically large parallel electric field arises due to the inconsistency between electrostatic potential calculated from the perturbed density and vector potential calculated from the perturbed canonical flow. Finally, the gyrokinetic particle simulations of the Alfvén waves in sheared cylinder have superior numerical properties compared with the fluid simulations, which suffer from numerical difficulties associated with singular mode structures.

Study of nonlinear interaction between bunched beam and intermediate cavities in a relativistic klystron amplifier

NASA Astrophysics Data System (ADS)

Wu, Y.; Xu, Z.; Li, Z. H.; Tang, C. X.

2012-07-01

In intermediate cavities of a relativistic klystron amplifier (RKA) driven by intense relativistic electron beam, the equivalent circuit model, which is widely adopted to investigate the interaction between bunched beam and the intermediate cavity in a conventional klystron design, is invalid due to the high gap voltage and the nonlinear beam loading in a RKA. According to Maxwell equations and Lorentz equation, the self-consistent equations for beam-wave interaction in the intermediate cavity are introduced to study the nonlinear interaction between bunched beam and the intermediate cavity in a RKA. Based on the equations, the effects of modulation depth and modulation frequency of the beam on the gap voltage amplitude and its phase are obtained. It is shown that the gap voltage is significantly lower than that estimated by the equivalent circuit model when the beam modulation is high. And the bandwidth becomes wider as the beam modulation depth increases. An S-band high gain relativistic klystron amplifier is designed based on the result. And the corresponding experiment is carried out on the linear transformer driver accelerator. The peak output power has achieved 1.2 GW with an efficiency of 28.6% and a gain of 46 dB in the corresponding experiment.

Wave-induced hydraulic forces on submerged aquatic plants in shallow lakes.

PubMed

Schutten, J; Dainty, J; Davy, A J

2004-03-01

Hydraulic pulling forces arising from wave action are likely to limit the presence of freshwater macrophytes in shallow lakes, particularly those with soft sediments. The aim of this study was to develop and test experimentally simple models, based on linear wave theory for deep water, to predict such forces on individual shoots. Models were derived theoretically from the action of the vertical component of the orbital velocity of the waves on shoot size. Alternative shoot-size descriptors (plan-form area or dry mass) and alternative distributions of the shoot material along its length (cylinder or inverted cone) were examined. Models were tested experimentally in a flume that generated sinusoidal waves which lasted 1 s and were up to 0.2 m high. Hydraulic pulling forces were measured on plastic replicas of Elodea sp. and on six species of real plants with varying morphology (Ceratophyllum demersum, Chara intermedia, Elodea canadensis, Myriophyllum spicatum, Potamogeton natans and Potamogeton obtusifolius). Measurements on the plastic replicas confirmed predicted relationships between force and wave phase, wave height and plant submergence depth. Predicted and measured forces were linearly related over all combinations of wave height and submergence depth. Measured forces on real plants were linearly related to theoretically derived predictors of the hydraulic forces (integrals of the products of the vertical orbital velocity raised to the power 1.5 and shoot size). The general applicability of the simplified wave equations used was confirmed. Overall, dry mass and plan-form area performed similarly well as shoot-size descriptors, as did the conical or cylindrical models of shoot distribution. The utility of the modelling approach in predicting hydraulic pulling forces from relatively simple plant and environmental measurements was validated over a wide range of forces, plant sizes and species.

Shear wave velocities of unconsolidated shallow sediments in the Gulf of Mexico

USGS Publications Warehouse

Lee, Myung W.

2013-01-01

Accurate shear-wave velocities for shallow sediments are important for a variety of seismic applications such as inver-sion and amplitude versus offset analysis. During the U.S. Department of Energy-sponsored Gas Hydrate Joint Industry Project Leg II, shear-wave velocities were measured at six wells in the Gulf of Mexico using the logging-while-drilling SonicScope acoustic tool. Because the tool measurement point was only 35 feet from the drill bit, the adverse effect of the borehole condition, which is severe for the shallow unconsolidated sediments in the Gulf of Mexico, was mini-mized and accurate shear-wave velocities of unconsolidated sediments were measured. Measured shear-wave velocities were compared with the shear-wave velocities predicted from the compressional-wave velocities using empirical formulas and the rock physics models based on the Biot-Gassmann theory, and the effectiveness of the two prediction methods was evaluated. Although the empirical equation derived from measured shear-wave data is accurate for predicting shear-wave velocities for depths greater than 500 feet in these wells, the three-phase Biot-Gassmann-theory -based theory appears to be optimum for predicting shear-wave velocities for shallow unconsolidated sediments in the Gulf of Mexico.

Theoretical monochromatic-wave-induced currents in intermediate water with viscosity and nonzero mass transport

NASA Technical Reports Server (NTRS)

Talay, T. A.

1975-01-01

Wave-induced mass-transport current theories with both zero and nonzero net mass (or volume) transport of the water column are reviewed. A relationship based on the Longuet-Higgens theory is derived for wave-induced, nonzero mass-transport currents in intermediate water depths for a viscous fluid. The relationship is in a form useful for experimental applications; therefore, some design criteria for experimental wave-tank tests are also presented. Sample parametric cases for typical wave-tank conditions and a typical ocean swell were assessed by using the relation in conjunction with an equation developed by Unluata and Mei for the maximum wave-induced volume transport. Calculations indicate that substantial changes in the wave-induced mass-transport current profiles may exist dependent upon the assumed net volume transport. A maximum volume transport, corresponding to an infinite channel or idealized ocean condition, produces the largest wave-induced mass-transport currents. These calculations suggest that wave-induced mass-transport currents may have considerable effects on pollution and suspended-sediments transport as well as buoy drift, the surface and midlayer water-column currents caused by waves increasing with increasing net volume transports. Some of these effects are discussed.

Dynamic Site Characterization and Correlation of Shear Wave Velocity with Standard Penetration Test ` N' Values for the City of Agartala, Tripura State, India

NASA Astrophysics Data System (ADS)

Sil, Arjun; Sitharam, T. G.

2014-08-01

Seismic site characterization is the basic requirement for seismic microzonation and site response studies of an area. Site characterization helps to gauge the average dynamic properties of soil deposits and thus helps to evaluate the surface level response. This paper presents a seismic site characterization of Agartala city, the capital of Tripura state, in the northeast of India. Seismically, Agartala city is situated in the Bengal Basin zone which is classified as a highly active seismic zone, assigned by Indian seismic code BIS-1893, Indian Standard Criteria for Earthquake Resistant Design of Structures, Part-1 General Provisions and Buildings. According to the Bureau of Indian Standards, New Delhi (2002), it is the highest seismic level (zone-V) in the country. The city is very close to the Sylhet fault (Bangladesh) where two major earthquakes ( M w > 7) have occurred in the past and affected severely this city and the whole of northeast India. In order to perform site response evaluation, a series of geophysical tests at 27 locations were conducted using the multichannel analysis of surface waves (MASW) technique, which is an advanced method for obtaining shear wave velocity ( V s) profiles from in situ measurements. Similarly, standard penetration test (SPT-N) bore log data sets have been obtained from the Urban Development Department, Govt. of Tripura. In the collected data sets, out of 50 bore logs, 27 were selected which are close to the MASW test locations and used for further study. Both the data sets ( V s profiles with depth and SPT-N bore log profiles) have been used to calculate the average shear wave velocity ( V s30) and average SPT-N values for the upper 30 m depth of the subsurface soil profiles. These were used for site classification of the study area recommended by the National Earthquake Hazard Reduction Program (NEHRP) manual. The average V s30 and SPT-N classified the study area as seismic site class D and E categories, indicating that the city is susceptible to site effects and liquefaction. Further, the different data set combinations between V s and SPT-N (corrected and uncorrected) values have been used to develop site-specific correlation equations by statistical regression, as ` V s' is a function of SPT- N value (corrected and uncorrected), considered with or without depth. However, after considering the data set pairs, a probabilistic approach has also been presented to develop a correlation using a quantile-quantile (Q-Q) plot. A comparison has also been made with the well known published correlations (for all soils) available in the literature. The present correlations closely agree with the other equations, but, comparatively, the correlation of shear wave velocity with the variation of depth and uncorrected SPT-N values provides a more suitable predicting model. Also the Q-Q plot agrees with all the other equations. In the absence of in situ measurements, the present correlations could be used to measure V s profiles of the study area for site response studies.

Pressure Wave Propagation along the Décollement of the Nankai Accretionary Wedge: Implications for Aseismic Slip Events

NASA Astrophysics Data System (ADS)

Joshi, A.; Appold, M. S.

2015-12-01

Seismic and hydrologic observations of the Nankai subduction zone made by the Ocean Drilling Program suggest that pore fluid pressures within the accretionary wedge décollement are highly overpressured to near lithostatic values below depths of 2 km beneath the sea floor as a result of sediment diagenesis and dehydration of the subducting oceanic plate. This overpressured zone is also observed to discharge pulses of high fluid pressure that migrate up-dip along the décollement at rates of 1's of km/day. These high pressure pulses along the décollement may cause large enough reductions in the local effective stress to account for aseismic slip events that have been found to propagate also at rates of 1's of km/day. Because elevated fluid pressure and correspondingly decreased effective stress can lead to a dilation of porosity, the pressure waves may become effective agents of fluid transport that can travel more quickly than fluids flowing in the background Darcian flow regime. The purpose of the present study was to seek theoretical confirmation that pressure waves are able to travel quickly enough to account for the seismic and hydrological observations documented. This confirmation was sought through a transient one-dimensional numerical solution to the differential fluid mass conservation equation for an elastic porous medium. Results of the numerical simulations show that when overpressures at depths greater than 2 km in the décollement exceed lithostatic pressure by at least 3%, pressure waves are formed that migrate up-dip at rates fast enough to account for aseismic slip over a broad range of geologic conditions. Pressure waves spawned from these depths in the décollement may travel fast enough to account for aseismic slip when overpressures there are as low as 99% of lithostatic pressure, but require low specific storage of 3×10-6 m-1, high sensitivity of permeability to effective stress, low permeability no higher than about 10-21 m2 at depths below 2 km in the décollement, and an accurate accounting of the decrease in fluid viscosity with increasing depth. Thus, pressure waves could account for aseismic slip in the Nankai accretionary wedge if conditions were near the limits of geologically reasonable ranges.

Efficient parallel seismic simulations including topography and 3-D material heterogeneities on locally refined composite grids

NASA Astrophysics Data System (ADS)

Petersson, Anders; Rodgers, Arthur

2010-05-01

The finite difference method on a uniform Cartesian grid is a highly efficient and easy to implement technique for solving the elastic wave equation in seismic applications. However, the spacing in a uniform Cartesian grid is fixed throughout the computational domain, whereas the resolution requirements in realistic seismic simulations usually are higher near the surface than at depth. This can be seen from the well-known formula h ≤ L-P which relates the grid spacing h to the wave length L, and the required number of grid points per wavelength P for obtaining an accurate solution. The compressional and shear wave lengths in the earth generally increase with depth and are often a factor of ten larger below the Moho discontinuity (at about 30 km depth), than in sedimentary basins near the surface. A uniform grid must have a grid spacing based on the small wave lengths near the surface, which results in over-resolving the solution at depth. As a result, the number of points in a uniform grid is unnecessarily large. In the wave propagation project (WPP) code, we address the over-resolution-at-depth issue by generalizing our previously developed single grid finite difference scheme to work on a composite grid consisting of a set of structured rectangular grids of different spacings, with hanging nodes on the grid refinement interfaces. The computational domain in a regional seismic simulation often extends to depth 40-50 km. Hence, using a refinement ratio of two, we need about three grid refinements from the bottom of the computational domain to the surface, to keep the local grid size in approximate parity with the local wave lengths. The challenge of the composite grid approach is to find a stable and accurate method for coupling the solution across the grid refinement interface. Of particular importance is the treatment of the solution at the hanging nodes, i.e., the fine grid points which are located in between coarse grid points. WPP implements a new, energy conserving, coupling procedure for the elastic wave equation at grid refinement interfaces. When used together with our single grid finite difference scheme, it results in a method which is provably stable, without artificial dissipation, for arbitrary heterogeneous isotropic elastic materials. The new coupling procedure is based on satisfying the summation-by-parts principle across refinement interfaces. From a practical standpoint, an important advantage of the proposed method is the absence of tunable numerical parameters, which seldom are appreciated by application experts. In WPP, the composite grid discretization is combined with a curvilinear grid approach that enables accurate modeling of free surfaces on realistic (non-planar) topography. The overall method satisfies the summation-by-parts principle and is stable under a CFL time step restriction. A feature of great practical importance is that WPP automatically generates the composite grid based on the user provided topography and the depths of the grid refinement interfaces. The WPP code has been verified extensively, for example using the method of manufactured solutions, by solving Lamb's problem, by solving various layer over half- space problems and comparing to semi-analytic (FK) results, and by simulating scenario earthquakes where results from other seismic simulation codes are available. WPP has also been validated against seismographic recordings of moderate earthquakes. WPP performs well on large parallel computers and has been run on up to 32,768 processors using about 26 Billion grid points (78 Billion DOF) and 41,000 time steps. WPP is an open source code that is available under the Gnu general public license.

On the generation and evolution of internal gravity waves

NASA Technical Reports Server (NTRS)

Lansing, F. S.; Maxworthy, T.

1984-01-01

The tidal generation and evolution of internal gravity waves is investigated experimentally and theoretically using a two-dimensional two-layer model. Time-dependent flow is created by moving a profile of maximum submerged depth 7.7 cm through a total stroke of 29 cm in water above a freon-kerosene mixture in an 8.6-m-long 30-cm-deep 20-cm-wide transparent channel, and the deformation of the fluid interface is recorded photographically. A theoretical model of the interface as a set of discrete vortices is constructed numerically; the rigid structures are represented by a source distribution; governing equations in Lagrangian form are obtained; and two integrodifferential equations relating baroclinic vorticity generation and source-density generation are derived. The experimental and computed results are shown in photographs and graphs, respectively, and found to be in good agreement at small Froude numbers. The reasons for small discrepancies in the position of the maximum interface displacement at large Froude numbers are examined.

Subsurface Void Characterization with 3-D Time Domain Full Waveform Tomography.

NASA Astrophysics Data System (ADS)

Nguyen, T. D.

2017-12-01

A new three dimensional full waveform inversion (3-D FWI) method is presented for subsurface site characterization at engineering scales (less than 30 m in depth). The method is based on a solution of 3-D elastic wave equations for forward modeling, and a cross-adjoint gradient approach for model updating. The staggered-grid finite-difference technique is used to solve the wave equations, together with implementation of the perfectly matched layer condition for boundary truncation. The gradient is calculated from the forward and backward wavefields. Reversed-in-time displacement residuals are induced as multiple sources at all receiver locations for the backward wavefield. The capability of the presented FWI method is tested on both synthetic and field experimental datasets. The test configuration uses 96 receivers and 117 shots at equal spacing (Fig 1). The inversion results from synthetic data show the ability of characterizing variable low- and high-velocity layers with embedded void (Figs 2-3). The synthetic study shows good potential for detection of voids and abnormalities in the field.

Fully- and weakly-nonlinear biperiodic traveling waves in shallow water

NASA Astrophysics Data System (ADS)

Hirakawa, Tomoaki; Okamura, Makoto

2018-04-01

We directly calculate fully nonlinear traveling waves that are periodic in two independent horizontal directions (biperiodic) in shallow water. Based on the Riemann theta function, we also calculate exact periodic solutions to the Kadomtsev-Petviashvili (KP) equation, which can be obtained by assuming weakly-nonlinear, weakly-dispersive, weakly-two-dimensional waves. To clarify how the accuracy of the biperiodic KP solution is affected when some of the KP approximations are not satisfied, we compare the fully- and weakly-nonlinear periodic traveling waves of various wave amplitudes, wave depths, and interaction angles. As the interaction angle θ decreases, the wave frequency and the maximum wave height of the biperiodic KP solution both increase, and the central peak sharpens and grows beyond the height of the corresponding direct numerical solutions, indicating that the biperiodic KP solution cannot qualitatively model direct numerical solutions for θ ≲ 45^\\circ . To remedy the weak two-dimensionality approximation, we apply the correction of Yeh et al (2010 Eur. Phys. J. Spec. Top. 185 97-111) to the biperiodic KP solution, which substantially improves the solution accuracy and results in wave profiles that are indistinguishable from most other cases.

New soliton solution to the longitudinal wave equation in a magneto-electro-elastic circular rod

NASA Astrophysics Data System (ADS)

Seadawy, Aly R.; Manafian, Jalil

2018-03-01

This paper examines the effectiveness of an integration scheme which called the extended trial equation method (ETEM) in exactly solving a well-known nonlinear equation of partial differential equations (PDEs). In this respect, the longitudinal wave equation (LWE) that arises in mathematical physics with dispersion caused by the transverse Poisson's effect in a magneto-electro-elastic (MEE) circular rod, which a series of exact traveling wave solutions for the aforementioned equation is formally extracted. Explicit new exact solutions are derived in different form such as dark solitons, bright solitons, solitary wave, periodic solitary wave, rational function, and elliptic function solutions of the longitudinal wave equation. The movements of obtained solutions are shown graphically, which helps to understand the physical phenomena of this longitudinal wave equation. Many other such types of nonlinear equations arising in non-destructive evaluation of structures made of the advanced MEE material can also be solved by this method.

Two dimensional modelling of flood flows and suspended sediment transport: the case of Brenta River

NASA Astrophysics Data System (ADS)

D'Alpaos, L.; Martini, P.; Carniello, L.

2003-04-01

The paper deals with numerical modelling of flood waves and suspended sediment in plain river basins. The two dimensional depth integrated momentum and continuity equations, modified to take into account of the bottom irregularities that strongly affect the hydrodynamic and the continuity in partially dry areas (for example, during the first stages of a plain flooding and in tidal flows), are solved with a standard Galerkin finite element method using a semi-implicit numerical scheme and considering the role both of the small channel network and the regulation dispositive on the flooding wave propagation. Transport of suspended sediment and bed evolution are coupled with the flood propagation through the convection-dispersion equation and the Exner's equation. Results of a real case study are presented in which the effects of extreme flood of Brenta River (Italy) are examinated. The flooded areas (urban and rural areas) are identified and a mitigation solution based on a diversion channel flowing into Venice Lagoon is proposed. We show that this solution strongly reduces the flood risk in the downstream areas and can provide an important sediment source to the Venice Lagoon. Finally, preliminary results of the sediment dispersion in the Venice Lagoon are presented.

Generating porosity spectrum of carbonate reservoirs using ultrasonic imaging log

NASA Astrophysics Data System (ADS)

Zhang, Jie; Nie, Xin; Xiao, Suyun; Zhang, Chong; Zhang, Chaomo; Zhang, Zhansong

2018-03-01

Imaging logging tools can provide us the borehole wall image. The micro-resistivity imaging logging has been used to obtain borehole porosity spectrum. However, the resistivity imaging logging cannot cover the whole borehole wall. In this paper, we propose a method to calculate the porosity spectrum using ultrasonic imaging logging data. Based on the amplitude attenuation equation, we analyze the factors affecting the propagation of wave in drilling fluid and formation and based on the bulk-volume rock model, Wyllie equation and Raymer equation, we establish various conversion models between the reflection coefficient β and porosity ϕ. Then we use the ultrasonic imaging logging and conventional wireline logging data to calculate the near-borehole formation porosity distribution spectrum. The porosity spectrum result obtained from ultrasonic imaging data is compared with the one from the micro-resistivity imaging data, and they turn out to be similar, but with discrepancy, which is caused by the borehole coverage and data input difference. We separate the porosity types by performing threshold value segmentation and generate porosity-depth distribution curves by counting with equal depth spacing on the porosity image. The practice result is good and reveals the efficiency of our method.

How to choose a subset of frequencies in frequency-domain finite-difference migration

NASA Astrophysics Data System (ADS)

Mulder, W. A.; Plessix, R.-E.

2004-09-01

Finite-difference migration with the two-way wave equation can be accelerated by an order of magnitude if the frequency domain rather than the time domain is used. This gain is mainly accomplished by using a subset of the available frequencies. The implicit assumption is that the data have a certain amount of redundancy in the frequency domain. The choice of frequencies cannot be arbitrary. If the frequencies are chosen with a constant increment and their spacing is too large, the well-known wrap-around that occurs when transforming back to the time domain will also show up in the migration to the depth domain, albeit in a more subtle way. Because migration involves propagation in a given background velocity model and summation over shots and receivers, the effects of wrap-around may disappear even when the Nyquist theorem is not obeyed. We have studied these effects analytically for the constant-velocity case and determined sampling conditions that avoid wrap-around artefacts. The conditions depend on the velocity, depth of the migration grid and offset range. They show that the spacing between subsequent frequencies can be larger than the inverse of the time range prescribed by the Nyquist theorem. A 2-D example has been used to test the validity of these conditions for a more realistic velocity model. Finite-difference migration with the one-way wave equation shows a similar behaviour.

Solitary waves, rogue waves and homoclinic breather waves for a (2 + 1)-dimensional generalized Kadomtsev-Petviashvili equation

NASA Astrophysics Data System (ADS)

Dong, Min-Jie; Tian, Shou-Fu; Yan, Xue-Wei; Zou, Li; Li, Jin

2017-10-01

We study a (2 + 1)-dimensional generalized Kadomtsev-Petviashvili (gKP) equation, which characterizes the formation of patterns in liquid drops. By using Bell’s polynomials, an effective way is employed to succinctly construct the bilinear form of the gKP equation. Based on the resulting bilinear equation, we derive its solitary waves, rogue waves and homoclinic breather waves, respectively. Our results can help enrich the dynamical behavior of the KP-type equations.

Dynamics of liquid films exposed to high-frequency surface vibration

NASA Astrophysics Data System (ADS)

Manor, Ofer; Rezk, Amgad R.; Friend, James R.; Yeo, Leslie Y.

2015-05-01

We derive a generalized equation that governs the spreading of liquid films under high-frequency (MHz-order) substrate vibration in the form of propagating surface waves and show that this single relationship is universally sufficient to collectively describe the rich and diverse dynamic phenomena recently observed for the transport of oil films under such substrate excitation, in particular, Rayleigh surface acoustic waves. In contrast to low-frequency (Hz- to kHz-order) vibration-induced wetting phenomena, film spreading at such high frequencies arises from convective drift generated by the viscous periodic flow localized in a region characterized by the viscous penetration depth β-1≡(2μ /ρ ω ) 1 /2 adjacent to the substrate that is invoked directly by its vibration; μ and ρ are the viscosity and the density of the liquid, respectively, and ω is the excitation frequency. This convective drift is responsible for driving the spreading of thin films of thickness h ≪kl-1 , which spread self-similarly as t1 /4 along the direction of the drift corresponding to the propagation direction of the surface wave, kl being the wave number of the compressional acoustic wave that forms in the liquid due to leakage of the surface wave energy from the substrate into the liquid and t the time. Films of greater thicknesses h ˜kl-1≫β-1 , in contrast, are observed to spread with constant velocity but in a direction that opposes the drift and surface wave propagation due to the attenuation of the acoustic wave in the liquid. The universal equation derived allows for the collective prediction of the spreading of these thin and thick films in opposing directions.

Rogue waves in the two dimensional nonlocal nonlinear Schrödinger equation and nonlocal Klein-Gordon equation.

PubMed

Liu, Wei; Zhang, Jing; Li, Xiliang

2018-01-01

In this paper, we investigate two types of nonlocal soliton equations with the parity-time (PT) symmetry, namely, a two dimensional nonlocal nonlinear Schrödinger (NLS) equation and a coupled nonlocal Klein-Gordon equation. Solitons and periodic line waves as exact solutions of these two nonlocal equations are derived by employing the Hirota's bilinear method. Like the nonlocal NLS equation, these solutions may have singularities. However, by suitable constraints of parameters, nonsingular breather solutions are generated. Besides, by taking a long wave limit of these obtained soliton solutions, rogue wave solutions and semi-rational solutions are derived. For the two dimensional NLS equation, rogue wave solutions are line rogue waves, which arise from a constant background with a line profile and then disappear into the same background. The semi-rational solutions shows intriguing dynamical behaviours: line rogue wave and line breather arise from a constant background together and then disappear into the constant background again uniformly. For the coupled nonlocal Klein-Gordon equation, rogue waves are localized in both space and time, semi-rational solutions are composed of rogue waves, breathers and periodic line waves. These solutions are demonstrated analytically to exist for special classes of nonlocal equations relevant to optical waveguides.

Rogue waves in the two dimensional nonlocal nonlinear Schrödinger equation and nonlocal Klein-Gordon equation

PubMed Central

Zhang, Jing; Li, Xiliang

2018-01-01

In this paper, we investigate two types of nonlocal soliton equations with the parity-time (PT) symmetry, namely, a two dimensional nonlocal nonlinear Schrödinger (NLS) equation and a coupled nonlocal Klein-Gordon equation. Solitons and periodic line waves as exact solutions of these two nonlocal equations are derived by employing the Hirota’s bilinear method. Like the nonlocal NLS equation, these solutions may have singularities. However, by suitable constraints of parameters, nonsingular breather solutions are generated. Besides, by taking a long wave limit of these obtained soliton solutions, rogue wave solutions and semi-rational solutions are derived. For the two dimensional NLS equation, rogue wave solutions are line rogue waves, which arise from a constant background with a line profile and then disappear into the same background. The semi-rational solutions shows intriguing dynamical behaviours: line rogue wave and line breather arise from a constant background together and then disappear into the constant background again uniformly. For the coupled nonlocal Klein-Gordon equation, rogue waves are localized in both space and time, semi-rational solutions are composed of rogue waves, breathers and periodic line waves. These solutions are demonstrated analytically to exist for special classes of nonlocal equations relevant to optical waveguides. PMID:29432495

Theory and observation of electromagnetic ion cyclotron triggered emissions in the magnetosphere

NASA Astrophysics Data System (ADS)

Omura, Yoshiharu; Pickett, Jolene; Grison, Benjamin; Santolik, Ondrej; Dandouras, Iannis; Engebretson, Mark; Décréau, Pierrette M. E.; Masson, Arnaud

2010-07-01

We develop a nonlinear wave growth theory of electromagnetic ion cyclotron (EMIC) triggered emissions observed in the inner magnetosphere. We first derive the basic wave equations from Maxwell's equations and the momentum equations for the electrons and ions. We then obtain equations that describe the nonlinear dynamics of resonant protons interacting with an EMIC wave. The frequency sweep rate of the wave plays an important role in forming the resonant current that controls the wave growth. Assuming an optimum condition for the maximum growth rate as an absolute instability at the magnetic equator and a self-sustaining growth condition for the wave propagating from the magnetic equator, we obtain a set of ordinary differential equations that describe the nonlinear evolution of a rising tone emission generated at the magnetic equator. Using the physical parameters inferred from the wave, particle, and magnetic field data measured by the Cluster spacecraft, we determine the dispersion relation for the EMIC waves. Integrating the differential equations numerically, we obtain a solution for the time variation of the amplitude and frequency of a rising tone emission at the equator. Assuming saturation of the wave amplitude, as is found in the observations, we find good agreement between the numerical solutions and the wave spectrum of the EMIC triggered emissions.

A numerical study of the 3-periodic wave solutions to KdV-type equations

NASA Astrophysics Data System (ADS)

Zhang, Yingnan; Hu, Xingbiao; Sun, Jianqing

2018-02-01

In this paper, by using the direct method of calculating periodic wave solutions proposed by Akira Nakamura, we present a numerical process to calculate the 3-periodic wave solutions to several KdV-type equations: the Korteweg-de Vries equation, the Sawada-Koterra equation, the Boussinesq equation, the Ito equation, the Hietarinta equation and the (2 + 1)-dimensional Kadomtsev-Petviashvili equation. Some detailed numerical examples are given to show the existence of the three-periodic wave solutions numerically.

Poincare oscillations and geostrophic adjustment in a rotating paraboloid

NASA Astrophysics Data System (ADS)

Kalashnik, M.; Kakhiani, V.; Patarashvili, K.; Tsakadze, S.

2009-10-01

Free liquid oscillations (Poincare oscillations) in a rotating paraboloid are investigated theoretically and experimentally. Within the framework of shallow-water theory, with account for the centrifugal force, expressions for the free oscillation frequencies are obtained and corrections to the frequencies related with the finiteness of the liquid depth are found. It is shown that in the rotating liquid, apart from the wave modes of free oscillations, a stationary vortex mode is also generated, that is, a process of geostrophic adjustment takes place. Solutions of the shallow-water equations which describe the wave dynamics of the adjustment process are presented. In the experiments performed the wave and vortex modes were excited by removing a previously immersed hemisphere from the central part of the paraboloid. Good agreement between theory and experiment was obtained. Address: alex_gaina@yahoo.com Database: phy

Unsplit complex frequency shifted perfectly matched layer for second-order wave equation using auxiliary differential equations.

PubMed

Gao, Yingjie; Zhang, Jinhai; Yao, Zhenxing

2015-12-01

The complex frequency shifted perfectly matched layer (CFS-PML) can improve the absorbing performance of PML for nearly grazing incident waves. However, traditional PML and CFS-PML are based on first-order wave equations; thus, they are not suitable for second-order wave equation. In this paper, an implementation of CFS-PML for second-order wave equation is presented using auxiliary differential equations. This method is free of both convolution calculations and third-order temporal derivatives. As an unsplit CFS-PML, it can reduce the nearly grazing incidence. Numerical experiments show that it has better absorption than typical PML implementations based on second-order wave equation.

Nonlinear acoustic wave equations with fractional loss operators.

PubMed

Prieur, Fabrice; Holm, Sverre

2011-09-01

Fractional derivatives are well suited to describe wave propagation in complex media. When introduced in classical wave equations, they allow a modeling of attenuation and dispersion that better describes sound propagation in biological tissues. Traditional constitutive equations from solid mechanics and heat conduction are modified using fractional derivatives. They are used to derive a nonlinear wave equation which describes attenuation and dispersion laws that match observations. This wave equation is a generalization of the Westervelt equation, and also leads to a fractional version of the Khokhlov-Zabolotskaya-Kuznetsov and Burgers' equations. © 2011 Acoustical Society of America

Linear shoaling of free-surface waves in multi-layer non-hydrostatic models

NASA Astrophysics Data System (ADS)

Bai, Yefei; Cheung, Kwok Fai

2018-01-01

The capability to describe shoaling over sloping bottom is fundamental to modeling of coastal wave transformation. The linear shoaling gradient provides a metric to measure this property in non-hydrostatic models with layer-integrated formulations. The governing equations in Boussinesq form facilitate derivation of the linear shoaling gradient, which is in the form of a [ 2 P + 2 , 2 P ] expansion of the water depth parameter kd with P equal to 1 for a one-layer model and (4 N - 4) for an N-layer model. The expansion reproduces the analytical solution from Airy wave theory at the shallow water limit and maintains a reasonable approximation up to kd = 1.2 and 2 for the one and two-layer models. Additional layers provide rapid and monotonic convergence of the shoaling gradient into deep water. Numerical experiments of wave propagation over a plane slope illustrate manifestation of the shoaling errors through the transformation processes from deep to shallow water. Even though outside the zone of active wave transformation, shoaling errors from deep to intermediate water are cumulative to produce appreciable impact to the wave amplitude in shallow water.

Classifying bilinear differential equations by linear superposition principle

NASA Astrophysics Data System (ADS)

Zhang, Lijun; Khalique, Chaudry Masood; Ma, Wen-Xiu

2016-09-01

In this paper, we investigate the linear superposition principle of exponential traveling waves to construct a sub-class of N-wave solutions of Hirota bilinear equations. A necessary and sufficient condition for Hirota bilinear equations possessing this specific sub-class of N-wave solutions is presented. We apply this result to find N-wave solutions to the (2+1)-dimensional KP equation, a (3+1)-dimensional generalized Kadomtsev-Petviashvili (KP) equation, a (3+1)-dimensional generalized BKP equation and the (2+1)-dimensional BKP equation. The inverse question, i.e., constructing Hirota Bilinear equations possessing N-wave solutions, is considered and a refined 3-step algorithm is proposed. As examples, we construct two very general kinds of Hirota bilinear equations of order 4 possessing N-wave solutions among which one satisfies dispersion relation and another does not satisfy dispersion relation.

Regional correlations of VS30 averaged over depths less than and greater than 30 meters

USGS Publications Warehouse

Boore, David M.; Thompson, Eric M.; Cadet, Héloïse

2011-01-01

Using velocity profiles from sites in Japan, California, Turkey, and Europe, we find that the time-averaged shear-wave velocity to 30 m (VS30), used as a proxy for site amplification in recent ground-motion prediction equations (GMPEs) and building codes, is strongly correlated with average velocities to depths less than 30 m (VSz, with z being the averaging depth). The correlations for sites in Japan (corresponding to the KiK-net network) show that VSz is systematically larger for a given VSz than for profiles from the other regions. The difference largely results from the placement of the KiK-net station locations on rock and rocklike sites, whereas stations in the other regions are generally placed in urban areas underlain by sediments. Using the KiK-net velocity profiles, we provide equations relating VS30 to VSz for z ranging from 5 to 29 m in 1-m increments. These equations (and those for California velocity profiles given in Boore, 2004b) can be used to estimate VS30 from VSz for sites in which velocity profiles do not extend to 30 m. The scatter of the residuals decreases with depth, but, even for an averaging depth of 5 m, a variation in logVS30 of ±1 standard deviation maps into less than a 20% uncertainty in ground motions given by recent GMPEs at short periods. The sensitivity of the ground motions to VS30 uncertainty is considerably larger at long periods (but is less than a factor of 1.2 for averaging depths greater than about 20 m). We also find that VS30 is correlated with VSz for z as great as 400 m for sites of the KiK-net network, providing some justification for using VS30 as a site-response variable for predicting ground motions at periods for which the wavelengths far exceed 30 m.

Imaging hydraulic fractures at Median Tectonic Line, Japan using multiply generated and scattered tube waves in a shallow VSP experiment

NASA Astrophysics Data System (ADS)

Minato, Shohei; Ghose, Ranajit; Tsuji, Takeshi; Ikeda, Michiharu; Onishi, Kozo

2016-04-01

Tube waves are low frequency guided waves that propagate along a fluid-filled borehole. The analysis of tube waves is a promising approach to image and characterize hydraulic fractures intersecting a borehole. It exploits tube waves generated by an external seismic wavefield which compresses fractures and injects fluid into the borehole. It also utilizes the attenuation of tube waves due to fluid exchange between the fracture and the borehole, which creates scattered waves (reflection and transmission). Conventional approaches consider tube waves due to a single fracture. However, when the spacing between multiple fractures is short relative to the wavelength of the tube waves, the generated and scattered tube waves interfere with each other, making it difficult to isolate the effect of a single fracture. The analysis of closely spaced fractures is important in highly fractured areas, such as a fault zone. In this study, we explore the possibility of prediction and utilization of generated and scattered tube waves due to multiple fractures. We derive a new integral equation of the full tube wavefield using 1D wavefield representation theory incorporating nonwelded interfaces. We adapt the recent developments in modeling tube wave generation/scattering at a fracture. In these models, a fracture is represented as a parallel wall or a thin poloelastic layer. This allowed us to consider the effects of a dynamic fracture aperture with fracture compliances and the permeability. The representation also leads to a new imaging method for the hydraulic fractures, using multiply-generated and scattered tube waves. This is achieved by applying an inverse operator to the observed tube waves, which focuses the tube waves to the depth where they are generated and/or scattered. The inverse operator is constructed by a tube wave Green's function with a known propagation velocity. The Median Tectonic Line (MTL) is the most significant fault in Japan, extending NE-SW for over 1000 km across the Japanese Islands. We observed multiple tube waves in a P-wave VSP experiment in a 250 m deep, vertical borehole located on the MTL at Shikoku, Japan. The borehole televiewer and the core studies show that below 40 m depth, the Sambagawa metamorphic rocks contain highly fractured zones which consist of more than 100 open fractures and more than 30 cataclasites. We predict the full tube wavefield using the values of fracture depth and thickness known from the borehole televiewer. We model the open fractures as parallel-wall fractures and the cataclasites as thin poroelastic layers. Furthermore, we estimate the depth of the hydraulic fractures by applying the inverse operator. The results show that the tube waves could be generated and scattered at these permeable structures. Our preliminary results also indicate the possibility that the effect of the open fractures is more dominant in the generation and scattering of tube waves than that of the cataclasites in this field. The formulation and the results presented in this study and the following discussion will be useful in analysis of tube waves in highly fractured zones, in order to localize and characterize hydraulic fractures.

Traveling waves and conservation laws for highly nonlinear wave equations modeling Hertz chains

NASA Astrophysics Data System (ADS)

Przedborski, Michelle; Anco, Stephen C.

2017-09-01

A highly nonlinear, fourth-order wave equation that models the continuum theory of long wavelength pulses in weakly compressed, homogeneous, discrete chains with a general power-law contact interaction is studied. For this wave equation, all solitary wave solutions and all nonlinear periodic wave solutions, along with all conservation laws, are derived. The solutions are explicitly parameterized in terms of the asymptotic value of the wave amplitude in the case of solitary waves and the peak of the wave amplitude in the case of nonlinear periodic waves. All cases in which the solution expressions can be stated in an explicit analytic form using elementary functions are worked out. In these cases, explicit expressions for the total energy and total momentum for all solutions are obtained as well. The derivation of the solutions uses the conservation laws combined with an energy analysis argument to reduce the wave equation directly to a separable first-order differential equation that determines the wave amplitude in terms of the traveling wave variable. This method can be applied more generally to other highly nonlinear wave equations.

Kinematics and depth-integrated terms in surf zone waves from laboratory measurement

NASA Astrophysics Data System (ADS)

Stansby, Peter K.; Feng, Tong

2005-04-01

Kinematics of nominally periodic surf zone waves have been measured in the laboratory using LDA (laser Doppler anemometry), above trough level as well as below, for weakly plunging breakers transforming into bores in shallower water. The aim was to determine, through phase- or ensemble-averaging, periodic flow structures in a two-dimensional vertical plane, from large-scale down to small-scale vortical structures. Coherent multiple vortical structures were evident at the initiation of breaking, becoming elongated along the surface during bore propagation. The initial region is likely to become more extensive as waves become more strongly plunging and could explain the difference in turbulence characteristics between plunging and spilling breakers observed elsewhere. Comparison of vorticity magnitudes with hydraulic-jump measurements showed some similarities during the initial stages of breaking, but these quickly grew less as breaking progressed into shallower water. Period-averaged kinematics and vorticity were also obtained showing shoreward mass transport above trough level and undertow below, with a thick layer of vorticity at trough level and a thin layer of vorticity of opposite rotation at the bed. There were also concentrated regions of mean vorticity near the end of the plunging region. Residual turbulence of relatively high frequency was presented as Reynolds stresses, showing marked anisotrophy. Dynamic pressure (pressure minus its hydrostatic component) was determined from the kinematics. The magnitudes of different effects were evaluated through the depth-integrated Reynolds-averaged Navier-Stokes (RANS) equations, which may be reduced to nine terms (the standard inviscid terms of the shallow-water equations conserving mass and momentum with hydrostatic pressure, and six additional terms), assuming that the complex, often aerated, free surface is treated as a simple interface. All terms were evaluated, assuming that a space/time transformation was justified with a slowly varying phase speed, and the net balance was always small in relation to the maxima of the larger terms. Terms due to dynamic pressure and vertical dispersion (due to the vertical variation of velocity) were as significant as the three terms in the inviscid shallow-water equations; terms involving residual turbulence were insignificant. The r.m.s. (root mean square) variation of each along the slope is highly irregular, with the inertia term due to (Eulerian) acceleration always greatest. This is consistent with complex, though repetitive, coherent structures. Modelling the flow with the shallow-water equations, using the surface elevation variation at the break point as input, nevertheless gave a good prediction of the wave height variation up the slope.

THE FUNDAMENTAL SOLUTIONS FOR MULTI-TERM MODIFIED POWER LAW WAVE EQUATIONS IN A FINITE DOMAIN.

PubMed

Jiang, H; Liu, F; Meerschaert, M M; McGough, R J

2013-01-01

Fractional partial differential equations with more than one fractional derivative term in time, such as the Szabo wave equation, or the power law wave equation, describe important physical phenomena. However, studies of these multi-term time-space or time fractional wave equations are still under development. In this paper, multi-term modified power law wave equations in a finite domain are considered. The multi-term time fractional derivatives are defined in the Caputo sense, whose orders belong to the intervals (1, 2], [2, 3), [2, 4) or (0, n ) ( n > 2), respectively. Analytical solutions of the multi-term modified power law wave equations are derived. These new techniques are based on Luchko's Theorem, a spectral representation of the Laplacian operator, a method of separating variables and fractional derivative techniques. Then these general methods are applied to the special cases of the Szabo wave equation and the power law wave equation. These methods and techniques can also be extended to other kinds of the multi-term time-space fractional models including fractional Laplacian.

Calculation of Seismic Waves from Explosions with Tectonic Stresses and Topography

NASA Astrophysics Data System (ADS)

Stevens, J. L.; O'Brien, M.

2017-12-01

We investigate the effects of explosion depth, tectonic stresses and topography on seismic waves from underground nuclear explosions. We perform three-dimensional nonlinear calculations of an explosion at several depths in the topography of the North Korean test site. We also perform a large number of two-dimensional axisymmetric calculations of explosions at depths from 150 to 1000 meters in four earth structures, with compressive and tensile tectonic stresses and with no tectonic stresses. We use the representation theorem to propagate the results of these calculations and calculate seismic waves at regional and teleseismic distances. We find that P-waves are not strongly affected by any of these effects because the initial downgoing P-wave is unaffected by interaction with the free surface. Surface waves, however, are strongly affected by all of these effects. There is an optimal depth at which surface waves are maximized at the base of a mountain and at or slightly below normal containment depth. At deeper depths, increasing overburden pressure reduces the surface waves. At shallower depths, interaction with the free surface reduces the surface waves. For explosions inside a mountain, displacement of the sides of the mountain reduces surface waves. Compressive prestress reduces surface waves substantially, while tensile prestress increases surface waves. The North Korean explosions appear to be at an optimal depth, in a region of extension, and beneath a mountain, all of which increase surface wave amplitudes.

High resolution crustal image of South California Continental Borderland: Reverse time imaging including multiples

NASA Astrophysics Data System (ADS)

Bian, A.; Gantela, C.

2014-12-01

Strong multiples were observed in marine seismic data of Los Angeles Regional Seismic Experiment (LARSE).It is crucial to eliminate these multiples in conventional ray-based or one-way wave-equation based depth image methods. As long as multiples contain information of target zone along travelling path, it's possible to use them as signal, to improve the illumination coverage thus enhance the image quality of structural boundaries. Reverse time migration including multiples is a two-way wave-equation based prestack depth image method that uses both primaries and multiples to map structural boundaries. Several factors, including source wavelet, velocity model, back ground noise, data acquisition geometry and preprocessing workflow may influence the quality of image. The source wavelet is estimated from direct arrival of marine seismic data. Migration velocity model is derived from integrated model building workflow, and the sharp velocity interfaces near sea bottom needs to be preserved in order to generate multiples in the forward and backward propagation steps. The strong amplitude, low frequency marine back ground noise needs to be removed before the final imaging process. High resolution reverse time image sections of LARSE Lines 1 and Line 2 show five interfaces: depth of sea-bottom, base of sedimentary basins, top of Catalina Schist, a deep layer and a possible pluton boundary. Catalina Schist shows highs in the San Clemente ridge, Emery Knoll, Catalina Ridge, under Catalina Basin on both the lines, and a minor high under Avalon Knoll. The high of anticlinal fold in Line 1 is under the north edge of Emery Knoll and under the San Clemente fault zone. An area devoid of any reflection features are interpreted as sides of an igneous plume.

Finite Difference Modeling of Wave Progpagation in Acoustic TiltedTI Media

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhang, Linbin; Rector III, James W.; Hoversten, G. Michael

2005-03-21

Based on an acoustic assumption (shear wave velocity is zero) and a dispersion relation, we derive an acoustic wave equation for P-waves in tilted transversely isotropic (TTI) media (transversely isotropic media with a tilted symmetry axis). This equation has fewer parameters than an elastic wave equation in TTI media and yields an accurate description of P-wave traveltimes and spreading-related attenuation. Our TTI acoustic wave equation is a fourth-order equation in time and space. We demonstrate that the acoustic approximation allows the presence of shear waves in the solution. The substantial differences in traveltime and amplitude between data created using VTImore » and TTI assumptions is illustrated in examples.« less

Stress measurement in thick plates using nonlinear ultrasonics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Abbasi, Zeynab, E-mail: zabbas5@uic.edu, E-mail: dozevin@uic.edu; Ozevin, Didem, E-mail: zabbas5@uic.edu, E-mail: dozevin@uic.edu

2015-03-31

In this paper the interaction between nonlinear ultrasonic characteristics and stress state of complex loaded thick steel plates using fundamental theory of nonlinear ultrasonics is investigated in order to measure the stress state at a given cross section. The measurement concept is based on phased array placement of ultrasonic transmitter-receiver to scan three angles of a given cross section using Rayleigh waves. The change in the ultrasonic data in thick steel plates is influenced by normal and shear stresses; therefore, three measurements are needed to solve the equations simultaneously. Different thickness plates are studied in order to understand the interactionmore » of Rayleigh wave penetration depth and shear stress. The purpose is that as the thickness becomes smaller, the shear stress becomes negligible at the angled measurement. For thicker cross section, shear stress becomes influential if the depth of penetration of Rayleigh wave is greater than the half of the thickness. The influences of plate thickness and ultrasonic frequency on the identification of stress tensor are numerically studied in 3D structural geometry and Murnaghan material model. The experimental component of this study includes uniaxial loading of the plate while measuring ultrasonic wave at three directions (perpendicular, parallel and angled to the loading direction). Instead of rotating transmitter-receiver pair for each test, a device capable of measuring the three angles is designed.« less

Hawking radiation by Kerr black holes and conformal symmetry.

PubMed

Agullo, Ivan; Navarro-Salas, José; Olmo, Gonzalo J; Parker, Leonard

2010-11-19

The exponential blueshift associated with the event horizon of a black hole makes conformal symmetry play a fundamental role in accounting for its thermal properties. Using a derivation based on two-point functions, we show that the full spectrum of thermal radiation of scalar particles by Kerr black holes can be explicitly derived on the basis of a conformal symmetry arising in the wave equation near the horizon. The simplicity of our approach emphasizes the depth of the connection between conformal symmetry and black hole radiance.

Impact of errors in short wave radiation and its attenuation on modeled upper ocean heat content

DTIC Science & Technology

Photosynthetically available radiation (PAR) and its attenuation with the depth represent a forcing (source) term in the governing equation for the...and vertical attenuation of PAR have on the upper ocean model heat content. In the Monterey Bay area, we show that with a decrease in water clarity...attenuation coefficient. For Jerlov’s type IA water (attenuation coefficient is 0.049 m1), the relative error in surface PAR introduces an error

Exact traveling wave solutions of modified KdV-Zakharov-Kuznetsov equation and viscous Burgers equation.

PubMed

Islam, Md Hamidul; Khan, Kamruzzaman; Akbar, M Ali; Salam, Md Abdus

2014-01-01

Mathematical modeling of many physical systems leads to nonlinear evolution equations because most physical systems are inherently nonlinear in nature. The investigation of traveling wave solutions of nonlinear partial differential equations (NPDEs) plays a significant role in the study of nonlinear physical phenomena. In this article, we construct the traveling wave solutions of modified KDV-ZK equation and viscous Burgers equation by using an enhanced (G '/G) -expansion method. A number of traveling wave solutions in terms of unknown parameters are obtained. Derived traveling wave solutions exhibit solitary waves when special values are given to its unknown parameters. 35C07; 35C08; 35P99.

An approach to rogue waves through the cnoidal equation

NASA Astrophysics Data System (ADS)

Lechuga, Antonio

2014-05-01

Lately it has been realized the importance of rogue waves in some events happening in open seas. Extreme waves and extreme weather could explain some accidents, but not all of them. Every now and then inflicted damages on ships only can be reported to be caused by anomalous and elusive waves, such as rogue waves. That's one of the reason why they continue attracting considerable interest among researchers. In the frame of the Nonlinear Schrödinger equation(NLS), Witham(1974) and Dingemans and Otta (2001)gave asymptotic solutions in moving coordinates that transformed the NLS equation in a ordinary differential equation that is the Duffing or cnoidal wave equation. Applying the Zakharov equation, Stiassnie and Shemer(2004) and Shemer(2010)got also a similar equation. It's well known that this ordinary equation can be solved in elliptic functions. The main aim of this presentation is to sort out the domains of the solutions of this equation, that, of course, are linked to the corresponding solutions of the partial differential equations(PDEs). That being, Lechuga(2007),a simple way to look for anomalous waves as it's the case with some "chaotic" solutions of the Duffing equation.

Wave equations in conformal gravity

NASA Astrophysics Data System (ADS)

Du, Juan-Juan; Wang, Xue-Jing; He, You-Biao; Yang, Si-Jiang; Li, Zhong-Heng

2018-05-01

We study the wave equation governing massless fields of all spins (s = 0, 1 2, 1, 3 2 and 2) in the most general spherical symmetric metric of conformal gravity. The equation is separable, the solution of the angular part is a spin-weighted spherical harmonic, and the radial wave function may be expressed in terms of solutions of the Heun equation which has four regular singular points. We also consider various special cases of the metric and find that the angular wave functions are the same for all cases, the actual shape of the metric functions affects only the radial wave function. It is interesting to note that each radial equation can be transformed into a known ordinary differential equation (i.e. Heun equation, or confluent Heun equation, or hypergeometric equation). The results show that there are analytic solutions for all the wave equations of massless spin fields in the spacetimes of conformal gravity. This is amazing because exact solutions are few and far between for other spacetimes.

Peculiarities of spreading of acoustic waves over a shelf with decreasing depth

NASA Astrophysics Data System (ADS)

Dolgikh, G. I.; Budrin, S. S.; Ovcharenko, V. V.; Plotnikov, A. A.

2016-09-01

We analyze experimental data collected in Vityaz Bay of the Sea of Japan during study of the peculiarities of spreading of hydroacoustic waves over a shelf with decreasing depth. We found that the waves propagate over a shelf with depths greater than half of the hydroacoustic wave according to the law of cylindrical divergence with least losses of the wave energy. If the depths are shallower than half of the hydroacoustic wave, they spread along the water-bottom boundary as Rayleigh waves of decaying and undamped types with significant absorption of the wave energy by the bottom.

Rogue periodic waves of the modified KdV equation

NASA Astrophysics Data System (ADS)

Chen, Jinbing; Pelinovsky, Dmitry E.

2018-05-01

Rogue periodic waves stand for rogue waves on a periodic background. Two families of travelling periodic waves of the modified Korteweg–de Vries (mKdV) equation in the focusing case are expressed by the Jacobian elliptic functions dn and cn. By using one-fold and two-fold Darboux transformations of the travelling periodic waves, we construct new explicit solutions for the mKdV equation. Since the dn-periodic wave is modulationally stable with respect to long-wave perturbations, the new solution constructed from the dn-periodic wave is a nonlinear superposition of an algebraically decaying soliton and the dn-periodic wave. On the other hand, since the cn-periodic wave is modulationally unstable with respect to long-wave perturbations, the new solution constructed from the cn-periodic wave is a rogue wave on the cn-periodic background, which generalizes the classical rogue wave (the so-called Peregrine’s breather) of the nonlinear Schrödinger equation. We compute the magnification factor for the rogue cn-periodic wave of the mKdV equation and show that it remains constant for all amplitudes. As a by-product of our work, we find explicit expressions for the periodic eigenfunctions of the spectral problem associated with the dn and cn periodic waves of the mKdV equation.

Observed variability in the upper layers at the Equator, 90°E in the Indian Ocean during 2001-2008, 1: zonal currents

NASA Astrophysics Data System (ADS)

Rao, R. R.; Horii, T.; Masumoto, Y.; Mizuno, K.

2017-08-01

The observed variability of zonal currents (ZC) at the Equator, 90°E shows a strong seasonal cycle in the near-surface 40-350 m water column with periodic east-west reversals most pronounced at semiannual frequency. Superposed on this, a strong intraseasonal variability of 30-90 day periodicity is also prominently seen in the near-surface layer (40-80 m) almost throughout the year with the only exception of February-March. An eastward flowing equatorial undercurrent (EUC) is present in the depth range of 80-160 m during March-April and October-November. The observed intraseasonal variability in the near-surface layer is primarily determined by the equatorial zonal westerly wind bursts (WWBs) through local frictional coupling between the zonal flow in the surface layer and surface zonal winds and shows large interannual variability. The eastward flowing EUC maintained by the ZPG set up by the east-west slope of the thermocline remotely controlled by the zonal wind (ZW) and zonally propagating wave fields also shows significant interannual variability. This observed variability on interannual time scales appears to be controlled by the corresponding variability in the alongshore winds off the Somalia coast during the preceding boreal winter, the ZW field along the equator, and the associated zonally propagating Kelvin and Rossby waves. The salinity induced vertical stratification observed in the near-surface layer through barrier layer thickness (BLT) effects also shows a significant influence on the ZC field on intraseasonal time scale. Interestingly, among all the 8 years (2001-2008), relatively weaker annual cycle is seen in both ZC in the 40-350 m water column and boreal spring sea surface temperature (SST) only during 2001 and 2008 along the equator caused through propagating wave dynamics.

Observations of experimental and numerical waveforms of piezoelectric signals generated in bovine cancellous bone by ultrasound waves

NASA Astrophysics Data System (ADS)

Hosokawa, Atsushi

2018-07-01

Experimental and numerical waveforms of piezoelectric signals generated in the bovine cancellous bone by ultrasound waves at 1.0 MHz were observed. The experimental observations were performed using a “piezoelectric cell (PE-cell)”, in which an air-saturated cancellous bone specimen was electrically shielded. The PE-cell was used to receive burst ultrasound waves. The numerical observations were performed using a piezoelectric finite-difference time-domain (PE-FDTD) method, which was an elastic FDTD method with piezoelectric constitutive equations. The cancellous bone model was reconstructed from the three-dimensional X-ray microcomputed tomographic image of the specimen used in the experiments. Both experimental and numerical results showed that the repetitive piezoelectric signals could be generated by the multireflected ultrasound waves within the cancellous bone specimen. Moreover, it was shown that the output piezoelectric signal in the PE-cell could be the overlap of the local signals in the trabecular elements at various depths (or thicknesses) in the cancellous bone specimen.

An estimate of equatorial wave energy flux at 9- to 90-day periods in the Central Pacific

NASA Technical Reports Server (NTRS)

Eriksen, Charles C.; Richman, James G.

1988-01-01

Deep fluctuations in current along the equator in the Central Pacific are dominated by coherent structures which correspond closely to narrow-band propagating equatorial waves. Currents were measured roughly at 1500 and 3000 m depths at five moorings between 144 and 148 deg W from January 1981 to March 1983, as part of the Pacific Equatorial Ocean Dynamics program. In each frequency band resolved, a single complex empirical orthogonal function accounts for half to three quarters of the observed variance in either zonal or meridional current. Dispersion for equatorial first meridional Rossby and Rossby gravity waves is consistent with the observed vertical-zonal coherence structure. The observations indicate that energy flux is westward and downward in long first meridional mode Rossby waves at periods 45 days and longer, and eastward and downward in short first meridional mode Rossby waves and Rossby-gravity waves at periods 30 days and shorter. A local minimum in energy flux occurs at periods corresponding to a maximum in upper-ocean meridional current energy contributed by tropical instability waves. Total vertical flux across the 9- to 90-day period range is 2.5 kW/m.

Propagation of nonlinear shock waves for the generalised Oskolkov equation and its dynamic motions in the presence of an external periodic perturbation

NASA Astrophysics Data System (ADS)

Ak, Turgut; Aydemir, Tugba; Saha, Asit; Kara, Abdul Hamid

2018-06-01

Propagation of nonlinear shock waves for the generalised Oskolkov equation and dynamic motions of the perturbed Oskolkov equation are investigated. Employing the unified method, a collection of exact shock wave solutions for the generalised Oskolkov equations is presented. Collocation finite element method is applied to the generalised Oskolkov equation for checking the accuracy of the proposed method by two test problems including the motion of shock wave and evolution of waves with Gaussian and undular bore initial conditions. Considering an external periodic perturbation, the dynamic motions of the perturbed generalised Oskolkov equation are studied depending on the system parameters with the help of phase portrait and time series plot. The perturbed generalised Oskolkov equation exhibits period-3, quasiperiodic and chaotic motions for some special values of the system parameters, whereas the generalised Oskolkov equation presents shock waves in the absence of external periodic perturbation.

Widespread imaging of the lower crust, Moho, and upper mantle from Rayleigh waves: A comparison of the Cascadia and Aleutian-Alaska subduction zones

NASA Astrophysics Data System (ADS)

Haney, M. M.; Tsai, V. C.; Ward, K. M.

2016-12-01

Recently, Haney and Tsai (2015) developed a new approach to Rayleigh-wave inversion based on assumptions that are similar to those used in the formulation of the Dix equation in reflection seismology. Here we apply the Dix technique to Rayleigh-wave phase-velocity maps by Ekstrom (2013) and Ward (2015) of the contiguous US and Alaska, respectively, at periods between 12 and 45 s. We refine the initial Dix result with subsequent nonlinear inversion to estimate Moho depth together with shear-wave velocity of the lower crust and upper mantle. In the contiguous US, the Moho we image agrees well with recent receiver function studies. There is an apparent deepening of the Moho to the west of the Cascades volcanic chain that we interpret as the waveguide interface transitioning to the slab due to the continental Moho becoming transparent above the mantle forearc. This feature abruptly terminates at the southern extent of the Cascadia subduction zone. We compare the depths of this "apparent Moho" with published estimates of the depth to the Juan de Fuca Plate since, owing to the paucity of tectonic earthquakes, the Slab1.0 model is not defined in Cascadia. Our result in Alaska is the first regional Moho map derived explicitly from seismic waves. We find that crustal thickness is generally correlated with topography, with thicker crust beneath mountain ranges in southern Alaska. North of the Denali Fault, the Moho is smoother than to the south and located at typical depths of 30-35 km. There are also indications that the waveguide interface we solve for beneath Prince William Sound is actually the subducting slab instead of the continental Moho. The slab structure beneath Prince William Sound extends further east than the Pacific slab represented in the Slab1.0 model. Using the limited number of broadband seismometers in the Aleutian Islands, we obtain preliminary estimates for the crustal structure beneath the western portion of the Aleutian-Alaska subduction zone.

Adapting HYDRUS-1D to Simulate Overland Flow and Reactive Transport During Sheet Flow Deviations

NASA Astrophysics Data System (ADS)

Liang, J.; Bradford, S. A.; Simunek, J.; Hartmann, A.

2017-12-01

The HYDRUS-1D code is a popular numerical model for solving the Richards equation for variably-saturated water flow and solute transport in porous media. This code was adapted to solve rather than the Richards equation for subsurface flow the diffusion wave equation for overland flow at the soil surface. The numerical results obtained by the new model produced an excellent agreement with the analytical solution of the kinematic wave equation. Model tests demonstrated its applicability to simulate the transport and fate of many different solutes, such as non-adsorbing tracers, nutrients, pesticides, and microbes. However, the diffusion wave or kinematic wave equations describe surface runoff as sheet flow with a uniform depth and velocity across the slope. In reality, overland water flow and transport processes are rarely uniform. Local soil topography, vegetation, and spatial soil heterogeneity control directions and magnitudes of water fluxes, and strongly influence runoff characteristics. There is increasing evidence that variations in soil surface characteristics influence the distribution of overland flow and transport of pollutants. These spatially varying surface characteristics are likely to generate non-equilibrium flow and transport processes. HYDRUS-1D includes a hierarchical series of models of increasing complexity to account for both physical equilibrium and non-equilibrium, e.g., dual-porosity and dual-permeability models, up to a dual-permeability model with immobile water. The same conceptualization as used for the subsurface was implemented to simulate non-equilibrium overland flow and transport at the soil surface. The developed model improves our ability to describe non-equilibrium overland flow and transport processes and to improves our understanding of factors that cause this behavior. The HYDRUS-1D overland flow and transport model was additionally also extended to simulate soil erosion. The HYDRUS-1D Soil Erosion Model has been verified by comparing with other soil erosion models. The model performed well when the average soil particle size is relatively large. The performance of the soil erosion model has been further validated by comparing with selected experimental datasets from the literature.

Parametric study of power absorption from electromagnetic waves by small ferrite spheres

NASA Technical Reports Server (NTRS)

Englert, Gerald W.

1989-01-01

Algebraic expressions in terms of elementary mathematical functions are derived for power absorption and dissipation by eddy currents and magnetic hysteresis in ferrite spheres. Skin depth is determined by using a variable inner radius in descriptive integral equations. Numerical results are presented for sphere diameters less than one wavelength. A generalized power absorption parameter for both eddy currents and hysteresis is expressed in terms of the independent parameters involving wave frequency, sphere radius, resistivity, and complex permeability. In general, the hysteresis phenomenon has a greater sensitivity to these independent parameters than do eddy currents over the ranges of independent parameters studied herein. Working curves are presented for obtaining power losses from input to the independent parameters.

Extremal inversion of lunar travel time data. [seismic velocity structure

NASA Technical Reports Server (NTRS)

Burkhard, N.; Jackson, D. D.

1975-01-01

The tau method, developed by Bessonova et al. (1974), of inversion of travel times is applied to lunar P-wave travel time data to find limits on the velocity structure of the moon. Tau is the singular solution to the Clairaut equation. Models with low-velocity zones, with low-velocity zones at differing depths, and without low-velocity zones, were found to be consistent with data and within the determined limits. Models with and without a discontinuity at about 25-km depth have been found which agree with all travel time data to within two standard deviations. In other words, the existence of the discontinuity and its size and location have not been uniquely resolved. Models with low-velocity channels are also possible.

High-frequency Born synthetic seismograms based on coupled normal modes

USGS Publications Warehouse

Pollitz, Fred F.

2011-01-01

High-frequency and full waveform synthetic seismograms on a 3-D laterally heterogeneous earth model are simulated using the theory of coupled normal modes. The set of coupled integral equations that describe the 3-D response are simplified into a set of uncoupled integral equations by using the Born approximation to calculate scattered wavefields and the pure-path approximation to modulate the phase of incident and scattered wavefields. This depends upon a decomposition of the aspherical structure into smooth and rough components. The uncoupled integral equations are discretized and solved in the frequency domain, and time domain results are obtained by inverse Fourier transform. Examples show the utility of the normal mode approach to synthesize the seismic wavefields resulting from interaction with a combination of rough and smooth structural heterogeneities. This approach is applied to an ∼4 Hz shallow crustal wave propagation around the site of the San Andreas Fault Observatory at Depth (SAFOD).

Wave-packet formation at the zero-dispersion point in the Gardner-Ostrovsky equation.

PubMed

Whitfield, A J; Johnson, E R

2015-05-01

The long-time effect of weak rotation on an internal solitary wave is the decay into inertia-gravity waves and the eventual emergence of a coherent, steadily propagating, nonlinear wave packet. There is currently no entirely satisfactory explanation as to why these wave packets form. Here the initial value problem is considered within the context of the Gardner-Ostrovsky, or rotation-modified extended Korteweg-de Vries, equation. The linear Gardner-Ostrovsky equation has maximum group velocity at a critical wave number, often called the zero-dispersion point. It is found here that a nonlinear splitting of the wave-number spectrum at the zero-dispersion point, where energy is shifted into the modulationally unstable regime of the Gardner-Ostrovsky equation, is responsible for the wave-packet formation. Numerical comparisons of the decay of a solitary wave in the Gardner-Ostrovsky equation and a derived nonlinear Schrödinger equation at the zero-dispersion point are used to confirm the spectral splitting.

Convective wave breaking in the KdV equation

NASA Astrophysics Data System (ADS)

Brun, Mats K.; Kalisch, Henrik

2018-03-01

The KdV equation is a model equation for waves at the surface of an inviscid incompressible fluid, and it is well known that the equation describes the evolution of unidirectional waves of small amplitude and long wavelength fairly accurately if the waves fall into the Boussinesq regime. The KdV equation allows a balance of nonlinear steepening effects and dispersive spreading which leads to the formation of steady wave profiles in the form of solitary waves and cnoidal waves. While these wave profiles are solutions of the KdV equation for any amplitude, it is shown here that there for both the solitary and the cnoidal waves, there are critical amplitudes for which the horizontal component of the particle velocity matches the phase velocity of the wave. Solitary or cnoidal solutions of the KdV equation which surpass these amplitudes feature incipient wave breaking as the particle velocity exceeds the phase velocity near the crest of the wave, and the model breaks down due to violation of the kinematic surface boundary condition. The condition for breaking can be conveniently formulated as a convective breaking criterion based on the local Froude number at the wave crest. This breaking criterion can also be applied to time-dependent situations, and one case of interest is the development of an undular bore created by an influx at a lateral boundary. It is shown that this boundary forcing leads to wave breaking in the leading wave behind the bore if a certain threshold is surpassed.

Wave propagation problem for a micropolar elastic waveguide

NASA Astrophysics Data System (ADS)

Kovalev, V. A.; Murashkin, E. V.; Radayev, Y. N.

2018-04-01

A propagation problem for coupled harmonic waves of translational displacements and microrotations along the axis of a long cylindrical waveguide is discussed at present study. Microrotations modeling is carried out within the linear micropolar elasticity frameworks. The mathematical model of the linear (or even nonlinear) micropolar elasticity is also expanded to a field theory model by variational least action integral and the least action principle. The governing coupled vector differential equations of the linear micropolar elasticity are given. The translational displacements and microrotations in the harmonic coupled wave are decomposed into potential and vortex parts. Calibrating equations providing simplification of the equations for the wave potentials are proposed. The coupled differential equations are then reduced to uncoupled ones and finally to the Helmholtz wave equations. The wave equations solutions for the translational and microrotational waves potentials are obtained for a high-frequency range.

Inversion of Surface-wave Dispersion Curves due to Low-velocity-layer Models

NASA Astrophysics Data System (ADS)

Shen, C.; Xia, J.; Mi, B.

2016-12-01

A successful inversion relies on exact forward modeling methods. It is a key step to accurately calculate multi-mode dispersion curves of a given model in high-frequency surface-wave (Rayleigh wave and Love wave) methods. For normal models (shear (S)-wave velocity increasing with depth), their theoretical dispersion curves completely match the dispersion spectrum that is generated based on wave equation. For models containing a low-velocity-layer, however, phase velocities calculated by existing forward-modeling algorithms (e.g. Thomson-Haskell algorithm, Knopoff algorithm, fast vector-transfer algorithm and so on) fail to be consistent with the dispersion spectrum at a high frequency range. They will approach a value that close to the surface-wave velocity of the low-velocity-layer under the surface layer, rather than that of the surface layer when their corresponding wavelengths are short enough. This phenomenon conflicts with the characteristics of surface waves, which results in an erroneous inverted model. By comparing the theoretical dispersion curves with simulated dispersion energy, we proposed a direct and essential solution to accurately compute surface-wave phase velocities due to low-velocity-layer models. Based on the proposed forward modeling technique, we can achieve correct inversion for these types of models. Several synthetic data proved the effectiveness of our method.

Symmetry Reductions and Group-Invariant Radial Solutions to the n-Dimensional Wave Equation

NASA Astrophysics Data System (ADS)

Feng, Wei; Zhao, Songlin

2018-01-01

In this paper, we derive explicit group-invariant radial solutions to a class of wave equation via symmetry group method. The optimal systems of one-dimensional subalgebras for the corresponding radial wave equation are presented in terms of the known point symmetries. The reductions of the radial wave equation into second-order ordinary differential equations (ODEs) with respect to each symmetry in the optimal systems are shown. Then we solve the corresponding reduced ODEs explicitly in order to write out the group-invariant radial solutions for the wave equation. Finally, several analytical behaviours and smoothness of the resulting solutions are discussed.

A one-dimensional model of the semiannual oscillation driven by convectively forced gravity waves

NASA Technical Reports Server (NTRS)

Sassi, Fabrizio; Garcia, Rolando R.

1994-01-01

A one-dimensional model that solves the time-dependent equations for the zonal mean wind and a wave of specified zonal wavenumber has been used to illustrate the ability of gravity waves forced by time-dependent tropospheric heating to produce a semiannual oscillation (SAO) in the middle atmosphere. When the heating has a strong diurnal cycle, as observed over tropical landmasses, gravity waves with zonal wavelengths of a few thousand kilometers and phase velocities in the range +/- 40-50 m/sec are excited efficiently by the maximum vertical projection criterion (vertical wavelength approximately equals 2 x forcing depth). Calculations show that these waves can account for large zonal mean wind accelerations in the middle atmosphere, resulting in realistic stratopause and mesopause oscillations. Calculations of the temporal evolution of a quasi-conserved tracer indicate strong down-welling in the upper stratosphere near the equinoxes, which is associated with the descent of the SAO westerlies. In the upper mesosphere, there is a semiannual oscillation in tracer mixing ratio driven by seasonal variability in eddy mixing, which increases at the solstices and decreases at the equinoxes.

Insights into Volcanic Tremor: A Linear Stability Analysis of Waves Propagating Along Fluid-Filled Cracks

NASA Astrophysics Data System (ADS)

Lipovsky, B.; Dunham, E. M.

2012-12-01

Crack waves are guided waves along fluid-filled cracks that propagate with phase velocity less than the sound wave speed. Chouet (JGR, 1986) and Ferrazzini and Aki (JGR, 1977) have shown that such waves could explain volcanic tremor in terms of the resonant modes of a finite length magma-filled crack. Based on an idealized lumped-parameter model, Julian (JGR, 1994) further proposed that the steady flow of a viscous magma in a volcanic conduit is unstable to perturbations, leading to self-excited oscillations of the conduit walls and radiation of seismic waves. Our objective is to evaluate the possibility of self-excited oscillations within a rigorous, continuum framework. Our specific focus has been on basaltic fissure eruptions. In a typical basaltic fissure system, the magnitudes of the wave restoring forces, fluid compressibility and wall elasticity, are highly depth dependent. Because of the elevated fluid compressibility from gas exsolution at shallow depths, fluid pressure perturbations in this regime propagate as acoustic waves with effectively rigid conduit walls. Below the exsolution depth, the conduit walls are more compliant relative to the magma compressibility and perturbations propagate as dispersive crack waves. Viscous magma flow through such a fissure will evolve to a fully developed state characterized by a parabolic velocity profile in several to tens of seconds. This time scale is greater than harmonic tremor periods, typically 0.1 to 1 second. A rigorous treatment of the wave response to pressure perturbations therefore requires a general analysis of conduit flow that is not in a fully developed state. We present a linearized analysis of the coupled fluid and elastic response to general flow perturbations. We assume that deformation of the wall is linear elastic. As our focus is on wavelengths greatly exceeding the crack width, fluid flow is described by a quasi-one dimensional, or width-averaged, model. We account for conservation of magma mass and momentum including compressibility and viscous drag. Our analysis further assumes small perturbations about a steady background flow, a linearized isothermal equation of state, and a nominally constant width channel. We confirm Julian's results that sufficiently rapid flow through a deformable-walled conduit is unstable to perturbations in the form of crack waves. Instability occurs when drag reduction from opening the conduit exceeds the increase in drag from increased fluid velocity. Crack waves are most unstable at long wavelengths, where the conduit becomes more compliant. In the long wavelength limit, we find a simple expression for the critical flow speed beyond which crack waves are unstable: u = c / 2, where c is the crack wave phase velocity. The instability condition is remarkably independent of viscosity. This result more rigorously confirms the conclusion of Dunham and Ogden (2012, J. App. Mech.), who found the same instability criterion under the limiting assumption of fully developed flow. In a typical basaltic system the occurrence of this instability requires flow speeds exceeding ~50 m/s at depths where magma is primarily liquid melt with little exsolved gas. At these depths, flow speeds of this order are unlikely to occur. We conclude that harmonic tremor due to self-excited oscillations is unlikely to occur in nature.

Modeling Tsunami Wave Generation Using a Two-layer Granular Landslide Model

NASA Astrophysics Data System (ADS)

Ma, G.; Kirby, J. T., Jr.; Shi, F.; Grilli, S. T.; Hsu, T. J.

2016-12-01

Tsunamis can be generated by subaerial or submarine landslides in reservoirs, lakes, fjords, bays and oceans. Compared to seismogenic tsunamis, landslide or submarine mass failure (SMF) tsunamis are normally characterized by relatively shorter wave lengths and stronger wave dispersion, and potentially may generate large wave amplitudes locally and high run-up along adjacent coastlines. Due to a complex interplay between the landslide and tsunami waves, accurate simulation of landslide motion as well as tsunami generation is a challenging task. We develop and test a new two-layer model for granular landslide motion and tsunami wave generation. The landslide is described as a saturated granular flow, accounting for intergranular stresses governed by Coulomb friction. Tsunami wave generation is simulated by the three-dimensional non-hydrostatic wave model NHWAVE, which is capable of capturing wave dispersion efficiently using a small number of discretized vertical levels. Depth-averaged governing equations for the granular landslide are derived in a slope-oriented coordinate system, taking into account the dynamic interaction between the lower-layer granular landslide and upper-layer water motion. The model is tested against laboratory experiments on impulsive wave generation by subaerial granular landslides. Model results illustrate a complex interplay between the granular landslide and tsunami waves, and they reasonably predict not only the tsunami wave generation but also the granular landslide motion from initiation to deposition.

Resolving the depth of fluorescent light by structured illumination and shearing interferometry

NASA Astrophysics Data System (ADS)

Schindler, Johannes; Elmaklizi, Ahmed; Voit, Florian; Hohmann, Ansgar; Schau, Philipp; Brodhag, Nicole; Krauter, Philipp; Frenner, Karsten; Kienle, Alwin; Osten, Wolfgang

2016-03-01

A method for the depth-sensitive detection of fluorescent light is presented. It relies on a structured illumination restricting the excitation volume and on an interferometric detection of the wave front curvature. The illumination with two intersecting beams of a white-light laser separated in a Sagnac interferometer coupled to the microscope provides a coarse confinement in lateral and axial direction. The depth reconstruction is carried out by evaluating shearing interferograms produced with a Michelson interferometer. This setup can also be used with spatially and temporally incoherent light as emitted by fluorophores. A simulation workflow of the method was developed using a combination of a solution of Maxwell's equations with the Monte Carlo method. These simulations showed the principal feasibility of the method. The method is validated by measurements at reference samples with characterized material properties, locations and sizes of fluorescent regions. It is demonstrated that sufficient signal quality can be obtained for materials with scattering properties comparable to dental enamel while maintaining moderate illumination powers in the milliwatt range. The depth reconstruction is demonstrated for a range of distances and penetration depths of several hundred micrometers.

Periodic wave, breather wave and travelling wave solutions of a (2 + 1)-dimensional B-type Kadomtsev-Petviashvili equation in fluids or plasmas

NASA Astrophysics Data System (ADS)

Hu, Wen-Qiang; Gao, Yi-Tian; Jia, Shu-Liang; Huang, Qian-Min; Lan, Zhong-Zhou

2016-11-01

In this paper, a (2 + 1)-dimensional B-type Kadomtsev-Petviashvili equation is investigated, which has been presented as a model for the shallow water wave in fluids or the electrostatic wave potential in plasmas. By virtue of the binary Bell polynomials, the bilinear form of this equation is obtained. With the aid of the bilinear form, N -soliton solutions are obtained by the Hirota method, periodic wave solutions are constructed via the Riemann theta function, and breather wave solutions are obtained according to the extended homoclinic test approach. Travelling waves are constructed by the polynomial expansion method as well. Then, the relations between soliton solutions and periodic wave solutions are strictly established, which implies the asymptotic behaviors of the periodic waves under a limited procedure. Furthermore, we obtain some new solutions of this equation by the standard extended homoclinic test approach. Finally, we give a generalized form of this equation, and find that similar analytical solutions can be obtained from the generalized equation with arbitrary coefficients.

Effect of Liquid Viscosity on Dispersion of Quasi-Lamb Waves in an Elastic-Layer-Viscous-Liquid-Layer System

NASA Astrophysics Data System (ADS)

Guz, A. N.; Bagno, A. M.

2017-07-01

The dispersion curves are constructed and propagation of quasi-Lamb waves are studied for wide range of frequencies based on the Navier -Stokes three-dimensional linearized equations for a viscous liquid and linear equations of the classical theory of elasticity for an elastic layer. For a thick liquid layer, the effect of the viscosity of the liquid and the thickness of elastic and liquid layers on the phase velocities and attenuation coefficients of quasi-Lamb modes is analyzed. It is shown that in the case of a thick liquid layer for all modes, there are elastic layers of certain thickness with minimal effect of liquid viscosity on the phase velocities and attenuation coefficients of modes. It is also discovered that for some modes, there are both certain thicknesses and certain ranges of thickness where the effect of liquid viscosity on the phase velocities and attenuation coefficients of these modes is considerable. We ascertain that liquid viscosity promotes decrease of the penetration depth of the lowest quasi-Lamb mode into the liquid. The developed approach and the obtained results make it possible to ascertain for wave processes the limits of applicability of the model of ideal compressible fluid. Numerical results in the form of graphs are adduced and analyzed.

Should tsunami simulations include a nonzero initial horizontal velocity?

NASA Astrophysics Data System (ADS)

Lotto, Gabriel C.; Nava, Gabriel; Dunham, Eric M.

2017-08-01

Tsunami propagation in the open ocean is most commonly modeled by solving the shallow water wave equations. These equations require initial conditions on sea surface height and depth-averaged horizontal particle velocity or, equivalently, horizontal momentum. While most modelers assume that initial velocity is zero, Y.T. Song and collaborators have argued for nonzero initial velocity, claiming that horizontal displacement of a sloping seafloor imparts significant horizontal momentum to the ocean. They show examples in which this effect increases the resulting tsunami height by a factor of two or more relative to models in which initial velocity is zero. We test this claim with a "full-physics" integrated dynamic rupture and tsunami model that couples the elastic response of the Earth to the linearized acoustic-gravitational response of a compressible ocean with gravity; the model self-consistently accounts for seismic waves in the solid Earth, acoustic waves in the ocean, and tsunamis (with dispersion at short wavelengths). Full-physics simulations of subduction zone megathrust ruptures and tsunamis in geometries with a sloping seafloor confirm that substantial horizontal momentum is imparted to the ocean. However, almost all of that initial momentum is carried away by ocean acoustic waves, with negligible momentum imparted to the tsunami. We also compare tsunami propagation in each simulation to that predicted by an equivalent shallow water wave simulation with varying assumptions regarding initial velocity. We find that the initial horizontal velocity conditions proposed by Song and collaborators consistently overestimate the tsunami amplitude and predict an inconsistent wave profile. Finally, we determine tsunami initial conditions that are rigorously consistent with our full-physics simulations by isolating the tsunami waves from ocean acoustic and seismic waves at some final time, and backpropagating the tsunami waves to their initial state by solving the adjoint problem. The resulting initial conditions have negligible horizontal velocity.[Figure not available: see fulltext.

Should tsunami models use a nonzero initial condition for horizontal velocity?

NASA Astrophysics Data System (ADS)

Nava, G.; Lotto, G. C.; Dunham, E. M.

2017-12-01

Tsunami propagation in the open ocean is most commonly modeled by solving the shallow water wave equations. These equations require two initial conditions: one on sea surface height and another on depth-averaged horizontal particle velocity or, equivalently, horizontal momentum. While most modelers assume that initial velocity is zero, Y.T. Song and collaborators have argued for nonzero initial velocity, claiming that horizontal displacement of a sloping seafloor imparts significant horizontal momentum to the ocean. They show examples in which this effect increases the resulting tsunami height by a factor of two or more relative to models in which initial velocity is zero. We test this claim with a "full-physics" integrated dynamic rupture and tsunami model that couples the elastic response of the Earth to the linearized acoustic-gravitational response of a compressible ocean with gravity; the model self-consistently accounts for seismic waves in the solid Earth, acoustic waves in the ocean, and tsunamis (with dispersion at short wavelengths). We run several full-physics simulations of subduction zone megathrust ruptures and tsunamis in geometries with a sloping seafloor, using both idealized structures and a more realistic Tohoku structure. Substantial horizontal momentum is imparted to the ocean, but almost all momentum is carried away in the form of ocean acoustic waves. We compare tsunami propagation in each full-physics simulation to that predicted by an equivalent shallow water wave simulation with varying assumptions regarding initial conditions. We find that the initial horizontal velocity conditions proposed by Song and collaborators consistently overestimate the tsunami amplitude and predict an inconsistent wave profile. Finally, we determine tsunami initial conditions that are rigorously consistent with our full-physics simulations by isolating the tsunami waves (from ocean acoustic and seismic waves) at some final time, and backpropagating the tsunami waves to their initial state by solving the adjoint problem. The resulting initial conditions have negligible horizontal velocity.

The role of shear and tensile failure in dynamically triggered landslides

USGS Publications Warehouse

Gipprich, T.L.; Snieder, R.K.; Jibson, R.W.; Kimman, W.

2008-01-01

Dynamic stresses generated by earthquakes can trigger landslides. Current methods of landslide analysis such as pseudo-static analysis and Newmark's method focus on the effects of earthquake accelerations on the landslide mass to characterize dynamic landslide behaviour. One limitation of these methods is their use Mohr-Coulomb failure criteria, which only accounts for shear failure, but the role of tensile failure is not accounted for. We develop a limit-equilibrium model to investigate the dynamic stresses generated by a given ground motion due to a plane wave and use this model to assess the role of shear and tensile failure in the initiation of slope instability. We do so by incorporating a modified Griffith failure envelope, which combines shear and tensile failure into a single criterion. Tests of dynamic stresses in both homogeneous and layered slopes demonstrate that two modes of failure exist, tensile failure in the uppermost meters of a slope and shear failure at greater depth. Further, we derive equations that express the dynamic stress in the near-surface in the acceleration measured at the surface. These equations are used to approximately define the depth range for each mechanism of failure. The depths at which these failure mechanisms occur suggest that shear and tensile failure might collaborate in generating slope failure. ?? 2007 The Authors Journal compilation ?? 2007 RAS.

Kinetic effects on Alfven wave nonlinearity. II - The modified nonlinear wave equation

NASA Technical Reports Server (NTRS)

Spangler, Steven R.

1990-01-01

A previously developed Vlasov theory is used here to study the role of resonant particle and other kinetic effects on Alfven wave nonlinearity. A hybrid fluid-Vlasov equation approach is used to obtain a modified version of the derivative nonlinear Schroedinger equation. The differences between a scalar model for the plasma pressure and a tensor model are discussed. The susceptibilty of the modified nonlinear wave equation to modulational instability is studied. The modulational instability normally associated with the derivative nonlinear Schroedinger equation will, under most circumstances, be restricted to left circularly polarized waves. The nonlocal term in the modified nonlinear wave equation engenders a new modulational instability that is independent of beta and the sense of circular polarization. This new instability may explain the occurrence of wave packet steepening for all values of the plasma beta in the vicinity of the earth's bow shock.

A wave equation migration method for receiver function imaging: 2. Application to the Japan subduction zone

NASA Astrophysics Data System (ADS)

Chen, Ling; Wen, Lianxing; Zheng, Tianyu

2005-11-01

The newly developed wave equation poststack depth migration method for receiver function imaging is applied to study the subsurface structures of the Japan subduction zone using the Fundamental Research on Earthquakes and Earth's Interior Anomalies (FREESIA) broadband data. Three profiles are chosen in the subsurface imaging, two in northeast (NE) Japan to study the subducting Pacific plate and one in southwest (SW) Japan to study the Philippine Sea plate. The descending Pacific plate in NE Japan is well imaged within a depth range of 50-150 km. The slab image exhibits a little more steeply dipping angle (˜32°) in the south than in the north (˜27°), although the general characteristics between the two profiles in NE Japan are similar. The imaged Philippine Sea plate in eastern SW Japan, in contrast, exhibits a much shallower subduction angle (˜19°) and is only identifiable at the uppermost depths of no more than 60 km. Synthetic tests indicate that the top 150 km of the migrated images of the Pacific plate is well resolved by our seismic data, but the resolution of deep part of the slab images becomes poor due to the limited data coverage. Synthetic tests also suggest that the breakdown of the Philippine Sea plate at shallow depths reflects the real structural features of the subduction zone, rather than caused by insufficient coverage of data. Comparative studies on both synthetics and real data images show the possibility of retrieval of fine-scale structures from high-frequency contributions if high-frequency noise can be effectively suppressed and a small bin size can be used in future studies. The derived slab geometry and image feature also appear to have relatively weak dependence on overlying velocity structure. The observed seismicity in the region confirms the geometries inferred from the migrated images for both subducting plates. Moreover, the deep extent of the Pacific plate image and the shallow breakdown of the Philippine Sea plate image are observed to correlate well with the depth extent of the seismicity beneath NE and SW Japan. Such a correlation supports the inference that the specific appearance of slabs and intermediate-depth earthquakes are a consequence of temperature-dependent dehydration induced metamorphism occurring in the hydrated descending oceanic crust.

Extended nonlinear Schrödinger equation with higher-order odd and even terms and its rogue wave solutions.

PubMed

Ankiewicz, Adrian; Wang, Yan; Wabnitz, Stefan; Akhmediev, Nail

2014-01-01

We consider an extended nonlinear Schrödinger equation with higher-order odd (third order) and even (fourth order) terms with variable coefficients. The resulting equation has soliton solutions and approximate rogue wave solutions. We present these solutions up to second order. Moreover, specific constraints on the parameters of higher-order terms provide integrability of the resulting equation, providing a corresponding Lax pair. Particular cases of this equation are the Hirota and the Lakshmanan-Porsezian-Daniel equations. The resulting integrable equation admits exact rogue wave solutions. In particular cases, mentioned above, these solutions are reduced to the rogue wave solutions of the corresponding equations.

Several reverse-time integrable nonlocal nonlinear equations: Rogue-wave solutions

NASA Astrophysics Data System (ADS)

Yang, Bo; Chen, Yong

2018-05-01

A study of rogue-wave solutions in the reverse-time nonlocal nonlinear Schrödinger (NLS) and nonlocal Davey-Stewartson (DS) equations is presented. By using Darboux transformation (DT) method, several types of rogue-wave solutions are constructed. Dynamics of these rogue-wave solutions are further explored. It is shown that the (1 + 1)-dimensional fundamental rogue-wave solutions in the reverse-time NLS equation can be globally bounded or have finite-time blowing-ups. It is also shown that the (2 + 1)-dimensional line rogue waves in the reverse-time nonlocal DS equations can be bounded for all space and time or develop singularities in critical time. In addition, the multi- and higher-order rogue waves exhibit richer structures, most of which have no counterparts in the corresponding local nonlinear equations.

Multiple branches of travelling waves for the Gross–Pitaevskii equation

NASA Astrophysics Data System (ADS)

Chiron, David; Scheid, Claire

2018-06-01

Explicit solitary waves are known to exist for the Kadomtsev–Petviashvili-I (KP-I) equation in dimension 2. We first address numerically the question of their Morse index. The results confirm that the lump solitary wave has Morse index one and that the other explicit solutions correspond to excited states. We then turn to the 2D Gross–Pitaevskii (GP) equation, which in some long wave regime converges to the KP-I equation. Numerical simulations have already shown that a branch of travelling waves of GP converges to a ground state of KP-I, expected to be the lump. In this work, we perform numerical simulations showing that other explicit solitary waves solutions to the KP-I equation give rise to new branches of travelling waves of GP corresponding to excited states.

Computational methods and traveling wave solutions for the fourth-order nonlinear Ablowitz-Kaup-Newell-Segur water wave dynamical equation via two methods and its applications

NASA Astrophysics Data System (ADS)

Ali, Asghar; Seadawy, Aly R.; Lu, Dianchen

2018-05-01

The aim of this article is to construct some new traveling wave solutions and investigate localized structures for fourth-order nonlinear Ablowitz-Kaup-Newell-Segur (AKNS) water wave dynamical equation. The simple equation method (SEM) and the modified simple equation method (MSEM) are applied in this paper to construct the analytical traveling wave solutions of AKNS equation. The different waves solutions are derived by assigning special values to the parameters. The obtained results have their importance in the field of physics and other areas of applied sciences. All the solutions are also graphically represented. The constructed results are often helpful for studying several new localized structures and the waves interaction in the high-dimensional models.

Shock Waves in a Bose-Einstein Condensate

NASA Technical Reports Server (NTRS)

Kulikov, Igor; Zak, Michail

2005-01-01

A paper presents a theoretical study of shock waves in a trapped Bose-Einstein condensate (BEC). The mathematical model of the BEC in this study is a nonlinear Schroedinger equation (NLSE) in which (1) the role of the wave function of a single particle in the traditional Schroedinger equation is played by a space- and time-dependent complex order parameter (x,t) proportional to the square root of the density of atoms and (2) the atoms engage in a repulsive interaction characterized by a potential proportional to | (x,t)|2. Equations that describe macroscopic perturbations of the BEC at zero temperature are derived from the NLSE and simplifying assumptions are made, leading to equations for the propagation of sound waves and the transformation of sound waves into shock waves. Equations for the speeds of shock waves and the relationships between jumps of velocity and density across shock fronts are derived. Similarities and differences between this theory and the classical theory of sound waves and shocks in ordinary gases are noted. The present theory is illustrated by solving the equations for the example of a shock wave propagating in a cigar-shaped BEC.

Numerical study of the Kadomtsev-Petviashvili equation and dispersive shock waves

NASA Astrophysics Data System (ADS)

Grava, T.; Klein, C.; Pitton, G.

2018-02-01

A detailed numerical study of the long time behaviour of dispersive shock waves in solutions to the Kadomtsev-Petviashvili (KP) I equation is presented. It is shown that modulated lump solutions emerge from the dispersive shock waves. For the description of dispersive shock waves, Whitham modulation equations for KP are obtained. It is shown that the modulation equations near the soliton line are hyperbolic for the KPII equation while they are elliptic for the KPI equation leading to a focusing effect and the formation of lumps. Such a behaviour is similar to the appearance of breathers for the focusing nonlinear Schrödinger equation in the semiclassical limit.

Applications of exact traveling wave solutions of Modified Liouville and the Symmetric Regularized Long Wave equations via two new techniques

NASA Astrophysics Data System (ADS)

Lu, Dianchen; Seadawy, Aly R.; Ali, Asghar

2018-06-01

In this current work, we employ novel methods to find the exact travelling wave solutions of Modified Liouville equation and the Symmetric Regularized Long Wave equation, which are called extended simple equation and exp(-Ψ(ξ))-expansion methods. By assigning the different values to the parameters, different types of the solitary wave solutions are derived from the exact traveling wave solutions, which shows the efficiency and precision of our methods. Some solutions have been represented by graphical. The obtained results have several applications in physical science.

Nonlocal symmetries, solitary waves and cnoidal periodic waves of the (2+1)-dimensional breaking soliton equation

NASA Astrophysics Data System (ADS)

Zou, Li; Tian, Shou-Fu; Feng, Lian-Li

2017-12-01

In this paper, we consider the (2+1)-dimensional breaking soliton equation, which describes the interaction of a Riemann wave propagating along the y-axis with a long wave along the x-axis. By virtue of the truncated Painlevé expansion method, we obtain the nonlocal symmetry, Bäcklund transformation and Schwarzian form of the equation. Furthermore, by using the consistent Riccati expansion (CRE), we prove that the breaking soliton equation is solvable. Based on the consistent tan-function expansion, we explicitly derive the interaction solutions between solitary waves and cnoidal periodic waves.

Technique for estimating depth of floods in Tennessee

USGS Publications Warehouse

Gamble, C.R.

1983-01-01

Estimates of flood depths are needed for design of roadways across flood plains and for other types of construction along streams. Equations for estimating flood depths in Tennessee were derived using data for 150 gaging stations. The equations are based on drainage basin size and can be used to estimate depths of the 10-year and 100-year floods for four hydrologic areas. A method also was developed for estimating depth of floods having recurrence intervals between 10 and 100 years. Standard errors range from 22 to 30 percent for the 10-year depth equations and from 23 to 30 percent for the 100-year depth equations. (USGS)

Numerical and Experimental Study on the Effect of Coral Reef and Beach Vegetation on Reduction of Long Wave Run-Up

NASA Astrophysics Data System (ADS)

Mohandie, R. K.; Teng, M. H.

2009-12-01

Numerical and experimental studies were carried out to examine the mitigating capabilities of coral reefs and vegetations on tsunami and storm surge inundation. For long waves propagating over variable depth such as that over a reef, the nonlinear and dispersive Boussinesq equations were applied. For run-up onto dry land where the nonlinear effect dominates, the nonlinear and nondispersive shallow water equations were used. Long waves with various amplitudes and wavelengths propagating over coral reefs of different length and height were investigated to quantify under which conditions a coral reef may be effective in reducing the wave impact. It was observed that a reef can make a long wave separate into several smaller waves and it can also cause wave breaking resulting in energy dissipation. Our data suggest that both wave separation and breaking induced by coral reefs are effective at mitigating long wave run-up, with the latter being noticeably more effective than the former. As expected, it was observed that the higher the coral reef height, the more the reduction in wave run-up especially when the reef height is greater than 50% of the water depth. For reefs to be effective as a barrier for long waves such as tsunamis and storm surges, it was found that the reefs must be sufficiently long in the wave propagation direction, for example, with its length to be at least of the same magnitude as the wavelength or longer. In this study, it was shown that an effective reef can reduce the long wave run-up by as much as 25% and 50% by wave separation and wave breaking, respectively. Three types of vegetation, namely, grass, shrub and coconut trees, were modeled and tested in a wave tank against various initial wave amplitude and beach slopes in the Hydraulics Lab at the University of Hawaii (UH) to examine each particular type’s effectiveness in reducing wave run-up and to determine its roughness coefficient for wave run-up through numerical simulation and experimental measurement. These roughness coefficients were shown to be higher than the traditional Manning’s coefficient values for vegetation in channel flows. Also, the coefficients were shown to be a function of the ratio of the initial wave amplitude over the vegetation height and are relatively independent of the beach slope. The vegetation spacing and tree diameters in the lab models were selected based on the typical spacing and tree diameter observed in the field through a reduced scale. All three types of vegetation were found to be effective in reducing wave run-up especially on mildly sloped beaches with a reduction rate ranging from 20% to more than 50%. A numerical simulation that incorporated the effects of coral reef and the combined vegetation types showed that on a 5 degree slope the reduction in run-up was 61% as compared to an unprotected scenario. A larger scale experimental study on coconut and bushes in the NSF-funded tsunami basin at the OSU also showed these vegetations are effective at reducing wave run-up. These results can be helpful in achieving a better understanding of the role that coral reefs and vegetation play in tsunami and storm surge mitigation.

Spatial and temporal variations of wave energy in the nearshore waters of the central west coast of India

NASA Astrophysics Data System (ADS)

Amrutha, M. M.; Sanil Kumar, V.

2016-12-01

Assessment of wave power potential at different water depths and time is required for identifying a wave power plant location. This study examines the variation in wave power off the central west coast of India at water depths of 30, 9 and 5 m based on waverider buoy measured wave data. The study shows a significant reduction ( ˜ 10 to 27 %) in wave power at 9 m water depth compared to 30 m and the wave power available at 5 m water depth is 20 to 23 % less than that at 9 m. At 9 m depth, the seasonal mean value of the wave power varied from 1.6 kW m-1 in the post-monsoon period (ONDJ) to 15.2 kW m-1 in the Indian summer monsoon (JJAS) period. During the Indian summer monsoon period, the variation of wave power in a day is up to 32 kW m-1. At 9 m water depth, the mean annual wave power is 6 kW m-1 and interannual variations up to 19.3 % are observed during 2009-2014. High wave energy ( > 20 kW m-1) at the study area is essentially from the directional sector 245-270° and also 75 % of the total annual wave energy is from this narrow directional sector, which is advantageous while aligning the wave energy converter.

Rogue-wave solutions of the Zakharov equation

NASA Astrophysics Data System (ADS)

Rao, Jiguang; Wang, Lihong; Liu, Wei; He, Jingsong

2017-12-01

Using the bilinear transformation method, we derive general rogue-wave solutions of the Zakharov equation. We present these Nth-order rogue-wave solutions explicitly in terms of Nth-order determinants whose matrix elements have simple expressions. We show that the fundamental rogue wave is a line rogue wave with a line profile on the plane ( x, y) arising from a constant background at t ≪ 0 and then gradually tending to the constant background for t ≫ 0. Higher-order rogue waves arising from a constant background and later disappearing into it describe the interaction of several fundamental line rogue waves. We also consider different structures of higher-order rogue waves. We present differences between rogue waves of the Zakharov equation and of the first type of the Davey-Stewartson equation analytically and graphically.

Evaluating the Effects of Riboflavin/UV-A and Rose-Bengal/Green Light Cross-Linking of the Rabbit Cornea by Noncontact Optical Coherence Elastography

PubMed Central

Singh, Manmohan; Li, Jiasong; Han, Zhaolong; Vantipalli, Srilatha; Liu, Chih-Hao; Wu, Chen; Raghunathan, Raksha; Aglyamov, Salavat R.; Twa, Michael D.; Larin, Kirill V.

2016-01-01

Purpose The purpose of this study was to use noncontact optical coherence elastography (OCE) to evaluate and compare changes in biomechanical properties that occurred in rabbit cornea in situ after corneal collagen cross-linking by either of two techniques: ultraviolet-A (UV-A)/riboflavin or rose-Bengal/green light. Methods Low-amplitude (≤10 μm) elastic waves were induced in mature rabbit corneas by a focused air pulse. Elastic wave propagation was imaged by a phase-stabilized swept source OCE (PhS-SSOCE) system. Corneas were then cross-linked by either of two methods: UV-A/riboflavin (UV-CXL) or rose-Bengal/green light (RGX). Phase velocities of the elastic waves were fitted to a previously developed modified Rayleigh-Lamb frequency equation to obtain the viscoelasticity of the corneas before and after the cross-linking treatments. Micro-scale depth-resolved phase velocity distribution revealed the depth-wise heterogeneity of both cross-linking techniques. Results Under standard treatment settings, UV-CXL significantly increased the stiffness of the corneas by ∼47% (P < 0.05), but RGX did not produce statistically significant increases. The shear viscosities were unaffected by either cross-linking technique. The depth-wise phase velocities showed that UV-CXL affected the anterior ∼34% of the corneas, whereas RGX affected only the anterior ∼16% of the corneas. Conclusions UV-CXL significantly strengthens the cornea, whereas RGX does not, and the effects of cross-linking by UV-CXL reach deeper into the cornea than cross-linking effects of RGX under similar conditions. PMID:27409461

Characteristics of solitary waves, quasiperiodic solutions, homoclinic breather solutions and rogue waves in the generalized variable-coefficient forced Kadomtsev-Petviashvili equation

NASA Astrophysics Data System (ADS)

Yan, Xue-Wei; Tian, Shou-Fu; Dong, Min-Jie; Zou, Li

2017-12-01

In this paper, the generalized variable-coefficient forced Kadomtsev-Petviashvili (gvcfKP) equation is investigated, which can be used to characterize the water waves of long wavelength relating to nonlinear restoring forces. Using a dependent variable transformation and combining the Bell’s polynomials, we accurately derive the bilinear expression for the gvcfKP equation. By virtue of bilinear expression, its solitary waves are computed in a very direct method. By using the Riemann theta function, we derive the quasiperiodic solutions for the equation under some limitation factors. Besides, an effective way can be used to calculate its homoclinic breather waves and rogue waves, respectively, by using an extended homoclinic test function. We hope that our results can help enrich the dynamical behavior of the nonlinear wave equations with variable-coefficient.

Nonlinear modes of the tensor Dirac equation and CPT violation

NASA Technical Reports Server (NTRS)

Reifler, Frank J.; Morris, Randall D.

1993-01-01

Recently, it has been shown that Dirac's bispinor equation can be expressed, in an equivalent tensor form, as a constrained Yang-Mills equation in the limit of an infinitely large coupling constant. It was also shown that the free tensor Dirac equation is a completely integrable Hamiltonian system with Lie algebra type Poisson brackets, from which Fermi quantization can be derived directly without using bispinors. The Yang-Mills equation for a finite coupling constant is investigated. It is shown that the nonlinear Yang-Mills equation has exact plane wave solutions in one-to-one correspondence with the plane wave solutions of Dirac's bispinor equation. The theory of nonlinear dispersive waves is applied to establish the existence of wave packets. The CPT violation of these nonlinear wave packets, which could lead to new observable effects consistent with current experimental bounds, is investigated.

Sensitivity of high-frequency Rayleigh-wave data revisited

USGS Publications Warehouse

Xia, J.; Miller, R.D.; Ivanov, J.

2007-01-01

Rayleigh-wave phase velocity of a layered earth model is a function of frequency and four groups of earth properties: P-wave velocity, S-wave velocity (Vs), density, and thickness of layers. Analysis of the Jacobian matrix (or the difference method) provides a measure of dispersion curve sensitivity to earth properties. Vs is the dominant influence for the fundamental mode (Xia et al., 1999) and higher modes (Xia et al., 2003) of dispersion curves in a high frequency range (>2 Hz) followed by layer thickness. These characteristics are the foundation of determining S-wave velocities by inversion of Rayleigh-wave data. More applications of surface-wave techniques show an anomalous velocity layer such as a high-velocity layer (HVL) or a low-velocity layer (LVL) commonly exists in near-surface materials. Spatial location (depth) of an anomalous layer is usually the most important information that surface-wave techniques are asked to provide. Understanding and correctly defining the sensitivity of high-frequency Rayleigh-wave data due to depth of an anomalous velocity layer are crucial in applying surface-wave techniques to obtain a Vs profile and/or determine the depth of an anomalous layer. Because depth is not a direct earth property of a layered model, changes in depth will result in changes in other properties. Modeling results show that sensitivity at a given depth calculated by the difference method is dependent on the Vs difference (contrast) between an anomalous layer and surrounding layers. The larger the contrast is, the higher the sensitivity due to depth of the layer. Therefore, the Vs contrast is a dominant contributor to sensitivity of Rayleigh-wave data due to depth of an anomalous layer. Modeling results also suggest that the most sensitive depth for an HVL is at about the middle of the depth to the half-space, but for an LVL it is near the ground surface. ?? 2007 Society of Exploration Geophysicists.

Classification of the Lie and Noether point symmetries for the Wave and the Klein-Gordon equations in pp-wave spacetimes

NASA Astrophysics Data System (ADS)

Paliathanasis, A.; Tsamparlis, M.; Mustafa, M. T.

2018-02-01

A complete classification of the Lie and Noether point symmetries for the Klein-Gordon and the wave equation in pp-wave spacetimes is obtained. The classification analysis is carried out by reducing the problem of the determination of the point symmetries to the problem of existence of conformal killing vectors on the pp-wave spacetimes. Employing the existing results for the isometry classes of the pp-wave spacetimes, the functional form of the potential is determined for which the Klein-Gordon equation admits point symmetries and Noetherian conservation law. Finally the Lie and Noether point symmetries of the wave equation are derived.

Wave‐induced Hydraulic Forces on Submerged Aquatic Plants in Shallow Lakes

PubMed Central

SCHUTTEN, J.; DAINTY, J.; DAVY, A. J.

2004-01-01

• Background and Aims Hydraulic pulling forces arising from wave action are likely to limit the presence of freshwater macrophytes in shallow lakes, particularly those with soft sediments. The aim of this study was to develop and test experimentally simple models, based on linear wave theory for deep water, to predict such forces on individual shoots. • Methods Models were derived theoretically from the action of the vertical component of the orbital velocity of the waves on shoot size. Alternative shoot‐size descriptors (plan‐form area or dry mass) and alternative distributions of the shoot material along its length (cylinder or inverted cone) were examined. Models were tested experimentally in a flume that generated sinusoidal waves which lasted 1 s and were up to 0·2 m high. Hydraulic pulling forces were measured on plastic replicas of Elodea sp. and on six species of real plants with varying morphology (Ceratophyllum demersum, Chara intermedia, Elodea canadensis, Myriophyllum spicatum, Potamogeton natans and Potamogeton obtusifolius). • Key Results Measurements on the plastic replicas confirmed predicted relationships between force and wave phase, wave height and plant submergence depth. Predicted and measured forces were linearly related over all combinations of wave height and submergence depth. Measured forces on real plants were linearly related to theoretically derived predictors of the hydraulic forces (integrals of the products of the vertical orbital velocity raised to the power 1·5 and shoot size). • Conclusions The general applicability of the simplified wave equations used was confirmed. Overall, dry mass and plan‐form area performed similarly well as shoot‐size descriptors, as did the conical or cylindrical models of shoot distribution. The utility of the modelling approach in predicting hydraulic pulling forces from relatively simple plant and environmental measurements was validated over a wide range of forces, plant sizes and species. PMID:14988098

Modelling of Charles Darwin's tsunami reports

NASA Astrophysics Data System (ADS)

Galiev, Shamil

2010-05-01

Darwin landed at Valdivia and Concepcion, Chile, just before, during, and after a great 1835 earthquake. He described his impressions and results of the earthquake-induced natural catastrophe in The Voyage of the Beagle. His description of the tsunami could easily be read as a report from Indonesia or Sri Lanka, after the catastrophic tsunami of 26 December 2004. In particular, Darwin emphasised the dependence of earthquake-induced waves on a form of the coast and the coastal depth: ‘… Talcuhano and Callao are situated at the head of great shoaling bays, and they have always suffered from this phenomenon; whereas, the town of Valparaiso, which is seated close on the border of a profound ocean... has never been overwhelmed by one of these terrific deluges…' . He reports also, that ‘… the whole body of the sea retires from the coast, and then returns in great waves of overwhelming force ...' (we cite the Darwin's sentences following researchspace. auckland. ac. nz/handle/2292/4474). The coastal evolution of a tsunami was analytically studied in many publications (see, for example, Synolakis, C.E., Bernard, E.N., 2006. Philos. Trans. R. Soc., Ser. A, 364, 2231-2265; Tinti, S., Tonini, R. 205. J.Fluid Mech., 535, 11-21). However, the Darwin's reports and the influence of the coastal depth on the formation and the evolution of the steep front and the profile of tsunami did not practically discuss. Recently, a mathematical theory of these phenomena was presented in researchspace. auckland. ac. nz/handle/2292/4474. The theory describes the waves which are excited due to nonlinear effects within a shallow coastal zone. The tsunami elevation is described by two components: . Here is the linear (prime) component. It describes the wave coming from the deep ocean. is the nonlinear component. This component may become very important near the coastal line. After that the theory of the shallow waves is used. This theory yields the linear equation for and the weakly-nonlinear equation for . The last equation contains the forcing term which is generated by nonlinearity and depends on . The nonlinear shock-like solution for is constructed which is valid within the narrow coastal zone. Then the tsunami evolution near a coast is studied. It is found that the coastal evolution strongly depends on the profile of the bottom and the distance from the coastline. Far from this the wave surface is smooth and the wave is long enough. The wave profile begins to change quickly, if the coastal water is shallow. The steep (discontinuous) front of the tsunami can be generated. The water level reduces ahead of the front, or the ebb can appear there. Then this front begins to move away from the coast - into the ocean. This direction is opposite to the motion of the whole wave. The amplitude of the front is increased. The water wall is formed. This process explains the catastrophic effect of a tsunami, when a water-wall appears instantly. The wave, having two steep peaks, may be generated in the case of very shallow water. In contrast with this, the tsunami, practically, does not change, if the coastal water is deep. On the whole, the conclusions agree with the Darwin's reports.

Evaluation of the Sparton tight-tolerance AXBT

NASA Technical Reports Server (NTRS)

Boyd, Janice D.; Linzell, Robert S.

1993-01-01

Forty-six near-simultaneous pairs of conductivity - temperature - depth (CTD) and Sparton 'tight tolerance' air expendable bathythermograph (AXBT) temperature profiles were obtained in summer 1991 from a location in the Sargasso Sea. The data were analyzed to assess the temperature and depth accuracies of the Sparton AXBTs. The tight-tolerance criterion was not achieved using the manufacturer's equations but may have been achieved using customized equations computed from the CTD data. The temperature data from the customized equations had a one standard deviation error of 0.13 C. A customized elapsed fall time-to-depth conversion equation was found to be z = 1.620t - 2.2384 x 10(exp -4) t(exp 2) + 1.291 x 10(exp -7) t(exp 3), with z the depth in meters and t the elapsed fall time after probe release in seconds. The standard deviation of the depth error was about 5 m; a rule of thumb for estimating maximum bounds on the depth error below 100 m could be expressed as +/-2% of depth or +/- 10 m, whichever is greater. This equation gave greater depth accuracy than either the manufacturer's supplied equation or the navy standard equation.

Weierstrass traveling wave solutions for dissipative Benjamin, Bona, and Mahony (BBM) equation

NASA Astrophysics Data System (ADS)

Mancas, Stefan C.; Spradlin, Greg; Khanal, Harihar

2013-08-01

In this paper the effect of a small dissipation on waves is included to find exact solutions to the modified Benjamin, Bona, and Mahony (BBM) equation by viscosity. Using Lyapunov functions and dynamical systems theory, we prove that when viscosity is added to the BBM equation, in certain regions there still exist bounded traveling wave solutions in the form of solitary waves, periodic, and elliptic functions. By using the canonical form of Abel equation, the polynomial Appell invariant makes the equation integrable in terms of Weierstrass ℘ functions. We will use a general formalism based on Ince's transformation to write the general solution of dissipative BBM in terms of ℘ functions, from which all the other known solutions can be obtained via simplifying assumptions. Using ODE (ordinary differential equations) analysis we show that the traveling wave speed is a bifurcation parameter that makes transition between different classes of waves.

Alternative stable qP wave equations in TTI media with their applications for reverse time migration

NASA Astrophysics Data System (ADS)

Zhou, Yang; Wang, Huazhong; Liu, Wenqing

2015-10-01

Numerical instabilities may arise if the spatial variation of symmetry axis is handled improperly when implementing P-wave modeling and reverse time migration in heterogeneous tilted transversely isotropic (TTI) media, especially in the cases where fast changes exist in TTI symmetry axis’ directions. Based on the pseudo-acoustic approximation to anisotropic elastic wave equations in Cartesian coordinates, alternative second order qP (quasi-P) wave equations in TTI media are derived in this paper. Compared with conventional stable qP wave equations, the proposed equations written in stress components contain only spatial derivatives of wavefield variables (stress components) and are free from spatial derivatives involving media parameters. These lead to an easy and efficient implementation for stable P-wave modeling and imaging. Numerical experiments demonstrate the stability and computational efficiency of the presented equations in complex TTI media.

Improving Short Wave Breaking Behavior In Surfbeat Models

NASA Astrophysics Data System (ADS)

Roelvink, J.; Daly, C.; Vandongeren, A. R.; van Thiel de Vries, J.; McCall, R.

2009-12-01

In present surfzone modeling three approaches are widely applied: short-wave resolving models, ‘surfbeat’ models, which resolve wave energy modulations on the time-scale of wave groups and their associated infragravity waves, and wave averaged models. In all three approaches, wave breaking is a process that is highly schematized and governed by several empirical coefficients. In this presentation we will focus on the breaking process in ‘surfbeat’ models, such as XBeach (Roelvink et al, 2009). These models need to describe the short wave dissipation by breaking as a function of the slowly-varying short wave energy or wave height. The model usually applied is that by Roelvink (1993), which combines a probability that waves are breaking as function of wave heigth over water depth ratio H/h with a bore-type dissipation formulation similar to that by Battjes and Janssen (1978). A drawback of such a formulation is that there is no ‘memory’ in the breaking process, and the amount of breaking instantly varies with the water depth (though the wave height itself does have a memory). For cases with bichromatic waves, or for long-period swell, this does not reflect reality enough: waves that start breaking do not instantly stop breaking once the water depth increases, but continue until some lower threshold is reached. This concept was captured in Dally’s (1992) wave-by-wave approach, where individual waves are tracked in a probabilistic setting. We have now implemented a similar formulation in XBeach, where the property that waves are breaking is tracked; it is switched on when H/h exceeds a first criterion; this property is propagated using an advection equation and when H/h gets below a second criterion breaking is switched off. This formulation can do two things the previous one can’t: maintain groupiness inside the surf zone and have a maximum of wave breaking in the trough after a steep bar, as was observed for instance in Arcilla et al’s (1994) test 1C. Obviously this has important consequences for the forcing of both long waves and mean currents. In our presentation we will show results of comparisons of both formulations. References. Arcilla, A.S., Roelvink, J.A., O'Connor, B.A. Reniers, A., and Jimenez. J.A. The Delta Flume '93 Experiment. Coastal Dynamics '94. Arcilla, Stive and Kraus (eds), ASCE, New York, pp. 488-502. Battjes, J.A. and J.P.F.M. Janssen, (1978), Energy loss and set-up due to breaking in random waves, Proc. 16th Int. Coastal Eng. Conf., Hamburg, vol. 1: 569-587. Dally, W.R. (1992) Random breaking waves: Field verification of a wave-by-wave algorithm for engineering application. Coastal Engineering, Volume 16, Issue 4, March 1992, Pages 369-397. Roelvink, Dano, Ad Reniers, Ap van Dongeren, Jaap van Thiel de Vries, Robert McCall, Jamie Lescinski. Modelling storm impacts on beaches, dunes and barrier islands, Coast. Eng. (2009), doi:10.1016/j.coastaleng.2009.08.006 Roelvink, J.A. Dissipation in random wave groups incident on a beach. Coastal Eng., 19 (1993) pp. 127-150.

Regional correlations of V s30 and velocities averaged over depths less than and greater than 30 meters

USGS Publications Warehouse

Boore, D.M.; Thompson, E.M.; Cadet, H.

2011-01-01

Using velocity profiles from sites in Japan, California, Turkey, and Europe, we find that the time-averaged shear-wave velocity to 30 m (V S30), used as a proxy for site amplification in recent ground-motion prediction equations (GMPEs) and building codes, is strongly correlated with average velocities to depths less than 30 m (V Sz, with z being the averaging depth). The correlations for sites in Japan (corresponding to the KiK-net network) show that V S30 is systematically larger for a given V Sz than for profiles from the other regions. The difference largely results from the placement of the KiK-net station locations on rock and rocklike sites, whereas stations in the other regions are generally placed in urban areas underlain by sediments. Using the KiK-net velocity profiles, we provide equations relating V S30 to V Sz for z ranging from 5 to 29 m in 1-m increments. These equations (and those for California velocity profiles given in Boore, 2004b) can be used to estimate V S30 from V Sz for sites in which velocity profiles do not extend to 30 m. The scatter of the residuals decreases with depth, but, even for an averaging depth of 5 m, a variation in log V S30 of 1 standard deviation maps into less than a 20% uncertainty in ground motions given by recent GMPEs at short periods. The sensitivity of the ground motions to V S30 uncertainty is considerably larger at long periods (but is less than a factor of 1.2 for averaging depths greater than about 20 m). We also find that V S30 is correlated with V Sz for z as great as 400 m for sites of the KiK-net network, providing some justification for using V S30 as a site-response variable for predicting ground motions at periods for which the wavelengths far exceed 30 m.

Assessment of Reinforced Concrete Surface Breaking Crack Using Rayleigh Wave Measurement.

PubMed

Lee, Foo Wei; Chai, Hwa Kian; Lim, Kok Sing

2016-03-05

An improved single sided Rayleigh wave (R-wave) measurement was suggested to characterize surface breaking crack in steel reinforced concrete structures. Numerical simulations were performed to clarify the behavior of R-waves interacting with surface breaking crack with different depths and degrees of inclinations. Through analysis of simulation results, correlations between R-wave parameters of interest and crack characteristics (depth and degree of inclination) were obtained, which were then validated by experimental measurement of concrete specimens instigated with vertical and inclined artificial cracks of different depths. Wave parameters including velocity and amplitude attenuation for each case were studied. The correlations allowed us to estimate the depth and inclination of cracks measured experimentally with acceptable discrepancies, particularly for cracks which are relatively shallow and when the crack depth is smaller than the wavelength.

Nonlocal Reformulations of Water and Internal Waves and Asymptotic Reductions

NASA Astrophysics Data System (ADS)

Ablowitz, Mark J.

2009-09-01

Nonlocal reformulations of the classical equations of water waves and two ideal fluids separated by a free interface, bounded above by either a rigid lid or a free surface, are obtained. The kinematic equations may be written in terms of integral equations with a free parameter. By expressing the pressure, or Bernoulli, equation in terms of the surface/interface variables, a closed system is obtained. An advantage of this formulation, referred to as the nonlocal spectral (NSP) formulation, is that the vertical component is eliminated, thus reducing the dimensionality and fixing the domain in which the equations are posed. The NSP equations and the Dirichlet-Neumann operators associated with the water wave or two-fluid equations can be related to each other and the Dirichlet-Neumann series can be obtained from the NSP equations. Important asymptotic reductions obtained from the two-fluid nonlocal system include the generalizations of the Benney-Luke and Kadomtsev-Petviashvili (KP) equations, referred to as intermediate-long wave (ILW) generalizations. These 2+1 dimensional equations possess lump type solutions. In the water wave problem high-order asymptotic series are obtained for two and three dimensional gravity-capillary solitary waves. In two dimensions, the first term in the asymptotic series is the well-known hyperbolic secant squared solution of the KdV equation; in three dimensions, the first term is the rational lump solution of the KP equation.

Orbital stability of solitary waves for Kundu equation

NASA Astrophysics Data System (ADS)

Zhang, Weiguo; Qin, Yinghao; Zhao, Yan; Guo, Boling

In this paper, we consider the Kundu equation which is not a standard Hamiltonian system. The abstract orbital stability theory proposed by Grillakis et al. (1987, 1990) cannot be applied directly to study orbital stability of solitary waves for this equation. Motivated by the idea of Guo and Wu (1995), we construct three invariants of motion and use detailed spectral analysis to obtain orbital stability of solitary waves for Kundu equation. Since Kundu equation is more complex than the derivative Schrödinger equation, we utilize some techniques to overcome some difficulties in this paper. It should be pointed out that the results obtained in this paper are more general than those obtained by Guo and Wu (1995). We present a sufficient condition under which solitary waves are orbitally stable for 2c+sυ<0, while Guo and Wu (1995) only considered the case 2c+sυ>0. We obtain the results on orbital stability of solitary waves for the derivative Schrödinger equation given by Colin and Ohta (2006) as a corollary in this paper. Furthermore, we obtain orbital stability of solitary waves for Chen-Lee-Lin equation and Gerdjikov-Ivanov equation, respectively.

Generalized perturbation (n, M)-fold Darboux transformations and multi-rogue-wave structures for the modified self-steepening nonlinear Schrödinger equation.

PubMed

Wen, Xiao-Yong; Yang, Yunqing; Yan, Zhenya

2015-07-01

In this paper, a simple and constructive method is presented to find the generalized perturbation (n,M)-fold Darboux transformations (DTs) of the modified nonlinear Schrödinger (MNLS) equation in terms of fractional forms of determinants. In particular, we apply the generalized perturbation (1,N-1)-fold DTs to find its explicit multi-rogue-wave solutions. The wave structures of these rogue-wave solutions of the MNLS equation are discussed in detail for different parameters, which display abundant interesting wave structures, including the triangle and pentagon, etc., and may be useful to study the physical mechanism of multirogue waves in optics. The dynamical behaviors of these multi-rogue-wave solutions are illustrated using numerical simulations. The same Darboux matrix can also be used to investigate the Gerjikov-Ivanov equation such that its multi-rogue-wave solutions and their wave structures are also found. The method can also be extended to find multi-rogue-wave solutions of other nonlinear integrable equations.

Effect of magnetic quantization on ion acoustic waves ultra-relativistic dense plasma

NASA Astrophysics Data System (ADS)

Javed, Asif; Rasheed, A.; Jamil, M.; Siddique, M.; Tsintsadze, N. L.

2017-11-01

In this paper, we have studied the influence of magnetic quantization of orbital motion of the electrons on the profile of linear and nonlinear ion-acoustic waves, which are propagating in the ultra-relativistic dense magneto quantum plasmas. We have employed both Thomas Fermi and Quantum Magneto Hydrodynamic models (along with the Poisson equation) of quantum plasmas. To investigate the large amplitude nonlinear structure of the acoustic wave, Sagdeev-Pseudo-Potential approach has been adopted. The numerical analysis of the linear dispersion relation and the nonlinear acoustic waves has been presented by drawing their graphs that highlight the effects of plasma parameters on these waves in both the linear and the nonlinear regimes. It has been noticed that only supersonic ion acoustic solitary waves can be excited in the above mentioned quantum plasma even when the value of the critical Mach number is less than unity. Both width and depth of Sagdeev potential reduces on increasing the magnetic quantization parameter η. Whereas the amplitude of the ion acoustic soliton reduces on increasing η, its width appears to be directly proportional to η. The present work would be helpful to understand the excitation of nonlinear ion-acoustic waves in the dense astrophysical environments such as magnetars and in intense-laser plasma interactions.

Series expansion solutions for the multi-term time and space fractional partial differential equations in two- and three-dimensions

NASA Astrophysics Data System (ADS)

Ye, H.; Liu, F.; Turner, I.; Anh, V.; Burrage, K.

2013-09-01

Fractional partial differential equations with more than one fractional derivative in time describe some important physical phenomena, such as the telegraph equation, the power law wave equation, or the Szabo wave equation. In this paper, we consider two- and three-dimensional multi-term time and space fractional partial differential equations. The multi-term time-fractional derivative is defined in the Caputo sense, whose order belongs to the interval (1,2],(2,3],(3,4] or (0, m], and the space-fractional derivative is referred to as the fractional Laplacian form. We derive series expansion solutions based on a spectral representation of the Laplacian operator on a bounded region. Some applications are given for the two- and three-dimensional telegraph equation, power law wave equation and Szabo wave equation.

Travelling-wave solutions of a weakly nonlinear two-dimensional higher-order Kadomtsev-Petviashvili dynamical equation for dispersive shallow-water waves

NASA Astrophysics Data System (ADS)

Seadawy, Aly R.

2017-01-01

The propagation of three-dimensional nonlinear irrotational flow of an inviscid and incompressible fluid of the long waves in dispersive shallow-water approximation is analyzed. The problem formulation of the long waves in dispersive shallow-water approximation lead to fifth-order Kadomtsev-Petviashvili (KP) dynamical equation by applying the reductive perturbation theory. By using an extended auxiliary equation method, the solitary travelling-wave solutions of the two-dimensional nonlinear fifth-order KP dynamical equation are derived. An analytical as well as a numerical solution of the two-dimensional nonlinear KP equation are obtained and analyzed with the effects of external pressure flow.

Super-rogue waves in simulations based on weakly nonlinear and fully nonlinear hydrodynamic equations.

PubMed

Slunyaev, A; Pelinovsky, E; Sergeeva, A; Chabchoub, A; Hoffmann, N; Onorato, M; Akhmediev, N

2013-07-01

The rogue wave solutions (rational multibreathers) of the nonlinear Schrödinger equation (NLS) are tested in numerical simulations of weakly nonlinear and fully nonlinear hydrodynamic equations. Only the lowest order solutions from 1 to 5 are considered. A higher accuracy of wave propagation in space is reached using the modified NLS equation, also known as the Dysthe equation. This numerical modeling allowed us to directly compare simulations with recent results of laboratory measurements in Chabchoub et al. [Phys. Rev. E 86, 056601 (2012)]. In order to achieve even higher physical accuracy, we employed fully nonlinear simulations of potential Euler equations. These simulations provided us with basic characteristics of long time evolution of rational solutions of the NLS equation in the case of near-breaking conditions. The analytic NLS solutions are found to describe the actual wave dynamics of steep waves reasonably well.

Local energy decay for linear wave equations with variable coefficients

NASA Astrophysics Data System (ADS)

Ikehata, Ryo

2005-06-01

A uniform local energy decay result is derived to the linear wave equation with spatial variable coefficients. We deal with this equation in an exterior domain with a star-shaped complement. Our advantage is that we do not assume any compactness of the support on the initial data, and its proof is quite simple. This generalizes a previous famous result due to Morawetz [The decay of solutions of the exterior initial-boundary value problem for the wave equation, Comm. Pure Appl. Math. 14 (1961) 561-568]. In order to prove local energy decay, we mainly apply two types of ideas due to Ikehata-Matsuyama [L2-behaviour of solutions to the linear heat and wave equations in exterior domains, Sci. Math. Japon. 55 (2002) 33-42] and Todorova-Yordanov [Critical exponent for a nonlinear wave equation with damping, J. Differential Equations 174 (2001) 464-489].

Pure quasi-P wave equation and numerical solution in 3D TTI media

NASA Astrophysics Data System (ADS)

Zhang, Jian-Min; He, Bing-Shou; Tang, Huai-Gu

2017-03-01

Based on the pure quasi-P wave equation in transverse isotropic media with a vertical symmetry axis (VTI media), a quasi-P wave equation is obtained in transverse isotropic media with a tilted symmetry axis (TTI media). This is achieved using projection transformation, which rotates the direction vector in the coordinate system of observation toward the direction vector for the coordinate system in which the z-component is parallel to the symmetry axis of the TTI media. The equation has a simple form, is easily calculated, is not influenced by the pseudo-shear wave, and can be calculated reliably when δ is greater than ɛ. The finite difference method is used to solve the equation. In addition, a perfectly matched layer (PML) absorbing boundary condition is obtained for the equation. Theoretical analysis and numerical simulation results with forward modeling prove that the equation can accurately simulate a quasi-P wave in TTI medium.

Two-dimensional numerical simulations of shoaling internal solitary waves at the ASIAEX site in the South China Sea

NASA Astrophysics Data System (ADS)

Lamb, K. G.; Warn-Varnas, A.

2015-05-01

The interaction of barotropic tides with Luzon Strait topography generates some of the world's largest internal solitary waves which eventually shoal and dissipate on the western side of the northern South China Sea. Two-dimensional numerical simulations of the shoaling of a single internal solitary wave at the site of the Asian Seas International Acoustic Experiment (ASIAEX) have been undertaken in order to investigate the sensitivity of the shoaling process to the stratification and the underlying bathymetry and to explore the influence of rotation. The bulk of the simulations are inviscid; however, exploratory simulations using a vertical eddy-viscosity confined to a near bottom layer, along with a no-slip boundary condition, suggest that viscous effects may become important in water shallower than about 200 m. A shoaling solitary wave fissions into several waves. At depths of 200-300 m the front of the leading waves become nearly parallel to the bottom and develop a very steep back as has been observed. The leading waves are followed by waves of elevation (pedestals) that are conjugate to the waves of depression ahead and behind them. Horizontal resolutions of at least 50 m are required to simulate these well. Wave breaking was found to occur behind the second or third of the leading solitary waves, never at the back of the leading wave. Comparisons of the shoaling of waves started at depths of 1000 and 3000 m show significant differences and the shoaling waves can be significantly non-adiabatic even at depths greater than 2000 m. When waves reach a depth of 200 m, their amplitudes can be more than 50% larger than the largest possible solitary wave at that depth. The shoaling behaviour is sensitive to the presence of small-scale features in the bathymetry: a 200 m high bump at 700 m depth can result in the generation of many mode-two waves and of higher mode waves. Sensitivity to the stratification is considered by using three stratifications based on summer observations. They primarily differ in the depth of the thermocline. The generation of mode-two waves and the behaviour of the waves in shallow water is sensitive to this depth. Rotation affects the shoaling waves by reducing the amplitude of the leading waves via the radiation of long trailing inertia-gravity waves. The nonlinear-dispersive evolution of these inertia-gravity waves results in the formation of secondary mode-one wave packets.

Nonlinear dynamics of resonant electrons interacting with coherent Langmuir waves

NASA Astrophysics Data System (ADS)

Tobita, Miwa; Omura, Yoshiharu

2018-03-01

We study the nonlinear dynamics of resonant particles interacting with coherent waves in space plasmas. Magnetospheric plasma waves such as whistler-mode chorus, electromagnetic ion cyclotron waves, and hiss emissions contain coherent wave structures with various discrete frequencies. Although these waves are electromagnetic, their interaction with resonant particles can be approximated by equations of motion for a charged particle in a one-dimensional electrostatic wave. The equations are expressed in the form of nonlinear pendulum equations. We perform test particle simulations of electrons in an electrostatic model with Langmuir waves and a non-oscillatory electric field. We solve equations of motion and study the dynamics of particles with different values of inhomogeneity factor S defined as a ratio of the non-oscillatory electric field intensity to the wave amplitude. The simulation results demonstrate deceleration/acceleration, thermalization, and trapping of particles through resonance with a single wave, two waves, and multiple waves. For two-wave and multiple-wave cases, we describe the wave-particle interaction as either coherent or incoherent based on the probability of nonlinear trapping.

On an Acoustic Wave Equation Arising in Non-Equilibrium Gasdynamics. Classroom Notes

ERIC Educational Resources Information Center

Chandran, Pallath

2004-01-01

The sixth-order wave equation governing the propagation of one-dimensional acoustic waves in a viscous, heat conducting gaseous medium subject to relaxation effects has been considered. It has been reduced to a system of lower order equations corresponding to the finite speeds occurring in the equation, following a method due to Whitham. The lower…

High-frequency homogenization for travelling waves in periodic media.

PubMed

Harutyunyan, Davit; Milton, Graeme W; Craster, Richard V

2016-07-01

We consider high-frequency homogenization in periodic media for travelling waves of several different equations: the wave equation for scalar-valued waves such as acoustics; the wave equation for vector-valued waves such as electromagnetism and elasticity; and a system that encompasses the Schrödinger equation. This homogenization applies when the wavelength is of the order of the size of the medium periodicity cell. The travelling wave is assumed to be the sum of two waves: a modulated Bloch carrier wave having crystal wavevector [Formula: see text] and frequency ω 1 plus a modulated Bloch carrier wave having crystal wavevector [Formula: see text] and frequency ω 2 . We derive effective equations for the modulating functions, and then prove that there is no coupling in the effective equations between the two different waves both in the scalar and the system cases. To be precise, we prove that there is no coupling unless ω 1 = ω 2 and [Formula: see text] where Λ =(λ 1 λ 2 …λ d ) is the periodicity cell of the medium and for any two vectors [Formula: see text] the product a ⊙ b is defined to be the vector ( a 1 b 1 , a 2 b 2 ,…, a d b d ). This last condition forces the carrier waves to be equivalent Bloch waves meaning that the coupling constants in the system of effective equations vanish. We use two-scale analysis and some new weak-convergence type lemmas. The analysis is not at the same level of rigour as that of Allaire and co-workers who use two-scale convergence theory to treat the problem, but has the advantage of simplicity which will allow it to be easily extended to the case where there is degeneracy of the Bloch eigenvalue.

A more fundamental approach to the derivation of nonlinear acoustic wave equations with fractional loss operators (L).

PubMed

Prieur, Fabrice; Vilenskiy, Gregory; Holm, Sverre

2012-10-01

A corrected derivation of nonlinear wave propagation equations with fractional loss operators is presented. The fundamental approach is based on fractional formulations of the stress-strain and heat flux definitions but uses the energy equation and thermodynamic identities to link density and pressure instead of an erroneous fractional form of the entropy equation as done in Prieur and Holm ["Nonlinear acoustic wave equations with fractional loss operators," J. Acoust. Soc. Am. 130(3), 1125-1132 (2011)]. The loss operator of the obtained nonlinear wave equations differs from the previous derivations as well as the dispersion equation, but when approximating for low frequencies the expressions for the frequency dependent attenuation and velocity dispersion remain unchanged.

Multi-Hamiltonian structure of equations of hydrodynamic type

NASA Astrophysics Data System (ADS)

Gümral, H.; Nutku, Y.

1990-11-01

The discussion of the Hamiltonian structure of two-component equations of hydrodynamic type is completed by presenting the Hamiltonian operators for Euler's equation governing the motion of plane sound waves of finite amplitude and another quasilinear second-order wave equation. There exists a doubly infinite family of conserved Hamiltonians for the equations of gas dynamics that degenerate into one, namely, the Benney sequence, for shallow-water waves. Infinite sequences of conserved quantities for these equations are also presented. In the case of multicomponent equations of hydrodynamic type, it is shown, that Kodama's generalization of the shallow-water equations admits bi-Hamiltonian structure.

Nonparaxial wave beams and packets with general astigmatism

NASA Astrophysics Data System (ADS)

Kiselev, A. P.; Plachenov, A. B.; Chamorro-Posada, P.

2012-04-01

We present exact solutions of the wave equation involving an arbitrary wave form with a phase closely similar to the general astigmatic phase of paraxial wave optics. Special choices of the wave form allow general astigmatic beamlike and pulselike waves with a Gaussian-type unrestricted localization in space and time. These solutions are generalizations of the known Bateman-type waves obtained from the connection existing between beamlike solutions of the paraxial parabolic equation and relatively undistorted wave solutions of the wave equation. As a technical tool, we present a full description of parametrizations of 2×2 symmetric matrices with positive imaginary part, which arise in the theory of Gaussian beams.

Stability of dust ion acoustic solitary waves in a collisionless unmagnetized nonthermal plasma in presence of isothermal positrons

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sardar, Sankirtan; Bandyopadhyay, Anup, E-mail: abandyopadhyay1965@gmail.com; Das, K. P.

A three-dimensional KP (Kadomtsev Petviashvili) equation is derived here describing the propagation of weakly nonlinear and weakly dispersive dust ion acoustic wave in a collisionless unmagnetized plasma consisting of warm adiabatic ions, static negatively charged dust grains, nonthermal electrons, and isothermal positrons. When the coefficient of the nonlinear term of the KP-equation vanishes an appropriate modified KP (MKP) equation describing the propagation of dust ion acoustic wave is derived. Again when the coefficient of the nonlinear term of this MKP equation vanishes, a further modified KP equation is derived. Finally, the stability of the solitary wave solutions of the KPmore » and the different modified KP equations are investigated by the small-k perturbation expansion method of Rowlands and Infeld [J. Plasma Phys. 3, 567 (1969); 8, 105 (1972); 10, 293 (1973); 33, 171 (1985); 41, 139 (1989); Sov. Phys. - JETP 38, 494 (1974)] at the lowest order of k, where k is the wave number of a long-wavelength plane-wave perturbation. The solitary wave solutions of the different evolution equations are found to be stable at this order.« less

A unifying fractional wave equation for compressional and shear waves.

PubMed

Holm, Sverre; Sinkus, Ralph

2010-01-01

This study has been motivated by the observed difference in the range of the power-law attenuation exponent for compressional and shear waves. Usually compressional attenuation increases with frequency to a power between 1 and 2, while shear wave attenuation often is described with powers less than 1. Another motivation is the apparent lack of partial differential equations with desirable properties such as causality that describe such wave propagation. Starting with a constitutive equation which is a generalized Hooke's law with a loss term containing a fractional derivative, one can derive a causal fractional wave equation previously given by Caputo [Geophys J. R. Astron. Soc. 13, 529-539 (1967)] and Wismer [J. Acoust. Soc. Am. 120, 3493-3502 (2006)]. In the low omegatau (low-frequency) case, this equation has an attenuation with a power-law in the range from 1 to 2. This is consistent with, e.g., attenuation in tissue. In the often neglected high omegatau (high-frequency) case, it describes attenuation with a power-law between 0 and 1, consistent with what is observed in, e.g., dynamic elastography. Thus a unifying wave equation derived properly from constitutive equations can describe both cases.

Techniques for estimating flood-depth frequency relations for streams in West Virginia

USGS Publications Warehouse

Wiley, J.B.

1987-01-01

Multiple regression analyses are applied to data from 119 U.S. Geological Survey streamflow stations to develop equations that estimate baseline depth (depth of 50% flow duration) and 100-yr flood depth on unregulated streams in West Virginia. Drainage basin characteristics determined from the 100-yr flood depth analysis were used to develop 2-, 10-, 25-, 50-, and 500-yr regional flood depth equations. Two regions with distinct baseline depth equations and three regions with distinct flood depth equations are delineated. Drainage area is the most significant independent variable found in the central and northern areas of the state where mean basin elevation also is significant. The equations are applicable to any unregulated site in West Virginia where values of independent variables are within the range evaluated for the region. Examples of inapplicable sites include those in reaches below dams, within and directly upstream from bridge or culvert constrictions, within encroached reaches, in karst areas, and where streams flow through lakes or swamps. (Author 's abstract)

Quantitative subsurface analysis using frequency modulated thermal wave imaging

NASA Astrophysics Data System (ADS)

Subhani, S. K.; Suresh, B.; Ghali, V. S.

2018-01-01

Quantitative depth analysis of the anomaly with an enhanced depth resolution is a challenging task towards the estimation of depth of the subsurface anomaly using thermography. Frequency modulated thermal wave imaging introduced earlier provides a complete depth scanning of the object by stimulating it with a suitable band of frequencies and further analyzing the subsequent thermal response using a suitable post processing approach to resolve subsurface details. But conventional Fourier transform based methods used for post processing unscramble the frequencies with a limited frequency resolution and contribute for a finite depth resolution. Spectral zooming provided by chirp z transform facilitates enhanced frequency resolution which can further improves the depth resolution to axially explore finest subsurface features. Quantitative depth analysis with this augmented depth resolution is proposed to provide a closest estimate to the actual depth of subsurface anomaly. This manuscript experimentally validates this enhanced depth resolution using non stationary thermal wave imaging and offers an ever first and unique solution for quantitative depth estimation in frequency modulated thermal wave imaging.

Investigation on the cavitation effect of underwater shock near different boundaries

NASA Astrophysics Data System (ADS)

Xiao, Wei; Wei, Hai-peng; Feng, Liang

2017-08-01

When the shock wave of underwater explosion propagates to the surfaces of different boundaries, it gets reflected. Then, a negative pressure area is formed by the superposition of the incident wave and reflected wave. Cavitation occurs when the value of the negative pressure falls below the vapor pressure of water. An improved numerical model based on the spectral element method is applied to investigate the cavitation effect of underwater shock near different boundaries, mainly including the feature of cavitation effect near different boundaries and the influence of different parameters on cavitation effect. In the implementation of the improved numerical model, the bilinear equation of state is used to deal with the fluid field subjected to cavitation, and the field separation technique is employed to avoid the distortion of incident wave propagating through the mesh and the second-order doubly asymptotic approximation is applied to simulate the non-reflecting boundary. The main results are as follows. As the peak pressure and decay constant of shock wave increases, the range of cavitation domain increases, and the duration of cavitation increases. As the depth of water increases, the influence of cavitation on the dynamic response of spherical shell decreases.

The Extended Parabolic Equation Method and Implication of Results for Atmospheric Millimeter-Wave and Optical Propagation

NASA Technical Reports Server (NTRS)

Manning, Robert M.

2004-01-01

The extended wide-angle parabolic wave equation applied to electromagnetic wave propagation in random media is considered. A general operator equation is derived which gives the statistical moments of an electric field of a propagating wave. This expression is used to obtain the first and second order moments of the wave field and solutions are found that transcend those which incorporate the full paraxial approximation at the outset. Although these equations can be applied to any propagation scenario that satisfies the conditions of application of the extended parabolic wave equation, the example of propagation through atmospheric turbulence is used. It is shown that in the case of atmospheric wave propagation and under the Markov approximation (i.e., the -correlation of the fluctuations in the direction of propagation), the usual parabolic equation in the paraxial approximation is accurate even at millimeter wavelengths. The methodology developed here can be applied to any qualifying situation involving random propagation through turbid or plasma environments that can be represented by a spectral density of permittivity fluctuations.

Dust acoustic solitary waves in a dusty plasma with two kinds of nonthermal ions at different temperatures

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dorranian, Davoud; Sabetkar, Akbar

The nonlinear dust acoustic solitary waves in a dusty plasma with two nonthermal ion species at different temperatures is studied analytically. Using reductive perturbation method, the Kadomtsev-Petviashivili (KP) equation is derived, and the effects of nonthermal coefficient, ions temperature, and ions number density on the amplitude and width of soliton in dusty plasma are investigated. It is shown that the amplitude of solitary wave of KP equation diverges at critical points of plasma parameters. The modified KP equation is also derived, and from there, the soliton like solutions of modified KP equation with finite amplitude is extracted. Results show thatmore » generation of rarefactive or compressive solitary waves strongly depends on the number and temperature of nonthermal ions. Results of KP equation confirm that for different magnitudes of ions temperature (mass) and number density, mostly compressive solitary waves are generated in a dusty plasma. In this case, the amplitude of solitary wave is decreased, while the width of solitary waves is increased. According to the results of modified KP equation for some certain magnitudes of parameters, there is a condition for generation of an evanescent solitary wave in a dusty plasma.« less

Evolution of nonlinear waves in a blood-filled artery with an aneurysm

NASA Astrophysics Data System (ADS)

Nikolova, E. V.; Jordanov, I. P.; Dimitrova, Z. I.; Vitanov, N. K.

2017-10-01

We discuss propagation of traveling waves in a blood-filled hyper-elastic artery with a local dilatation (an aneurysm). The processes in the injured artery are modeled by an equation of the motion of the arterial wall and by equations of the motion of the fluid (the blood). Taking into account the specific arterial geometry and applying the reductive perturbation method in long-wave approximation we reduce the model equations to a version of the perturbed Korteweg-de Vries kind equation with variable coefficients. Exact traveling-wave solutions of this equation are obtained by the modified method of simplest equation where the differential equation of Abel is used as a simplest equation. A particular case of the obtained exact solution is numerically simulated and discussed from the point of view of arterial disease mechanics.

Multi-Periodic Waves in Shallow Water

DTIC Science & Technology

1992-09-01

models-the Kadomtsev - Petviashvili (KP) equation . The KP equation describes the evolu- tion of weakly nonlinear, weakly two-dimensional waves on water of...experimentally. The analytical model is a family of periodic solutions of the Kadomtsev -Petviashuili equation . The experiments demonstrate the accuracy... Petviashvili Equation (with Norman Schef- fner & Harvey Segur). Proceedings, Nonlinear Water Waves Workshop, University of Bristol. England, 1991. Resonant

On the Mathematical Modeling of Single and Multiple Scattering of Ultrasonic Guided Waves by Small Scatterers: A Structural Health Monitoring Measurement Model

NASA Astrophysics Data System (ADS)

Strom, Brandon William

In an effort to assist in the paradigm shift from schedule based maintenance to conditioned based maintenance, we derive measurement models to be used within structural health monitoring algorithms. Our models are physics based, and use scattered Lamb waves to detect and quantify pitting corrosion. After covering the basics of Lamb waves and the reciprocity theorem, we develop a technique for the scattered wave solution. The first application is two-dimensional, and is employed in two different ways. The first approach integrates a traction distribution and replaces it by an equivalent force. The second approach is higher order and uses the actual traction distribution. We find that the equivalent force version of the solution technique holds well for small pits at low frequencies. The second application is three-dimensional. The equivalent force caused by the scattered wave of an arbitrary equivalent force is calculated. We obtain functions for the scattered wave displacements as a function of equivalent forces, equivalent forces as a function of incident wave, and scattered wave amplitudes as a function of incident amplitude. The third application uses self-consistency to derive governing equations for the scattered waves due to multiple corrosion pits. We decouple the implicit set of equations and solve explicitly by using a recursive series solution. Alternatively, we solve via an undetermined coefficient method which results in an interaction operator and solution via matrix inversion. The general solution is given for N pits including mode conversion. We show that the two approaches are equivalent, and give a solution for three pits. Various approximations are advanced to simplify the problem while retaining the leading order physics. As a final application, we use the multiple scattering model to investigate resonance of Lamb waves. We begin with a one-dimensional problem and progress to a three-dimensional problem. A directed graph enables interpretation of the interaction operator, and we show that a series solution converges due to loss of energy in the system. We see that there are four causes of resonance and plot the modulation depth as a function of spacing between the pits.

From the paddle to the beach - A Boussinesq shallow water numerical wave tank based on Madsen and Sørensen's equations

NASA Astrophysics Data System (ADS)

Orszaghova, Jana; Borthwick, Alistair G. L.; Taylor, Paul H.

2012-01-01

This article describes a one-dimensional numerical model of a shallow-water flume with an in-built piston paddle moving boundary wavemaker. The model is based on a set of enhanced Boussinesq equations and the nonlinear shallow water equations. Wave breaking is described approximately, by locally switching to the nonlinear shallow water equations when a critical wave steepness is reached. The moving shoreline is calculated as part of the solution. The piston paddle wavemaker operates on a movable grid, which is Lagrangian on the paddle face and Eulerian away from the paddle. The governing equations are, however, evolved on a fixed mapped grid, and the newly calculated solution is transformed back onto the moving grid via a domain mapping technique. Validation test results are compared against analytical solutions, confirming correct discretisation of the governing equations, wave generation via the numerical paddle, and movement of the wet/dry front. Simulations are presented that reproduce laboratory experiments of wave runup on a plane beach and wave overtopping of a laboratory seawall, involving solitary waves and compact wave groups. In practice, the numerical model is suitable for simulating the propagation of weakly dispersive waves and can additionally model any associated inundation, overtopping or inland flooding within the same simulation.

Pure quasi-P-wave calculation in transversely isotropic media using a hybrid method

NASA Astrophysics Data System (ADS)

Wu, Zedong; Liu, Hongwei; Alkhalifah, Tariq

2018-07-01

The acoustic approximation for anisotropic media is widely used in current industry imaging and inversion algorithms mainly because Pwaves constitute the majority of the energy recorded in seismic exploration. The resulting acoustic formulae tend to be simpler, resulting in more efficient implementations, and depend on fewer medium parameters. However, conventional solutions of the acoustic wave equation with higher-order derivatives suffer from shear wave artefacts. Thus, we derive a new acoustic wave equation for wave propagation in transversely isotropic (TI) media, which is based on a partially separable approximation of the dispersion relation for TI media and free of shear wave artefacts. Even though our resulting equation is not a partial differential equation, it is still a linear equation. Thus, we propose to implement this equation efficiently by combining the finite difference approximation with spectral evaluation of the space-independent parts. The resulting algorithm provides solutions without the constraint ɛ ≥ δ. Numerical tests demonstrate the effectiveness of the approach.

The Gassmann-Burgers Model to Simulate Seismic Waves at the Earth Crust And Mantle

NASA Astrophysics Data System (ADS)

Carcione, José M.; Poletto, Flavio; Farina, Biancamaria; Craglietto, Aronne

2017-03-01

The upper part of the crust shows generally brittle behaviour while deeper zones, including the mantle, may present ductile behaviour, depending on the pressure-temperature conditions; moreover, some parts are melted. Seismic waves can be used to detect these conditions on the basis of reflection and transmission events. Basically, from the elastic-plastic point of view the seismic properties (seismic velocity and density) depend on effective pressure and temperature. Confining and pore pressures have opposite effects on these properties, such that very small effective pressures (the presence of overpressured fluids) may substantially decrease the P- and S-wave velocities, mainly the latter, by opening of cracks and weakening of grain contacts. Similarly, high temperatures induce the same effect by partial melting. To model these effects, we consider a poro-viscoelastic model based on Gassmann equations and Burgers mechanical model to represent the properties of the rock frame and describe ductility in which deformation takes place by shear plastic flow. The Burgers elements allow us to model the effects of seismic attenuation, velocity dispersion and steady-state creep flow, respectively. The stiffness components of the brittle and ductile media depend on stress and temperature through the shear viscosity, which is obtained by the Arrhenius equation and the octahedral stress criterion. Effective pressure effects are taken into account in the dry-rock moduli using exponential functions whose parameters are obtained by fitting experimental data as a function of confining pressure. Since fluid effects are important, the density and bulk modulus of the saturating fluids (water and steam) are modeled using the equations provided by the NIST website, including supercritical behaviour. The theory allows us to obtain the phase velocity and quality factor as a function of depth and geological pressure and temperature as well as time frequency. We then obtain the PS and SH equations of motion recast in the velocity-stress formulation, including memory variables to avoid the computation of time convolutions. The equations correspond to isotropic anelastic and inhomogeneous media and are solved by a direct grid method based on the Runge-Kutta time stepping technique and the Fourier pseudospectral method. The algorithm is tested with success against known analytical solutions for different shear viscosities. An example shows how anomalous conditions of pressure and temperature can in principle be detected with seismic waves.

Vertical Mixing In Western Lake Constance Due To Long Internal Waves

NASA Astrophysics Data System (ADS)

Boehrer, B.

Current profiles in the pelagic waters of western Lake Constance have been broken up into modes of the internal wave equation [1,2]. All current profiles can be well represented by a combination of the first and second mode wave. The temporal vari- ation of the modal composition with the interaction of the first and second mode im- plies current shear at varying depths. From current and density profiles, the gradient Richardson number can be evaluated in its spatial and temporal pattern with occa- tional occurence of supercritical values at all depths, also in the deep hypolimnion. An empiric connection between gradient Richardson number and diapycnical mixing [3] is applied to yield a profile of vertical transport coefficients, which can be com- pared with transport coefficients from gradient flux calculations of temperature and electrical conductivity profiles [4]. [1] B. Boehrer, J. Ilmberger and K.O. Münnich (2000): Vertical Structure of Current in Western Lake Constance, JGR-Oceans, 105 (12), 28823-28835 [2] B. Boehrer (2000): Modal Response of a Deep Stratified Lake: Western Lake Con- stance, JGR-Oceans, 105 (12), 28837-28845 [3] H. Peeters, M.C. Gregg and J.M. Toole (1988): On the parameterization of equa- torial turbulence, JGR, 93, 1199-1218 [4] G. Heinz, J. Ilmberger and M. Schimmele (1990): Vertical Mixing in Überlinger See, western part of Lake Constance, Aquat. Sci., 52(3), 256-268

Experimental tsunami deposits: Linking hydrodynamics to sediment entrainment, advection lengths and downstream fining

NASA Astrophysics Data System (ADS)

Johnson, Joel P. L.; Delbecq, Katie; Kim, Wonsuck; Mohrig, David

2016-01-01

A goal of paleotsunami research is to quantitatively reconstruct wave hydraulics from sediment deposits in order to better understand coastal hazards. Simple models have been proposed to predict wave heights and velocities, based largely on deposit grain size distributions (GSDs). Although seemingly consistent with some recent tsunamis, little independent data exist to test these equations. We conducted laboratory experiments to evaluate inversion assumptions and uncertainties. A computer-controlled lift gate instantaneously released 6.5 m3 of water into a 32 m flume with shallow ponded water, creating a hydraulic bore that transported sand from an upstream source dune. Differences in initial GSDs and ponded water depths influenced entrainment, transport, and deposition. While the source dune sand was fully suspendable based on size alone, experimental tsunamis produced deposits dominated by bed load sand transport in the upstream 1/3 of the flume and suspension-dominated transport downstream. The suspension deposits exhibited downstream fining and thinning. At 95% confidence, a published advection-settling model predicts time-averaged flow depths to approximately a factor of two, and time-averaged downstream flow velocities to within a factor of 1.5. Finally, reasonable scaling is found between flume and field cases by comparing flow depths, inundation distances, Froude numbers, Rouse numbers and grain size trends in suspension-dominated tsunami deposits, justifying laboratory study of sediment transport and deposition by tsunamis.

Progress Towards a Comprehensive Site Database for Taiwan Strong Motion Network

NASA Astrophysics Data System (ADS)

Kuo, C. H.; Lin, C. M.; Chang, S. C.; Wen, K. L.

2016-12-01

Site effect is usually treated as a simple site parameter like Vs30, which is a value of average shear wave velocity for the top 30 m of layers, in Ground Motion Prediction Equations (GMPEs) and engineering seismology. Although debates on usage of Vs30 for its advantage and disadvantage are still an open question, it has become the most widely be used site parameter in ground motion prediction, seismic hazard analysis, and building codes. Depth to the horizons with shear wave velocity of larger than 1.0 km/s (or 1.5 km/s, 2.5 km/s), the so called Z1.0 (or Z1.5, Z2.5), was recently introduced to the GMPEs of the Next Generation of Attenuation Equations (NGA) project in order to make up for the insufficient of Vs30 especially in regions covered by large thickness of sediments. However this kind of data is still rare and quite difficult to be acquired. This parameter is only available in Japan, California, and part region of Turkey at present. The high-frequency attenuation factor, i.e. kappa, is considered a significant parameter controlling attenuation of high-frequency seismic waves. High correlation is believed between kappa and local site conditions. S-wave velocity profiles of the Engineering Geology Database for TSMIP (EGDT) were measured using suspension PS-logging at more than 450 strong ground motion stations throughout Taiwan. Accurate Vs30 is therefore provided by the site database. Although the depths of most stations were only 35 m, Z1.0 still can be derived at dozens of stations near basin edges or piedmont area from EGDT. Several techniques including microtremor array, receiver function, and HVSR inversion have been used to obtain S-wave velocity profiles at strong motion stations and thus the parameter Z1.0 can be derived. A relationship between Vs30 and Z1.0 for Taiwan is consequently evaluated and further compared with those for Japan and California. Kappa at strong motion stations was calculated and a special correlation with Vs30 is found. The achievement in the progress toward a comprehensive site database for a national strong motion network is quite important for engineering seismology and national seismic hazard analysis.

Weakly Nonlinear Description of Parametric Instabilities in Vibrating Flows

NASA Technical Reports Server (NTRS)

Knobloch, E.; Vega, J. M.

1999-01-01

This project focuses on the effects of weak dissipation on vibrational flows in microgravity and in particular on (a) the generation of mean flows through viscous effects and their reaction on the flows themselves, and (b) the effects of finite group velocity and dispersion on the resulting dynamics in large domains. The basic mechanism responsible for the generation of such flows is nonlinear and was identified by Schlichting [21] and Longuet-Higgins. However, only recently has it become possible to describe such flows self-consistently in terms of amplitude equations for the parametrically excited waves coupled to a mean flow equation. The derivation of these equations is nontrivial because the limit of zero viscosity is singular. This project focuses on various aspects of this singular problem (i.e., the limit C equivalent to (nu)((g)(h(exp 3)))exp -1/2 << 1,where nu is the kinematic viscosity and h is the liquid depth) in the weakly nonlinear regime. A number of distinct cases is identified depending on the values of the Bond number, the size of the nonlinear terms, distance above threshold and the length scales of interest. The theory provides a quantitative explanation of a number of experiments on the vibration modes of liquid bridges and related experiments on parametric excitation of capillary waves in containers of both small and large aspect ratio. The following is a summary of results obtained thus far.

On the three dimensional structure of stratospheric material transport associated with various types of waves

NASA Astrophysics Data System (ADS)

Kinoshita, T.; Sato, K.

2016-12-01

The Transformed Eulerian-Mean (TEM) equations were derived by Andrews and McIntyre (1976, 1978) and have been widely used to examine wave-mean flow interaction in the meridional cross section. According to previous studies, the Brewer-Dobson circulation in the stratosphere is driven by planetary waves, baroclinic waves, and inertia-gravity waves, and that the meridional circulation from the summer hemisphere to the winter hemisphere in the mesosphere is mainly driven by gravity waves (e.g., Garcia and Boville 1994; Plumb and Semeniuk 2003; Watanabe et al. 2008; Okamoto et al. 2011). However, the TEM equations do not provide the three-dimensional view of the transport, so that the three dimensional TEM equations have been formulated (Hoskins et al. 1983, Trenberth 1986, Plumb 1985, 1986, Takaya and Nakamura 1997, 2001, Miyahara 2006, Kinoshita et al. 2010, Noda 2010, Kinoshita and Sato 2013a, b, and Noda 2014). On the other hand, the TEM equations cannot properly treat the lower boundary and unstable waves. The Mass-weighted Isentropic Mean (MIM) equations derived by Iwasaki (1989, 1990) are the equations that overcome those problems and the formulation of three-dimensional MIM equations have been studied. The present study applies the three-dimensional TEM and MIM equations to the ERA-Interim reanalysis data and examines the climatological character of three-dimensional structure of Stratospheric Brewer-Dobson circulation. Next, we will discuss how to treat the flow associated with spatial structure of stationary waves.

Statistical comparison of methods for estimating sediment thickness from Horizontal-to-Vertical Spectral Ratio (HVSR) seismic methods: An example from Tylerville, Connecticut, USA

USGS Publications Warehouse

Johnson, Carole D.; Lane, John W.

2016-01-01

Determining sediment thickness and delineating bedrock topography are important for assessing groundwater availability and characterizing contamination sites. In recent years, the horizontal-to-vertical spectral ratio (HVSR) seismic method has emerged as a non-invasive, cost-effective approach for estimating the thickness of unconsolidated sediments above bedrock. Using a three-component seismometer, this method uses the ratio of the average horizontal- and vertical-component amplitude spectrums to produce a spectral ratio curve with a peak at the fundamental resonance frequency. The HVSR method produces clear and repeatable resonance frequency peaks when there is a sharp contrast (>2:1) in acoustic impedance at the sediment/bedrock boundary. Given the resonant frequency, sediment thickness can be determined either by (1) using an estimate of average local sediment shear-wave velocity or by (2) application of a power-law regression equation developed from resonance frequency observations at sites with a range of known depths to bedrock. Two frequently asked questions about the HVSR method are (1) how accurate are the sediment thickness estimates? and (2) how much do sediment thickness/bedrock depth estimates change when using different published regression equations? This paper compares and contrasts different approaches for generating HVSR depth estimates, through analysis of HVSR data acquired in the vicinity of Tylerville, Connecticut, USA.

Electrokinetic instability in microchannel ferrofluid/water co-flows

PubMed Central

Song, Le; Yu, Liandong; Zhou, Yilong; Antao, Asher Reginald; Prabhakaran, Rama Aravind; Xuan, Xiangchun

2017-01-01

Electrokinetic instability refers to unstable electric field-driven disturbance to fluid flows, which can be harnessed to promote mixing for various electrokinetic microfluidic applications. This work presents a combined numerical and experimental study of electrokinetic ferrofluid/water co-flows in microchannels of various depths. Instability waves are observed at the ferrofluid and water interface when the applied DC electric field is beyond a threshold value. They are generated by the electric body force that acts on the free charge induced by the mismatch of ferrofluid and water electric conductivities. A nonlinear depth-averaged numerical model is developed to understand and simulate the interfacial electrokinetic behaviors. It considers the top and bottom channel walls’ stabilizing effects on electrokinetic flow through the depth averaging of three-dimensional transport equations in a second-order asymptotic analysis. This model is found accurate to predict both the observed electrokinetic instability patterns and the measured threshold electric fields for ferrofluids of different concentrations in shallow microchannels. PMID:28406228

Computational technique and performance of Transient Inundation Model for Rivers--2 Dimensional (TRIM2RD) : a depth-averaged two-dimensional flow model

USGS Publications Warehouse

Fulford, Janice M.

2003-01-01

A numerical computer model, Transient Inundation Model for Rivers -- 2 Dimensional (TrimR2D), that solves the two-dimensional depth-averaged flow equations is documented and discussed. The model uses a semi-implicit, semi-Lagrangian finite-difference method. It is a variant of the Trim model and has been used successfully in estuarine environments such as San Francisco Bay. The abilities of the model are documented for three scenarios: uniform depth flows, laboratory dam-break flows, and large-scale riverine flows. The model can start computations from a ?dry? bed and converge to accurate solutions. Inflows are expressed as source terms, which limits the use of the model to sufficiently long reaches where the flow reaches equilibrium with the channel. The data sets used by the investigation demonstrate that the model accurately propagates flood waves through long river reaches and simulates dam breaks with abrupt water-surface changes.

Zero-Inertial Recession for a Kinematic Wave Model

USDA-ARS?s Scientific Manuscript database

Kinematic-wave models of surface irrigation assume a fixed relationship between depth and discharge (typically, normal depth). When surface irrigation inflow is cut off, the calculated upstream flow depth goes to zero, since the discharge is zero. For short time steps, use of the Kinematic Wave mode...

A 20-Year High-Resolution Wave Resource Assessment of Japan with Wave-Current Interactions

NASA Astrophysics Data System (ADS)

Webb, A.; Waseda, T.; Kiyomatsu, K.

2016-02-01

Energy harvested from surface ocean waves and tidal currents has the potential to be a significant source of green energy, particularly for countries with extensive coastlines such as Japan. As part of a larger marine renewable energy project*, The University of Tokyo (in cooperation with JAMSTEC) has conducted a state-of-the-art wave resource assessment (with uncertainty estimates) to assist with wave generator site identification and construction in Japan. This assessment will be publicly available and is based on a large-scale NOAA WAVEWATCH III (version 4.18) simulation using NCEP and JAMSTEC forcings. It includes several key components to improve model skill: a 20-year simulation to reduce aleatory uncertainty, a four-nested-layer approach to resolve a 1 km shoreline, and finite-depth and current effects included in all wave power density calculations. This latter component is particularly important for regions near strong currents such as the Kuroshio. Here, we will analyze the different wave power density equations, discuss the model setup, and present results from the 20-year assessment (with a focus on the role of wave-current interactions). Time permitting, a comparison will also be made with simulations using JMA MSM 5 km winds. *New Energy and Industrial Technology Development Organization (NEDO): "Research on the Framework and Infrastructure of Marine Renewable Energy; an Energy Potential Assessment"

High-frequency Born synthetic seismograms based on coupled normal modes

USGS Publications Warehouse

Pollitz, F.

2011-01-01

High-frequency and full waveform synthetic seismograms on a 3-D laterally heterogeneous earth model are simulated using the theory of coupled normal modes. The set of coupled integral equations that describe the 3-D response are simplified into a set of uncoupled integral equations by using the Born approximation to calculate scattered wavefields and the pure-path approximation to modulate the phase of incident and scattered wavefields. This depends upon a decomposition of the aspherical structure into smooth and rough components. The uncoupled integral equations are discretized and solved in the frequency domain, and time domain results are obtained by inverse Fourier transform. Examples show the utility of the normal mode approach to synthesize the seismic wavefields resulting from interaction with a combination of rough and smooth structural heterogeneities. This approach is applied to an ~4 Hz shallow crustal wave propagation around the site of the San Andreas Fault Observatory at Depth (SAFOD). ?? The Author Geophysical Journal International ?? 2011 RAS.

Nonlinear Drift-Kinetic Equation in the Presence of a Circularly Polarized Wave

NASA Technical Reports Server (NTRS)

Khazanov, G. V.; Krivorutsky, E. N.; Whitaker, Ann F. (Technical Monitor)

2001-01-01

Equations of the single particle motion and nonlinear kinetic equation for plasma in the presence of a circularly polarized wave of arbitrary frequency in the drift approximation are presented. The nonstationarity and inhomogeneity of the plasma-wave system are taken into account.

On the exact solutions of high order wave equations of KdV type (I)

NASA Astrophysics Data System (ADS)

Bulut, Hasan; Pandir, Yusuf; Baskonus, Haci Mehmet

2014-12-01

In this paper, by means of a proper transformation and symbolic computation, we study high order wave equations of KdV type (I). We obtained classification of exact solutions that contain soliton, rational, trigonometric and elliptic function solutions by using the extended trial equation method. As a result, the motivation of this paper is to utilize the extended trial equation method to explore new solutions of high order wave equation of KdV type (I). This method is confirmed by applying it to this kind of selected nonlinear equations.

Solitary wave solutions of two-dimensional nonlinear Kadomtsev-Petviashvili dynamic equation in dust-acoustic plasmas

NASA Astrophysics Data System (ADS)

Seadawy, Aly R.

2017-09-01

Nonlinear two-dimensional Kadomtsev-Petviashvili (KP) equation governs the behaviour of nonlinear waves in dusty plasmas with variable dust charge and two temperature ions. By using the reductive perturbation method, the two-dimensional dust-acoustic solitary waves (DASWs) in unmagnetized cold plasma consisting of dust fluid, ions and electrons lead to a KP equation. We derived the solitary travelling wave solutions of the two-dimensional nonlinear KP equation by implementing sech-tanh, sinh-cosh, extended direct algebraic and fraction direct algebraic methods. We found the electrostatic field potential and electric field in the form travelling wave solutions for two-dimensional nonlinear KP equation. The solutions for the KP equation obtained by using these methods can be demonstrated precisely and efficiency. As an illustration, we used the readymade package of Mathematica program 10.1 to solve the original problem. These solutions are in good agreement with the analytical one.

Nonextensive statistics and skin depth of transverse wave in collisional plasma

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hashemzadeh, M., E-mail: hashemzade@gmail.com

Skin depth of transverse wave in a collisional plasma is studied taking into account the nonextensive electron distribution function. Considering the kinetic theory for charge particles and using the Bhatnagar-Gross-Krook collision model, a generalized transverse dielectric permittivity is obtained. The transverse dispersion relation in different frequency ranges is investigated. Obtaining the imaginary part of the wave vector from the dispersion relation, the skin depth for these frequency ranges is also achieved. Profiles of the skin depth show that by increasing the q parameter, the penetration depth decreases. In addition, the skin depth increases by increasing the electron temperature. Finally, itmore » is found that in the high frequency range and high electron temperature, the penetration depth decreases by increasing the collision frequency. In contrast, by increasing the collision frequency in a highly collisional frequency range, the skin depth of transverse wave increases.« less

Wave propagation through an inhomogeneous slab sandwiched by the piezoelectric and the piezomagnetic half spaces.

PubMed

Jiao, Fengyu; Wei, Peijun; Li, Li

2017-01-01

Wave propagation through a gradient slab sandwiched by the piezoelectric and the piezomagnetic half spaces are studied in this paper. First, the secular equations in the transverse isotropic piezoelectric/piezomagnetic half spaces are derived from the general dynamic equation. Then, the state vectors at piezoelectric and piezomagnetic half spaces are related to the amplitudes of various possible waves. The state transfer equation of the functionally graded slab is derived from the equations of motion by the reduction of order, and the transfer matrix of the functionally gradient slab is obtained by solving the state transfer equation with the spatial-varying coefficient. Finally, the continuous interface conditions are used to lead to the resultant algebraic equations. The algebraic equations are solved to obtain the amplitude ratios of various waves which are further used to obtain the energy reflection and transmission coefficients of various waves. The numerical results are shown graphically and are validated by the energy conservation law. Based on the numerical results on the fives of gradient profiles, the influences of the graded slab on the wave propagation are discussed. It is found that the reflection and transmission coefficients are obviously dependent upon the gradient profile. The various surface waves are more sensitive to the gradient profile than the bulk waves. Copyright © 2016 Elsevier B.V. All rights reserved.

The limitation and applicability of Musher-Sturman equation to two dimensional lower hybrid wave collapse

NASA Technical Reports Server (NTRS)

Tam, Sunny W. Y.; Chang, Tom

1995-01-01

The existence of localized regions of intense lower hybrid waves in the auroral ionosphere recently observed by rocket and satellite experiments can be understood by the study of a non-linear two-timescale coupling process. In this Letter, we demonstrate that the leading non-linear term in the standard Musher-Sturman equation vanishes identically in strict two-dimensions (normal to the magnetic field). Instead, the new two-dimensional equation is characterized by a much weaker non-linear term which arises from the ponderomotive force perpendicular to the magnetic field, particularly that due to the ions. The old and new equations are compared by means of time-evolution calculations of wave fields. The results exhibit a remarkable difference in the evolution of the waves as governed by the two equations. Such dissimilar outcomes motivate our investigation of the limitation of Musher-Sturman equation in quasi-two-dimensions. Only within all these limits can Musher-Sturman equation adequately describe the collapse of lower hybrid waves.

Multiple and exact soliton solutions of the perturbed Korteweg-de Vries equation of long surface waves in a convective fluid via Painlevé analysis, factorization, and simplest equation methods.

PubMed

Selima, Ehab S; Yao, Xiaohua; Wazwaz, Abdul-Majid

2017-06-01

In this research, the surface waves of a horizontal fluid layer open to air under gravity field and vertical temperature gradient effects are studied. The governing equations of this model are reformulated and converted to a nonlinear evolution equation, the perturbed Korteweg-de Vries (pKdV) equation. We investigate the latter equation, which includes dispersion, diffusion, and instability effects, in order to examine the evolution of long surface waves in a convective fluid. Dispersion relation of the pKdV equation and its properties are discussed. The Painlevé analysis is applied not only to check the integrability of the pKdV equation but also to establish the Bäcklund transformation form. In addition, traveling wave solutions and a general form of the multiple-soliton solutions of the pKdV equation are obtained via Bäcklund transformation, the simplest equation method using Bernoulli, Riccati, and Burgers' equations as simplest equations, and the factorization method.

Dynamic response of a riser under excitation of internal waves

NASA Astrophysics Data System (ADS)

Lou, Min; Yu, Chenglong; Chen, Peng

2015-12-01

In this paper, the dynamic response of a marine riser under excitation of internal waves is studied. With the linear approximation, the governing equation of internal waves is given. Based on the rigid-lid boundary condition assumption, the equation is solved by Thompson-Haskell method. Thus the velocity field of internal waves is obtained by the continuity equation. Combined with the modified Morison formula, using finite element method, the motion equation of riser is solved in time domain with Newmark-β method. The computation programs are compiled to solve the differential equations in time domain. Then we get the numerical results, including riser displacement and transfiguration. It is observed that the internal wave will result in circular shear flow, and the first two modes have a dominant effect on dynamic response of the marine riser. In the high mode, the response diminishes rapidly. In different modes of internal waves, the deformation of riser has different shapes, and the location of maximum displacement shifts. Studies on wave parameters indicate that the wave amplitude plays a considerable role in response displacement of riser, while the wave frequency contributes little. Nevertheless, the internal waves of high wave frequency will lead to a high-frequency oscillation of riser; it possibly gives rise to fatigue crack extension and partial fatigue failure.

Theoretical Studies of Alfven Waves and Energetic Particle Physics in Fusion Plasmas

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chen, Liu

This report summarizes major theoretical findings in the linear as well as nonlinear physics of Alfvén waves and energetic particles in magnetically confined fusion plasmas. On the linear physics, a variational formulation, based on the separation of singular and regular spatial scales, for drift-Alfvén instabilities excited by energetic particles is established. This variational formulation is then applied to derive the general fishbone-like dispersion relations corresponding to the various Alfvén eigenmodes and energetic-particle modes. It is further employed to explore in depth the low-frequency Alfvén eigenmodes and demonstrate the non-perturbative nature of the energetic particles. On the nonlinear physics, new novelmore » findings are obtained on both the nonlinear wave-wave interactions and nonlinear wave-energetic particle interactions. It is demonstrated that both the energetic particles and the fine radial mode structures could qualitatively affect the nonlinear evolution of Alfvén eigenmodes. Meanwhile, a theoretical approach based on the Dyson equation is developed to treat self-consistently the nonlinear interactions between Alfvén waves and energetic particles, and is then applied to explain simulation results of energetic-particle modes. Relevant list of journal publications on the above findings is also included.« less

Fluid dynamics of liquids on Titans surface

NASA Astrophysics Data System (ADS)

Ori, Gian Gabriele; Marinangeli, Lucia; Baliva, Antonio; Bressan, Mario; Strom, Robert G.

1998-10-01

On the surface of Titan liquids can be present in three types of environments : (i) oceans, (ii) seas and lakes, and (iii) fluvial channels. The liquid in these environments will be affected by several types of motion: progressive (tidal) waves, wind-generated waves and unidirectional currents. The physical parameters of the liquid on Titans surface can be reconstructed using the Peng-Robinson equation of state. The total energy of the waves, both tidal and wind, depends on the gravity and liquid density ; both values are lower on Titan than on Earth. Thus, the same total energy will produce larger waves on Titan. This is also valid also for the progressive waves, as it is confirmed by the physical relationship between horizontal velocity, wave amplitude, and depth of the liquid. Wind-driven waves also will tend to be larger, because the viscosity of the liquid (which is lower on Titan) controls the deformation of the liquid under shear stress. Wind-generated waves would be rather large, but the dimension of the liquid basin limits the size of the waves ; in small lakes or seas the wave power cannot reach large values. Unidirectional currents are also affected by the liquid properties. Both the relations from driving and resting forces and the Reynolds number suggests that the flows exhibit a large erosional capacity and that, theoretically, a true fluvial network could be formed. However, caution should be exercised, because the cohesion of the sedimentary interface can armour bottom and induce laterally extensive, unchanelled sheet flows with small erosional capacity.

Existence and Stability of Traveling Waves for Degenerate Reaction-Diffusion Equation with Time Delay

NASA Astrophysics Data System (ADS)

Huang, Rui; Jin, Chunhua; Mei, Ming; Yin, Jingxue

2018-01-01

This paper deals with the existence and stability of traveling wave solutions for a degenerate reaction-diffusion equation with time delay. The degeneracy of spatial diffusion together with the effect of time delay causes us the essential difficulty for the existence of the traveling waves and their stabilities. In order to treat this case, we first show the existence of smooth- and sharp-type traveling wave solutions in the case of c≥c^* for the degenerate reaction-diffusion equation without delay, where c^*>0 is the critical wave speed of smooth traveling waves. Then, as a small perturbation, we obtain the existence of the smooth non-critical traveling waves for the degenerate diffusion equation with small time delay τ >0 . Furthermore, we prove the global existence and uniqueness of C^{α ,β } -solution to the time-delayed degenerate reaction-diffusion equation via compactness analysis. Finally, by the weighted energy method, we prove that the smooth non-critical traveling wave is globally stable in the weighted L^1 -space. The exponential convergence rate is also derived.

Existence and Stability of Traveling Waves for Degenerate Reaction-Diffusion Equation with Time Delay

NASA Astrophysics Data System (ADS)

Huang, Rui; Jin, Chunhua; Mei, Ming; Yin, Jingxue

2018-06-01

This paper deals with the existence and stability of traveling wave solutions for a degenerate reaction-diffusion equation with time delay. The degeneracy of spatial diffusion together with the effect of time delay causes us the essential difficulty for the existence of the traveling waves and their stabilities. In order to treat this case, we first show the existence of smooth- and sharp-type traveling wave solutions in the case of c≥c^* for the degenerate reaction-diffusion equation without delay, where c^*>0 is the critical wave speed of smooth traveling waves. Then, as a small perturbation, we obtain the existence of the smooth non-critical traveling waves for the degenerate diffusion equation with small time delay τ >0. Furthermore, we prove the global existence and uniqueness of C^{α ,β }-solution to the time-delayed degenerate reaction-diffusion equation via compactness analysis. Finally, by the weighted energy method, we prove that the smooth non-critical traveling wave is globally stable in the weighted L^1-space. The exponential convergence rate is also derived.

Asymptotic analysis of numerical wave propagation in finite difference equations

NASA Technical Reports Server (NTRS)

Giles, M.; Thompkins, W. T., Jr.

1983-01-01

An asymptotic technique is developed for analyzing the propagation and dissipation of wave-like solutions to finite difference equations. It is shown that for each fixed complex frequency there are usually several wave solutions with different wavenumbers and the slowly varying amplitude of each satisfies an asymptotic amplitude equation which includes the effects of smoothly varying coefficients in the finite difference equations. The local group velocity appears in this equation as the velocity of convection of the amplitude. Asymptotic boundary conditions coupling the amplitudes of the different wave solutions are also derived. A wavepacket theory is developed which predicts the motion, and interaction at boundaries, of wavepackets, wave-like disturbances of finite length. Comparison with numerical experiments demonstrates the success and limitations of the theory. Finally an asymptotic global stability analysis is developed.

Observations and Simulations of the Impact of Wave-Current Interaction on Wave Direction in the Surf Zone

NASA Astrophysics Data System (ADS)

Hopkins, Julia; Elgar, Steve; Raubenheimer, Britt

2017-04-01

Accurately characterizing the interaction of waves and currents can improve predictions of wave propagation and subsequent sediment transport in the nearshore. Along the southern shoreline of Martha's Vineyard, MA, waves propagate across strong tidal currents as they shoal, providing an ideal environment for investigating wave-current interaction. Wave directions and mean currents observed for two 1-month-long periods in 7- and 2-m water depths along 11 km of the Martha's Vineyard shoreline have strong tidal modulations. Wave directions shift by as much as 70 degrees over a tidal cycle in 7 m depth, and by as much as 25 degrees in 2 m depth. The magnitude of the tidal modulations in the wave field decreases alongshore to the west, consistent with the observed decrease in tidal currents from 2.1 to 0.2 m/s. The observations are reproduced accurately by a numerical model (SWAN and Deflt3D-FLOW) that simulates waves and currents over the observed bathymetry. Model simulations with and without wave-current interaction and tidal depth changes demonstrate that the observed tidal modulations of the wave field primarily are caused by wave-current interaction and not by tidal changes to water depths over the nearby complex shoals. Sediment transport estimates from simulated wave conditions using a range of tidal currents and offshore wave fields indicate that the modulation of the wave field at Martha's Vineyard can impact the direction of wave-induced alongshore sediment transport, sometimes driving transport opposing the direction of the offshore incident wave field. As such, the observations and model simulations suggest the importance of wave-current interaction to tidally averaged transport in mixed-energy wave-and-current nearshore environments. Supported by ASD(R&E), NSF, NOAA (Sea Grant), and ONR.

A reflection TIE system for 3D inspection of wafer structures

NASA Astrophysics Data System (ADS)

Yan, Yizhen; Qu, Weijuan; Yan, Lei; Wang, Zhaomin; Zhao, Hongying

2017-10-01

A reflection TIE system consisting of a reflecting microscope and a 4f relay system is presented in this paper, with which the transport of intensity equation (TIE) is applied to reconstruct the three-dimensional (3D) profile of opaque micro objects like wafer structures for 3D inspection. As the shape of an object can affect the phases of waves, the 3D information of the object can be easily acquired with the multiple phases at different refocusing planes. By electronically controlled refocusing, multi-focal images can be captured and used in solving TIE to obtain the phase and depth of the object. In order to validate the accuracy and efficiency of the proposed system, the phase and depth values of several samples are calculated, and the experimental results is presented to demonstrate the performance of the system.

Formation of wave packets in the Ostrovsky equation for both normal and anomalous dispersion

PubMed Central

Grimshaw, Roger; Stepanyants, Yury; Alias, Azwani

2016-01-01

It is well known that the Ostrovsky equation with normal dispersion does not support steady solitary waves. An initial Korteweg–de Vries solitary wave decays adiabatically through the radiation of long waves and is eventually replaced by an envelope solitary wave whose carrier wave and envelope move with different velocities (phase and group velocities correspondingly). Here, we examine the same initial condition for the Ostrovsky equation with anomalous dispersion, when the wave frequency increases with wavenumber in the limit of very short waves. The essential difference is that now there exists a steady solitary wave solution (Ostrovsky soliton), which in the small-amplitude limit can be described asymptotically through the solitary wave solution of a nonlinear Schrödinger equation, based at that wavenumber where the phase and group velocities coincide. Long-time numerical simulations show that the emergence of this steady envelope solitary wave is a very robust feature. The initial Korteweg–de Vries solitary wave transforms rapidly to this envelope solitary wave in a seemingly non-adiabatic manner. The amplitude of the Ostrovsky soliton strongly correlates with the initial Korteweg–de Vries solitary wave. PMID:26997887

An investigation into the bedrock depth in the Eskisehir Quaternary Basin (Turkey) using the microtremor method

NASA Astrophysics Data System (ADS)

Tün, M.; Pekkan, E.; Özel, O.; Guney, Y.

2016-10-01

Amplification can occur in a graben as a result of strong earthquake-induced ground motion. Thus, in seismic hazard and seismic site response studies, it is of the utmost importance to determine the geometry of the bedrock depth. The main objectives of this study were to determine the bedrock depth and map the depth-to-bedrock ratio for use in land use planning in regard to the mitigation of earthquake hazards in the Eskişehir Basin. The fundamental resonance frequencies (fr) of 318 investigation sites in the Eskişehir Basin were determined through case studies, and the 2-D S-wave velocity structure down to the bedrock depth was explored. Single-station microtremor data were collected from the 318 sites, as well as microtremor array data from nine sites, seismic reflection data from six sites, deep-drilling log data from three sites and shallow drilling log data from ten sites in the Eskişehir Graben. The fundamental resonance frequencies of the Eskişehir Basin sites were obtained from the microtremor data using the horizontal-to vertical (H/V) spectral ratio (HVSR) method. The phase velocities of the Rayleigh waves were estimated from the microtremor data using the spatial autocorrelation (SPAC) method. The fundamental resonance frequency range at the deepest point of the Eskişehir Basin was found to be 0.23-0.35 Hz. Based on the microtremor array measurements and the 2-D S-wave velocity profiles obtained using the SPAC method, a bedrock level with an average velocity of 1300 m s-1 was accepted as the bedrock depth limit in the region. The log data from a deep borehole and a seismic reflection cross-section of the basement rocks of the Eskişehir Basin were obtained and permitted a comparison of bedrock levels. Tests carried out using a multichannel walk-away technique permitted a seismic reflection cross-section to be obtained up to a depth of 1500-2000 m using an explosive energy source. The relationship between the fundamental resonance frequency in the Eskişehir Basin and the results of deep drilling, shallow drilling, shear wave velocity measurement and sedimentary cover depth measurement obtained from the seismic reflection section was expressed in the form of a nonlinear regression equation. An empirical relationship between fr, the thickness of sediments and the bedrock depth is suggested for use in future microzonation studies of sites in the region. The results revealed a maximum basin depth of 1000 m, located in the northeast of the Eskişehir Basin, and the SPAC and HVSR results indicated that within the study area the basin is characterized by a thin local sedimentary cover with low shear wave velocity overlying stiff materials, resulting in a sharp velocity contrast. The thicknesses of the old Quaternary and Tertiary fluvial sediments within the basin serve as the primary data sources in seismic hazard and seismic site response studies, and these results add to the body of available seismic hazard data contributing to a seismic microzonation of the Eskişehir Graben in advance of the severe earthquakes expected in the Anatolian Region.

Spatiotemporal optical dark X solitary waves.

PubMed

Baronio, Fabio; Chen, Shihua; Onorato, Miguel; Trillo, Stefano; Wabnitz, Stefan; Kodama, Yuji

2016-12-01

We introduce spatiotemporal optical dark X solitary waves of the (2+1)D hyperbolic nonlinear Schrödinger equation (NLSE), which rules wave propagation in a self-focusing and normally dispersive medium. These analytical solutions are derived by exploiting the connection between the NLSE and a well-known equation of hydrodynamics, namely the type II Kadomtsev-Petviashvili (KP-II) equation. As a result, families of shallow water X soliton solutions of the KP-II equation are mapped into optical dark X solitary wave solutions of the NLSE. Numerical simulations show that optical dark X solitary waves may propagate for long distances (tens of nonlinear lengths) before they eventually break up, owing to the modulation instability of the continuous wave background. This finding opens a novel path for the excitation and control of X solitary waves in nonlinear optics.

A Self-Consistent Model of the Interacting Ring Current Ions and Electromagnetic Ion Cyclotron Waves, Initial Results: Waves and Precipitating Fluxes

NASA Technical Reports Server (NTRS)

Khazanov, G. V.; Gamayunov, K. V.; Jordanova, V. K.; Krivorutsky, E. N.

2002-01-01

Initial results from a newly developed model of the interacting ring current ions and ion cyclotron waves are presented. The model is based on the system of two kinetic equations: one equation describes the ring current ion dynamics, and another equation describes wave evolution. The system gives a self-consistent description of the ring current ions and ion cyclotron waves in a quasilinear approach. These equations for the ion phase space distribution function and for the wave power spectral density were solved on aglobal magnetospheric scale undernonsteady state conditions during the 2-5 May 1998 storm. The structure and dynamics of the ring current proton precipitating flux regions and the ion cyclotron wave-active zones during extreme geomagnetic disturbances on 4 May 1998 are presented and discussed in detail.

Dirac and Klein-Gordon-Fock equations in Grumiller’s spacetime

NASA Astrophysics Data System (ADS)

Al-Badawi, A.; Sakalli, I.

We study the Dirac and the chargeless Klein-Gordon-Fock equations in the geometry of Grumiller’s spacetime that describes a model for gravity of a central object at large distances. The Dirac equation is separated into radial and angular equations by adopting the Newman-Penrose formalism. The angular part of the both wave equations are analytically solved. For the radial equations, we managed to reduce them to one dimensional Schrödinger-type wave equations with their corresponding effective potentials. Fermions’s potentials are numerically analyzed by serving their some characteristic plots. We also compute the quasinormal frequencies of the chargeless and massive scalar waves. With the aid of those quasinormal frequencies, Bekenstein’s area conjecture is tested for the Grumiller black hole. Thus, the effects of the Rindler acceleration on the waves of fermions and scalars are thoroughly analyzed.

Tsunami generation and associated waves in the water column and seabed due to an asymmetric earthquake motion within an anisotropic substratum

NASA Astrophysics Data System (ADS)

Bagheri, Amirhossein; Greenhalgh, Stewart; Khojasteh, Ali; Rahimian, Mohammad; Attarnejad, Reza

2016-10-01

In this paper, closed-form integral expressions are derived to describe how surface gravity waves (tsunamis) are generated when general asymmetric ground displacement (due to earthquake rupturing), involving both horizontal and vertical components of motion, occurs at arbitrary depth within the interior of an anisotropic subsea solid beneath the ocean. In addition, we compute the resultant hydrodynamic pressure within the seawater and the elastic wavefield within the seabed at any position. The method of potential functions and an integral transform approach, accompanied by a special contour integration scheme, are adopted to handle the equations of motion and produce the numerical results. The formulation accounts for any number of possible acoustic-gravity modes and is valid for both shallow and deep water situations as well as for any focal depth of the earthquake source. Phase and group velocity dispersion curves are developed for surface gravity (tsunami mode), acoustic-gravity, Rayleigh, and Scholte waves. Several asymptotic cases which arise from the general analysis are discussed and compared to existing solutions. The role of effective parameters such as hypocenter location and frequency of excitation is examined and illustrated through several figures which show the propagation pattern in the vertical and horizontal directions. Attention is directed to the unexpected contribution from the horizontal ground motion. The results have important application in several fields such as tsunami hazard prediction, marine seismology, and offshore and coastal engineering. In a companion paper, we examine the effect of ocean stratification on the appearance and character of internal and surface gravity waves.

A comparative study of diffraction of shallow-water waves by high-level IGN and GN equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhao, B.B.; Ertekin, R.C.; College of Shipbuilding Engineering, Harbin Engineering University, 150001 Harbin

2015-02-15

This work is on the nonlinear diffraction analysis of shallow-water waves, impinging on submerged obstacles, by two related theories, namely the classical Green–Naghdi (GN) equations and the Irrotational Green–Naghdi (IGN) equations, both sets of equations being at high levels and derived for incompressible and inviscid flows. Recently, the high-level Green–Naghdi equations have been applied to some wave transformation problems. The high-level IGN equations have also been used in the last decade to study certain wave propagation problems. However, past works on these theories used different numerical methods to solve these nonlinear and unsteady sets of differential equations and at differentmore » levels. Moreover, different physical problems have been solved in the past. Therefore, it has not been possible to understand the differences produced by these two sets of theories and their range of applicability so far. We are thus motivated to make a direct comparison of the results produced by these theories by use of the same numerical method to solve physically the same wave diffraction problems. We focus on comparing these two theories by using similar codes; only the equations used are different but other parts of the codes, such as the wave-maker, damping zone, discretion method, matrix solver, etc., are exactly the same. This way, we eliminate many potential sources of differences that could be produced by the solution of different equations. The physical problems include the presence of various submerged obstacles that can be used for example as breakwaters or to represent the continental shelf. A numerical wave tank is created by placing a wavemaker on one end and a wave absorbing beach on the other. The nonlinear and unsteady sets of differential equations are solved by the finite-difference method. The results are compared with different equations as well as with the available experimental data.« less

A comparative study of diffraction of shallow-water waves by high-level IGN and GN equations

NASA Astrophysics Data System (ADS)

Zhao, B. B.; Ertekin, R. C.; Duan, W. Y.

2015-02-01

This work is on the nonlinear diffraction analysis of shallow-water waves, impinging on submerged obstacles, by two related theories, namely the classical Green-Naghdi (GN) equations and the Irrotational Green-Naghdi (IGN) equations, both sets of equations being at high levels and derived for incompressible and inviscid flows. Recently, the high-level Green-Naghdi equations have been applied to some wave transformation problems. The high-level IGN equations have also been used in the last decade to study certain wave propagation problems. However, past works on these theories used different numerical methods to solve these nonlinear and unsteady sets of differential equations and at different levels. Moreover, different physical problems have been solved in the past. Therefore, it has not been possible to understand the differences produced by these two sets of theories and their range of applicability so far. We are thus motivated to make a direct comparison of the results produced by these theories by use of the same numerical method to solve physically the same wave diffraction problems. We focus on comparing these two theories by using similar codes; only the equations used are different but other parts of the codes, such as the wave-maker, damping zone, discretion method, matrix solver, etc., are exactly the same. This way, we eliminate many potential sources of differences that could be produced by the solution of different equations. The physical problems include the presence of various submerged obstacles that can be used for example as breakwaters or to represent the continental shelf. A numerical wave tank is created by placing a wavemaker on one end and a wave absorbing beach on the other. The nonlinear and unsteady sets of differential equations are solved by the finite-difference method. The results are compared with different equations as well as with the available experimental data.

Phase Inversion: Inferring Solar Subphotospheric Flow and Other Asphericity from the Distortion of Acoustic Waves

NASA Technical Reports Server (NTRS)

Gough, Douglas; Merryfield, William J.; Toomre, Juri

1998-01-01

A method is proposed for analyzing an almost monochromatic train of waves propagating in a single direction in an inhomogeneous medium that is not otherwise changing in time. An effective phase is defined in terms of the Hilbert transform of the wave function, which is related, via the JWKB approximation, to the spatial variation of the background state against which the wave is propagating. The contaminating effect of interference between the truly monochromatic components of the train is eliminated using its propagation properties. Measurement errors, provided they are uncorrelated, are manifest as rapidly varying noise; although that noise can dominate the raw phase-processed signal, it can largely be removed by low-pass filtering. The intended purpose of the analysis is to determine the distortion of solar oscillations induced by horizontal structural variation and material flow. It should be possible to apply the method directly to sectoral modes. The horizontal phase distortion provides a measure of longitudinally averaged properties of the Sun in the vicinity of the equator, averaged also in radius down to the depth to which the modes penetrate. By combining such averages from different modes, the two-dimensional variation can be inferred by standard inversion techniques. After taking due account of horizontal refraction, it should be possible to apply the technique also to locally sectoral modes that propagate obliquely to the equator and thereby build a network of lateral averages at each radius, from which the full three-dimensional structure of the Sun can, in principle, be determined as an inverse Radon transform.

Numerical simulation and experimental research on interaction of micro-defects and laser ultrasonic signal

NASA Astrophysics Data System (ADS)

Guo, Hualing; Zheng, Bin; Liu, Hui

2017-11-01

In the present research, the mechanism governing the interaction between laser-generated ultrasonic wave and the micro-defects on an aluminum plate has been studied by virtue of numerical simulation as well as practical experiments. Simulation results indicate that broadband ultrasonic waves are caused mainly by surface waves, and that the surface waves produced by micro-defects could be utilized for the detection of micro-defects because these waves reflect as much information of the defects as possible. In the research, a laser-generated ultrasonic wave testing system with a surface wave probe has been established for the detection of micro-defects, and the surface waves produced by the defects with different depths on an aluminum plate have been tested by using the system. The interaction between defect depth and the maximum amplitude of the surface wave and that between defect depth and the center frequency of the surface wave have also been analyzed in detail. Research results indicate that, when the defect depth is less than half of the wavelength of the surface wave, the maximum amplitude and the center frequency of the surface wave are in linear proportion to the defect depth. Sound consistency of experimental results with theoretical simulation indicates that the system as established in the present research could be adopted for the quantitative detection of micro-defects.

Floodtide pulses after low tides in shallow subembayments adjacent to deep channels

USGS Publications Warehouse

Warner, J.C.; Schoellhamer, D.H.; Ruhl, C.A.; Burau, J.R.

2004-01-01

In shallow waters surface gravity waves (tides) propagate with a speed proportional to the square root of water depth (c=g(h+η)). As the ratio of free surface displacement to mean depth (η/h) approaches unity the wave will travel noticeably faster at high tide than at low tide, creating asymmetries in the tidal form. This physical process is explained analytically by the increased significance of friction and the nonlinear terms in the continuity and momentum equations. In a tidal system comprising a shallow bay adjacent to a deeper channel, tidal asymmetries will be more prevalent in the shallow bay. Thus strong barotropic gradients can be generated between the two, producing rapid accelerations of currents into the bay (relative to other bay tidal processes) and create a maximum peak in the flood tide that we describe as a floodtide pulse. These floodtide pulses can promote a landward flux of suspended-sediment into the bay. In Grizzly Bay (part of northern San Francisco Bay, USA), field observations verify the occurrence of floodtide pulses during the lowest low tides of the year. No pulses were observed in neighboring Honker Bay, which has an average depth ~30 cm greater than Grizzly Bay. Numerical simulations of northern San Francisco Bay using realistic bathymetry demonstrated that floodtide pulses occurred in Grizzly Bay but not in Honker Bay, consistent with the observations. Both observations and numerical simulations show that floodtide pulses promote a landward flux of sediment into Grizzly Bay. Numerical simulations of an idealized bay-channel system quantify the importance of mean depth and friction in creating these floodtide pulses. 

Waves and instabilities in plasmas

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chen, L.

1987-01-01

The contents of this book are: Plasma as a Dielectric Medium; Nyquist Technique; Absolute and Convective Instabilities; Landau Damping and Phase Mixing; Particle Trapping and Breakdown of Linear Theory; Solution of Viasov Equation via Guilding-Center Transformation; Kinetic Theory of Magnetohydrodynamic Waves; Geometric Optics; Wave-Kinetic Equation; Cutoff and Resonance; Resonant Absorption; Mode Conversion; Gyrokinetic Equation; Drift Waves; Quasi-Linear Theory; Ponderomotive Force; Parametric Instabilities; Problem Sets for Homework, Midterm and Final Examinations.

Modeling RF Fields in Hot Plasmas with Parallel Full Wave Code

NASA Astrophysics Data System (ADS)

Spencer, Andrew; Svidzinski, Vladimir; Zhao, Liangji; Galkin, Sergei; Kim, Jin-Soo

2016-10-01

FAR-TECH, Inc. is developing a suite of full wave RF plasma codes. It is based on a meshless formulation in configuration space with adapted cloud of computational points (CCP) capability and using the hot plasma conductivity kernel to model the nonlocal plasma dielectric response. The conductivity kernel is calculated by numerically integrating the linearized Vlasov equation along unperturbed particle trajectories. Work has been done on the following calculations: 1) the conductivity kernel in hot plasmas, 2) a monitor function based on analytic solutions of the cold-plasma dispersion relation, 3) an adaptive CCP based on the monitor function, 4) stencils to approximate the wave equations on the CCP, 5) the solution to the full wave equations in the cold-plasma model in tokamak geometry for ECRH and ICRH range of frequencies, and 6) the solution to the wave equations using the calculated hot plasma conductivity kernel. We will present results on using a meshless formulation on adaptive CCP to solve the wave equations and on implementing the non-local hot plasma dielectric response to the wave equations. The presentation will include numerical results of wave propagation and absorption in the cold and hot tokamak plasma RF models, using DIII-D geometry and plasma parameters. Work is supported by the U.S. DOE SBIR program.

An Operator Method for Field Moments from the Extended Parabolic Wave Equation and Analytical Solutions of the First and Second Moments for Atmospheric Electromagnetic Wave Propagation

NASA Technical Reports Server (NTRS)

Manning, Robert M.

2004-01-01

The extended wide-angle parabolic wave equation applied to electromagnetic wave propagation in random media is considered. A general operator equation is derived which gives the statistical moments of an electric field of a propagating wave. This expression is used to obtain the first and second order moments of the wave field and solutions are found that transcend those which incorporate the full paraxial approximation at the outset. Although these equations can be applied to any propagation scenario that satisfies the conditions of application of the extended parabolic wave equation, the example of propagation through atmospheric turbulence is used. It is shown that in the case of atmospheric wave propagation and under the Markov approximation (i.e., the delta-correlation of the fluctuations in the direction of propagation), the usual parabolic equation in the paraxial approximation is accurate even at millimeter wavelengths. The comprehensive operator solution also allows one to obtain expressions for the longitudinal (generalized) second order moment. This is also considered and the solution for the atmospheric case is obtained and discussed. The methodology developed here can be applied to any qualifying situation involving random propagation through turbid or plasma environments that can be represented by a spectral density of permittivity fluctuations.

The Shock and Vibration Digest. Volume 16, Number 11

DTIC Science & Technology

1984-11-01

wave [19], a secular equation for Rayleigh waves on ing, seismic risk, and related problems are discussed. the surface of an anisotropic half-space...waves in an !so- tive equation of an elastic-plastic rack medium was....... tropic linear elastic half-space with plane material used; the coefficient...pair of semi-linear hyperbolic partial differential -- " Conditions under which the equations of motion equations governing slow variations in amplitude

Nonlinear and linear wave equations for propagation in media with frequency power law losses

NASA Astrophysics Data System (ADS)

Szabo, Thomas L.

2003-10-01

The Burgers, KZK, and Westervelt wave equations used for simulating wave propagation in nonlinear media are based on absorption that has a quadratic dependence on frequency. Unfortunately, most lossy media, such as tissue, follow a more general frequency power law. The authors first research involved measurements of loss and dispersion associated with a modification to Blackstock's solution to the linear thermoviscous wave equation [J. Acoust. Soc. Am. 41, 1312 (1967)]. A second paper by Blackstock [J. Acoust. Soc. Am. 77, 2050 (1985)] showed the loss term in the Burgers equation for plane waves could be modified for other known instances of loss. The authors' work eventually led to comprehensive time-domain convolutional operators that accounted for both dispersion and general frequency power law absorption [Szabo, J. Acoust. Soc. Am. 96, 491 (1994)]. Versions of appropriate loss terms were developed to extend the standard three nonlinear wave equations to these more general losses. Extensive experimental data has verified the predicted phase velocity dispersion for different power exponents for the linear case. Other groups are now working on methods suitable for solving wave equations numerically for these types of loss directly in the time domain for both linear and nonlinear media.

Fast and local non-linear evolution of steep wave-groups on deep water: A comparison of approximate models to fully non-linear simulations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Adcock, T. A. A.; Taylor, P. H.

2016-01-15

The non-linear Schrödinger equation and its higher order extensions are routinely used for analysis of extreme ocean waves. This paper compares the evolution of individual wave-packets modelled using non-linear Schrödinger type equations with packets modelled using fully non-linear potential flow models. The modified non-linear Schrödinger Equation accurately models the relatively large scale non-linear changes to the shape of wave-groups, with a dramatic contraction of the group along the mean propagation direction and a corresponding extension of the width of the wave-crests. In addition, as extreme wave form, there is a local non-linear contraction of the wave-group around the crest whichmore » leads to a localised broadening of the wave spectrum which the bandwidth limited non-linear Schrödinger Equations struggle to capture. This limitation occurs for waves of moderate steepness and a narrow underlying spectrum.« less

The picosecond structure of ultra-fast rogue waves

NASA Astrophysics Data System (ADS)

Klein, Avi; Shahal, Shir; Masri, Gilad; Duadi, Hamootal; Sulimani, Kfir; Lib, Ohad; Steinberg, Hadar; Kolpakov, Stanislav A.; Fridman, Moti

2018-02-01

We investigated ultrafast rogue waves in fiber lasers and found three different patterns of rogue waves: single- peaks, twin-peaks, and triple-peaks. The statistics of the different patterns as a function of the pump power of the laser reveals that the probability for all rogue waves patterns increase close to the laser threshold. We developed a numerical model which prove that the ultrafast rogue waves patterns result from both the polarization mode dispersion in the fiber and the non-instantaneous nature of the saturable absorber. This discovery reveals that there are three different types of rogue waves in fiber lasers: slow, fast, and ultrafast, which relate to three different time-scales and are governed by three different sets of equations: the laser rate equations, the nonlinear Schrodinger equation, and the saturable absorber equations, accordingly. This discovery is highly important for analyzing rogue waves and other extreme events in fiber lasers and can lead to realizing types of rogue waves which were not possible so far such as triangular rogue waves.

Reduction of the equation for lower hybrid waves in a plasma to a nonlinear Schroedinger equation

NASA Technical Reports Server (NTRS)

Karney, C. F. F.

1977-01-01

Equations describing the nonlinear propagation of waves in an anisotropic plasma are rarely exactly soluble. However it is often possible to make approximations that reduce the exact equations into a simpler equation. The use of MACSYMA to make such approximations, and so reduce the equation describing lower hybrid waves into the nonlinear Schrodinger equation which is soluble by the inverse scattering method is demonstrated. MACSYMA is used at several stages in the calculation only because there is a natural division between calculations that are easiest done by hand, and those that are easiest done by machine.

Technique for handling wave propagation specific effects in biological tissue: mapping of the photon transport equation to Maxwell's equations.

PubMed

Handapangoda, Chintha C; Premaratne, Malin; Paganin, David M; Hendahewa, Priyantha R D S

2008-10-27

A novel algorithm for mapping the photon transport equation (PTE) to Maxwell's equations is presented. Owing to its accuracy, wave propagation through biological tissue is modeled using the PTE. The mapping of the PTE to Maxwell's equations is required to model wave propagation through foreign structures implanted in biological tissue for sensing and characterization of tissue properties. The PTE solves for only the magnitude of the intensity but Maxwell's equations require the phase information as well. However, it is possible to construct the phase information approximately by solving the transport of intensity equation (TIE) using the full multigrid algorithm.

A theory for predicting boundary impedance and resonance frequencies of slotted-wall wind tunnels, including plenum effects

NASA Technical Reports Server (NTRS)

Barger, R. L.

1981-01-01

Wave-induced resonance associated with the geometry of wind-tunnel test sections can occur. A theory that uses acoustic impedance concepts to predict resonance modes in a two dimensional, slotted wall wind tunnel with a plenum chamber is described. The equation derived is consistent with known results for limiting conditions. The computed resonance modes compare well with appropriate experimental data. When the theory is applied to perforated wall test sections, it predicts the experimentally observed closely spaced modes that occur when the wavelength is not long compared with he plenum depth.

The Dynamics and Evolution of Poles and Rogue Waves for Nonlinear Schrödinger Equations*

NASA Astrophysics Data System (ADS)

Chiu, Tin Lok; Liu, Tian Yang; Chan, Hiu Ning; Wing Chow, Kwok

2017-09-01

Rogue waves are unexpectedly large deviations from equilibrium or otherwise calm positions in physical systems, e.g. hydrodynamic waves and optical beam intensities. The profiles and points of maximum displacements of these rogue waves are correlated with the movement of poles of the exact solutions extended to the complex plane through analytic continuation. Such links are shown to be surprisingly precise for the first order rogue wave of the nonlinear Schrödinger (NLS) and the derivative NLS equations. A computational study on the second order rogue waves of the NLS equation also displays remarkable agreements.

Analytic solutions for Long's equation and its generalization

NASA Astrophysics Data System (ADS)

Humi, Mayer

2017-12-01

Two-dimensional, steady-state, stratified, isothermal atmospheric flow over topography is governed by Long's equation. Numerical solutions of this equation were derived and used by several authors. In particular, these solutions were applied extensively to analyze the experimental observations of gravity waves. In the first part of this paper we derive an extension of this equation to non-isothermal flows. Then we devise a transformation that simplifies this equation. We show that this simplified equation admits solitonic-type solutions in addition to regular gravity waves. These new analytical solutions provide new insights into the propagation and amplitude of gravity waves over topography.

Nonlinear waves of a nonlocal modified KdV equation in the atmospheric and oceanic dynamical system

NASA Astrophysics Data System (ADS)

Tang, Xiao-yan; Liang, Zu-feng; Hao, Xia-zhi

2018-07-01

A new general nonlocal modified KdV equation is derived from the nonlinear inviscid dissipative and equivalent barotropic vorticity equation in a β-plane. The nonlocal property is manifested in the shifted parity and delayed time reversal symmetries. Exact solutions of the nonlocal modified KdV equation are obtained including periodic waves, kink waves, solitary waves, kink- and/or anti-kink-cnoidal periodic wave interaction solutions, which can be utilized to describe various two-place and time-delayed correlated events. As an illustration, a special approximate solution is applied to theoretically capture the salient features of two correlated dipole blocking events in atmospheric dynamical systems.

Explicit and exact nontraveling wave solutions of the (3+1)-dimensional potential Yu-Toda-Sasa-Fukuyama equation

NASA Astrophysics Data System (ADS)

Yuan, Na

2018-04-01

With the aid of the symbolic computation, we present an improved ( G ‧ / G ) -expansion method, which can be applied to seek more types of exact solutions for certain nonlinear evolution equations. In illustration, we choose the (3 + 1)-dimensional potential Yu-Toda-Sasa-Fukuyama equation to demonstrate the validity and advantages of the method. As a result, abundant explicit and exact nontraveling wave solutions are obtained including two solitary waves solutions, nontraveling wave solutions and dromion soliton solutions. Some particular localized excitations and the interactions between two solitary waves are researched. The method can be also applied to other nonlinear partial differential equations.

Numerical solution of the wave equation with variable wave speed on nonconforming domains by high-order difference potentials

NASA Astrophysics Data System (ADS)

Britt, S.; Tsynkov, S.; Turkel, E.

2018-02-01

We solve the wave equation with variable wave speed on nonconforming domains with fourth order accuracy in both space and time. This is accomplished using an implicit finite difference (FD) scheme for the wave equation and solving an elliptic (modified Helmholtz) equation at each time step with fourth order spatial accuracy by the method of difference potentials (MDP). High-order MDP utilizes compact FD schemes on regular structured grids to efficiently solve problems on nonconforming domains while maintaining the design convergence rate of the underlying FD scheme. Asymptotically, the computational complexity of high-order MDP scales the same as that for FD.

Dispersive traveling wave solutions of the Equal-Width and Modified Equal-Width equations via mathematical methods and its applications

NASA Astrophysics Data System (ADS)

Lu, Dianchen; Seadawy, Aly R.; Ali, Asghar

2018-06-01

The Equal-Width and Modified Equal-Width equations are used as a model in partial differential equations for the simulation of one-dimensional wave transmission in nonlinear media with dispersion processes. In this article we have employed extend simple equation method and the exp(-varphi(ξ)) expansion method to construct the exact traveling wave solutions of equal width and modified equal width equations. The obtained results are novel and have numerous applications in current areas of research in mathematical physics. It is exposed that our method, with the help of symbolic computation, provides a effective and powerful mathematical tool for solving different kind nonlinear wave problems.

Constraints on the anisotropic contributions to velocity discontinuities at ∼60 km depth beneath the Pacific

PubMed Central

Harmon, Nicholas

2017-01-01

Abstract Strong, sharp, negative seismic discontinuities, velocity decreases with depth, are observed beneath the Pacific seafloor at ∼60 km depth. It has been suggested that these are caused by an increase in radial anisotropy with depth, which occurs in global surface wave models. Here we test this hypothesis in two ways. We evaluate whether an increase in surface wave radial anisotropy with depth is robust with synthetic resolution tests. We do this by fitting an example surface wave data set near the East Pacific Rise. We also estimate the apparent isotropic seismic velocity discontinuities that could be caused by changes in radial anisotropy in S‐to‐P and P‐to‐S receiver functions and SS precursors using synthetic seismograms. We test one model where radial anisotropy is caused by olivine alignment and one model where it is caused by compositional layering. The result of our surface wave inversion suggests strong shallow azimuthal anisotropy beneath 0–10 Ma seafloor, which would also have a radial anisotropy signature. An increase in radial anisotropy with depth at 60 km depth is not well‐resolved in surface wave models, and could be artificially observed. Shallow isotropy underlain by strong radial anisotropy could explain moderate apparent velocity drops (<6%) in SS precursor imaging, but not receiver functions. The effect is diminished if strong anisotropy also exists at 0–60 km depth as suggested by surface waves. Overall, an increase in radial anisotropy with depth may not exist at 60 km beneath the oceans and does not explain the scattered wave observations. PMID:29097907

Constraints on the anisotropic contributions to velocity discontinuities at ∼60 km depth beneath the Pacific.

PubMed

Rychert, Catherine A; Harmon, Nicholas

2017-08-01

Strong, sharp, negative seismic discontinuities, velocity decreases with depth, are observed beneath the Pacific seafloor at ∼60 km depth. It has been suggested that these are caused by an increase in radial anisotropy with depth, which occurs in global surface wave models. Here we test this hypothesis in two ways. We evaluate whether an increase in surface wave radial anisotropy with depth is robust with synthetic resolution tests. We do this by fitting an example surface wave data set near the East Pacific Rise. We also estimate the apparent isotropic seismic velocity discontinuities that could be caused by changes in radial anisotropy in S-to-P and P-to-S receiver functions and SS precursors using synthetic seismograms. We test one model where radial anisotropy is caused by olivine alignment and one model where it is caused by compositional layering. The result of our surface wave inversion suggests strong shallow azimuthal anisotropy beneath 0-10 Ma seafloor, which would also have a radial anisotropy signature. An increase in radial anisotropy with depth at 60 km depth is not well-resolved in surface wave models, and could be artificially observed. Shallow isotropy underlain by strong radial anisotropy could explain moderate apparent velocity drops (<6%) in SS precursor imaging, but not receiver functions. The effect is diminished if strong anisotropy also exists at 0-60 km depth as suggested by surface waves. Overall, an increase in radial anisotropy with depth may not exist at 60 km beneath the oceans and does not explain the scattered wave observations.

Explicit solutions from eigenfunction symmetry of the Korteweg-de Vries equation.

PubMed

Hu, Xiao-Rui; Lou, Sen-Yue; Chen, Yong

2012-05-01

In nonlinear science, it is very difficult to find exact interaction solutions among solitons and other kinds of complicated waves such as cnoidal waves and Painlevé waves. Actually, even if for the most well-known prototypical models such as the Kortewet-de Vries (KdV) equation and the Kadomtsev-Petviashvili (KP) equation, this kind of problem has not yet been solved. In this paper, the explicit analytic interaction solutions between solitary waves and cnoidal waves are obtained through the localization procedure of nonlocal symmetries which are related to Darboux transformation for the well-known KdV equation. The same approach also yields some other types of interaction solutions among different types of solutions such as solitary waves, rational solutions, Bessel function solutions, and/or general Painlevé II solutions.

Time dependent wave envelope finite difference analysis of sound propagation

NASA Technical Reports Server (NTRS)

Baumeister, K. J.

1984-01-01

A transient finite difference wave envelope formulation is presented for sound propagation, without steady flow. Before the finite difference equations are formulated, the governing wave equation is first transformed to a form whose solution tends not to oscillate along the propagation direction. This transformation reduces the required number of grid points by an order of magnitude. Physically, the transformed pressure represents the amplitude of the conventional sound wave. The derivation for the wave envelope transient wave equation and appropriate boundary conditions are presented as well as the difference equations and stability requirements. To illustrate the method, example solutions are presented for sound propagation in a straight hard wall duct and in a two dimensional straight soft wall duct. The numerical results are in good agreement with exact analytical results.

The stability of freak waves with regard to external impact and perturbation of initial data

NASA Astrophysics Data System (ADS)

Smirnova, Anna; Shamin, Roman

2014-05-01

We investigate solutions of the equations, describing freak waves, in perspective of stability with regard to external impact and perturbation of initial data. The modeling of freak waves is based on numerical solution of equations describing a non-stationary potential flow of the ideal fluid with a free surface. We consider the two-dimensional infinitely deep flow. For waves modeling we use the equations in conformal variables. The variant of these equations is offered in [1]. Mathematical correctness of these equations was discussed in [2]. These works establish the uniqueness of solutions, offer the effective numerical solution calculation methods, prove the numerical convergence of these methods. The important aspect of numerical modeling of freak waves is the stability of solutions, describing these waves. In this work we study the questions of stability with regards to external impact and perturbation of initial data. We showed the stability of freak waves numerical model, corresponding to the external impact. We performed series of computational experiments with various freak wave initial data and random external impact. This impact means the power density on free surface. In each experiment examine two waves: the wave that was formed by external impact and without one. In all the experiments we see the stability of equation`s solutions. The random external impact practically does not change the time of freak wave formation and its form. Later our work progresses to the investigation of solution's stability under perturbations of initial data. We take the initial data that provide a freak wave and get the numerical solution. In common we take the numerical solution of equation with perturbation of initial data. The computing experiments showed that the freak waves equations solutions are stable under perturbations of initial data.So we can make a conclusion that freak waves are stable relatively external perturbation and perturbation of initial data both. 1. Zakharov V.E., Dyachenko A.I., Vasilyev O.A. New method for numerical simulation of a nonstationary potential flow of incompressible fluid with a free surface// Eur. J.~Mech. B Fluids. 2002. V. 21. P. 283-291. 2. R.V. Shamin. Dynamics of an Ideal Liquid with a Free Surface in Conformal Variables // Journal of Mathematical Sciences, Vol. 160, No. 5, 2009. P. 537-678. 3. R.V. Shamin, V.E. Zakharov, A.I. Dyachenko. How probability for freak wave formation can be found // THE EUROPEAN PHYSICAL JOURNAL - SPECIAL TOPICS Volume 185, Number 1, 113-124, DOI: 10.1140/epjst/e2010-01242-y

Stability and instability of periodic travelling wave solutions for the critical Korteweg-de Vries and nonlinear Schrödinger equations

NASA Astrophysics Data System (ADS)

Angulo Pava, Jaime; Natali, Fábio M. Amorin

2009-04-01

In this paper we establish new results about the existence, stability, and instability of periodic travelling wave solutions related to the critical Korteweg-de Vries equation ut+5u4ux+u=0, and the critical nonlinear Schrödinger equation ivt+v+|v=0. The periodic travelling wave solutions obtained in our study tend to the classical solitary wave solutions in the infinite wavelength scenario. The stability approach is based on the theory developed by Angulo & Natali in [J. Angulo, F. Natali, Positivity properties of the Fourier transform and the stability of periodic travelling wave solutions, SIAM J. Math. Anal. 40 (2008) 1123-1151] for positive periodic travelling wave solutions associated to dispersive evolution equations of Korteweg-de Vries type. The instability approach is based on an extension to the periodic setting of arguments found in Bona & Souganidis & Strauss [J.L. Bona, P.E. Souganidis, W.A. Strauss, Stability and instability of solitary waves of Korteweg-de Vries type, Proc. Roy. Soc. London Ser. A 411 (1987) 395-412]. Regarding the critical Schrödinger equation stability/instability theories similar to the critical Korteweg-de Vries equation are obtained by using the classical Grillakis & Shatah & Strauss theory in [M. Grillakis, J. Shatah, W. Strauss, Stability theory of solitary waves in the presence of symmetry II, J. Funct. Anal. 94 (1990) 308-348; M. Grillakis, J. Shatah, W. Strauss, Stability theory of solitary waves in the presence of symmetry I, J. Funct. Anal. 74 (1987) 160-197]. The arguments presented in this investigation have prospects for the study of the stability of periodic travelling wave solutions of other nonlinear evolution equations.

A highly accurate finite-difference method with minimum dispersion error for solving the Helmholtz equation

NASA Astrophysics Data System (ADS)

Wu, Zedong; Alkhalifah, Tariq

2018-07-01

Numerical simulation of the acoustic wave equation in either isotropic or anisotropic media is crucial to seismic modeling, imaging and inversion. Actually, it represents the core computation cost of these highly advanced seismic processing methods. However, the conventional finite-difference method suffers from severe numerical dispersion errors and S-wave artifacts when solving the acoustic wave equation for anisotropic media. We propose a method to obtain the finite-difference coefficients by comparing its numerical dispersion with the exact form. We find the optimal finite difference coefficients that share the dispersion characteristics of the exact equation with minimal dispersion error. The method is extended to solve the acoustic wave equation in transversely isotropic (TI) media without S-wave artifacts. Numerical examples show that the method is highly accurate and efficient.

Mass, Energy, Space And Time Systemic Theory---MEST

NASA Astrophysics Data System (ADS)

Cao, Dayong

2010-03-01

Things have their physical system of the mass, energy, space and time of themselves-MEST. The matter have the physical systemic moel like that the mass-energy is center and the space-time is around. The time is from the frequency of wave, the space is from the amplitude of wave. What is the physical effection of the wave. The gravity and inertial force is from the wave. Not only the planets have the mass and the kinetic energy, but also it have the wave and the wave energy. According to the equivalence principle of the general relativity, there is the equation: ma=mg and mv^2 /2= δmc^2. The energy equation of the planets: E=mv^2=mgr (v is velocity) be bring put forward. In quantum mechanics, according to the quantum light theory and the de Broglie's theory , there are the equation of the wave: E=hν, p=h/λ (h is Planck constant, p is momentum, λ is the wavelengh), and there is the equation of the wave: E=mc^2. So the energy equation of the planets: E=mv^2 = mv^2 /2 + δmc^2 (mv^2 /2= δmc^2 ) be bring put forward. The equation: δmc^2 show that the planets have the wave of itself, and the wave give the planets the energy. So it do not fall from the heaven. When the matter go into the heaven, it need get the wave energy (like the potential energy). So we can make a new light-flight with the light-driving force.

Sensitivity of Rogue Waves Predictions to the Oceanic Stratification

NASA Astrophysics Data System (ADS)

Guo, Qiuchen; Alam, Mohammad-Reza

2014-11-01

Oceanic rogue waves are short-lived very large amplitude waves (a giant crest typically followed or preceded by a deep trough) that appear and disappear suddenly in the ocean causing damages to ships and offshore structures. Assuming that the state of the ocean at the present time is perfectly known, then the upcoming rogue waves can be predicted via numerically solving the equations that govern the evolution of the waves. The state of the art radar technology can now provide accurate wave height measurement over large spatial domains and when combined with advanced wave-field reconstruction techniques together render deterministic details of the current state of the ocean (i.e. surface elevation and velocity field) at any given moment of the time with a very high accuracy. The ocean water density is, however, stratified (mainly due to the salinity and temperature differences). This density stratification, with today's technology, is very difficult to be measured accurately. As a result in most predictive schemes these density variations are neglected. While the overall effect of the stratification on the average state of the ocean may not be significant, here we show that these density variations can strongly affect the prediction of oceanic rogue waves. Specifically, we consider a broadband oceanic spectrum in a two-layer density stratified fluid, and study via extensive statistical analysis the effects of strength of the stratification (difference between densities) and the depth of the thermocline on the prediction of upcoming rogue waves.

Dispersive solitary wave solutions of Kadomtsev-Petviashvili and modified Kadomtsev-Petviashvili dynamical equations in unmagnetized dust plasma

NASA Astrophysics Data System (ADS)

Seadawy, A. R.; El-Rashidy, K.

2018-03-01

The Kadomtsev-Petviashvili (KP) and modified KP equations are two of the most universal models in nonlinear wave theory, which arises as a reduction of system with quadratic nonlinearity which admit weakly dispersive waves. The generalized extended tanh method and the F-expansion method are used to derive exact solitary waves solutions of KP and modified KP equations. The region of solutions are displayed graphically.

Circularly polarized few-cycle optical rogue waves: rotating reduced Maxwell-Bloch equations.

PubMed

Xu, Shuwei; Porsezian, K; He, Jingsong; Cheng, Yi

2013-12-01

The rotating reduced Maxwell-Bloch (RMB) equations, which describe the propagation of few-cycle optical pulses in a transparent media with two isotropic polarized electronic field components, are derived from a system of complete Maxwell-Bloch equations without using the slowly varying envelope approximations. Two hierarchies of the obtained rational solutions, including rogue waves, which are also called few-cycle optical rogue waves, of the rotating RMB equations are constructed explicitly through degenerate Darboux transformation. In addition to the above, the dynamical evolution of the first-, second-, and third-order few-cycle optical rogue waves are constructed with different patterns. For an electric field E in the three lower-order rogue waves, we find that rogue waves correspond to localized large amplitude oscillations of the polarized electric fields. Further a complementary relationship of two electric field components of rogue waves is discussed in terms of analytical formulas as well as numerical figures.

Exact finite difference schemes for the non-linear unidirectional wave equation

NASA Technical Reports Server (NTRS)

Mickens, R. E.

1985-01-01

Attention is given to the construction of exact finite difference schemes for the nonlinear unidirectional wave equation that describes the nonlinear propagation of a wave motion in the positive x-direction. The schemes constructed for these equations are compared with those obtained by using the usual procedures of numerical analysis. It is noted that the order of the exact finite difference models is equal to the order of the differential equation.

An algorithm for solving the perturbed gas dynamic equations

NASA Technical Reports Server (NTRS)

Davis, Sanford

1993-01-01

The present application of a compact, higher-order central-difference approximation to the linearized Euler equations illustrates the multimodal character of these equations by means of computations for acoustic, vortical, and entropy waves. Such dissipationless central-difference methods are shown to propagate waves exhibiting excellent phase and amplitude resolution on the basis of relatively large time-steps; they can be applied to wave problems governed by systems of first-order partial differential equations.

Investigation of Solitary wave solutions for Vakhnenko-Parkes equation via exp-function and Exp(-ϕ(ξ))-expansion method.

PubMed

Roshid, Harun-Or; Kabir, Md Rashed; Bhowmik, Rajandra Chadra; Datta, Bimal Kumar

2014-01-01

In this paper, we have described two dreadfully important methods to solve nonlinear partial differential equations which are known as exp-function and the exp(-ϕ(ξ)) -expansion method. Recently, there are several methods to use for finding analytical solutions of the nonlinear partial differential equations. The methods are diverse and useful for solving the nonlinear evolution equations. With the help of these methods, we are investigated the exact travelling wave solutions of the Vakhnenko- Parkes equation. The obtaining soliton solutions of this equation are described many physical phenomena for weakly nonlinear surface and internal waves in a rotating ocean. Further, three-dimensional plots of the solutions such as solitons, singular solitons, bell type solitary wave i.e. non-topological solitons solutions and periodic solutions are also given to visualize the dynamics of the equation.

A Survey of Synoptic Waves over West Africa

NASA Astrophysics Data System (ADS)

Cheng, Yuan-Ming; Thorncroft, Chris D.; Kiladis, George N.

2017-04-01

Motivated by the pronounced wave-to-wave variability in African easterly wave (AEW) circulation, the three-dimensional structure of synoptic waves over West Africa is revisited with an Empirical Orthogonal Function (EOF) approach to isolate the dominant wave pattern. In this talk we present results of EOF analyses conducted with brightness temperature (Tb) derived from satellite observation and meridional wind at multiple levels from reanalysis data to examine the characteristics and variability of synoptic waves. The structure of waves is extracted by projecting the wind fields and Tb onto the principle components associated with EOF patterns of appropriately filtered parameters. The Tb EOF shows a confined AEW circulation centered around 7.5°N and a distinct evolution of convection within the wave in line with previous research. However, in striking contrast to the confined flow pattern in the Tb EOF, the EOF of 700-hPa meridional wind is distinguished by a meridionally broad AEW circulation. While the peak in circulation is centered around 10°N, there is marked cross-equatorial flow that is associated with an antisymmetric geopotential signature across the equator. This suggests the presence of a mixed Rossby-gravity wave (MRG) structure consistent with Matsuno's shallow water theory. Granted that the vast majority of studies on MRGs focus on the central and western Pacific region, this "hybrid" between AEWs and MRGs over West Africa and Atlantic sector has received little attention and more work regarding the nature and causes of its wave structure and behavior is needed. In addition, an upper-level synoptic wave is captured by EOFs of 200-hPa meridional wind. The kinematic fields reveal a continental-scale wave straddling the equator that resembles an MRG. This upper-level MRG appears to develop in situ over the Horn of Africa and intensifies as it moves across the continent. The associated lower-level structure shows an AEW-like circulation but with a larger spatial extent. This finding motivates the need for more in-depth investigations of synoptic wave variability over the region including an assessment of the direction of causality between the upper-level MRG and the lower-level AEW. This study highlights the various synoptic wave structures over West Africa and their interaction with AEWs. The results suggest the variability of AEW activity could be modulated by, in addition to the large-scale environment, other synoptic waves in the region. We will pursue the EOF approach to shed light on the characteristics and causes of the variability in synoptic wave activity over West Africa.

Generalization of the Euler-type solution to the wave equation

NASA Astrophysics Data System (ADS)

Borisov, Victor V.

2001-08-01

Generalization of the Euler-type solution to the wave equation is given. Peculiarities of the space-time structure of obtained waves are considered. For some particular cases interpretation of these waves as `subliminal' and `superluminal' is discussed. The possibility of description of electromagnetic waves by means of the scalar solutions is shown.

Probability density functions for radial anisotropy: implications for the upper 1200 km of the mantle

NASA Astrophysics Data System (ADS)

Beghein, Caroline; Trampert, Jeannot

2004-01-01

The presence of radial anisotropy in the upper mantle, transition zone and top of the lower mantle is investigated by applying a model space search technique to Rayleigh and Love wave phase velocity models. Probability density functions are obtained independently for S-wave anisotropy, P-wave anisotropy, intermediate parameter η, Vp, Vs and density anomalies. The likelihoods for P-wave and S-wave anisotropy beneath continents cannot be explained by a dry olivine-rich upper mantle at depths larger than 220 km. Indeed, while shear-wave anisotropy tends to disappear below 220 km depth in continental areas, P-wave anisotropy is still present but its sign changes compared to the uppermost mantle. This could be due to an increase with depth of the amount of pyroxene relative to olivine in these regions, although the presence of water, partial melt or a change in the deformation mechanism cannot be ruled out as yet. A similar observation is made for old oceans, but not for young ones where VSH> VSV appears likely down to 670 km depth and VPH> VPV down to 400 km depth. The change of sign in P-wave anisotropy seems to be qualitatively correlated with the presence of the Lehmann discontinuity, generally observed beneath continents and some oceans but not beneath ridges. Parameter η shows a similar age-related depth pattern as shear-wave anisotropy in the uppermost mantle and it undergoes the same change of sign as P-wave anisotropy at 220 km depth. The ratio between dln Vs and dln Vp suggests that a chemical component is needed to explain the anomalies in most places at depths greater than 220 km. More tests are needed to infer the robustness of the results for density, but they do not affect the results for anisotropy.

On the integrable elliptic cylindrical Kadomtsev-Petviashvili equation.

PubMed

Khusnutdinova, K R; Klein, C; Matveev, V B; Smirnov, A O

2013-03-01

There exist two versions of the Kadomtsev-Petviashvili (KP) equation, related to the Cartesian and cylindrical geometries of the waves. In this paper, we derive and study a new version, related to the elliptic cylindrical geometry. The derivation is given in the context of surface waves, but the derived equation is a universal integrable model applicable to generic weakly nonlinear weakly dispersive waves. We also show that there exist nontrivial transformations between all three versions of the KP equation associated with the physical problem formulation, and use them to obtain new classes of approximate solutions for water waves.

Two dimensional cylindrical fast magnetoacoustic solitary waves in a dust plasma

DOE Office of Scientific and Technical Information (OSTI.GOV)

Liu Haifeng; Wang Shiqing; Engineering and Technical College of Chengdu University of Technology, Leshan 614000

2011-04-15

The nonlinear fast magnetoacoustic solitary waves in a dust plasma with the combined effects of bounded cylindrical geometry and transverse perturbation are investigated in a new equation. In this regard, cylindrical Kadomtsev-Petviashvili (CKP) equation is derived using the small amplitude perturbation expansion method. Under a suitable coordinate transformation, the CKP equation can be solved analytically. It is shown that the dust cylindrical fast magnetoacoustic solitary waves can exist in the CKP equation. The present investigation may have relevance in the study of nonlinear electromagnetic soliton waves both in laboratory and astrophysical plasmas.

Dispersion relations with crossing symmetry for {pi}{pi}D- and F1-wave amplitudes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kaminski, R.

Results of implementation of dispersion relations with imposed crossing symmetry condition to description of {pi}{pi}D and F1 wave amplitudes are presented. We use relations with only one subtraction what leads to small uncertainties of results and to strong constraints for tested {pi}{pi} amplitudes. Presented equations are similar to those with one subtraction (so called GKPY equations) and to those with two subtractions (the Roy's equations) for the S and P waves. Numerical calculations are done with the S and P wave input amplitudes tested already with use of the Roy's and GKPY equations.

Effect of water depth on wind-wave frequency spectrum I. Spectral form

NASA Astrophysics Data System (ADS)

Wen, Sheng-Chang; Guan, Chang-Long; Sun, Shi-Cai; Wu, Ke-Jian; Zhang, Da-Cuo

1996-06-01

Wen et al's method developed to obtain wind-wave frequency spectrum in deep water was used to derive the spectrum in finite depth water. The spectrum S(ω) (ω being angular frequency) when normalized with the zeroth moment m 0 and peak frequency {ie97-1}, contains in addition to the peakness factor {ie97-2} a depth parameter η=(2π m o)1/2/ d ( d being water depth), so the spectrum behavior can be studied for different wave growth stages and water depths.

Modified method of simplest equation: Powerful tool for obtaining exact and approximate traveling-wave solutions of nonlinear PDEs

NASA Astrophysics Data System (ADS)

Vitanov, Nikolay K.

2011-03-01

We discuss the class of equations ∑i,j=0mAij(u){∂iu}/{∂ti}∂+∑k,l=0nBkl(u){∂ku}/{∂xk}∂=C(u) where Aij( u), Bkl( u) and C( u) are functions of u( x, t) as follows: (i) Aij, Bkl and C are polynomials of u; or (ii) Aij, Bkl and C can be reduced to polynomials of u by means of Taylor series for small values of u. For these two cases the above-mentioned class of equations consists of nonlinear PDEs with polynomial nonlinearities. We show that the modified method of simplest equation is powerful tool for obtaining exact traveling-wave solution of this class of equations. The balance equations for the sub-class of traveling-wave solutions of the investigated class of equations are obtained. We illustrate the method by obtaining exact traveling-wave solutions (i) of the Swift-Hohenberg equation and (ii) of the generalized Rayleigh equation for the cases when the extended tanh-equation or the equations of Bernoulli and Riccati are used as simplest equations.

Trends of Abutment-Scour Prediction Equations Applied to 144 Field Sites in South Carolina

USGS Publications Warehouse

Benedict, Stephen T.; Deshpande, Nikhil; Aziz, Nadim M.; Conrads, Paul

2006-01-01

The U.S. Geological Survey conducted a study in cooperation with the Federal Highway Administration in which predicted abutment-scour depths computed with selected predictive equations were compared with field measurements of abutment-scour depth made at 144 bridges in South Carolina. The assessment used five equations published in the Fourth Edition of 'Evaluating Scour at Bridges,' (Hydraulic Engineering Circular 18), including the original Froehlich, the modified Froehlich, the Sturm, the Maryland, and the HIRE equations. An additional unpublished equation also was assessed. Comparisons between predicted and observed scour depths are intended to illustrate general trends and order-of-magnitude differences for the prediction equations. Field measurements were taken during non-flood conditions when the hydraulic conditions that caused the scour generally are unknown. The predicted scour depths are based on hydraulic conditions associated with the 100-year flow at all sites and the flood of record for 35 sites. Comparisons showed that predicted scour depths frequently overpredict observed scour and at times were excessive. The comparison also showed that underprediction occurred, but with less frequency. The performance of these equations indicates that they are poor predictors of abutment-scour depth in South Carolina, and it is probable that poor performance will occur when the equations are applied in other geographic regions. Extensive data and graphs used to compare predicted and observed scour depths in this study were compiled into spreadsheets and are included in digital format with this report. In addition to the equation-comparison data, Water-Surface Profile Model tube-velocity data, soil-boring data, and selected abutment-scour data are included in digital format with this report. The digital database was developed as a resource for future researchers and is especially valuable for evaluating the reasonableness of future equations that may be developed.

Quantitative Estimation of Seismic Velocity Changes Using Time-Lapse Seismic Data and Elastic-Wave Sensitivity Approach

NASA Astrophysics Data System (ADS)

Denli, H.; Huang, L.

2008-12-01

Quantitative monitoring of reservoir property changes is essential for safe geologic carbon sequestration. Time-lapse seismic surveys have the potential to effectively monitor fluid migration in the reservoir that causes geophysical property changes such as density, and P- and S-wave velocities. We introduce a novel method for quantitative estimation of seismic velocity changes using time-lapse seismic data. The method employs elastic sensitivity wavefields, which are the derivatives of elastic wavefield with respect to density, P- and S-wave velocities of a target region. We derive the elastic sensitivity equations from analytical differentiations of the elastic-wave equations with respect to seismic-wave velocities. The sensitivity equations are coupled with the wave equations in a way that elastic waves arriving in a target reservoir behave as a secondary source to sensitivity fields. We use a staggered-grid finite-difference scheme with perfectly-matched layers absorbing boundary conditions to simultaneously solve the elastic-wave equations and the elastic sensitivity equations. By elastic-wave sensitivities, a linear relationship between relative seismic velocity changes in the reservoir and time-lapse seismic data at receiver locations can be derived, which leads to an over-determined system of equations. We solve this system of equations using a least- square method for each receiver to obtain P- and S-wave velocity changes. We validate the method using both surface and VSP synthetic time-lapse seismic data for a multi-layered model and the elastic Marmousi model. Then we apply it to the time-lapse field VSP data acquired at the Aneth oil field in Utah. A total of 10.5K tons of CO2 was injected into the oil reservoir between the two VSP surveys for enhanced oil recovery. The synthetic and field data studies show that our new method can quantitatively estimate changes in seismic velocities within a reservoir due to CO2 injection/migration.

Almost analytical Karhunen-Loeve representation of irregular waves based on the prolate spheroidal wave functions

NASA Astrophysics Data System (ADS)

Lee, Gibbeum; Cho, Yeunwoo

2017-11-01

We present an almost analytical new approach to solving the matrix eigenvalue problem or the integral equation in Karhunen-Loeve (K-L) representation of random data such as irregular ocean waves. Instead of solving this matrix eigenvalue problem purely numerically, which may suffer from the computational inaccuracy for big data, first, we consider a pair of integral and differential equations, which are related to the so-called prolate spheroidal wave functions (PSWF). For the PSWF differential equation, the pair of the eigenvectors (PSWF) and eigenvalues can be obtained from a relatively small number of analytical Legendre functions. Then, the eigenvalues in the PSWF integral equation are expressed in terms of functional values of the PSWF and the eigenvalues of the PSWF differential equation. Finally, the analytically expressed PSWFs and the eigenvalues in the PWSF integral equation are used to form the kernel matrix in the K-L integral equation for the representation of exemplary wave data; ordinary irregular waves and rogue waves. We found that the present almost analytical method is better than the conventional data-independent Fourier representation and, also, the conventional direct numerical K-L representation in terms of both accuracy and computational cost. This work was supported by the National Research Foundation of Korea (NRF). (NRF-2017R1D1A1B03028299).

Soliton solutions to the fifth-order Korteweg-de Vries equation and their applications to surface and internal water waves

NASA Astrophysics Data System (ADS)

Khusnutdinova, K. R.; Stepanyants, Y. A.; Tranter, M. R.

2018-02-01

We study solitary wave solutions of the fifth-order Korteweg-de Vries equation which contains, besides the traditional quadratic nonlinearity and third-order dispersion, additional terms including cubic nonlinearity and fifth order linear dispersion, as well as two nonlinear dispersive terms. An exact solitary wave solution to this equation is derived, and the dependence of its amplitude, width, and speed on the parameters of the governing equation is studied. It is shown that the derived solution can represent either an embedded or regular soliton depending on the equation parameters. The nonlinear dispersive terms can drastically influence the existence of solitary waves, their nature (regular or embedded), profile, polarity, and stability with respect to small perturbations. We show, in particular, that in some cases embedded solitons can be stable even with respect to interactions with regular solitons. The results obtained are applicable to surface and internal waves in fluids, as well as to waves in other media (plasma, solid waveguides, elastic media with microstructure, etc.).

Nonlinear coherent structures of Alfvén wave in a collisional plasma

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jana, Sayanee; Chakrabarti, Nikhil; Ghosh, Samiran

2016-07-15

The Alfvén wave dynamics is investigated in the framework of two-fluid approach in a compressible collisional magnetized plasma. In the finite amplitude limit, the dynamics of the nonlinear Alfvén wave is found to be governed by a modified Korteweg-de Vries Burgers equation (mKdVB). In this mKdVB equation, the electron inertia is found to act as a source of dispersion, and the electron-ion collision serves as a dissipation. The collisional dissipation is eventually responsible for the Burgers term in mKdVB equation. In the long wavelength limit, this weakly nonlinear Alfvén wave is shown to be governed by a damped nonlinear Schrödingermore » equation. Furthermore, these nonlinear equations are analyzed by means of analytical calculation and numerical simulation to elucidate the various aspects of the phase-space dynamics of the nonlinear wave. Results reveal that nonlinear Alfvén wave exhibits the dissipation mediated shock, envelope, and breather like structures. Numerical simulations also predict the formation of dissipative Alfvénic rogue wave, giant breathers, and rogue wave holes. These results are discussed in the context of the space plasma.« less

Prediction of Skin Temperature Distribution in Cosmetic Laser Surgery

NASA Astrophysics Data System (ADS)

Ting, Kuen; Chen, Kuen-Tasnn; Cheng, Shih-Feng; Lin, Wen-Shiung; Chang, Cheng-Ren

2008-01-01

The use of lasers in cosmetic surgery has increased dramatically in the past decade. To achieve minimal damage to tissues, the study of the temperature distribution of skin in laser irradiation is very important. The phenomenon of the thermal wave effect is significant due to the highly focused light energy of lasers in very a short time period. The conventional Pennes equation does not take the thermal wave effect into account, which the thermal relaxation time (τ) is neglected, so it is not sufficient to solve instantaneous heating and cooling problem. The purpose of this study is to solve the thermal wave equation to determine the realistic temperature distribution during laser surgery. The analytic solutions of the thermal wave equation are compared with those of the Pennes equation. Moreover, comparisons are made between the results of the above equations and the results of temperature measurement using an infrared thermal image instrument. The thermal wave equation could likely to predict the skin temperature distribution in cosmetic laser surgery.

Nonlinear Waves In A Stenosed Elastic Tube Filled With Viscous Fluid: Forced Perturbed Korteweg-De Vries Equation

NASA Astrophysics Data System (ADS)

Gaik*, Tay Kim; Demiray, Hilmi; Tiong, Ong Chee

In the present work, treating the artery as a prestressed thin-walled and long circularly cylindrical elastic tube with a mild symmetrical stenosis and the blood as an incompressible Newtonian fluid, we have studied the pro pagation of weakly nonlinear waves in such a composite medium, in the long wave approximation, by use of the reductive perturbation method. By intro ducing a set of stretched coordinates suitable for the boundary value type of problems and expanding the field variables into asymptotic series of the small-ness parameter of nonlinearity and dispersion, we obtained a set of nonlinear differential equations governing the terms at various order. By solving these nonlinear differential equations, we obtained the forced perturbed Korteweg-de Vries equation with variable coefficient as the nonlinear evolution equation. By use of the coordinate transformation, it is shown that this type of nonlinear evolution equation admits a progressive wave solution with variable wave speed.

Optical Kerr spatiotemporal dark extreme waves

NASA Astrophysics Data System (ADS)

Wabnitz, Stefan; Kodama, Yuji; Baronio, Fabio

2018-02-01

We study the existence and propagation of multidimensional dark non-diffractive and non-dispersive spatiotemporal optical wave-packets in nonlinear Kerr media. We report analytically and confirm numerically the properties of spatiotemporal dark lines, X solitary waves and lump solutions of the (2 + 1)D nonlinear Schr odinger equation (NLSE). Dark lines, X waves and lumps represent holes of light on a continuous wave background. These solitary waves are derived by exploiting the connection between the (2 + 1)D NLSE and a well-known equation of hydrodynamics, namely the (2+1)D Kadomtsev-Petviashvili (KP) equation. This finding opens a novel path for the excitation and control of spatiotemporal optical solitary and rogue waves, of hydrodynamic nature.

Nonlinear Drift-Kinetic Equation in the Presence of a Circularly Polarized Wave

NASA Technical Reports Server (NTRS)

Khazanov, G. V.; Krivorutsky, E. N.; Six, N. Frank (Technical Monitor)

2002-01-01

Equations of the single particle motion and nonlinear kinetic equation for plasma in the presence of a circularly polarized wave of arbitrary frequency in the drift approximation are presented. The nonstationarity and inhomogeneity of the plasma-wave system are taken into account. The time dependent part of the ponderomotive force is discussed.

Exact traveling wave solutions for system of nonlinear evolution equations.

PubMed

Khan, Kamruzzaman; Akbar, M Ali; Arnous, Ahmed H

2016-01-01

In this work, recently deduced generalized Kudryashov method is applied to the variant Boussinesq equations, and the (2 + 1)-dimensional breaking soliton equations. As a result a range of qualitative explicit exact traveling wave solutions are deduced for these equations, which motivates us to develop, in the near future, a new approach to obtain unsteady solutions of autonomous nonlinear evolution equations those arise in mathematical physics and engineering fields. It is uncomplicated to extend this method to higher-order nonlinear evolution equations in mathematical physics. And it should be possible to apply the same method to nonlinear evolution equations having more general forms of nonlinearities by utilizing the traveling wave hypothesis.

Traveltime delay relative to the maximum energy of the wave train for dispersive tsunamis propagating across the Pacific Ocean: the case of 2010 and 2015 Chilean Tsunamis

NASA Astrophysics Data System (ADS)

Poupardin, A.; Heinrich, P.; Hébert, H.; Schindelé, F.; Jamelot, A.; Reymond, D.; Sugioka, H.

2018-05-01

This paper evaluates the importance of frequency dispersion in the propagation of recent trans-Pacific tsunamis. Frequency dispersion induces a time delay for the most energetic waves, which increases for long propagation distances and short source dimensions. To calculate this time delay, propagation of tsunamis is simulated and analyzed from spectrograms of time-series at specific gauges in the Pacific Ocean. One- and two-dimensional simulations are performed by solving either shallow water or Boussinesq equations and by considering realistic seismic sources. One-dimensional sensitivity tests are first performed in a constant-depth channel to study the influence of the source width. Two-dimensional tests are then performed in a simulated Pacific Ocean with a 4000-m constant depth and by considering tectonic sources of 2010 and 2015 Chilean earthquakes. For these sources, both the azimuth and the distance play a major role in the frequency dispersion of tsunamis. Finally, simulations are performed considering the real bathymetry of the Pacific Ocean. Multiple reflections, refractions as well as shoaling of waves result in much more complex time series for which the effects of the frequency dispersion are hardly discernible. The main point of this study is to evaluate frequency dispersion in terms of traveltime delays by calculating spectrograms for a time window of 6 hours after the arrival of the first wave. Results of the spectral analysis show that the wave packets recorded by pressure and tide sensors in the Pacific Ocean seem to be better reproduced by the Boussinesq model than the shallow water model and approximately follow the theoretical dispersion relationship linking wave arrival times and frequencies. Additionally, a traveltime delay is determined above which effects of frequency dispersion are considered to be significant in terms of maximum surface elevations.

Electromagnetic Ion Cyclotron Wavefields in a Realistic Dipole Field

NASA Astrophysics Data System (ADS)

Denton, R. E.

2018-02-01

The latitudinal distribution and properties of electromagnetic ion cyclotron (EMIC) waves determine the total effect of those waves on relativistic electrons. Here we describe the latitudinal variation of EMIC waves simulated self-consistently in a dipole magnetic field for a plasmasphere or plume-like plasma at geostationary orbit with cold H+, He+, and O+ and hot protons with temperature anisotropy. The waves grow as they propagate away from the magnetic equator to higher latitude, while the wave vector turns outward radially and the polarization becomes linear. We calculate the detailed wave spectrum in four latitudinal ranges varying from magnetic latitude (MLAT) close to 0° (magnetic equator) up to 21°. The strongest waves are propagating away from the magnetic equator, but some wave power propagating toward the magnetic equator is observed due to local generation (especially close to the magnetic equator) or reflection. The He band waves, which are generated relatively high up on their dispersion surface, are able to propagate all the way to MLAT = 21°, but the H band waves experience frequency filtering, with no equatorial waves propagating to MLAT = 21° and only the higher-frequency waves propagating to MLAT = 14°. The result is that the wave power averaged k∥, which determines the relativistic electron minimum resonance energy, scales like the inverse of the local magnetic field for the He mode, whereas it is almost constant for the H mode. While the perpendicular wave vector turns outward, it broadens. These wavefields should be useful for simulations of radiation belt particle dynamics.

A Relation Between the Eikonal Equation Associated to a Potential Energy Surface and a Hyperbolic Wave Equation.

PubMed

Bofill, Josep Maria; Quapp, Wolfgang; Caballero, Marc

2012-12-11

The potential energy surface (PES) of a molecule can be decomposed into equipotential hypersurfaces. We show in this article that the hypersurfaces are the wave fronts of a certain hyperbolic partial differential equation, a wave equation. It is connected with the gradient lines, or the steepest descent, or the steepest ascent lines of the PES. The energy seen as a reaction coordinate plays the central role in this treatment.

Nonlinear extraordinary wave in dense plasma

DOE Office of Scientific and Technical Information (OSTI.GOV)

Krasovitskiy, V. B., E-mail: krasovit@mail.ru; Turikov, V. A.

2013-10-15

Conditions for the propagation of a slow extraordinary wave in dense magnetized plasma are found. A solution to the set of relativistic hydrodynamic equations and Maxwell’s equations under the plasma resonance conditions, when the phase velocity of the nonlinear wave is equal to the speed of light, is obtained. The deviation of the wave frequency from the resonance frequency is accompanied by nonlinear longitudinal-transverse oscillations. It is shown that, in this case, the solution to the set of self-consistent equations obtained by averaging the initial equations over the period of high-frequency oscillations has the form of an envelope soliton. Themore » possibility of excitation of a nonlinear wave in plasma by an external electromagnetic pulse is confirmed by numerical simulations.« less

An ansatz for solving nonlinear partial differential equations in mathematical physics.

PubMed

Akbar, M Ali; Ali, Norhashidah Hj Mohd

2016-01-01

In this article, we introduce an ansatz involving exact traveling wave solutions to nonlinear partial differential equations. To obtain wave solutions using direct method, the choice of an appropriate ansatz is of great importance. We apply this ansatz to examine new and further general traveling wave solutions to the (1+1)-dimensional modified Benjamin-Bona-Mahony equation. Abundant traveling wave solutions are derived including solitons, singular solitons, periodic solutions and general solitary wave solutions. The solutions emphasize the nobility of this ansatz in providing distinct solutions to various tangible phenomena in nonlinear science and engineering. The ansatz could be more efficient tool to deal with higher dimensional nonlinear evolution equations which frequently arise in many real world physical problems.

Study on monostable and bistable reaction-diffusion equations by iteration of travelling wave maps

NASA Astrophysics Data System (ADS)

Yi, Taishan; Chen, Yuming

2017-12-01

In this paper, based on the iterative properties of travelling wave maps, we develop a new method to obtain spreading speeds and asymptotic propagation for monostable and bistable reaction-diffusion equations. Precisely, for Dirichlet problems of monostable reaction-diffusion equations on the half line, by making links between travelling wave maps and integral operators associated with the Dirichlet diffusion kernel (the latter is NOT invariant under translation), we obtain some iteration properties of the Dirichlet diffusion and some a priori estimates on nontrivial solutions of Dirichlet problems under travelling wave transformation. We then provide the asymptotic behavior of nontrivial solutions in the space-time region for Dirichlet problems. These enable us to develop a unified method to obtain results on heterogeneous steady states, travelling waves, spreading speeds, and asymptotic spreading behavior for Dirichlet problem of monostable reaction-diffusion equations on R+ as well as of monostable/bistable reaction-diffusion equations on R.

Spatio-temporal evolutions of non-orthogonal equatorial wave modes derived from observations

NASA Astrophysics Data System (ADS)

Barton, Cory

Equatorial waves have been studied extensively due to their importance to the tropical climate and weather systems. Historically, their activity is diagnosed mainly in the wavenumber-frequency domain. Recently, many studies have projected observational data onto parabolic cylinder functions (PCFs), which represent the meridional structure of individual wave modes, to attain time-dependent spatial wave structures. The non-orthogonality of wave modes has yet posed a problem when attempting to separate data into wave fields where the waves project onto the same structure functions. We propose the development and application of a new methodology for equatorial wave expansion of instantaneous flows using the full equatorial wave spectrum. By creating a mapping from the meridional structure function amplitudes to the equatorial wave class amplitudes, we are able to diagnose instantaneous wave fields and determine their evolution. Because all meridional modes are shared by some subset of the wave classes, we require constraints on the wave class amplitudes to yield a closed system with a unique solution for all waves' spatial structures, including IG waves. A synthetic field is analyzed using this method to determine its accuracy for data of a single vertical mode. The wave class spectra diagnosed using this method successfully match the correct dispersion curves even if the incorrect depth is chosen for the spatial decomposition. In the case of more than one depth scale, waves with varying equivalent depth may be similarly identified using the dispersion curves. The primary vertical mode is the 200 m equivalent depth mode, which is that of the peak projection response. A distinct spectral power peak along the Kelvin wave dispersion curve for this value validates our choice of equivalent depth, although the possibility of depth varying with time and height is explored. The wave class spectra diagnosed assuming this depth scale mostly match their expected dispersion curves, showing that this method successfully partitions the wave spectra by calculating wave amplitudes in physical space. This is particularly striking because the time evolution, and therefore the frequency characteristics, is determined simply by a timeseries of independently-diagnosed instantaneous horizontal fields. We use the wave fields diagnosed by this method to study wave evolution in the context of the stratospheric QBO of zonal wind, confirming the continuous evolution of the selection mechanism for equatorial waves in the middle atmosphere. The amplitude cycle synchronized with the background zonal wind as predicted by QBO theory is present in the wave class fields even though the dynamics are not forced by the method itself. We have additionally identified a time-evolution of the zonal wavenumber spectrum responsible for the amplitude variability in physical space. Similar to the temporal characteristics, the vertical structures are also the result of a simple height cross-section through multiple independently-diagnosed levels.

Helical localized wave solutions of the scalar wave equation.

PubMed

Overfelt, P L

2001-08-01

A right-handed helical nonorthogonal coordinate system is used to determine helical localized wave solutions of the homogeneous scalar wave equation. Introducing the characteristic variables in the helical system, i.e., u = zeta - ct and v = zeta + ct, where zeta is the coordinate along the helical axis, we can use the bidirectional traveling plane wave representation and obtain sets of elementary bidirectional helical solutions to the wave equation. Not only are these sets bidirectional, i.e., based on a product of plane waves, but they may also be broken up into right-handed and left-handed solutions. The elementary helical solutions may in turn be used to create general superpositions, both Fourier and bidirectional, from which new solutions to the wave equation may be synthesized. These new solutions, based on the helical bidirectional superposition, are members of the class of localized waves. Examples of these new solutions are a helical fundamental Gaussian focus wave mode, a helical Bessel-Gauss pulse, and a helical acoustic directed energy pulse train. Some of these solutions have the interesting feature that their shape and localization properties depend not only on the wave number governing propagation along the longitudinal axis but also on the normalized helical pitch.

Target-in-the-loop beam control: basic considerations for analysis and wave-front sensing

NASA Astrophysics Data System (ADS)

Vorontsov, Mikhail A.; Kolosov, Valeriy

2005-01-01

Target-in-the-loop (TIL) wave propagation geometry represents perhaps the most challenging case for adaptive optics applications that are related to maximization of irradiance power density on extended remotely located surfaces in the presence of dynamically changing refractive-index inhomogeneities in the propagation medium. We introduce a TIL propagation model that uses a combination of the parabolic equation describing coherent outgoing-wave propagation, and the equation describing evolution of the mutual correlation function (MCF) for the backscattered wave (return wave). The resulting evolution equation for the MCF is further simplified by use of the smooth-refractive-index approximation. This approximation permits derivation of the transport equation for the return-wave brightness function, analyzed here by the method of characteristics (brightness function trajectories). The equations for the brightness function trajectories (ray equations) can be efficiently integrated numerically. We also consider wave-front sensors that perform sensing of speckle-averaged characteristics of the wave-front phase (TIL sensors). Analysis of the wave-front phase reconstructed from Shack-Hartmann TIL sensor measurements shows that an extended target introduces a phase modulation (target-induced phase) that cannot be easily separated from the atmospheric-turbulence-related phase aberrations. We also show that wave-front sensing results depend on the extended target shape, surface roughness, and outgoing-beam intensity distribution on the target surface. For targets with smooth surfaces and nonflat shapes, the target-induced phase can contain aberrations. The presence of target-induced aberrations in the conjugated phase may result in a deterioration of adaptive system performance.

Target-in-the-loop beam control: basic considerations for analysis and wave-front sensing.

PubMed

Vorontsov, Mikhail A; Kolosov, Valeriy

2005-01-01

Target-in-the-loop (TIL) wave propagation geometry represents perhaps the most challenging case for adaptive optics applications that are related to maximization of irradiance power density on extended remotely located surfaces in the presence of dynamically changing refractive-index inhomogeneities in the propagation medium. We introduce a TIL propagation model that uses a combination of the parabolic equation describing coherent outgoing-wave propagation, and the equation describing evolution of the mutual correlation function (MCF) for the backscattered wave (return wave). The resulting evolution equation for the MCF is further simplified by use of the smooth-refractive-index approximation. This approximation permits derivation of the transport equation for the return-wave brightness function, analyzed here by the method of characteristics (brightness function trajectories). The equations for the brightness function trajectories (ray equations) can be efficiently integrated numerically. We also consider wave-front sensors that perform sensing of speckle-averaged characteristics of the wave-front phase (TIL sensors). Analysis of the wave-front phase reconstructed from Shack-Hartmann TIL sensor measurements shows that an extended target introduces a phase modulation (target-induced phase) that cannot be easily separated from the atmospheric-turbulence-related phase aberrations. We also show that wave-front sensing results depend on the extended target shape, surface roughness, and outgoing-beam intensity distribution on the target surface. For targets with smooth surfaces and nonflat shapes, the target-induced phase can contain aberrations. The presence of target-induced aberrations in the conjugated phase may result in a deterioration of adaptive system performance.

Exploring the Alfven-Wave Acceleration of Auroral Electrons in the Laboratory

NASA Astrophysics Data System (ADS)

Schroeder, James William Ryan

Inertial Alfven waves occur in plasmas where the Alfven speed is greater than the electron thermal speed and the scale of wave field structure across the background magnetic field is comparable to the electron skin depth. Such waves have an electric field aligned with the background magnetic field that can accelerate electrons. It is likely that electrons are accelerated by inertial Alfven waves in the auroral magnetosphere and contribute to the generation of auroras. While rocket and satellite measurements show a high level of coincidence between inertial Alfven waves and auroral activity, definitive measurements of electrons being accelerated by inertial Alfven waves are lacking. Continued uncertainty stems from the difficulty of making a conclusive interpretation of measurements from spacecraft flying through a complex and transient process. A laboratory experiment can avoid some of the ambiguity contained in spacecraft measurements. Experiments have been performed in the Large Plasma Device (LAPD) at UCLA. Inertial Alfven waves were produced while simultaneously measuring the suprathermal tails of the electron distribution function. Measurements of the distribution function use resonant absorption of whistler mode waves. During a burst of inertial Alfven waves, the measured portion of the distribution function oscillates at the Alfven wave frequency. The phase space response of the electrons is well-described by a linear solution to the Boltzmann equation. Experiments have been repeated using electrostatic and inductive Alfven wave antennas. The oscillation of the distribution function is described by a purely Alfvenic model when the Alfven wave is produced by the inductive antenna. However, when the electrostatic antenna is used, measured oscillations of the distribution function are described by a model combining Alfvenic and non-Alfvenic effects. Indications of a nonlinear interaction between electrons and inertial Alfven waves are present in recent data.

Thermophysical Fluid Dynamics: the Key to the Structures of Fluid Objects

NASA Astrophysics Data System (ADS)

Houben, H.

2013-12-01

It has become customary to model the hydrodynamics of fluid planets like Jupiter and Saturn by spinning up general circulation models until they reach a statistical steady state. This approach is physically sound, based on the thermodynamic expectation that the system will eventually achieve a state of maximum entropy, but the models have not been specifically designed for this purpose. Over the course of long integrations, numerical artifacts can drive the system to a state that does not correspond to the physically realistic end state. A different formulation of the governing equations promises better results. The equations of motion are recast as scalar conservation laws in which the diabatic and irreversible terms (both entropy-changing) are clearly identified. The balance between these terms defines the steady state of the system analytically, without the need for any temporal integrations. The conservation of mass in this system is trivial. Conservation of angular momentum replaces the zonal momentum equation and determines the zonal wind from a balance between the tidal torque and frictional dissipation. The principle of wave-mean flow non-interaction is preserved. Bernoulli's Theorem replaces the energy equation. The potential temperature structure is determined by the balance between work done against friction and heat transfer by convection and radiation. An equation of state and the traditional momentum equations in the meridional plane are sufficient to complete the model. Based on the assumption that the final state vertical and meridional winds are small compared to the zonal wind (in any case they are impossible to predict ab initio as they are driven by wave flux convergences), these last equations determine the pressure and density (and hence gravity) fields of the basic state. The thermal wind relation (in its most general form with the axial derivative of the zonal wind balancing the baroclinicity) is preserved. The model is not hydrostatic (in the sense used in planetary modeling) and the zonal wind is not constant on cylinders. Rather, the zonal wind falls off more rapidly with depth --- at least as fast as r3. A similar reformulation of the equations of magnetohydrodynamics is possible. It is found that wave-mean flow non-interaction extends to Alfven waves. Bernoulli's Theorem is augmented by the Poynting Theorem. The components of the traditional dynamo equation can be written as conservation laws. Only a single element of the alpha tensor contributes to the generation of axisymmetric magnetic fields and the mean meridional circulation provides a significant feedback, quenching the omega effect and limiting the amplitudes of non-axisymmetric fields. Thus analytic models are available for all the state variables of Jupiter and Saturn. The unknown independent variables are terms in the equation of state, the eddy viscosity and heat transport coefficients, the magnetic resistivity, and the strength of the tidal torques (which are dependent on the vertical structure of the planet's troposphere). By making new measurements of the atmospheric structure and higher order gravitational moments of Jupiter, JUNO has the potential to constrain these unknowns and contribute greatly to our understanding of the interior of that planet.

Model Parameterization and P-wave AVA Direct Inversion for Young's Impedance

NASA Astrophysics Data System (ADS)

Zong, Zhaoyun; Yin, Xingyao

2017-05-01

AVA inversion is an important tool for elastic parameters estimation to guide the lithology prediction and "sweet spot" identification of hydrocarbon reservoirs. The product of the Young's modulus and density (named as Young's impedance in this study) is known as an effective lithology and brittleness indicator of unconventional hydrocarbon reservoirs. Density is difficult to predict from seismic data, which renders the estimation of the Young's impedance inaccurate in conventional approaches. In this study, a pragmatic seismic AVA inversion approach with only P-wave pre-stack seismic data is proposed to estimate the Young's impedance to avoid the uncertainty brought by density. First, based on the linearized P-wave approximate reflectivity equation in terms of P-wave and S-wave moduli, the P-wave approximate reflectivity equation in terms of the Young's impedance is derived according to the relationship between P-wave modulus, S-wave modulus, Young's modulus and Poisson ratio. This equation is further compared to the exact Zoeppritz equation and the linearized P-wave approximate reflectivity equation in terms of P- and S-wave velocities and density, which illustrates that this equation is accurate enough to be used for AVA inversion when the incident angle is within the critical angle. Parameter sensitivity analysis illustrates that the high correlation between the Young's impedance and density render the estimation of the Young's impedance difficult. Therefore, a de-correlation scheme is used in the pragmatic AVA inversion with Bayesian inference to estimate Young's impedance only with pre-stack P-wave seismic data. Synthetic examples demonstrate that the proposed approach is able to predict the Young's impedance stably even with moderate noise and the field data examples verify the effectiveness of the proposed approach in Young's impedance estimation and "sweet spots" evaluation.

Development and testing of a simple inertial formulation of the shallow water equations for flood inundation modelling

NASA Astrophysics Data System (ADS)

Fewtrell, Timothy; Bates, Paul; Horritt, Matthew

2010-05-01

This abstract describes the development of a new set of equations derived from 1D shallow water theory for use in 2D storage cell inundation models. The new equation set is designed to be solved explicitly at very low computational cost, and is here tested against a suite of four analytical and numerical test cases of increasing complexity. In each case the predicted water depths compare favourably to analytical solutions or to benchmark results from the optimally stable diffusive storage cell code of Hunter et al. (2005). For the most complex test involving the fine spatial resolution simulation of flow in a topographically complex urban area the Root Mean Squared Difference between the new formulation and the model of Hunter et al. is ~1 cm. However, unlike diffusive storage cell codes where the stable time step scales with (1-?x)2 the new equation set developed here represents shallow water wave propagation and so the stability is controlled by the Courant-Freidrichs-Lewy condition such that the stable time step instead scales with 1-?x. This allows use of a stable time step that is 1-3 orders of magnitude greater for typical cell sizes than that possible with diffusive storage cell models and results in commensurate reductions in model run times. The maximum speed up achieved over a diffusive storage cell model was 1120x in these tests, although the actual value seen will depend on model resolution and water depth and surface gradient. Solutions using the new equation set are shown to be relatively grid-independent for the conditions considered given the numerical diffusion likely at coarse model resolution. In addition, the inertial formulation appears to have an intuitively correct sensitivity to friction, however small instabilities and increased errors on predicted depth were noted when Manning's n = 0.01. These small instabilities are likely to be a result of the numerical scheme employed, whereby friction is acting to stabilise the solution although this scheme is still widely used in practice. The new equations are likely to find widespread application in many types of flood inundation modelling and should provide a useful additional tool, alongside more established model formulations, for a variety of flood risk management studies.

FAST TRACK COMMUNICATION Quasi self-adjoint nonlinear wave equations

NASA Astrophysics Data System (ADS)

Ibragimov, N. H.; Torrisi, M.; Tracinà, R.

2010-11-01

In this paper we generalize the classification of self-adjoint second-order linear partial differential equation to a family of nonlinear wave equations with two independent variables. We find a class of quasi self-adjoint nonlinear equations which includes the self-adjoint linear equations as a particular case. The property of a differential equation to be quasi self-adjoint is important, e.g. for constructing conservation laws associated with symmetries of the differential equation.

Wave equations on anti self dual (ASD) manifolds

NASA Astrophysics Data System (ADS)

Bashingwa, Jean-Juste; Kara, A. H.

2017-11-01

In this paper, we study and perform analyses of the wave equation on some manifolds with non diagonal metric g_{ij} which are of neutral signatures. These include the invariance properties, variational symmetries and conservation laws. In the recent past, wave equations on the standard (space time) Lorentzian manifolds have been performed but not on the manifolds from metrics of neutral signatures.

Exact traveling wave solutions of the KP-BBM equation by using the new approach of generalized (G'/G)-expansion method.

PubMed

Alam, Md Nur; Akbar, M Ali

2013-01-01

The new approach of the generalized (G'/G)-expansion method is an effective and powerful mathematical tool in finding exact traveling wave solutions of nonlinear evolution equations (NLEEs) in science, engineering and mathematical physics. In this article, the new approach of the generalized (G'/G)-expansion method is applied to construct traveling wave solutions of the Kadomtsev-Petviashvili-Benjamin-Bona-Mahony (KP-BBM) equation. The solutions are expressed in terms of the hyperbolic functions, the trigonometric functions and the rational functions. By means of this scheme, we found some new traveling wave solutions of the above mentioned equation.

High-frequency sound waves to eliminate a horizon in the mixmaster universe.

NASA Technical Reports Server (NTRS)

Chitre, D. M.

1972-01-01

From the linear wave equation for small-amplitude sound waves in a curved space-time, there is derived a geodesiclike differential equation for sound rays to describe the motion of wave packets. These equations are applied in the generic, nonrotating, homogeneous closed-model universe (the 'mixmaster universe,' Bianchi type IX). As for light rays described by Doroshkevich and Novikov (DN), these sound rays can circumnavigate the universe near the singularity to remove particle horizons only for a small class of these models and in special directions. Although these results parallel those of DN, different Hamiltonian methods are used for treating the Einstein equations.

Unstable solitary-wave solutions of the generalized Benjamin-Bona-Mahony equation

DOE Office of Scientific and Technical Information (OSTI.GOV)

McKinney, W.R.; Restrepo, J.M.; Bona, J.L.

1994-06-01

The evolution of solitary waves of the gBBM equation is investigated computationally. The experiments confirm previously derived theoretical stability estimates and, more importantly, yield insights into their behavior. For example, highly energetic unstable solitary waves when perturbed are shown to evolve into several stable solitary waves.

The nonlinear Schrödinger equation and the propagation of weakly nonlinear waves in optical fibers and on the water surface

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chabchoub, A., E-mail: achabchoub@swin.edu.au; Kibler, B.; Finot, C.

2015-10-15

The dynamics of waves in weakly nonlinear dispersive media can be described by the nonlinear Schrödinger equation (NLSE). An important feature of the equation is that it can be derived in a number of different physical contexts; therefore, analogies between different fields, such as for example fiber optics, water waves, plasma waves and Bose–Einstein condensates, can be established. Here, we investigate the similarities between wave propagation in optical Kerr media and water waves. In particular, we discuss the modulation instability (MI) in both media. In analogy to the water wave problem, we derive for Kerr-media the Benjamin–Feir index, i.e. amore » nondimensional parameter related to the probability of formation of rogue waves in incoherent wave trains.« less

KP Equation in a Three-Dimensional Unmagnetized Warm Dusty Plasma with Variable Dust Charge

NASA Astrophysics Data System (ADS)

El-Shorbagy, Kh. H.; Mahassen, Hania; El-Bendary, Atef Ahmed

2017-12-01

In this work, we investigate the propagation of three-dimensional nonlinear dust-acoustic and dust-Coulomb waves in an unmagnetized warm dusty plasma consisting of electrons, ions, and charged dust particles. The grain charge fluctuation is incorporated through the current balance equation. Using the perturbation method, a Kadomtsev-Petviashvili (KP) equation is obtained. It has been shown that the charge fluctuation would modify the wave structures, and the waves in such systems are unstable due to high-order long wave perturbations.

Physical properties of hydrated tissue determined by surface interferometry of laser-induced thermoelastic deformation

NASA Astrophysics Data System (ADS)

Dark, Marta L.; Perelman, Lev T.; Itzkan, Irving; Schaffer, Jonathan L.; Feld, Michael S.

2000-02-01

Knee meniscus is a hydrated tissue; it is a fibrocartilage of the knee joint composed primarily of water. We present results of interferometric surface monitoring by which we measure physical properties of human knee meniscal cartilage. The physical response of biological tissue to a short laser pulse is primarily thermomechanical. When the pulse is shorter than characteristic times (thermal diffusion time and acoustic relaxation time) stresses build and propagate as acoustic waves in the tissue. The tissue responds to the laser-induced stress by thermoelastic expansion. Solving the thermoelastic wave equation numerically predicts the correct laser-induced expansion. By comparing theory with experimental data, we can obtain the longitudinal speed of sound, the effective optical penetration depth and the Grüneisen coefficient. This study yields information about the laser-tissue interaction and determines properties of the meniscus samples that could be used as diagnostic parameters.

Secondary Bifurcation and Change of Type for Three Dimensional Standing Waves in Shallow Water.

DTIC Science & Technology

1986-02-01

field of standing K-P waves. A set of two non-interacting (to first order) solutions of the K-P equation ( Kadomtsev - Petviashvili 1970). The K-P equation ...P equation was first derived by Kadomtsev & Petviashvili (1970) in their study of the stability of solitary waves to transverse perturbations. A...Scientists, Springer-Verlag 6. B.A. Dubrovin (1981), "Theta Functions and Non-linear Equations ", Russian Mat. Surveys, 36, 11-92 7 B.B. Kadomtsev

Soliton and quasi-periodic wave solutions for b-type Kadomtsev-Petviashvili equation

NASA Astrophysics Data System (ADS)

Singh, Manjit; Gupta, R. K.

2017-11-01

In this paper, truncated Laurent expansion is used to obtain the bilinear equation of a nonlinear evolution equation. As an application of Hirota's method, multisoliton solutions are constructed from the bilinear equation. Extending the application of Hirota's method and employing multidimensional Riemann theta function, one and two-periodic wave solutions are also obtained in a straightforward manner. The asymptotic behavior of one and two-periodic wave solutions under small amplitude limits is presented, and their relations with soliton solutions are also demonstrated.

A Numerical Method for Predicting Rayleigh Surface Wave Velocity in Anisotropic Crystals (Postprint)

DTIC Science & Technology

2017-09-05

generalized version of the equations are very difficult to derive, even in symbolic math languages such as Mathematica. As a result, the equations are...formalism, Math . Mech. Solids 9 (1) (2004) 5–15. [8] M. Destrade, The explicit secular equation for surface acoustic waves in monoclinic elastic crystals...Q. J. Mech. Appl. Math . 55 (2) (2002) 297–311. [10] D. Taylor, Surface waves in anisotropic media: the secular equation and its numerical solution

A novel approach for solitary wave solutions of the generalized fractional Zakharov-Kuznetsov equation

NASA Astrophysics Data System (ADS)

Batool, Fiza; Akram, Ghazala

2018-01-01

In this article the solitary wave solutions of generalized fractional Zakharov-Kuznetsov (GZK) equation which appear in the electrical transmission line model are investigated. The (G'/G)-expansion method is used to obtain the solitary solutions of fractional GZK equation via local fractional derivative. Three classes of solutions, hyperbolic, trigonometric and rational wave solutions of the associated equation are characterized with some free parameters. The obtained solutions reveal that the proposed technique is effective and powerful.

Statistics of extreme waves in the framework of one-dimensional Nonlinear Schrodinger Equation

NASA Astrophysics Data System (ADS)

Agafontsev, Dmitry; Zakharov, Vladimir

2013-04-01

We examine the statistics of extreme waves for one-dimensional classical focusing Nonlinear Schrodinger (NLS) equation, iΨt + Ψxx + |Ψ |2Ψ = 0, (1) as well as the influence of the first nonlinear term beyond Eq. (1) - the six-wave interactions - on the statistics of waves in the framework of generalized NLS equation accounting for six-wave interactions, dumping (linear dissipation, two- and three-photon absorption) and pumping terms, We solve these equations numerically in the box with periodically boundary conditions starting from the initial data Ψt=0 = F(x) + ?(x), where F(x) is an exact modulationally unstable solution of Eq. (1) seeded by stochastic noise ?(x) with fixed statistical properties. We examine two types of initial conditions F(x): (a) condensate state F(x) = 1 for Eq. (1)-(2) and (b) cnoidal wave for Eq. (1). The development of modulation instability in Eq. (1)-(2) leads to formation of one-dimensional wave turbulence. In the integrable case the turbulence is called integrable and relaxes to one of infinite possible stationary states. Addition of six-wave interactions term leads to appearance of collapses that eventually are regularized by the dumping terms. The energy lost during regularization of collapses in (2) is restored by the pumping term. In the latter case the system does not demonstrate relaxation-like behavior. We measure evolution of spectra Ik =< |Ψk|2 >, spatial correlation functions and the PDFs for waves amplitudes |Ψ|, concentrating special attention on formation of "fat tails" on the PDFs. For the classical integrable NLS equation (1) with condensate initial condition we observe Rayleigh tails for extremely large waves and a "breathing region" for middle waves with oscillations of the frequency of waves appearance with time, while nonintegrable NLS equation with dumping and pumping terms (2) with the absence of six-wave interactions α = 0 demonstrates perfectly Rayleigh PDFs without any oscillations with time. In case of the cnoidal wave initial condition we observe severely non-Rayleigh PDFs for the classical NLS equation (1) with the regions corresponding to 2-, 3- and so on soliton collisions clearly seen of the PDFs. Addition of six-wave interactions in Eq. (2) for condensate initial condition results in appearance of non-Rayleigh addition to the PDFs that increase with six-wave interaction constant α and disappears with the absence of six-wave interactions α = 0. References: [1] D.S. Agafontsev, V.E. Zakharov, Rogue waves statistics in the framework of one-dimensional Generalized Nonlinear Schrodinger Equation, arXiv:1202.5763v3.

Effect of EMIC Wave Normal Angle Distribution on Relativistic Electron Scattering Based on the Newly Developed Self-consistent RC/EMIC Waves Model by Khazanov et al. [2006

NASA Technical Reports Server (NTRS)

Khazanov, G. V.; Gallagher, D. L.; Gamayunov, K.

2007-01-01

It is well known that the effects of EMIC waves on RC ion and RB electron dynamics strongly depend on such particle/wave characteristics as the phase-space distribution function, frequency, wave-normal angle, wave energy, and the form of wave spectral energy density. Therefore, realistic characteristics of EMIC waves should be properly determined by modeling the RC-EMIC waves evolution self-consistently. Such a selfconsistent model progressively has been developing by Khaznnov et al. [2002-2006]. It solves a system of two coupled kinetic equations: one equation describes the RC ion dynamics and another equation describes the energy density evolution of EMIC waves. Using this model, we present the effectiveness of relativistic electron scattering and compare our results with previous work in this area of research.

Rogue-wave bullets in a composite (2+1)D nonlinear medium.

PubMed

Chen, Shihua; Soto-Crespo, Jose M; Baronio, Fabio; Grelu, Philippe; Mihalache, Dumitru

2016-07-11

We show that nonlinear wave packets localized in two dimensions with characteristic rogue wave profiles can propagate in a third dimension with significant stability. This unique behavior makes these waves analogous to light bullets, with the additional feature that they propagate on a finite background. Bulletlike rogue-wave singlet and triplet are derived analytically from a composite (2+1)D nonlinear wave equation. The latter can be interpreted as the combination of two integrable (1+1)D models expressed in different dimensions, namely, the Hirota equation and the complex modified Korteweg-de Vries equation. Numerical simulations confirm that the generation of rogue-wave bullets can be observed in the presence of spontaneous modulation instability activated by quantum noise.

Analytical and numerical solution for wave reflection from a porous wave absorber

NASA Astrophysics Data System (ADS)

Magdalena, Ikha; Roque, Marian P.

2018-03-01

In this paper, wave reflection from a porous wave absorber is investigated theoretically and numerically. The equations that we used are based on shallow water type model. Modification of motion inside the absorber is by including linearized friction term in momentum equation and introducing a filtered velocity. Here, an analytical solution for wave reflection coefficient from a porous wave absorber over a flat bottom is derived. Numerically, we solve the equations using the finite volume method on a staggered grid. To validate our numerical model, comparison of the numerical reflection coefficient is made against the analytical solution. Further, we implement our numerical scheme to study the evolution of surface waves pass through a porous absorber over varied bottom topography.

Depth-variant azimuthal anisotropy in Tibet revealed by surface wave tomography

NASA Astrophysics Data System (ADS)

Pandey, Shantanu; Yuan, Xiaohui; Debayle, Eric; Tilmann, Frederik; Priestley, Keith; Li, Xueqing

2015-06-01

Azimuthal anisotropy derived from multimode Rayleigh wave tomography in China exhibits depth-dependent variations in Tibet, which can be explained as induced by the Cenozoic India-Eurasian collision. In west Tibet, the E-W fast polarization direction at depths <100 km is consistent with the accumulated shear strain in the Tibetan lithosphere, whereas the N-S fast direction at greater depths is aligned with Indian Plate motion. In northeast Tibet, depth-consistent NW-SE directions imply coupled deformation throughout the whole lithosphere, possibly also involving the underlying asthenosphere. Significant anisotropy at depths of 225 km in southeast Tibet reflects sublithospheric deformation induced by northward and eastward lithospheric subduction beneath the Himalaya and Burma, respectively. The multilayer anisotropic surface wave model can explain some features of SKS splitting measurements in Tibet, with differences probably attributable to the limited back azimuthal coverage of most SKS studies in Tibet and the limited horizontal resolution of the surface wave results.

Evaluation of pier-scour equations for coarse-bed streams

USGS Publications Warehouse

Chase, Katherine J.; Holnbeck, Stephen R.

2004-01-01

Streambed scour at bridge piers is among the leading causes of bridge failure in the United States. Several pier-scour equations have been developed to calculate potential scour depths at existing and proposed bridges. Because many pier-scour equations are based on data from laboratory flumes and from cohesionless silt- and sand-bottomed streams, they tend to overestimate scour for piers in coarse-bed materials. Several equations have been developed to incorporate the mitigating effects of large particle sizes on pier scour, but further investigations are needed to evaluate how accurately pier-scour depths calculated by these equations match measured field data. This report, prepared in cooperation with the Montana Department of Transportation, describes the evaluation of five pier-scour equations for coarse-bed streams. Pier-scour and associated bridge-geometry, bed-material, and streamflow-measurement data at bridges over coarse-bed streams in Montana, Alaska, Maryland, Ohio, and Virginia were selected from the Bridge Scour Data Management System. Pier scour calculated using the Simplified Chinese equation, the Froehlich equation, the Froehlich design equation, the HEC-18/Jones equation and the HEC-18/Mueller equation for flood events with approximate recurrence intervals of less than 2 to 100 years were compared to 42 pier-scour measurements. Comparison of results showed that pier-scour depths calculated with the HEC-18/Mueller equation were seldom smaller than measured pier-scour depths. In addition, pier-scour depths calculated using the HEC-18/Mueller equation were closer to measured scour than for the other equations that did not underestimate pier scour. However, more data are needed from coarse-bed streams and from less frequent flood events to further evaluate pier-scour equations.

Temporal evolutions and stationary waves for dissipative Benjamin-Ono equation

NASA Astrophysics Data System (ADS)

Feng, Bao-Feng; Kawahara, Takuji

2000-05-01

Initial value problems as well as stationary solitary and periodic waves are investigated for dissipative Benjamin-Ono (DBO) equation. Multi-hump stationary waves and their structures are identified numerically and the stability regions of stationary periodic waves are also examined numerically. These results elucidate a close relation between irregular behaviours in the initial value problem and the multiplicity of stationary waves.

Wave equation datuming applied to S-wave reflection seismic data

NASA Astrophysics Data System (ADS)

Tinivella, U.; Giustiniani, M.; Nicolich, R.

2018-05-01

S-wave high-resolution reflection seismic data was processed using Wave Equation Datuming technique in order to improve signal/noise ratio, attenuating coherent noise, and seismic resolution and to solve static corrections problems. The application of this algorithm allowed obtaining a good image of the shallow subsurface geological features. Wave Equation Datuming moves shots and receivers from a surface to another datum (the datum plane), removing time shifts originated by elevation variation and/or velocity changes in the shallow subsoil. This algorithm has been developed and currently applied to P wave, but it reveals the capacity to highlight S-waves images when used to resolve thin layers in high-resolution prospecting. A good S-wave image facilitates correlation with well stratigraphies, optimizing cost/benefit ratio of any drilling. The application of Wave Equation Datuming requires a reliable velocity field, so refraction tomography was adopted. The new seismic image highlights the details of the subsoil reflectors and allows an easier integration with borehole information and geological surveys than the seismic section obtained by conventional CMP reflection processing. In conclusion, the analysis of S-wave let to characterize the shallow subsurface recognizing levels with limited thickness once we have clearly attenuated ground roll, wind and environmental noise.

Non-autonomous multi-rogue waves for spin-1 coupled nonlinear Gross-Pitaevskii equation and management by external potentials.

PubMed

Li, Li; Yu, Fajun

2017-09-06

We investigate non-autonomous multi-rogue wave solutions in a three-component(spin-1) coupled nonlinear Gross-Pitaevskii(GP) equation with varying dispersions, higher nonlinearities, gain/loss and external potentials. The similarity transformation allows us to relate certain class of multi-rogue wave solutions of the spin-1 coupled nonlinear GP equation to the solutions of integrable coupled nonlinear Schrödinger(CNLS) equation. We study the effect of time-dependent quadratic potential on the profile and dynamic of non-autonomous rogue waves. With certain requirement on the backgrounds, some non-autonomous multi-rogue wave solutions exhibit the different shapes with two peaks and dip in bright-dark rogue waves. Then, the managements with external potential and dynamic behaviors of these solutions are investigated analytically. The results could be of interest in such diverse fields as Bose-Einstein condensates, nonlinear fibers and super-fluids.

A new mathematical approach for shock-wave solution in a dusty plasma

DOE Office of Scientific and Technical Information (OSTI.GOV)

Das, G.C.; Dwivedi, C.B.; Talukdar, M.

1997-12-01

The problem of nonlinear Burger equation in a plasma contaminated with heavy dust grains has been revisited. As discussed earlier [C. B. Dwivedi and B. P. Pandey, Phys. Plasmas {bold 2}, 9 (1995)], the Burger equation originates due to dust charge fluctuation dynamics. A new alternate mathematical approach based on a simple traveling wave formalism has been applied to find out the solution of the derived Burger equation, and the method recovers the known shock-wave solution. This technique, although having its own limitation, predicts successfully the salient features of the weak shock-wave structure in a dusty plasma with dust chargemore » fluctuation dynamics. It is emphasized that this approach of the traveling wave formalism is being applied for the first time to solve the nonlinear wave equation in plasmas. {copyright} {ital 1997 American Institute of Physics.}« less

Wave height estimates from pressure and velocity data at an intermediate depth in the presence of uniform currents

NASA Astrophysics Data System (ADS)

Basu, Biswajit

2017-12-01

Bounds on estimates of wave heights (valid for large amplitudes) from pressure and flow measurements at an arbitrary intermediate depth have been provided. Two-dimensional irrotational steady water waves over a flat bed with a finite depth in the presence of underlying uniform currents have been considered in the analysis. Five different upper bounds based on a combination of pressure and velocity field measurements have been derived, though there is only one available lower bound on the wave height in the case of the speed of current greater than or less than the wave speed. This article is part of the theme issue 'Nonlinear water waves'.

A phase space approach to wave propagation with dispersion.

PubMed

Ben-Benjamin, Jonathan S; Cohen, Leon; Loughlin, Patrick J

2015-08-01

A phase space approximation method for linear dispersive wave propagation with arbitrary initial conditions is developed. The results expand on a previous approximation in terms of the Wigner distribution of a single mode. In contrast to this previously considered single-mode case, the approximation presented here is for the full wave and is obtained by a different approach. This solution requires one to obtain (i) the initial modal functions from the given initial wave, and (ii) the initial cross-Wigner distribution between different modal functions. The full wave is the sum of modal functions. The approximation is obtained for general linear wave equations by transforming the equations to phase space, and then solving in the new domain. It is shown that each modal function of the wave satisfies a Schrödinger-type equation where the equivalent "Hamiltonian" operator is the dispersion relation corresponding to the mode and where the wavenumber is replaced by the wavenumber operator. Application to the beam equation is considered to illustrate the approach.

Survey of Coherent Approximately 1 Hz Waves in Mercury's Inner Magnetosphere from MESSENGER Observations

NASA Technical Reports Server (NTRS)

Boardsen, Scott A.; Slavin, James A.; Anderson, Brian J.; Korth, Haje; Schriver, David; Solomon, Sean C.

2012-01-01

We summarize observations by the MESSENGER spacecraft of highly coherent waves at frequencies between 0.4 and 5 Hz in Mercury's inner magnetosphere. This survey covers the time period from 24 March to 25 September 2011, or 2.1 Mercury years. These waves typically exhibit banded harmonic structure that drifts in frequency as the spacecraft traverses the magnetic equator. The waves are seen at all magnetic local times, but their observed rate of occurrence is much less on the dayside, at least in part the result of MESSENGER's orbit. On the nightside, on average, wave power is maximum near the equator and decreases with increasing magnetic latitude, consistent with an equatorial source. When the spacecraft traverses the plasma sheet during its equatorial crossings, wave power is a factor of 2 larger than for equatorial crossings that do not cross the plasma sheet. The waves are highly transverse at large magnetic latitudes but are more compressional near the equator. However, at the equator the transverse component of these waves increases relative to the compressional component as the degree of polarization decreases. Also, there is a substantial minority of events that are transverse at all magnetic latitudes, including the equator. A few of these latter events could be interpreted as ion cyclotron waves. In general, the waves tend to be strongly linear and characterized by values of the ellipticity less than 0.3 and wave-normal angles peaked near 90 deg. Their maxima in wave power at the equator coupled with their narrow-band character suggests that these waves might be generated locally in loss cone plasma characterized by high values of the ratio beta of plasma pressure to magnetic pressure. Presumably both electromagnetic ion cyclotron waves and electromagnetic ion Bernstein waves can be generated by ion loss cone distributions. If proton beta decreases with increasing magnetic latitude along a field line, then electromagnetic ion Bernstein waves are predicted to transition from compressional to transverse, a pattern consistent with our observations. We hypothesize that these local instabilities can lead to enhanced ion precipitation and directly feed field-line resonances.

Localized light waves: Paraxial and exact solutions of the wave equation (a review)

NASA Astrophysics Data System (ADS)

Kiselev, A. P.

2007-04-01

Simple explicit localized solutions are systematized over the whole space of a linear wave equation, which models the propagation of optical radiation in a linear approximation. Much attention has been paid to exact solutions (which date back to the Bateman findings) that describe wave beams (including Bessel-Gauss beams) and wave packets with a Gaussian localization with respect to the spatial variables and time. Their asymptotics with respect to free parameters and at large distances are presented. A similarity between these exact solutions and harmonic in time fields obtained in the paraxial approximation based on the Leontovich-Fock parabolic equation has been studied. Higher-order modes are considered systematically using the separation of variables method. The application of the Bateman solutions of the wave equation to the construction of solutions to equations with dispersion and nonlinearity and their use in wavelet analysis, as well as the summation of Gaussian beams, are discussed. In addition, solutions localized at infinity known as the Moses-Prosser “acoustic bullets”, as well as their harmonic in time counterparts, “ X waves”, waves from complex sources, etc., have been considered. Everywhere possible, the most elementary mathematical formalism is used.

Modulational instability and dynamics of implicit higher-order rogue wave solutions for the Kundu equation

NASA Astrophysics Data System (ADS)

Wen, Xiao-Yong; Zhang, Guoqiang

2018-01-01

Under investigation in this paper is the Kundu equation, which may be used to describe the propagation process of ultrashort optical pulses in nonlinear optics. The modulational instability of the plane-wave for the possible reason of the formation of the rogue wave (RW) is studied for the system. Based on our proposed generalized perturbation (n,N - n)-fold Darboux transformation (DT), some new higher-order implicit RW solutions in terms of determinants are obtained by means of the generalized perturbation (1,N - 1)-fold DT, when choosing different special parameters, these results will reduce to the RW solutions of the Kaup-Newell (KN) equation, Chen-Lee-Liu (CLL) equation and Gerjikov-Ivanov (GI) equation, respectively. The relevant wave structures are shown graphically, which display abundant interesting wave structures. The dynamical behaviors and propagation stability of the first-order and second-order RW solutions are discussed by using numerical simulations, the higher-order nonlinear terms for the Kundu equation have an impact on the propagation instability of the RW. The method can also be extended to find the higher-order RW or rational solutions of other integrable nonlinear equations.

Generalized wave operators, weighted Killing fields, and perturbations of higher dimensional spacetimes

NASA Astrophysics Data System (ADS)

Araneda, Bernardo

2018-04-01

We present weighted covariant derivatives and wave operators for perturbations of certain algebraically special Einstein spacetimes in arbitrary dimensions, under which the Teukolsky and related equations become weighted wave equations. We show that the higher dimensional generalization of the principal null directions are weighted conformal Killing vectors with respect to the modified covariant derivative. We also introduce a modified Laplace–de Rham-like operator acting on tensor-valued differential forms, and show that the wave-like equations are, at the linear level, appropriate projections off shell of this operator acting on the curvature tensor; the projection tensors being made out of weighted conformal Killing–Yano tensors. We give off shell operator identities that map the Einstein and Maxwell equations into weighted scalar equations, and using adjoint operators we construct solutions of the original field equations in a compact form from solutions of the wave-like equations. We study the extreme and zero boost weight cases; extreme boost corresponding to perturbations of Kundt spacetimes (which includes near horizon geometries of extreme black holes), and zero boost to static black holes in arbitrary dimensions. In 4D our results apply to Einstein spacetimes of Petrov type D and make use of weighted Killing spinors.

A boundary integral approach to the scattering of nonplanar acoustic waves by rigid bodies

NASA Technical Reports Server (NTRS)

Gallman, Judith M.; Myers, M. K.; Farassat, F.

1990-01-01

The acoustic scattering of an incident wave by a rigid body can be described by a singular Fredholm integral equation of the second kind. This equation is derived by solving the wave equation using generalized function theory, Green's function for the wave equation in unbounded space, and the acoustic boundary condition for a perfectly rigid body. This paper will discuss the derivation of the wave equation, its reformulation as a boundary integral equation, and the solution of the integral equation by the Galerkin method. The accuracy of the Galerkin method can be assessed by applying the technique outlined in the paper to reproduce the known pressure fields that are due to various point sources. From the analysis of these simpler cases, the accuracy of the Galerkin solution can be inferred for the scattered pressure field caused by the incidence of a dipole field on a rigid sphere. The solution by the Galerkin technique can then be applied to such problems as a dipole model of a propeller whose pressure field is incident on a rigid cylinder. This is the groundwork for modeling the scattering of rotating blade noise by airplane fuselages.

Experimental study on the evolution of Peregrine breather with uniform-depth adverse currents

NASA Astrophysics Data System (ADS)

Liao, B.; Ma, Y.; Ma, X.; Dong, G.

2018-05-01

A series of laboratory experiments were performed to study the evolution of Peregrine breather (PB) in a wave flume in finite depth, and wave trains were initially generated in a region of quiescent water and then propagated into an adverse current region for which the current velocity strength gradually increased from zero to an approximately stable value. The PB is often considered as a prototype of oceanic freak waves that can focus wave energy into a single wave packet. In the experiment, the cases were selected with the relative water depths k0h (k0 is the wave number in quiescent water and h is the water depth) varying from 3.11 through 8.17, and the initial wave steepness k0a0 (a0 is the background wave amplitude) ranges between 0.065 and 0.120. The experimental results show the persistence of the breather evolution dynamics even in the presence of strong opposing currents. We have shown that the characteristic spectrum of the PB persists even on strong currents, thus making it a viable characteristic for prediction of freak waves. It was also found that the adverse currents tend to shift the focusing point upstream compared to the cases without currents. Furthermore, it was found that uniform-depth adverse currents can reduce the breather extension in time domain.

Traveling wave solutions and conservation laws for nonlinear evolution equation

NASA Astrophysics Data System (ADS)

Baleanu, Dumitru; Inc, Mustafa; Yusuf, Abdullahi; Aliyu, Aliyu Isa

2018-02-01

In this work, the Riccati-Bernoulli sub-ordinary differential equation and modified tanh-coth methods are used to reach soliton solutions of the nonlinear evolution equation. We acquire new types of traveling wave solutions for the governing equation. We show that the equation is nonlinear self-adjoint by obtaining suitable substitution. Therefore, we construct conservation laws for the equation using new conservation theorem. The obtained solutions in this work may be used to explain and understand the physical nature of the wave spreads in the most dispersive medium. The constraint condition for the existence of solitons is stated. Some three dimensional figures for some of the acquired results are illustrated.

Lapse-time-dependent coda-wave depth sensitivity to local velocity perturbations in 3-D heterogeneous elastic media

NASA Astrophysics Data System (ADS)

Obermann, Anne; Planès, Thomas; Hadziioannou, Céline; Campillo, Michel

2016-10-01

In the context of seismic monitoring, recent studies made successful use of seismic coda waves to locate medium changes on the horizontal plane. Locating the depth of the changes, however, remains a challenge. In this paper, we use 3-D wavefield simulations to address two problems: first, we evaluate the contribution of surface- and body-wave sensitivity to a change at depth. We introduce a thin layer with a perturbed velocity at different depths and measure the apparent relative velocity changes due to this layer at different times in the coda and for different degrees of heterogeneity of the model. We show that the depth sensitivity can be modelled as a linear combination of body- and surface-wave sensitivity. The lapse-time-dependent sensitivity ratio of body waves and surface waves can be used to build 3-D sensitivity kernels for imaging purposes. Second, we compare the lapse-time behaviour in the presence of a perturbation in horizontal and vertical slabs to address, for instance, the origin of the velocity changes detected after large earthquakes.

Diffusion phenomenon for linear dissipative wave equations in an exterior domain

NASA Astrophysics Data System (ADS)

Ikehata, Ryo

Under the general condition of the initial data, we will derive the crucial estimates which imply the diffusion phenomenon for the dissipative linear wave equations in an exterior domain. In order to derive the diffusion phenomenon for dissipative wave equations, the time integral method which was developed by Ikehata and Matsuyama (Sci. Math. Japon. 55 (2002) 33) plays an effective role.

Nonlinear Waves and Inverse Scattering

DTIC Science & Technology

1990-09-18

to be published Proceedings: conference Chaos in Australia (February 1990). 5. On the Kadomtsev Petviashvili Equation and Associated Constraints by...Scattering Transfoni (IST). IST is a method which alows one to’solve nonlinear wave equations by solving certain related direct and inverse scattering...problems. We use these results to find solutions to nonlinear wave equations much like one uses Fourier analysis for linear problems. Moreover the

Influence of optical activity on rogue waves propagating in chiral optical fibers.

PubMed

Temgoua, D D Estelle; Kofane, T C

2016-06-01

We derive the nonlinear Schrödinger (NLS) equation in chiral optical fiber with right- and left-hand nonlinear polarization. We use the similarity transformation to reduce the generalized chiral NLS equation to the higher-order integrable Hirota equation. We present the first- and second-order rational solutions of the chiral NLS equation with variable and constant coefficients, based on the modified Darboux transformation method. For some specific set of parameters, the features of chiral optical rogue waves are analyzed from analytical results, showing the influence of optical activity on waves. We also generate the exact solutions of the two-component coupled nonlinear Schrödinger equations, which describe optical activity effects on the propagation of rogue waves, and their properties in linear and nonlinear coupling cases are investigated. The condition of modulation instability of the background reveals the existence of vector rogue waves and the number of stable and unstable branches. Controllability of chiral optical rogue waves is examined by numerical simulations and may bring potential applications in optical fibers and in many other physical systems.

Ginzburg-Landau equation as a heuristic model for generating rogue waves

NASA Astrophysics Data System (ADS)

Lechuga, Antonio

2016-04-01

Envelope equations have many applications in the study of physical systems. Particularly interesting is the case 0f surface water waves. In steady conditions, laboratory experiments are carried out for multiple purposes either for researches or for practical problems. In both cases envelope equations are useful for understanding qualitative and quantitative results. The Ginzburg-Landau equation provides an excellent model for systems of that kind with remarkable patterns. Taking into account the above paragraph the main aim of our work is to generate waves in a water tank with almost a symmetric spectrum according to Akhmediev (2011) and thus, to produce a succession of rogue waves. The envelope of these waves gives us some patterns whose model is a type of Ginzburg-Landau equation, Danilov et al (1988). From a heuristic point of view the link between the experiment and the model is achieved. Further, the next step consists of changing generating parameters on the water tank and also the coefficients of the Ginzburg-Landau equation, Lechuga (2013) in order to reach a sufficient good approach.

Cyclotron maser and plasma wave growth in magnetic loops

NASA Technical Reports Server (NTRS)

Hamilton, Russell J.; Petrosian, Vahe

1990-01-01

Cyclotron maser and plasma wave growth which results from electrons accelerated in magnetic loops are studied. The evolution of the accelerated electron distribution is determined by solving the kinetic equation including Coulomb collisions and magnetic convergence. It is found that for modest values of the column depth of the loop the growth rates of instabilities are significantly reduced and that the reduction is much larger for the cyclotron modes than for the plasma wave modes. The large decrease in the growth rate with column depth suggests that solar coronal densities must be much lower than commonly accepted in order for the cyclotron maser to operate. The density depletion has to be similar to that which occurs during auroral kilometric radiation events in the magnetosphere. The resulting distributions are much more complicated than the idealized distributions used in many theoretical studies, but the fastest growing mode can still simply be determined by the ratio of electron plasma to gyrofrequency, U=omega(sub p)/Omega(sub e). However, the dominant modes are different than for the idealized situations with growth of the z-mode largest for U approximately less than 0.5, and second harmonic x-mode (s=2) or fundamental o-mode (s=1) the dominant modes for 0.5 approximately less than U approximately less than 1. The electron distributions typically contain more than one inverted feature which could give rise to wave growth. It is shown that this can result in simultaneous amplification of more than one mode with each mode driven by a different feature and can be observed, for example, by differences in the rise times of the right and left circularly polarized components of the associated spike bursts.

Mapping the Moho with seismic surface waves: Sensitivity, resolution, and recommended inversion strategies

NASA Astrophysics Data System (ADS)

Lebedev, Sergei; Adam, Joanne; Meier, Thomas

2013-04-01

Seismic surface waves have been used to study the Earth's crust since the early days of modern seismology. In the last decade, surface-wave crustal imaging has been rejuvenated by the emergence of new, array techniques (ambient-noise and teleseismic interferometry). The strong sensitivity of both Rayleigh and Love waves to the Moho is evident from a mere visual inspection of their dispersion curves or waveforms. Yet, strong trade-offs between the Moho depth and crustal and mantle structure in surface-wave inversions have prompted doubts regarding their capacity to resolve the Moho. Although the Moho depth has been an inversion parameter in numerous surface-wave studies, the resolution of Moho properties yielded by a surface-wave inversion is still somewhat uncertain and controversial. We use model-space mapping in order to elucidate surface waves' sensitivity to the Moho depth and the resolution of their inversion for it. If seismic wavespeeds within the crust and upper mantle are known, then Moho-depth variations of a few kilometres produce large (over 1 per cent) perturbations in phase velocities. However, in inversions of surface-wave data with no a priori information (wavespeeds not known), strong Moho-depth/shear-speed trade-offs will mask about 90 per cent of the Moho-depth signal, with remaining phase-velocity perturbations 0.1-0.2 per cent only. In order to resolve the Moho with surface waves alone, errors in the data must thus be small (up to 0.2 per cent for resolving continental Moho). If the errors are larger, Moho-depth resolution is not warranted and depends on error distribution with period, with errors that persist over broad period ranges particularly damaging. An effective strategy for the inversion of surface-wave data alone for the Moho depth is to, first, constrain the crustal and upper-mantle structure by inversion in a broad period range and then determine the Moho depth in inversion in a narrow period range most sensitive to it, with the first-step results used as reference. We illustrate this strategy with an application to data from the Kaapvaal Craton. Prior information on crustal and mantle structure reduces the trade-offs and thus enables resolving the Moho depth with noisier data; such information should be sought and used whenever available (as has been done, explicitly or implicitly, in many previous studies). Joint analysis or inversion of surface-wave and other data (receiver functions, topography, gravity) can reduce uncertainties further and facilitate Moho mapping. Alone or as a part of multi-disciplinary datasets, surface-wave data offer unique sensitivity to the crustal and upper-mantle structure and are becoming increasingly important in the seismic imaging of the crust and the Moho. Reference Lebedev, S., J. Adam, T. Meier. Mapping the Moho with seismic surface waves: A review, resolution analysis, and recommended inversion strategies. Tectonophysics, "Moho" special issue, 10.1016/j.tecto.2012.12.030, 2013.

Explicit Solutions and Bifurcations for a Class of Generalized Boussinesq Wave Equation

NASA Astrophysics Data System (ADS)

Ma, Zhi-Min; Sun, Yu-Huai; Liu, Fu-Sheng

2013-03-01

In this paper, the generalized Boussinesq wave equation utt — uxx + a(um)xx + buxxxx = 0 is investigated by using the bifurcation theory and the method of phase portraits analysis. Under the different parameter conditions, the exact explicit parametric representations for solitary wave solutions and periodic wave solutions are obtained.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Roberts, Jesse D.; Chang, Grace; Jones, Craig

The numerical model, SWAN (Simulating WAves Nearshore) , was used to simulate wave conditions in Kaneohe Bay, HI in order to determine the effects of wave energy converter ( WEC ) devices on the propagation of waves into shore. A nested SWAN model was validated then used to evaluate a range of initial wave conditions: significant wave heights (H s ) , peak periods (T p ) , and mean wave directions ( MWD) . Differences between wave height s in the presence and absence of WEC device s were assessed at locations in shore of the WEC array. Themore » maximum decrease in wave height due to the WEC s was predicted to be approximately 6% at 5 m and 10 m water depths. Th is occurred for model initiation parameters of H s = 3 m (for 5 m water depth) or 4 m (10 m water depth) , T p = 10 s, and MWD = 330deg . Subsequently, bottom orbital velocities were found to decrease by about 6%.« less

Modelling rogue waves through exact dynamical lump soliton controlled by ocean currents.

PubMed

Kundu, Anjan; Mukherjee, Abhik; Naskar, Tapan

2014-04-08

Rogue waves are extraordinarily high and steep isolated waves, which appear suddenly in a calm sea and disappear equally fast. However, though the rogue waves are localized surface waves, their theoretical models and experimental observations are available mostly in one dimension, with the majority of them admitting only limited and fixed amplitude and modular inclination of the wave. We propose two dimensions, exactly solvable nonlinear Schrödinger (NLS) equation derivable from the basic hydrodynamic equations and endowed with integrable structures. The proposed two-dimensional equation exhibits modulation instability and frequency correction induced by the nonlinear effect, with a directional preference, all of which can be determined through precise analytic result. The two-dimensional NLS equation allows also an exact lump soliton which can model a full-grown surface rogue wave with adjustable height and modular inclination. The lump soliton under the influence of an ocean current appears and disappears preceded by a hole state, with its dynamics controlled by the current term. These desirable properties make our exact model promising for describing ocean rogue waves.

Modelling rogue waves through exact dynamical lump soliton controlled by ocean currents

PubMed Central

Kundu, Anjan; Mukherjee, Abhik; Naskar, Tapan

2014-01-01

Rogue waves are extraordinarily high and steep isolated waves, which appear suddenly in a calm sea and disappear equally fast. However, though the rogue waves are localized surface waves, their theoretical models and experimental observations are available mostly in one dimension, with the majority of them admitting only limited and fixed amplitude and modular inclination of the wave. We propose two dimensions, exactly solvable nonlinear Schrödinger (NLS) equation derivable from the basic hydrodynamic equations and endowed with integrable structures. The proposed two-dimensional equation exhibits modulation instability and frequency correction induced by the nonlinear effect, with a directional preference, all of which can be determined through precise analytic result. The two-dimensional NLS equation allows also an exact lump soliton which can model a full-grown surface rogue wave with adjustable height and modular inclination. The lump soliton under the influence of an ocean current appears and disappears preceded by a hole state, with its dynamics controlled by the current term. These desirable properties make our exact model promising for describing ocean rogue waves. PMID:24711719

Joint Optimization of Vertical Component Gravity and Seismic P-wave First Arrivals by Simulated Annealing

NASA Astrophysics Data System (ADS)

Louie, J. N.; Basler-Reeder, K.; Kent, G. M.; Pullammanappallil, S. K.

2015-12-01

Simultaneous joint seismic-gravity optimization improves P-wave velocity models in areas with sharp lateral velocity contrasts. Optimization is achieved using simulated annealing, a metaheuristic global optimization algorithm that does not require an accurate initial model. Balancing the seismic-gravity objective function is accomplished by a novel approach based on analysis of Pareto charts. Gravity modeling uses a newly developed convolution algorithm, while seismic modeling utilizes the highly efficient Vidale eikonal equation traveltime generation technique. Synthetic tests show that joint optimization improves velocity model accuracy and provides velocity control below the deepest headwave raypath. Detailed first arrival picking followed by trial velocity modeling remediates inconsistent data. We use a set of highly refined first arrival picks to compare results of a convergent joint seismic-gravity optimization to the Plotrefa™ and SeisOpt® Pro™ velocity modeling packages. Plotrefa™ uses a nonlinear least squares approach that is initial model dependent and produces shallow velocity artifacts. SeisOpt® Pro™ utilizes the simulated annealing algorithm and is limited to depths above the deepest raypath. Joint optimization increases the depth of constrained velocities, improving reflector coherency at depth. Kirchoff prestack depth migrations reveal that joint optimization ameliorates shallow velocity artifacts caused by limitations in refraction ray coverage. Seismic and gravity data from the San Emidio Geothermal field of the northwest Basin and Range province demonstrate that joint optimization changes interpretation outcomes. The prior shallow-valley interpretation gives way to a deep valley model, while shallow antiformal reflectors that could have been interpreted as antiformal folds are flattened. Furthermore, joint optimization provides a clearer image of the rangefront fault. This technique can readily be applied to existing datasets and could replace the existing strategy of forward modeling to match gravity data.

Two-Dimensional Analysis of Cable Stayed Bridge under Wave Loading

NASA Astrophysics Data System (ADS)

Seeram, Madhuri; Manohar, Y.

2018-06-01

In the present study finite element analysis is performed for a modified fan type cable-stayed bridge using ANSYS Mechanical. A cable stayed bridge with two towers and main deck is considered for the present study. Dynamic analysis is performed to evaluate natural frequencies. The obtained natural frequencies and mode shapes of cable stayed bridge are compared to the existing results. Further studies have been conducted for offshore area application by increasing the pylon/tower height depending upon the water depth. Natural frequencies and mode shapes are evaluated for the cable stayed bridge for offshore area application. The results indicate that the natural periods are higher than the existing results due to the effect of increase in mass of the structure and decrease in stiffness of the pylon/tower. The cable stayed bridge is analyzed under various environmental loads such as dead, live, vehicle, seismic and wave loading. Morison equation is considered to evaluate the wave force. The sum of inertia and drag force is taken as the wave force distribution along the fluid interacting height of the pylon. Airy's wave theory is used to assess water particle kinematics, for the wave periods ranging from 5 to 20 s and unit wave height. The maximum wave force among the different regular waves is considered in the wave load case. The support reactions, moments and deflections for offshore area application are highlighted. It is observed that the maximum support reactions and support moments are obtained due to wave and earthquake loading respectively. Hence, it is concluded that the wave and earthquake forces shall be given significance in the design of cable stayed bridge.

Two-Dimensional Analysis of Cable Stayed Bridge under Wave Loading

NASA Astrophysics Data System (ADS)

Seeram, Madhuri; Manohar, Y.

2018-02-01

In the present study finite element analysis is performed for a modified fan type cable-stayed bridge using ANSYS Mechanical. A cable stayed bridge with two towers and main deck is considered for the present study. Dynamic analysis is performed to evaluate natural frequencies. The obtained natural frequencies and mode shapes of cable stayed bridge are compared to the existing results. Further studies have been conducted for offshore area application by increasing the pylon/tower height depending upon the water depth. Natural frequencies and mode shapes are evaluated for the cable stayed bridge for offshore area application. The results indicate that the natural periods are higher than the existing results due to the effect of increase in mass of the structure and decrease in stiffness of the pylon/tower. The cable stayed bridge is analyzed under various environmental loads such as dead, live, vehicle, seismic and wave loading. Morison equation is considered to evaluate the wave force. The sum of inertia and drag force is taken as the wave force distribution along the fluid interacting height of the pylon. Airy's wave theory is used to assess water particle kinematics, for the wave periods ranging from 5 to 20 s and unit wave height. The maximum wave force among the different regular waves is considered in the wave load case. The support reactions, moments and deflections for offshore area application are highlighted. It is observed that the maximum support reactions and support moments are obtained due to wave and earthquake loading respectively. Hence, it is concluded that the wave and earthquake forces shall be given significance in the design of cable stayed bridge.

A Semi-Implicit, Three-Dimensional Model for Estuarine Circulation

USGS Publications Warehouse

Smith, Peter E.

2006-01-01

A semi-implicit, finite-difference method for the numerical solution of the three-dimensional equations for circulation in estuaries is presented and tested. The method uses a three-time-level, leapfrog-trapezoidal scheme that is essentially second-order accurate in the spatial and temporal numerical approximations. The three-time-level scheme is shown to be preferred over a two-time-level scheme, especially for problems with strong nonlinearities. The stability of the semi-implicit scheme is free from any time-step limitation related to the terms describing vertical diffusion and the propagation of the surface gravity waves. The scheme does not rely on any form of vertical/horizontal mode-splitting to treat the vertical diffusion implicitly. At each time step, the numerical method uses a double-sweep method to transform a large number of small tridiagonal equation systems and then uses the preconditioned conjugate-gradient method to solve a single, large, five-diagonal equation system for the water surface elevation. The governing equations for the multi-level scheme are prepared in a conservative form by integrating them over the height of each horizontal layer. The layer-integrated volumetric transports replace velocities as the dependent variables so that the depth-integrated continuity equation that is used in the solution for the water surface elevation is linear. Volumetric transports are computed explicitly from the momentum equations. The resulting method is mass conservative, efficient, and numerically accurate.

Experimental investigation of change of energy of infragavity waves in dependence on spectral characteristics of an irregular wind waves in coastal zone

NASA Astrophysics Data System (ADS)

Saprykina, Yana; Divinskii, Boris

2013-04-01

An infragravity waves are long waves with periods of 20 - 300 s. Most essential influence of infragarvity waves on dynamic processes is in a coastal zone, where its energy can exceed the energy of wind waves. From practical point of view, the infragravity waves are important, firstly, due to their influence on sand transport processes in a coastal zone. For example, interacting with group structure of wind waves the infragravity waves can define position of underwater bars on sandy coast. Secondly, they are responsible on formation of long waves in harbors. Main source of infragravity waves is wave group structure defined by sub-nonlinear interactions of wind waves (Longuet-Higgins, Stewart, 1962). These infragravity waves are bound with groups of wind waves and propagate with wave group velocity. Another type of infragravity waves are formed in a surf zone as a result of migration a wave breaking point (Symonds, et al., 1982). What from described above mechanisms of formation of infragravity waves prevails, till now it is unknown. It is also unknown how energy of infragravity waves depends on energy of input wind waves and how it changes during nonlinear wave transformation in coastal zone. In our work on the basis of the analysis of data of field experiment and numerical simulation a contribution of infragravity waves in total wave energy in depending on integral characteristics of an irregular wave field in the conditions of a real bathymetry was investigated. For analysis the data of field experiment "Shkorpilovtsy-2007" (Black sea) and data of numerical modeling of Boussinesq type equation with extended dispersion characteristics (Madsen et al., 1997) were used. It was revealed that infragravity waves in a coastal zone are defined mainly by local group structure of waves, which permanently changes due to nonlinearity, shoaling and breaking processes. Free infragravity waves appearing after wave breaking exist together with bound infragravity waves. There are no clear total dependences of energy of infrragravity waves from energy of wind waves and mean period of infragravity waves from mean period of wind waves. But significant wave height of infragravity waves depends on relative water depth (wave height of wind waves divided on water depth). There are different types of this dependence for breaking and non-breaking waves. The influence of peak period, significant wave height and directional spreading of initial wave spectrum on these dependences are discussed. The peculiarities of spectra of infragravity waves for non-breaking, breaking and multibreaking wind waves are shown. This work is supported by the RFBR, project 12-05-00965. References: Longuet-Higgins, M. S., R. W. Stewart, 1962. Radiation stress and mass transport in gravity waves, with an application to surf beats. J. Fluid Mech., 13, pp. 481-504. Symonds G., D.A. Huntley, A.J. Bowen, 1982. Two dimensional surf beat: long wave generation by a time-varying breakpoint. J. of Geoph. Res., 87(C), pp.492-498. Madsen P.A., Sorensen O.R., Shaffer H.A. 1997. Surf zone dynamics simulated by a Boussinesq type model. Coastal Engineering, 32, p. 255-287.

Solitary-wave solutions of the Benjamin equation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Albert, J.P.; Bona, J.L.; Restrepo, J.M.

1999-10-01

Considered here is a model equation put forward by Benjamin that governs approximately the evolution of waves on the interface of a two-fluid system in which surface-tension effects cannot be ignored. The principal focus is the traveling-wave solutions called solitary waves, and three aspects will be investigated. A constructive proof of the existence of these waves together with a proof of their stability is developed. Continuation methods are used to generate a scheme capable of numerically approximating these solitary waves. The computer-generated approximations reveal detailed aspects of the structure of these waves. They are symmetric about their crests, but unlikemore » the classical Korteqeg-de Vries solitary waves, they feature a finite number of oscillations. The derivation of the equation is also revisited to get an idea of whether or not these oscillatory waves might actually occur in a natural setting.« less

A single-sided representation for the homogeneous Green's function of a unified scalar wave equation.

PubMed

Wapenaar, Kees

2017-06-01

A unified scalar wave equation is formulated, which covers three-dimensional (3D) acoustic waves, 2D horizontally-polarised shear waves, 2D transverse-electric EM waves, 2D transverse-magnetic EM waves, 3D quantum-mechanical waves and 2D flexural waves. The homogeneous Green's function of this wave equation is a combination of the causal Green's function and its time-reversal, such that their singularities at the source position cancel each other. A classical representation expresses this homogeneous Green's function as a closed boundary integral. This representation finds applications in holographic imaging, time-reversed wave propagation and Green's function retrieval by cross correlation. The main drawback of the classical representation in those applications is that it requires access to a closed boundary around the medium of interest, whereas in many practical situations the medium can be accessed from one side only. Therefore, a single-sided representation is derived for the homogeneous Green's function of the unified scalar wave equation. Like the classical representation, this single-sided representation fully accounts for multiple scattering. The single-sided representation has the same applications as the classical representation, but unlike the classical representation it is applicable in situations where the medium of interest is accessible from one side only.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Menikoff, Ralph

The Zel’dovich-von Neumann-Doering (ZND) profile of a detonation wave is derived. Two basic assumptions are required: i. An equation of state (EOS) for a partly burned explosive; P(V, e, λ). ii. A burn rate for the reaction progress variable; d/dt λ = R(V, e, λ). For a steady planar detonation wave the reactive flow PDEs can be reduced to ODEs. The detonation wave profile can be determined from an ODE plus algebraic equations for points on the partly burned detonation loci with a specified wave speed. Furthermore, for the CJ detonation speed the end of the reaction zone is sonic.more » A solution to the reactive flow equations can be constructed with a rarefaction wave following the detonation wave profile. This corresponds to an underdriven detonation wave, and the rarefaction is know as a Taylor wave.« less

On the solution of the generalized wave and generalized sine-Gordon equations

NASA Technical Reports Server (NTRS)

Ablowitz, M. J.; Beals, R.; Tenenblat, K.

1986-01-01

The generalized wave equation and generalized sine-Gordon equations are known to be natural multidimensional differential geometric generalizations of the classical two-dimensional versions. In this paper, a system of linear differential equations is associated with these equations, and it is shown how the direct and inverse problems can be solved for appropriately decaying data on suitable lines. An initial-boundary value problem is solved for these equations.

Twisted rogue-wave pairs in the Sasa-Satsuma equation.

PubMed

Chen, Shihua

2013-08-01

Exact explicit rogue wave solutions of the Sasa-Satsuma equation are obtained by use of a Darboux transformation. In addition to the double-peak structure and an analog of the Peregrine soliton, the rogue wave can exhibit an intriguing twisted rogue-wave pair that involves four well-defined zero-amplitude points. This exotic structure may enrich our understanding on the nature of rogue waves.

Influence of a weak gravitational wave on a bound system of two point-masses. [of binary stars

NASA Technical Reports Server (NTRS)

Turner, M. S.

1979-01-01

The problem of a weak gravitational wave impinging upon a nonrelativistic bound system of two point masses is considered. The geodesic equation for each mass is expanded in terms of two small parameters, v/c and dimensionless wave amplitude, in a manner similar to the post-Newtonian expansion; the geodesic equations are resolved into orbital and center-of-mass equations of motion. The effect of the wave on the orbit is determined by using Lagrange's planetary equations to calculate the time evolution of the orbital elements. The gauge properties of the solutions and, in particular, the gauge invariance of the secular effects are discussed.

An efficient Matlab script to calculate heterogeneous anisotropically elastic wave propagation in three dimensions

USGS Publications Warehouse

Boyd, O.S.

2006-01-01

We have created a second-order finite-difference solution to the anisotropic elastic wave equation in three dimensions and implemented the solution as an efficient Matlab script. This program allows the user to generate synthetic seismograms for three-dimensional anisotropic earth structure. The code was written for teleseismic wave propagation in the 1-0.1 Hz frequency range but is of general utility and can be used at all scales of space and time. This program was created to help distinguish among various types of lithospheric structure given the uneven distribution of sources and receivers commonly utilized in passive source seismology. Several successful implementations have resulted in a better appreciation for subduction zone structure, the fate of a transform fault with depth, lithospheric delamination, and the effects of wavefield focusing and defocusing on attenuation. Companion scripts are provided which help the user prepare input to the finite-difference solution. Boundary conditions including specification of the initial wavefield, absorption and two types of reflection are available. ?? 2005 Elsevier Ltd. All rights reserved.

Scour assessments and sediment-transport simulation for selected bridge sites in South Dakota

USGS Publications Warehouse

Niehus, C.A.

1996-01-01

Scour at bridges is a major concern in the design of new bridges and in the evaluation of structural stability of existing bridges. Equations for estimating pier, contraction, and abutment scour have been developed from numerous laboratory studies using sand-bed flumes, but little verification of these scour equations has been done for actual rivers with various bed conditions. This report describes the results of reconnaissance and detailed scour assessments and a sediment-transport simulation for selected bridge sites in South Dakota. Reconnaissance scour assessments were done during 1991 for 32 bridge sites. The reconnaissance assessments for each bridge site included compilation of general and structural data, field inspection to record and measure pertinent scour variables, and evaluation of scour susceptibility using various scour-index forms. Observed pier scour at the 32 sites ranged from 0 to 7 feet, observed contraction scour ranged from 0 to 4 feet, and observed abutment scour ranged from 0 to 10 feet. Thirteen bridge sites having high potential for scour were selected for detailed assessments, which were accomplished during 1992-95. These detailed assessments included prediction of scour depths for 2-, 100-, and 500-year flows using selected published scour equations; measurement of scour during high flows; comparison of measured and predicted scour; and identification of which scour equations best predict actual scour. The medians of predicted pier-scour depth at each of the 13 bridge sites (using 13 scour equations) ranged from 2.4 to 6.8 feet for the 2-year flows and ranged from 3.4 to 13.3 feet for the 500-year flows. The maximum pier scour measured during high flows ranged from 0 to 8.5 feet. Statistical comparison (Spearman rank correlation) of predicted pier-scour depths (using flow data col- lected during scour measurements) indicate that the Laursen, Shen (method b), Colorado State University, and Blench (method b) equations correlate closer with measured scour than do the other prediction equations. The predicted pier-scour depths using the Varzeliotis and Carstens equations have weak statistical rela- tions with measured scour depths. Medians of predicted pier-scour depth from the Shen (method a), Chitale, Bata, and Carstens equations are statistically equal to the median of measured pier-scour depths, based on the Wilcoxon signed-ranks test. The medians of contraction scour depth at each of the 13 bridge sites (using one equation) ranged from -0.1 foot for the 2- year flows to 23.2 feet for the 500-year flows. The maximum contraction scour measured during high flows ranged from 0 to 3.0 feet. The contraction- scour prediction equation substantially overestimated the scour depths in almost all comparisons with the measured scour depths. A significant reason for this discrepancy is due to the wide flood plain (as wide as 5,000 feet) at most of the bridge sites that were investigated. One possible way to reduce this effect for bridge design is to make a decision on what is the effective approach section and thereby limit the size of the bridge flow approach width. The medians of abutment-scour depth at each of the 13 bridge sites (using five equations) ranged from 8.2 to 16.5 feet for the 2-year flows and ranged from 5.7 to 41 feet for the 500-year flows. The maximum abutment scour measured during high flows ranged from 0 to 4.0 feet. The abutment-scour prediction equations also substantially overestimated the scour depths in almost all comparisons with the measured scour depths. The Liu and others (live bed) equation predicted abutment-scour depths substantially lower than the other four abutment-scour equations and closer to the actual measured scour depths. However, this equation at times predicted greater scour depths for 2-year flows than it did for 500-year flows, making its use highly questionable. Again, limiting the bridge flow approach width would produce more reasonable predicted abutment scour.

Influence of pitting defects on quality of high power laser light field

NASA Astrophysics Data System (ADS)

Ren, Huan; Zhang, Lin; Yang, Yi; Shi, Zhendong; Ma, Hua; Jiang, Hongzhen; Chen, Bo; Yang, XiaoYu; Zheng, Wanguo; Zhu, Rihong

2018-01-01

With the split-step-Fourier-transform method for solving the nonlinear paraxial wave equation, the intensity distribution of the light field when the pits diameter or depth change is obtained by using numerical simulation, include the intensity distribution inside optical element, the beam near-field, the different distances behind the element and the beam far-field. Results show that with the increase of pits diameter or depth, the light field peak intensity and the contrast inside of element corresponding enhancement. The contrast of the intensity distribution of the rear surface of the element will increase slightly. The peak intensity produced by a specific location element downstream of thermal effect will continue to increase, the damage probability in optics placed here is greatly increased. For the intensity distribution of the far-field, increase the pitting diameter or depth will cause the focal spot intensity distribution changes, and the energy of the spectrum center region increase constantly. This work provide a basis for quantitative design and inspection for pitting defects, which provides a reference for the design of optical path arrangement.

On the evolution of perturbations to solutions of the Kadomtsev-Petviashvilli equation using the Benney-Luke equation

NASA Astrophysics Data System (ADS)

Ablowitz, Mark J.; Curtis, Christopher W.

2011-05-01

The Benney-Luke equation, which arises as a long wave asymptotic approximation of water waves, contains the Kadomtsev-Petviashvilli (KP) equation as a leading-order maximal balanced approximation. The question analyzed is how the Benney-Luke equation modifies the so-called web solutions of the KP equation. It is found that the Benney-Luke equation introduces dispersive radiation which breaks each of the symmetric soliton-like humps well away from the interaction region of the KP web solution into a tail of multi-peaked oscillating profiles behind the main solitary hump. Computation indicates that the wave structure is modified near the center of the interaction region. Both analytical and numerical techniques are employed for working with non-periodic, non-decaying solutions on unbounded domains.

Exact solutions of unsteady Korteweg-de Vries and time regularized long wave equations.

PubMed

Islam, S M Rayhanul; Khan, Kamruzzaman; Akbar, M Ali

2015-01-01

In this paper, we implement the exp(-Φ(ξ))-expansion method to construct the exact traveling wave solutions for nonlinear evolution equations (NLEEs). Here we consider two model equations, namely the Korteweg-de Vries (KdV) equation and the time regularized long wave (TRLW) equation. These equations play significant role in nonlinear sciences. We obtained four types of explicit function solutions, namely hyperbolic, trigonometric, exponential and rational function solutions of the variables in the considered equations. It has shown that the applied method is quite efficient and is practically well suited for the aforementioned problems and so for the other NLEEs those arise in mathematical physics and engineering fields. PACS numbers: 02.30.Jr, 02.70.Wz, 05.45.Yv, 94.05.Fq.

Applied Analytical Methods for Solving Some Problems of Wave Propagation in the Coastal Areas

NASA Astrophysics Data System (ADS)

Gagoshidze, Shalva; Kodua, Manoni

2016-04-01

Analytical methods, easy for application, are proposed for the solution of the following four classical problems of coastline hydro mechanics: 1. Refraction of waves on coast slopes of arbitrary steepness; 2. Wave propagation in tapering water areas; 3. Longitudinal waves in open channels; 4. Long waves on uniform and non-uniform flows of water. The first three of these problems are solved by the direct Galerkin-Kantorovich method with a choice , of basic functions which completely satisfy all boundary conditions. This approach leads to obtaining new evolutionary equations which can be asymptotically solved by the WKB method. The WKB solution of the first problem enables us to easily determine the three-dimensional field of velocities and to construct the refraction picture of the wave surface near the coast having an arbitrary angle of slope to the horizon varying from 0° to 180°. This solution, in particular for a vertical cliff, fully agrees with Stoker's particular but difficult solution. Moreover, it is shown for the first time that our Schrödinger type evolutionary equation leads to the formation of the so-called "potential wells" if the angle of coast slope to the horizon exceeds 45°, while the angle given at infinity (i.e. at a large distance from the shore) between the wave crests and the coastline exceeds 75°. This theoretical result expressed in terms of elementary functions is well consistent with the experimental observations and with lot of aerial photographs of waves in the coastal zones of the oceans [1,2]. For the second problem we introduce the notions of "wide" and "narrow" water areas. It is shown that Green's law on the wave height growth holds only for the narrow part of the water area, whereas in the wide part the tapering of the water area leads to an insignificant decrease of the wave height. For the third problem, the bank slopes of trapezoidal channels are assumed to have an arbitrary angle of steepness. So far we have known the practically applicable solutions (obtained by MacDonald and Kelland) only for triangular channels whose lateral slopes to the horizon are 30°and 45°. For the fourth problem, a number of unique results are obtained by the correct linearization of shallow water equations. These results include in particular the following: the wave propagation against the flow is blocked by a stream with a Froude number Fr >2/3, but not with Fr > 1, as thought previously. New relations are derived for the conjugate depths of all types of hydraulic jumps and discontinuous roll-waves. References: 1.Stoker,J.J.1957 Water waves.The mathematical theory with application. New York: Interscience Publ., 567 p., (Figures 5.6.2, 5.6.3 and 5.6.5). 2.Hodgins,D.O., Le Blond, P.H. and Huntley, D.A., 1985, Shallow-water wave calculations. Canadian Contractor Report of Hydrography and Ocean Sciences, 10,75 p.,(Figure 3.5). The work supported by Grant Do/77/3-109/14 of the Georgian National Science Foundation

Progressive wave expansions and open boundary problems

NASA Technical Reports Server (NTRS)

Hagstrom, T.; Hariharan, S. I.

1995-01-01

In this paper we construct progressive wave expansions and asymptotic boundary conditions for wave-like equations in exterior domains, including applications to electromagnetics, compressible flows and aero-acoustics. The development of the conditions will be discussed in two parts. The first part will include derivations of asymptotic conditions based on the well-known progressive wave expansions for the two-dimensional wave equations. A key feature in the derivations is that the resulting family of boundary conditions involves a single derivative in the direction normal to the open boundary. These conditions are easy to implement and an application in electromagnetics will be presented. The second part of the paper will discuss the theory for hyperbolic systems in two dimensions. Here, the focus will be to obtain the expansions in a general way and to use them to derive a class of boundary conditions that involve only time derivatives or time and tangential derivatives. Maxwell's equations and the compressible Euler equations are used as examples. Simulations with the linearized Euler equations are presented to validate the theory.

Kinematic parameters of second-mode internal waves in the South China Sea

NASA Astrophysics Data System (ADS)

Kurkina, Oxana; Talipova, Tatiana; Kurkin, Andrey; Naumov, Alexander; Rybin, Artem

2017-04-01

Kinematic parameters of second-mode internal waves (in the framework of weakly nonlinear model of the Gardner equation) are calculated for the region of the South China Sea on a base of GDEM climatology. The prognostic parameters of the model include phase speed of long linear waves, coefficients of dispersion, quadratic and cubic nonlinearity, location (in vertical) of minimum, zero and maximum of the second vertical baroclinic mode and the ratio of its maximal and minimal values. All the parameters are presented in the form of geographical maps for winter (January) and summer (July) seasons. Frequence (in the sense of occurrence) histograms and scatter plots with depth are also given for all the parameters. Special attention is paid to the conditions of normalizing for internal waves of the second mode, as it possesses two extremes. Here some freedom exists, but for correct further modeling of internal waves within the Gardner model one has to fix and keep the same normalization (at maximum or at minimum) for whole a basin. Constructed arrays of prognostic parameters of second-mode internal waves are necessary for the estimations of shape and width (at fixed amplitude) of internal solitary and breather-like waves, limiting amplitudes of internal solitary waves of different families, for assessment of near-bed and near-surface flows induced by such waves, and for evaluation of transport distance for dissolved and suspended matter. The presented results of research are obtained with the support of the Russian Foundation for Basic Research grant 16-05-00049.

On critical behaviour in generalized Kadomtsev-Petviashvili equations

NASA Astrophysics Data System (ADS)

Dubrovin, B.; Grava, T.; Klein, C.

2016-10-01

An asymptotic description of the formation of dispersive shock waves in solutions to the generalized Kadomtsev-Petviashvili (KP) equation is conjectured. The asymptotic description based on a multiscales expansion is given in terms of a special solution to an ordinary differential equation of the Painlevé I hierarchy. Several examples are discussed numerically to provide strong evidence for the validity of the conjecture. The numerical study of the long time behaviour of these examples indicates persistence of dispersive shock waves in solutions to the (subcritical) KP equations, while in the supercritical KP equations a blow-up occurs after the formation of the dispersive shock waves.

Local-in-space blow-up criteria for a class of nonlinear dispersive wave equations

NASA Astrophysics Data System (ADS)

Novruzov, Emil

2017-11-01

This paper is concerned with blow-up phenomena for the nonlinear dispersive wave equation on the real line, ut -uxxt +[ f (u) ] x -[ f (u) ] xxx +[ g (u) + f″/(u) 2 ux2 ] x = 0 that includes the Camassa-Holm equation as well as the hyperelastic-rod wave equation (f (u) = ku2 / 2 and g (u) = (3 - k) u2 / 2) as special cases. We establish some a local-in-space blow-up criterion (i.e., a criterion involving only the properties of the data u0 in a neighborhood of a single point) simplifying and precising earlier blow-up criteria for this equation.

The Weyl-Lanczos equations and the Lanczos wave equation in four dimensions as systems in involution

NASA Astrophysics Data System (ADS)

Dolan, P.; Gerber, A.

2003-07-01

The Weyl-Lanczos equations in four dimensions form a system in involution. We compute its Cartan characters explicitly and use Janet-Riquier theory to confirm the results in the case of all space-times with a diagonal metric tensor and for the plane wave limit of space-times. We write the Lanczos wave equation as an exterior differential system and, with assistance from Janet-Riquier theory, we compute its Cartan characters and find that it forms a system in involution. We compare these Cartan characters with those of the Weyl-Lanczos equations. All results hold for the real analytic case.

The propagation of the shock wave from a strong explosion in a plane-parallel stratified medium: the Kompaneets approximation

NASA Astrophysics Data System (ADS)

Olano, C. A.

2009-11-01

Context: Using certain simplifications, Kompaneets derived a partial differential equation that states the local geometrical and kinematical conditions that each surface element of a shock wave, created by a point blast in a stratified gaseous medium, must satisfy. Kompaneets could solve his equation analytically for the case of a wave propagating in an exponentially stratified medium, obtaining the form of the shock front at progressive evolutionary stages. Complete analytical solutions of the Kompaneets equation for shock wave motion in further plane-parallel stratified media were not found, except for radially stratified media. Aims: We aim to analytically solve the Kompaneets equation for the motion of a shock wave in different plane-parallel stratified media that can reflect a wide variety of astrophysical contexts. We were particularly interested in solving the Kompaneets equation for a strong explosion in the interstellar medium of the Galactic disk, in which, due to intense winds and explosions of stars, gigantic gaseous structures known as superbubbles and supershells are formed. Methods: Using the Kompaneets approximation, we derived a pair of equations that we call adapted Kompaneets equations, that govern the propagation of a shock wave in a stratified medium and that permit us to obtain solutions in parametric form. The solutions provided by the system of adapted Kompaneets equations are equivalent to those of the Kompaneets equation. We solved the adapted Kompaneets equations for shock wave propagation in a generic stratified medium by means of a power-series method. Results: Using the series solution for a shock wave in a generic medium, we obtained the series solutions for four specific media whose respective density distributions in the direction perpendicular to the stratification plane are of an exponential, power-law type (one with exponent k=-1 and the other with k =-2) and a quadratic hyperbolic-secant. From these series solutions, we deduced exact solutions for the four media in terms of elemental functions. The exact solution for shock wave propagation in a medium of quadratic hyperbolic-secant density distribution is very appropriate to describe the growth of superbubbles in the Galactic disk. Member of the Carrera del Investigador Científico del CONICET, Argentina.

New exact periodic solitary-wave solutions for the new (3+1)-dimensional generalized Kadomtsev-Petviashvili equation in multi-temperature electron plasmas

NASA Astrophysics Data System (ADS)

Liu, Jian-Guo; Tian, Yu; Zeng, Zhi-Fang

2017-10-01

In this paper, we aim to introduce a new form of the (3+1)-dimensional generalized Kadomtsev-Petviashvili equation for the long waves of small amplitude with slow dependence on the transverse coordinate. By using the Hirota's bilinear form and the extended homoclinic test approach, new exact periodic solitary-wave solutions for the new (3+1)-dimensional generalized Kadomtsev-Petviashvili equation are presented. Moreover, the properties and characteristics for these new exact periodic solitary-wave solutions are discussed with some figures.

Travelling wave solutions and conservation laws for the Korteweg-de Vries-Bejamin-Bona-Mahony equation

NASA Astrophysics Data System (ADS)

Simbanefayi, Innocent; Khalique, Chaudry Masood

2018-03-01

In this work we study the Korteweg-de Vries-Benjamin-Bona-Mahony (KdV-BBM) equation, which describes the two-way propagation of waves. Using Lie symmetry method together with Jacobi elliptic function expansion and Kudryashov methods we construct its travelling wave solutions. Also, we derive conservation laws of the KdV-BBM equation using the variational derivative approach. In this method, we begin by computing second-order multipliers for the KdV-BBM equation followed by a derivation of the respective conservation laws for each multiplier.

Analytical studies on the Benney-Luke equation in mathematical physics

NASA Astrophysics Data System (ADS)

Islam, S. M. Rayhanul; Khan, Kamruzzaman; Woadud, K. M. Abdul Al

2018-04-01

The enhanced (G‧/G)-expansion method presents wide applicability to handling nonlinear wave equations. In this article, we find the new exact traveling wave solutions of the Benney-Luke equation by using the enhanced (G‧/G)-expansion method. This method is a useful, reliable, and concise method to easily solve the nonlinear evaluation equations (NLEEs). The traveling wave solutions have expressed in term of the hyperbolic and trigonometric functions. We also have plotted the 2D and 3D graphics of some analytical solutions obtained in this paper.

A nonlinear wave equation in nonadiabatic flame propagation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Booty, M.R.; Matalon, M.; Matkowsky, B.J.

1988-06-01

The authors derive a nonlinear wave equation from the diffusional thermal model of gaseous combustion to describe the evolution of a flame front. The equation arises as a long wave theory, for values of the volumeric heat loss in a neighborhood of the extinction point (beyond which planar uniformly propagating flames cease to exist), and for Lewis numbers near the critical value beyond which uniformly propagating planar flames lose stability via a degenerate Hopf bifurcation. Analysis of the equation suggests the possibility of a singularity developing in finite time.

Solitons and SeaSat,

DTIC Science & Technology

1984-08-01

the Kadomtsev - • . Petviashvili (1) equations . A derivation of Eq. (1) in the case of . " * internal waves is given in reference (2). An important...second statement is demonstrated to be false. The% Kadomtsev -.1etviashvile equation relevant to Internal Waves is shown not to have SOliL -solutions. This...more than one space dimension. The second statement is demonstrated to be false. The Kadomtsev -Petviashvile equation relevant to Internal Waves Is

Evidence for a continuous spectrum of equatorial waves in the Indian Ocean

NASA Astrophysics Data System (ADS)

Eriksen, Charles C.

1980-06-01

Seven-month records of current and temperature measurements from a moored array centered at 53°E on the equator in the Indian Ocean are consistent with a continuous spectrum of equatorially trapped internal inertial-gravity, mixed Rossby-gravity, and Kelvin waves. A model spectrum of free linear waves analogous to those for mid-latitude internal gravity waves is used to compute spectra of observed quantities at depths greater than about 2000 m. Model parameters are adjusted to fit general patterns in the observed spectra over periods from roughly 2 days to 1 month. Measurements at shallower depths presumably include forced motions which we have not attempted to model. This `straw-person' spectrum is consistent with the limited data available. The model spectru Ē (n, m, ω) = K · B(m) · C(n, ω), where Ē is an average local energy density in the equatorial wave guide which has amplitude K, wave number shape B(m) ∝ (1 + m/m*)-3, where m is vertical mode number and the bandwidth parameter m* is between 4 and 8, and frequency shape C(n, ω) ∝ [(2n + 1 + s2)½ · σ3]-1 where n is meridional mode number, and s and σ are dimensionless zonal wave number and frequency related by the usual dispersion relation. The scales are (β/cm)½ and (β · cm)½ for horizontal wave number and frequency, where cm is the Kelvin wave speed of the vertical mode m. At each frequency and vertical wave number, energy is partitioned equally among the available inertial gravity modes so that the field tends toward horizontal isotropy at high frequency. The transition between Kelvin and mixed Rossby-gravity motion at low frequency and inertial-gravity motion at high frequency occurs at a period of roughly 1 week. At periods in the range 1-3 weeks, the model spectrum which fits the observations suggests that mixed Rossby-gravity motion dominates; at shorter periods gravity motion dominates. The model results are consistent with the low vertical coherence lengths observed (roughly 80 m). Horizontal coherence over 2 km is consistent with isotropic energy flux. Evidence for net zontal energy flux is not found in this data, and the presence of a red wave number shape suggests that net flux will be difficult to observe from modest moored arrays. The equatorial wave spectrum does not match across the diurnal and semidiurnal tides to the high-frequency internal wave spectrum (the latter is roughly 1 decade higher).

Wave propagation through a flexoelectric piezoelectric slab sandwiched by two piezoelectric half-spaces.

PubMed

Jiao, Fengyu; Wei, Peijun; Li, Yueqiu

2018-01-01

Reflection and transmission of plane waves through a flexoelectric piezoelectric slab sandwiched by two piezoelectric half-spaces are studied in this paper. The secular equations in the flexoelectric piezoelectric material are first derived from the general governing equation. Different from the classical piezoelectric medium, there are five kinds of coupled elastic waves in the piezoelectric material with the microstructure effects taken into consideration. The state vectors are obtained by the summation of contributions from all possible partial waves. The state transfer equation of flexoelectric piezoelectric slab is derived from the motion equation by the reduction of order, and the transfer matrix of flexoelectric piezoelectric slab is obtained by solving the state transfer equation. By using the continuous conditions at the interface and the approach of partition matrix, we get the resultant algebraic equations in term of the transfer matrix from which the reflection and transmission coefficients can be calculated. The amplitude ratios and further the energy flux ratios of various waves are evaluated numerically. The numerical results are shown graphically and are validated by the energy conservation law. Based on these numerical results, the influences of two characteristic lengths of microstructure and the flexoelectric coefficients on the wave propagation are discussed. Copyright © 2017 Elsevier B.V. All rights reserved.

Microscopic Lagrangian description of warm plasmas. I - Linear wave propagation. II - Nonlinear wave interactions

NASA Technical Reports Server (NTRS)

Kim, H.; Crawford, F. W.

1977-01-01

It is pointed out that the conventional iterative analysis of nonlinear plasma wave phenomena, which involves a direct use of Maxwell's equations and the equations describing the particle dynamics, leads to formidable theoretical and algebraic complexities, especially for warm plasmas. As an effective alternative, the Lagrangian method may be applied. It is shown how this method may be used in the microscopic description of small-signal wave propagation and in the study of nonlinear wave interactions. The linear theory is developed for an infinite, homogeneous, collisionless, warm magnetoplasma. A summary is presented of a perturbation expansion scheme described by Galloway and Kim (1971), and Lagrangians to third order in perturbation are considered. Attention is given to the averaged-Lagrangian density, the action-transfer and coupled-mode equations, and the general solution of the coupled-mode equations.

Rogue waves in the multicomponent Mel'nikov system and multicomponent Schrödinger-Boussinesq system

NASA Astrophysics Data System (ADS)

Sun, Baonan; Lian, Zhan

2018-02-01

By virtue of the bilinear method and the KP hierarchy reduction technique, exact explicit rational solutions of the multicomponent Mel'nikov equation and the multicomponent Schrödinger-Boussinesq equation are constructed, which contain multicomponent short waves and single-component long wave. For the multicomponent Mel'nikov equation, the fundamental rational solutions possess two different behaviours: lump and rogue wave. It is shown that the fundamental (simplest) rogue waves are line localised waves which arise from the constant background with a line profile and then disappear into the constant background again. The fundamental line rogue waves can be classified into three: bright, intermediate and dark line rogue waves. Two subclasses of non-fundamental rogue waves, i.e., multirogue waves and higher-order rogue waves are discussed. The multirogue waves describe interaction of several fundamental line rogue waves, in which interesting wave patterns appear in the intermediate time. Higher-order rogue waves exhibit dynamic behaviours that the wave structures start from lump and then retreat back to it. Moreover, by taking the parameter constraints further, general higher-order rogue wave solutions for the multicomponent Schrödinger-Boussinesq system are generated.

Some new traveling wave exact solutions of the (2+1)-dimensional Boiti-Leon-Pempinelli equations.

PubMed

Qi, Jian-ming; Zhang, Fu; Yuan, Wen-jun; Huang, Zi-feng

2014-01-01

We employ the complex method to obtain all meromorphic exact solutions of complex (2+1)-dimensional Boiti-Leon-Pempinelli equations (BLP system of equations). The idea introduced in this paper can be applied to other nonlinear evolution equations. Our results show that all rational and simply periodic traveling wave exact solutions of the equations (BLP) are solitary wave solutions, the complex method is simpler than other methods, and there exist some rational solutions ur,2 (z) and simply periodic solutions us,2-6(z) which are not only new but also not degenerated successively by the elliptic function solutions. We believe that this method should play an important role for finding exact solutions in the mathematical physics. For these new traveling wave solutions, we give some computer simulations to illustrate our main results.

Rogue waves and unbounded solutions of the NLSE

NASA Astrophysics Data System (ADS)

Lechuga, Antonio

2017-04-01

Since the pioneering work of Zakharov has been generally admitted that rogue waves can be studied in the framework of the Nonlinear Schrödinger Equation (NLSE). Many researchers, Akhmediev, Peregrine, Matveev among others gave different solutions to this equation that, in some way, could be linked to rogue waves and also to its more important characteristic: its unexpectedness. Janssen (2003, 2004), Onorato (2004, 2006) and Waseda (2006) linked the coefficient of the nonlinear term of the Schrödinger equation with the Benjamin-Feir index (BFI) that, we know, is a measure of the modulational instability of the waves. From this point of view the value of this coefficient of the NLSE could be known from statistics. Thus the relationship between sea states and the mechanism of generation of rogue waves could be found out. Following the well-known Lie group theory researchers have been studying the Lie point symmetries of the NLSE: the scaling transformations, Galilean transformations and phase transformations. Basically these transformations turn the NLSE into a nonlinear ordinary differential equation called Duffing equation (also called eikonal equation). There are different ways to do this, but in most of them the independent variable that could be seen as a space variable is a kind of moving frame with the time incorporated in this way. The main aim of this work is to classify solutions of the Duffing equation (periodic and nonperiodic waves and also bounded and unbounded waves) bearing in mind that the coefficient of the nonlinear term in the NLSE is left unaltered in the process of the transformation.

Current structure of strongly nonlinear interfacial solitary waves

NASA Astrophysics Data System (ADS)

Semin, Sergey; Kurkina, Oxana; Kurkin, Andrey; Talipova, Tatiana; Pelinovsky, Efim; Churaev, Egor

2015-04-01

The characteristics of highly nonlinear solitary internal waves (solitons) in two-layer flow are computed within the fully nonlinear Navier-Stokes equations with use of numerical model of the Massachusetts Institute of Technology (MITgcm). The verification and adaptation of the model is based on the data from laboratory experiments [Carr & Davies, 2006]. The present paper also compares the results of our calculations with the computations performed in the framework of the fully nonlinear Bergen Ocean Model [Thiem et al, 2011]. The comparison of the computed soliton parameters with the predictions of the weakly nonlinear theory based on the Gardner equation is given. The occurrence of reverse flow in the bottom layer directly behind the soliton is confirmed in numerical simulations. The trajectories of Lagrangian particles in the internal soliton on the surface, on the interface and near the bottom are computed. The results demonstrated completely different trajectories at different depths of the model area. Thus, in the surface layer is observed the largest displacement of Lagrangian particles, which can be more than two and a half times larger than the characteristic width of the soliton. Located at the initial moment along the middle pycnocline fluid particles move along the elongated vertical loop at a distance of not more than one third of the width of the solitary wave. In the bottom layer of the fluid moves in the opposite direction of propagation of the internal wave, but under the influence of the reverse flow, when the bulk of the velocity field of the soliton ceases to influence the trajectory, it moves in the opposite direction. The magnitude of displacement of fluid particles in the bottom layer is not more than the half-width of the solitary wave. 1. Carr, M., and Davies, P.A. The motion of an internal solitary wave of depression over a fixed bottom boundary in a shallow, two-layer fluid. Phys. Fluids, 2006, vol. 18, No. 1, 1 - 10. 2. Thiem, O., Carr, M., Berntsen, J., and Davies, P.A. Numerical simulation of internal solitary wave-induced reverse flow and associated vortices in a shallow, two-layer fluid benthic boundary layer. Ocean Dynamics, 2011, vol. 61, No. 6, 857 - 872.

Dark- and bright-rogue-wave solutions for media with long-wave-short-wave resonance.

PubMed

Chen, Shihua; Grelu, Philippe; Soto-Crespo, J M

2014-01-01

Exact explicit rogue-wave solutions of intricate structures are presented for the long-wave-short-wave resonance equation. These vector parametric solutions feature coupled dark- and bright-field counterparts of the Peregrine soliton. Numerical simulations show the robustness of dark and bright rogue waves in spite of the onset of modulational instability. Dark fields originate from the complex interplay between anomalous dispersion and the nonlinearity driven by the coupled long wave. This unusual mechanism, not available in scalar nonlinear wave equation models, can provide a route to the experimental realization of dark rogue waves in, for instance, negative index media or with capillary-gravity waves.

Equivalent equations of motion for gravity and entropy

DOE Office of Scientific and Technical Information (OSTI.GOV)

Czech, Bartlomiej; Lamprou, Lampros; McCandlish, Samuel

We demonstrate an equivalence between the wave equation obeyed by the entanglement entropy of CFT subregions and the linearized bulk Einstein equation in Anti-de Sitter space. In doing so, we make use of the formalism of kinematic space and fields on this space. We show that the gravitational dynamics are equivalent to a gauge invariant wave-equation on kinematic space and that this equation arises in natural correspondence to the conformal Casimir equation in the CFT.

Equivalent equations of motion for gravity and entropy

DOE PAGES

Czech, Bartlomiej; Lamprou, Lampros; McCandlish, Samuel; ...

2017-02-01

We demonstrate an equivalence between the wave equation obeyed by the entanglement entropy of CFT subregions and the linearized bulk Einstein equation in Anti-de Sitter space. In doing so, we make use of the formalism of kinematic space and fields on this space. We show that the gravitational dynamics are equivalent to a gauge invariant wave-equation on kinematic space and that this equation arises in natural correspondence to the conformal Casimir equation in the CFT.

Unsteady streamflow simulation using a linear implicit finite-difference model

USGS Publications Warehouse

Land, Larry F.

1978-01-01

A computer program for simulating one-dimensional subcritical, gradually varied, unsteady flow in a stream has been developed and documented. Given upstream and downstream boundary conditions and channel geometry data, roughness coefficients, stage, and discharge can be calculated anywhere within the reach as a function of time. The program uses a linear implicit finite-difference technique that discritizes the partial differential equations. Then it arranges the coefficients of the continuity and momentum equations into a pentadiagonal matrix for solution. Because it is a reasonable compromise between computational accuracy, speed and ease of use,the technique is one of the most commonly used. The upstream boundary condition is a depth hydrograph. However, options also allow the boundary condition to be discharge or water-surface elevation. The downstream boundary condition is a depth which may be constant, self-setting, or unsteady. The reach may be divided into uneven increments and the cross sections may be nonprismatic and may vary from one to the other. Tributary and lateral inflow may enter the reach. The digital model will simulate such common problems as (1) flood waves, (2) releases from dams, and (3) channels where storage is a consideration. It may also supply the needed flow information for mass-transport simulation. (Woodard-USGS)

Novel approach for dam break flow modeling using computational intelligence

NASA Astrophysics Data System (ADS)

Seyedashraf, Omid; Mehrabi, Mohammad; Akhtari, Ali Akbar

2018-04-01

A new methodology based on the computational intelligence (CI) system is proposed and tested for modeling the classic 1D dam-break flow problem. The reason to seek for a new solution lies in the shortcomings of the existing analytical and numerical models. This includes the difficulty of using the exact solutions and the unwanted fluctuations, which arise in the numerical results. In this research, the application of the radial-basis-function (RBF) and multi-layer-perceptron (MLP) systems is detailed for the solution of twenty-nine dam-break scenarios. The models are developed using seven variables, i.e. the length of the channel, the depths of the up-and downstream sections, time, and distance as the inputs. Moreover, the depths and velocities of each computational node in the flow domain are considered as the model outputs. The models are validated against the analytical, and Lax-Wendroff and MacCormack FDM schemes. The findings indicate that the employed CI models are able to replicate the overall shape of the shock- and rarefaction-waves. Furthermore, the MLP system outperforms RBF and the tested numerical schemes. A new monolithic equation is proposed based on the best fitting model, which can be used as an efficient alternative to the existing piecewise analytic equations.

High Frequency Acoustic Propagation using Level Set Methods

DTIC Science & Technology

2007-01-01

solution of the high frequency approximation to the wave equation. Traditional solutions to the Eikonal equation in high frequency acoustics are...the Eikonal equation derived from the high frequency approximation to the wave equation, ucuH ∇±=∇ )(),( xx , with the nonnegative function c(x...For simplicity, we only consider the case ucuH ∇+=∇ )(),( xx . Two difficulties must be addressed when solving the Eikonal equation in a fixed

Soliton-cnoidal interactional wave solutions for the reduced Maxwell-Bloch equations

NASA Astrophysics Data System (ADS)

Huang, Li-Li; Qiao, Zhi-Jun; Chen, Yong

2018-02-01

Based on nonlocal symmetry method, localized excitations and interactional solutions are investigated for the reduced Maxwell-Bloch equations. The nonlocal symmetries of the reduced Maxwell-Bloch equations are obtained by the truncated Painleve expansion approach and the Mobious invariant property. The nonlocal symmetries are localized to a prolonged system by introducing suitable auxiliary dependent variables. The extended system can be closed and a novel Lie point symmetry system is constructed. By solving the initial value problems, a new type of finite symmetry transformations is obtained to derive periodic waves, Ma breathers and breathers travelling on the background of periodic line waves. Then rich exact interactional solutions are derived between solitary waves and other waves including cnoidal waves, rational waves, Painleve waves, and periodic waves through similarity reductions. In particular, several new types of localized excitations including rogue waves are found, which stem from the arbitrary function generated in the process of similarity reduction. By computer numerical simulation, the dynamics of these localized excitations and interactional solutions are discussed, which exhibit meaningful structures.

Analysis shear wave velocity structure obtained from surface wave methods in Bornova, Izmir

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pamuk, Eren, E-mail: eren.pamuk@deu.edu.tr; Akgün, Mustafa, E-mail: mustafa.akgun@deu.edu.tr; Özdağ, Özkan Cevdet, E-mail: cevdet.ozdag@deu.edu.tr

2016-04-18

Properties of the soil from the bedrock is necessary to describe accurately and reliably for the reduction of earthquake damage. Because seismic waves change their amplitude and frequency content owing to acoustic impedance difference between soil and bedrock. Firstly, shear wave velocity and depth information of layers on bedrock is needed to detect this changing. Shear wave velocity can be obtained using inversion of Rayleigh wave dispersion curves obtained from surface wave methods (MASW- the Multichannel Analysis of Surface Waves, ReMi-Refraction Microtremor, SPAC-Spatial Autocorrelation). While research depth is limeted in active source study, a passive source methods are utilized formore » deep depth which is not reached using active source methods. ReMi method is used to determine layer thickness and velocity up to 100 m using seismic refraction measurement systems.The research carried out up to desired depth depending on radius using SPAC which is utilized easily in conditions that district using of seismic studies in the city. Vs profiles which are required to calculate deformations in under static and dynamic loads can be obtained with high resolution using combining rayleigh wave dispersion curve obtained from active and passive source methods. In the this study, Surface waves data were collected using the measurements of MASW, ReMi and SPAC at the İzmir Bornova region. Dispersion curves obtained from surface wave methods were combined in wide frequency band and Vs-depth profiles were obtained using inversion. Reliability of the resulting soil profiles were provided by comparison with theoretical transfer function obtained from soil paremeters and observed soil transfer function from Nakamura technique and by examination of fitting between these functions. Vs values are changed between 200-830 m/s and engineering bedrock (Vs>760 m/s) depth is approximately 150 m.« less

Grating formation by a high power radio wave in near-equator ionosphere

DOE Office of Scientific and Technical Information (OSTI.GOV)

Singh, Rohtash; Sharma, A. K.; Tripathi, V. K.

2011-11-15

The formation of a volume grating in the near-equator regions of ionosphere due to a high power radio wave is investigated. The radio wave, launched from a ground based transmitter, forms a standing wave pattern below the critical layer, heating the electrons in a space periodic manner. The thermal conduction along the magnetic lines of force inhibits the rise in electron temperature, limiting the efficacy of heating to within a latitude of few degrees around the equator. The space periodic electron partial pressure leads to ambipolar diffusion creating a space periodic density ripple with wave vector along the vertical. Suchmore » a volume grating is effective to cause strong reflection of radio waves at a frequency one order of magnitude higher than the maximum plasma frequency in the ionosphere. Linearly mode converted plasma wave could scatter even higher frequency radio waves.« less

Relative Wave Energy based Adaptive Neuro-Fuzzy Inference System model for the Estimation of Depth of Anaesthesia.

PubMed

Benzy, V K; Jasmin, E A; Koshy, Rachel Cherian; Amal, Frank; Indiradevi, K P

2018-01-01

The advancement in medical research and intelligent modeling techniques has lead to the developments in anaesthesia management. The present study is targeted to estimate the depth of anaesthesia using cognitive signal processing and intelligent modeling techniques. The neurophysiological signal that reflects cognitive state of anaesthetic drugs is the electroencephalogram signal. The information available on electroencephalogram signals during anaesthesia are drawn by extracting relative wave energy features from the anaesthetic electroencephalogram signals. Discrete wavelet transform is used to decomposes the electroencephalogram signals into four levels and then relative wave energy is computed from approximate and detail coefficients of sub-band signals. Relative wave energy is extracted to find out the degree of importance of different electroencephalogram frequency bands associated with different anaesthetic phases awake, induction, maintenance and recovery. The Kruskal-Wallis statistical test is applied on the relative wave energy features to check the discriminating capability of relative wave energy features as awake, light anaesthesia, moderate anaesthesia and deep anaesthesia. A novel depth of anaesthesia index is generated by implementing a Adaptive neuro-fuzzy inference system based fuzzy c-means clustering algorithm which uses relative wave energy features as inputs. Finally, the generated depth of anaesthesia index is compared with a commercially available depth of anaesthesia monitor Bispectral index.

Exact Solutions of Atmospheric (2+1)-Dimensional Nonlinear Incompressible Non-hydrostatic Boussinesq Equations

NASA Astrophysics Data System (ADS)

Liu, Ping; Wang, Ya-Xiong; Ren, Bo; Li, Jin-Hua

2016-12-01

Exact solutions of the atmospheric (2+1)-dimensional nonlinear incompressible non-hydrostatic Boussinesq (INHB) equations are researched by Combining function expansion and symmetry method. By function expansion, several expansion coefficient equations are derived. Symmetries and similarity solutions are researched in order to obtain exact solutions of the INHB equations. Three types of symmetry reduction equations and similarity solutions for the expansion coefficient equations are proposed. Non-traveling wave solutions for the INHB equations are obtained by symmetries of the expansion coefficient equations. Making traveling wave transformations on expansion coefficient equations, we demonstrate some traveling wave solutions of the INHB equations. The evolutions on the wind velocities, temperature perturbation and pressure perturbation are demonstrated by figures, which demonstrate the periodic evolutions with time and space. Supported by the National Natural Science Foundation of China under Grant Nos. 11305031 and 11305106, and Training Programme Foundation for Outstanding Young Teachers in Higher Education Institutions of Guangdong Province under Grant No. Yq2013205

Applications of the ETEM for obtaining optical soliton solutions for the Lakshmanan-Porsezian-Daniel model

NASA Astrophysics Data System (ADS)

Manafian, Jalil; Foroutan, Mohammadreza; Guzali, Aref

2017-11-01

This paper examines the effectiveness of an integration scheme which is called the extended trial equation method (ETEM) for solving a well-known nonlinear equation of partial differential equations (PDEs). In this respect, the Lakshmanan-Porsezian-Daniel (LPD) equation with Kerr and power laws of nonlinearity which describes higher-order dispersion, full nonlinearity and spatiotemporal dispersion is considered, and as an achievement, a series of exact travelling-wave solutions for the aforementioned equation is formally extracted. Explicit new exact solutions are derived in different form such as dark solitons, bright solitons, solitary wave, periodic solitary wave, rational function, and elliptic function solutions of LPD equation. The movement of obtained solutions is shown graphically, which helps to understand the physical phenomena of this optical soliton equation. Many other such types of nonlinear equations arising in basic fabric of communications network technology and nonlinear optics can also be solved by this method.

Time domain viscoelastic full waveform inversion

NASA Astrophysics Data System (ADS)

Fabien-Ouellet, Gabriel; Gloaguen, Erwan; Giroux, Bernard

2017-06-01

Viscous attenuation can have a strong impact on seismic wave propagation, but it is rarely taken into account in full waveform inversion (FWI). When viscoelasticity is considered in time domain FWI, the displacement formulation of the wave equation is usually used instead of the popular velocity-stress formulation. However, inversion schemes rely on the adjoint equations, which are quite different for the velocity-stress formulation than for the displacement formulation. In this paper, we apply the adjoint state method to the isotropic viscoelastic wave equation in the velocity-stress formulation based on the generalized standard linear solid rheology. By applying linear transformations to the wave equation before deriving the adjoint state equations, we obtain two symmetric sets of partial differential equations for the forward and adjoint variables. The resulting sets of equations only differ by a sign change and can be solved by the same numerical implementation. We also investigate the crosstalk between parameter classes (velocity and attenuation) of the viscoelastic equation. More specifically, we show that the attenuation levels can be used to recover the quality factors of P and S waves, but that they are very sensitive to velocity errors. Finally, we present a synthetic example of viscoelastic FWI in the context of monitoring CO2 geological sequestration. We show that FWI based on our formulation can indeed recover P- and S-wave velocities and their attenuation levels when attenuation is high enough. Both changes in velocity and attenuation levels recovered with FWI can be used to track the CO2 plume during and after injection. Further studies are required to evaluate the performance of viscoelastic FWI on real data.

Semi-analytical Karhunen-Loeve representation of irregular waves based on the prolate spheroidal wave functions

NASA Astrophysics Data System (ADS)

Lee, Gibbeum; Cho, Yeunwoo

2018-01-01

A new semi-analytical approach is presented to solving the matrix eigenvalue problem or the integral equation in Karhunen-Loeve (K-L) representation of random data such as irregular ocean waves. Instead of direct numerical approach to this matrix eigenvalue problem, which may suffer from the computational inaccuracy for big data, a pair of integral and differential equations are considered, which are related to the so-called prolate spheroidal wave functions (PSWF). First, the PSWF is expressed as a summation of a small number of the analytical Legendre functions. After substituting them into the PSWF differential equation, a much smaller size matrix eigenvalue problem is obtained than the direct numerical K-L matrix eigenvalue problem. By solving this with a minimal numerical effort, the PSWF and the associated eigenvalue of the PSWF differential equation are obtained. Then, the eigenvalue of the PSWF integral equation is analytically expressed by the functional values of the PSWF and the eigenvalues obtained in the PSWF differential equation. Finally, the analytically expressed PSWFs and the eigenvalues in the PWSF integral equation are used to form the kernel matrix in the K-L integral equation for the representation of exemplary wave data such as ordinary irregular waves. It is found that, with the same accuracy, the required memory size of the present method is smaller than that of the direct numerical K-L representation and the computation time of the present method is shorter than that of the semi-analytical method based on the sinusoidal functions.

Long-term evolution of electron distribution function due to nonlinear resonant interaction with whistler mode waves

NASA Astrophysics Data System (ADS)

Artemyev, Anton V.; Neishtadt, Anatoly I.; Vasiliev, Alexei A.

2018-04-01

Accurately modelling and forecasting of the dynamics of the Earth's radiation belts with the available computer resources represents an important challenge that still requires significant advances in the theoretical plasma physics field of wave-particle resonant interaction. Energetic electron acceleration or scattering into the Earth's atmosphere are essentially controlled by their resonances with electromagnetic whistler mode waves. The quasi-linear diffusion equation describes well this resonant interaction for low intensity waves. During the last decade, however, spacecraft observations in the radiation belts have revealed a large number of whistler mode waves with sufficiently high intensity to interact with electrons in the nonlinear regime. A kinetic equation including such nonlinear wave-particle interactions and describing the long-term evolution of the electron distribution is the focus of the present paper. Using the Hamiltonian theory of resonant phenomena, we describe individual electron resonance with an intense coherent whistler mode wave. The derived characteristics of such a resonance are incorporated into a generalized kinetic equation which includes non-local transport in energy space. This transport is produced by resonant electron trapping and nonlinear acceleration. We describe the methods allowing the construction of nonlinear resonant terms in the kinetic equation and discuss possible applications of this equation.

Shock waves: The Maxwell-Cattaneo case.

PubMed

Uribe, F J

2016-03-01

Several continuum theories for shock waves give rise to a set of differential equations in which the analysis of the underlying vector field can be done using the tools of the theory of dynamical systems. We illustrate the importance of the divergences associated with the vector field by considering the ideas by Maxwell and Cattaneo and apply them to study shock waves in dilute gases. By comparing the predictions of the Maxwell-Cattaneo equations with shock wave experiments we are lead to the following conclusions: (a) For low compressions (low Mach numbers: M) the results from the Maxwell-Cattaneo equations provide profiles that are in fair agreement with the experiments, (b) as the Mach number is increased we find a range of Mach numbers (1.27 ≈ M(1) < M < M(2) ≈ 1.90) such that numerical shock wave solutions to the Maxwell-Cattaneo equations cannot be found, and (c) for greater Mach numbers (M>M_{2}) shock wave solutions can be found though they differ significantly from experiments.

Lagrangian geometrical optics of nonadiabatic vector waves and spin particles

DOE PAGES

Ruiz, D. E.; Dodin, I. Y.

2015-07-29

Linear vector waves, both quantum and classical, experience polarization-driven bending of ray trajectories and polarization dynamics that can be interpreted as the precession of the "wave spin". Here, both phenomena are governed by an effective gauge Hamiltonian vanishing in leading-order geometrical optics. This gauge Hamiltonian can be recognized as a generalization of the Stern-Gerlach Hamiltonian that is commonly known for spin-1/2 quantum particles. The corresponding reduced Lagrangians for continuous nondissipative waves and their geometrical-optics rays are derived from the fundamental wave Lagrangian. The resulting Euler-Lagrange equations can describe simultaneous interactions of N resonant modes, where N is arbitrary, and leadmore » to equations for the wave spin, which happens to be an (N 2 - 1)-dimensional spin vector. As a special case, classical equations for a Dirac particle (N = 2) are deduced formally, without introducing additional postulates or interpretations, from the Dirac quantum Lagrangian with the Pauli term. The model reproduces the Bargmann-Michel-Telegdi equations with added Stern-Gerlach force.« less

4-wave dynamics in kinetic wave turbulence

NASA Astrophysics Data System (ADS)

Chibbaro, Sergio; Dematteis, Giovanni; Rondoni, Lamberto

2018-01-01

A general Hamiltonian wave system with quartic resonances is considered, in the standard kinetic limit of a continuum of weakly interacting dispersive waves with random phases. The evolution equation for the multimode characteristic function Z is obtained within an ;interaction representation; and a perturbation expansion in the small nonlinearity parameter. A frequency renormalization is performed to remove linear terms that do not appear in the 3-wave case. Feynman-Wyld diagrams are used to average over phases, leading to a first order differential evolution equation for Z. A hierarchy of equations, analogous to the Boltzmann hierarchy for low density gases is derived, which preserves in time the property of random phases and amplitudes. This amounts to a general formalism for both the N-mode and the 1-mode PDF equations for 4-wave turbulent systems, suitable for numerical simulations and for investigating intermittency. Some of the main results which are developed here in detail have been tested numerically in a recent work.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Li Jibin; Qiao Zhijun

This paper deals with the following equation m{sub t}=(1/2)(1/m{sup k}){sub xxx}-(1/2)(1/m{sup k}){sub x}, which is proposed by Z. J. Qiao [J. Math. Phys. 48, 082701 (2007)] and Qiao and Liu [Chaos, Solitons Fractals 41, 587 (2009)]. By adopting the phase analysis method of planar dynamical systems and the theory of the singular traveling wave systems to the traveling wave solutions of the equation, it is shown that for different k, the equation may have infinitely many solitary wave solutions, periodic wave solutions, kink/antikink wave solutions, cusped solitary wave solutions, and breaking loop solutions. We discuss in a detail the casesmore » of k=-2,-(1/2),(1/2),2, and parametric representations of all possible bounded traveling wave solutions are given in the different (c,g)-parameter regions.« less

Low-frequency surface waves on semi-bounded magnetized quantum plasma

DOE Office of Scientific and Technical Information (OSTI.GOV)

Moradi, Afshin, E-mail: a.moradi@kut.ac.ir

2016-08-15

The propagation of low-frequency electrostatic surface waves on the interface between a vacuum and an electron-ion quantum plasma is studied in the direction perpendicular to an external static magnetic field which is parallel to the interface. A new dispersion equation is derived by employing both the quantum magnetohydrodynamic and Poisson equations. It is shown that the dispersion equations for forward and backward-going surface waves are different from each other.

Calculation Of Pneumatic Attenuation In Pressure Sensors

NASA Technical Reports Server (NTRS)

Whitmore, Stephen A.

1991-01-01

Errors caused by attenuation of air-pressure waves in narrow tubes calculated by method based on fundamental equations of flow. Changes in ambient pressure transmitted along narrow tube to sensor. Attenuation of high-frequency components of pressure wave calculated from wave equation derived from Navier-Stokes equations of viscous flow in tube. Developed to understand and compensate for frictional attenuation in narrow tubes used to connect aircraft pressure sensors with pressure taps on affected surfaces.

Electromagnetic or other directed energy pulse launcher

DOEpatents

Ziolkowski, Richard W.

1990-01-01

The physical realization of new solutions of wave propagation equations, such as Maxwell's equations and the scaler wave equation, produces localized pulses of wave energy such as electromagnetic or acoustic energy which propagate over long distances without divergence. The pulses are produced by driving each element of an array of radiating sources with a particular drive function so that the resultant localized packet of energy closely approximates the exact solutions and behaves the same.

Local Earthquake P-wave Tomography at Mount St. Helens with the iMUSH Broadband Array

NASA Astrophysics Data System (ADS)

Ulberg, C. W.; Creager, K. C.; Moran, S. C.; Abers, G. A.; Crosbie, K.; Crosson, R. S.; Denlinger, R. P.; Thelen, W. A.; Hansen, S. M.; Schmandt, B.; Kiser, E.; Levander, A.; Bachmann, O.

2016-12-01

We deployed 70 broadband seismometers in the summer of 2014 to image the seismic velocity structure beneath Mount St. Helens (MSH), Washington, as part of the collaborative imaging Magma Under St. Helens (iMUSH) project. Our goal is to illuminate the MSH magmatic system by integrating all portions of the iMUSH experiment, including active- and passive-source tomography, ambient-noise tomography, seismicity, receiver functions, magnetotellurics, and petrology. The broadband array has a diameter of 100 km centered on MSH with an average station spacing of 10 km, and was deployed through summer 2016. It is augmented by dozens of permanent stations in the area. We determine P-wave arrival times and also incorporate picks from the permanent network. There were more than 250 local events during the first year of iMUSH broadband recording, which have provided over 11,000 high-quality arrival times. The iMUSH experiment included 23 active shots in 2014 that were recorded with good signal-to-noise ratios across the entire array. Direct raypaths from local earthquakes and active shots reach 15-20 km depth beneath MSH. We use the program struct3DP to iteratively invert travel times to obtain a 3-D seismic velocity model and relocate hypocenters. Travel times are computed using a 3-D eikonal-equation solver. We are expanding our analysis to include S-wave arrivals from local events. The preliminary 3-D model shows low P-wave speeds along the St. Helens seismic zone, striking NNW-SSE of MSH from near the surface to where we lose resolution at 15-20km depth. This seismic zone coincides with a sharp boundary in Moho reflectivity that has been interpreted as the eastern boundary of a serpentinized mantle wedge (Hansen et al, 2016, submitted). We speculate that the seismic zone and low wave speeds are related to fluids rising from the eastern boundary of the wedge.

Traveling wave solutions of the Boussinesq equation via the new approach of generalized (G'/G)-expansion method.

PubMed

Alam, Md Nur; Akbar, M Ali; Roshid, Harun-Or-

2014-01-01

Exact solutions of nonlinear evolution equations (NLEEs) play a vital role to reveal the internal mechanism of complex physical phenomena. In this work, the exact traveling wave solutions of the Boussinesq equation is studied by using the new generalized (G'/G)-expansion method. Abundant traveling wave solutions with arbitrary parameters are successfully obtained by this method and the wave solutions are expressed in terms of the hyperbolic, trigonometric, and rational functions. It is shown that the new approach of generalized (G'/G)-expansion method is a powerful and concise mathematical tool for solving nonlinear partial differential equations in mathematical physics and engineering. 05.45.Yv, 02.30.Jr, 02.30.Ik.

FAST TRACK COMMUNICATION: Soliton solutions of the KP equation with V-shape initial waves

NASA Astrophysics Data System (ADS)

Kodama, Y.; Oikawa, M.; Tsuji, H.

2009-08-01

We consider the initial value problems of the Kadomtsev-Petviashvili (KP) equation for symmetric V-shape initial waves consisting of two semi-infinite line solitons with the same amplitude. Those are particularly important for studies of large amplitude waves such as tsunami in shallow water. Numerical simulations show that the solutions of the initial value problem approach asymptotically to certain exact solutions of the KP equation found recently in [1]. We then use a chord diagram to explain the asymptotic result. This provides an analytical method to study asymptotic behavior for the initial value problem of the KP equation. We also demonstrate a real experiment of shallow water waves which may represent the solution discussed in this communication.

Dynamic behavior of ion acoustic waves in electron-positron-ion magnetoplasmas with superthermal electrons and positrons

DOE Office of Scientific and Technical Information (OSTI.GOV)

Saha, Asit, E-mail: asit-saha123@rediffmail.com, E-mail: prasantachatterjee1@rediffmail.com; Department of Mathematics, Siksha Bhavana, Visva Bharati University, Santiniketan-731235; Pal, Nikhil

The dynamic behavior of ion acoustic waves in electron-positron-ion magnetoplasmas with superthermal electrons and positrons has been investigated in the framework of perturbed and non-perturbed Kadomtsev-Petviashili (KP) equations. Applying the reductive perturbation technique, we have derived the KP equation in electron-positron-ion magnetoplasma with kappa distributed electrons and positrons. Bifurcations of ion acoustic traveling waves of the KP equation are presented. Using the bifurcation theory of planar dynamical systems, the existence of the solitary wave solutions and the periodic traveling wave solutions has been established. Two exact solutions of these waves have been derived depending on the system parameters. Then, usingmore » the Hirota's direct method, we have obtained two-soliton and three-soliton solutions of the KP equation. The effect of the spectral index κ on propagations of the two-soliton and the three-soliton has been shown. Considering an external periodic perturbation, we have presented the quasi periodic behavior of ion acoustic waves in electron-positron-ion magnetoplasmas.« less

A Comparison of Martian Transient Wave Energetics in High and Low Optical Depth Environments

NASA Astrophysics Data System (ADS)

Battalio, J. M.; Szunyogh, I.; Lemmon, M. T.

2016-12-01

The local energetics of individual transient eddies from the Mars Analysis Correction Data Assimilation (MACDA) is compared between a year with a global-scale dust storm (MY 25) and two years of relatively low optical depth conditions. Eddies in each year are considered from a period of strong wave activity in the northern hemisphere before the winter solstice (Ls=170-240°). The local growth of eddies is typically triggered by geopotential flux convergence. While all waves exhibit some baroclinic growth, baroclinic energy conversion is weaker in the waves that occur during the global-scale dust storm. The weaker baroclinic energy conversion in these waves, however, is compensated by a more intense barotropic transfer of the kinetic energy from the mean flow to the waves: the contribution from barotropic energy conversion allows eddies during the global-scale dust storm to attain roughly the same maximum eddy kinetic energy as eddies during the low optical depth years. Individual eddies in the waves decay through a combination of barotropic conversion of the kinetic energy from the waves to the mean flow, geopotential flux divergence, and dissipation in both the high- and the low-optical-depth years.

Crust and upper mantle shear wave structure of Northeast Algeria from Rayleigh wave dispersion analysis

NASA Astrophysics Data System (ADS)

Radi, Zohir; Yelles-Chaouche, Abdelkrim; Corchete, Victor; Guettouche, Salim

2017-09-01

We resolve the crust and upper mantle structure beneath Northeast Algeria at depths of 0-400 km, using inversion of fundamental mode Rayleigh wave. Our data set consists of 490 earthquakes recorded between 2007 and 2014 by five permanent broadband seismic stations in the study area. Applying a combination of different filtering technics and inversion method shear wave velocities structure were determined as functions of depth. The resolved changes in Vs at 50 km depth are in perfect agreement with crustal thickness estimates, which reflect the study area's orogenic setting, partly overlying the collision zone between the African and Eurasian plates. The inferred Moho discontinuity depths are close to those estimated for other convergent areas. In addition, there is good agreement between our results and variations in orientations of regional seismic anisotropy. At depths of 80-180 km, negative Vs anomalies at station CBBR suggest the existence of a failed subduction slab.

Extremely Fast Numerical Integration of Ocean Surface Wave Dynamics: Building Blocks for a Higher Order Method

DTIC Science & Technology

2006-09-30

equation known as the Kadomtsev - Petviashvili (KP) equation ): (ηt + coηx +αηηx + βη )x +γηyy = 0 (4) where γ = co / 2 . The KdV equation ...using the spectral formulation of the Kadomtsev - Petviashvili equation , a standard equation for nonlinear, shallow water wave dynamics that is a... Petviashvili and nonlinear Schroedinger equations and higher order corrections have been developed as prerequisites to coding the Boussinesq and Euler

Multiphase wavetrains, singular wave interactions and the emergence of the Korteweg–de Vries equation

PubMed Central

Bridges, Thomas J.

2016-01-01

Multiphase wavetrains are multiperiodic travelling waves with a set of distinct wavenumbers and distinct frequencies. In conservative systems, such families are associated with the conservation of wave action or other conservation law. At generic points (where the Jacobian of the wave action flux is non-degenerate), modulation of the wavetrain leads to the dispersionless multiphase conservation of wave action. The main result of this paper is that modulation of the multiphase wavetrain, when the Jacobian of the wave action flux vector is singular, morphs the vector-valued conservation law into the scalar Korteweg–de Vries (KdV) equation. The coefficients in the emergent KdV equation have a geometrical interpretation in terms of projection of the vector components of the conservation law. The theory herein is restricted to two phases to simplify presentation, with extensions to any finite dimension discussed in the concluding remarks. Two applications of the theory are presented: a coupled nonlinear Schrödinger equation and two-layer shallow-water hydrodynamics with a free surface. Both have two-phase solutions where criticality and the properties of the emergent KdV equation can be determined analytically. PMID:28119546

Chirped solitary pulses for a nonic nonlinear Schrödinger equation on a continuous-wave background

NASA Astrophysics Data System (ADS)

Triki, Houria; Porsezian, K.; Choudhuri, Amitava; Dinda, P. Tchofo

2016-06-01

A class of derivative nonlinear Schrödinger equation with cubic-quintic-septic-nonic nonlinear terms describing the propagation of ultrashort optical pulses through a nonlinear medium with higher-order Kerr responses is investigated. An intensity-dependent chirp ansatz is adopted for solving the two coupled amplitude-phase nonlinear equations of the propagating wave. We find that the dynamics of field amplitude in this system is governed by a first-order nonlinear ordinary differential equation with a tenth-degree nonlinear term. We demonstrate that this system allows the propagation of a very rich variety of solitary waves (kink, dark, bright, and gray solitary pulses) which do not coexist in the conventional nonlinear systems that have appeared so far in the literature. The stability of the solitary wave solution under some violation on the parametric conditions is investigated. Moreover, we show that, unlike conventional systems, the nonlinear Schrödinger equation considered here meets the special requirements for the propagation of a chirped solitary wave on a continuous-wave background, involving a balance among group velocity dispersion, self-steepening, and higher-order nonlinearities of different nature.

Comparison between results of solution of Burgers' equation and Laplace's equation by Galerkin and least-square finite element methods

NASA Astrophysics Data System (ADS)

Adib, Arash; Poorveis, Davood; Mehraban, Farid

2018-03-01

In this research, two equations are considered as examples of hyperbolic and elliptic equations. In addition, two finite element methods are applied for solving of these equations. The purpose of this research is the selection of suitable method for solving each of two equations. Burgers' equation is a hyperbolic equation. This equation is a pure advection (without diffusion) equation. This equation is one-dimensional and unsteady. A sudden shock wave is introduced to the model. This wave moves without deformation. In addition, Laplace's equation is an elliptical equation. This equation is steady and two-dimensional. The solution of Laplace's equation in an earth dam is considered. By solution of Laplace's equation, head pressure and the value of seepage in the directions X and Y are calculated in different points of earth dam. At the end, water table is shown in the earth dam. For Burgers' equation, least-square method can show movement of wave with oscillation but Galerkin method can not show it correctly (the best method for solving of the Burgers' equation is discrete space by least-square finite element method and discrete time by forward difference.). For Laplace's equation, Galerkin and least square methods can show water table correctly in earth dam.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pasyanos, M; Gok, R; Zor, E

We investigate the crustal and upper mantle structure of eastern Turkey where the Anatolian, Arabian and Eurasian Plates meet and form a complex tectonic structure. The Bitlis suture is a continental collision zone between the Anatolian plateau and the Arabian plate. Broadband data available through the Eastern Turkey Seismic Experiment (ETSE) provided a unique opportunity for studying the high resolution velocity structure. Zor et al. found an average 46 km thick crust in Anatolian plateau using six-layered grid search inversion of the ETSE receiver functions. Receiver functions are sensitive to the velocity contrast of interfaces and the relative travel timemore » of converted and reverberated waves between those interfaces. The interpretation of receiver function alone with many-layered parameterization may result in an apparent depth-velocity tradeoff. In order to improve previous velocity model, we employed the joint inversion method with many layered parameterization of Julia et al. (2000) to the ETSE receiver functions. In this technique, the receiver function and surface-wave observations are combined into a single algebraic equation and each data set is weighted by an estimate of the uncertainty in the observations. We consider azimuthal changes of receiver functions and have stacked them into different groups. We calculated the receiver functions using iterative time-domain deconvolution technique and surface wave group velocity dispersion curves between 10-100 sec. We are making surface wave dispersion measurements at the ETSE stations and have incorporated them into a regional group velocity model. Preliminary results indicate a strong trend in the long period group velocity in the northeast. This indicates slow upper mantle velocities in the region consistent with Pn, Sn and receiver function results. We started with both the 1-D model that is obtained with the 12 tones dam explosion shot data recorded by ETSE network and the existing receiver function inversion results. In fact, we observe that the inversion results are independent at the starting model and converges well to the same final model. We don't observe a significant change at the first order discontinuities of model (e.g. Moho depth), but we obtain better defined depths to low velocity layers.« less

Numerical studies of the KP line-solitons

NASA Astrophysics Data System (ADS)

Chakravarty, S.; McDowell, T.; Osborne, M.

2017-03-01

The Kadomtsev-Petviashvili (KP) equation admits a class of solitary wave solutions localized along distinct rays in the xy-plane, called the line-solitons, which describe the interaction of shallow water waves on a flat surface. These wave interactions have been observed on long, flat beaches, as well as have been recreated in laboratory experiments. In this paper, the line-solitons are investigated via direct numerical simulations of the KP equation, and the interactions of the evolved solitary wave patterns are studied. The objective is to obtain greater insight into solitary wave interactions in shallow water and to determine the extent the KP equation is a good model in describing these nonlinear interactions.

Two-dimensional cylindrical ion-acoustic solitary and rogue waves in ultrarelativistic plasmas

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ata-ur-Rahman; National Centre for Physics at QAU Campus, Shahdrah Valley Road, Islamabad 44000; Ali, S.

2013-07-15

The propagation of ion-acoustic (IA) solitary and rogue waves is investigated in a two-dimensional ultrarelativistic degenerate warm dense plasma. By using the reductive perturbation technique, the cylindrical Kadomtsev–Petviashvili (KP) equation is derived, which can be further transformed into a Korteweg–de Vries (KdV) equation. The latter admits a solitary wave solution. However, when the frequency of the carrier wave is much smaller than the ion plasma frequency, the KdV equation can be transferred to a nonlinear Schrödinger equation to study the nonlinear evolution of modulationally unstable modified IA wavepackets. The propagation characteristics of the IA solitary and rogue waves are stronglymore » influenced by the variation of different plasma parameters in an ultrarelativistic degenerate dense plasma. The present results might be helpful to understand the nonlinear electrostatic excitations in astrophysical degenerate dense plasmas.« less

A Self-Consistent Model of the Interacting Ring Current Ions with Electromagnetic ICWs

NASA Technical Reports Server (NTRS)

Khazanov, G. V.; Gamayunov, K. V.; Jordanova, V. K.; Krivorutsky, E. N.; Whitaker, Ann F. (Technical Monitor)

2001-01-01

Initial results from a newly developed model of the interacting ring current ions and ion cyclotron waves are presented. The model is based on the system of two bound kinetic equations: one equation describes the ring current ion dynamics, and another equation describes wave evolution. The system gives a self-consistent description of ring current ions and ion cyclotron waves in a quasilinear approach. These two equations were solved on a global scale under non steady-state conditions during the May 2-5, 1998 storm. The structure and dynamics of the ring current proton precipitating flux regions and the wave active zones at three time cuts around initial, main, and late recovery phases of the May 4, 1998 storm phase are presented and discussed in detail. Comparisons of the model wave-ion data with the Polar/HYDRA and Polar/MFE instruments results are presented..

Equations for description of nonlinear standing waves in constant-cross-sectioned resonators.

PubMed

Bednarik, Michal; Cervenka, Milan

2014-03-01

This work is focused on investigation of applicability of two widely used model equations for description of nonlinear standing waves in constant-cross-sectioned resonators. The investigation is based on the comparison of numerical solutions of these model equations with solutions of more accurate model equations whose validity has been verified experimentally in a number of published papers.

Nonlinear Waves and Inverse Scattering

DTIC Science & Technology

1992-01-29

equations include the Kadomtsev - Petviashvili (K-P), Davey-Stewartson (D-S), 2+1 Toda, and Self-Dual Yang-Mills (SDYM) equations . We have uncovered a... Petviashvili Equation and Associated Constraints, M.J. Ablowitz and Javier Villaroel, Studies in Appl. Math. 85, (1991), 195-213. 12. On the Hamiltonian...nonlinear wave equations of physical significance, multidimensional inverse scattering, numer- ically induced instabilities and chaos, and forced

Sound Beams with Shockwave Pulses

NASA Astrophysics Data System (ADS)

Enflo, B. O.

2000-11-01

The beam equation for a sound beam in a diffusive medium, called the Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation, has a class of solutions, which are power series in the transverse variable with the terms given by a solution of a generalized Burgers’ equation. A free parameter in this generalized Burgers’ equation can be chosen so that the equation describes an N-wave which does not decay. If the beam source has the form of a spherical cap, then a beam with a preserved shock can be prepared. This is done by satisfying an inequality containing the spherical radius, the N-wave pulse duration, the N-wave pulse amplitude, and the sound velocity in the fluid.

Numerical and experimental results on the spectral wave transfer in finite depth

NASA Astrophysics Data System (ADS)

Benassai, Guido

2016-04-01

Determination of the form of the one-dimensional surface gravity wave spectrum in water of finite depth is important for many scientific and engineering applications. Spectral parameters of deep water and intermediate depth waves serve as input data for the design of all coastal structures and for the description of many coastal processes. Moreover, the wave spectra are given as an input for the response and seakeeping calculations of high speed vessels in extreme sea conditions and for reliable calculations of the amount of energy to be extracted by wave energy converters (WEC). Available data on finite depth spectral form is generally extrapolated from parametric forms applicable in deep water (e.g., JONSWAP) [Hasselmann et al., 1973; Mitsuyasu et al., 1980; Kahma, 1981; Donelan et al., 1992; Zakharov, 2005). The present paper gives a contribution in this field through the validation of the offshore energy spectra transfer from given spectral forms through the measurement of inshore wave heights and spectra. The wave spectra on deep water were recorded offshore Ponza by the Wave Measurement Network (Piscopia et al.,2002). The field regressions between the spectral parameters, fp and the nondimensional energy with the fetch length were evaluated for fetch-limited sea conditions. These regressions gave the values of the spectral parameters for the site of interest. The offshore wave spectra were transfered from the measurement station offshore Ponza to a site located offshore the Gulf of Salerno. The offshore local wave spectra so obtained were transfered on the coastline with the TMA model (Bouws et al., 1985). Finally the numerical results, in terms of significant wave heights, were compared with the wave data recorded by a meteo-oceanographic station owned by Naples Hydrographic Office on the coastline of Salerno in 9m depth. Some considerations about the wave energy to be potentially extracted by Wave Energy Converters were done and the results were discussed.

Millimeter Wave Generation by Relativistic Electron Beams.

DTIC Science & Technology

1984-12-01

frequency and wave vector matching relations for influence of various nonlinear effects on this instability is this four-wave interaction require...following coupled mode equations _ 6 = 6 _ (14)-- v vx (14) ." .’ for the lower hybrid sidebands: v - V 2 - The x component of the resultant vector equation...involves a purely growing modte, a four-wave interaction plitoces is analysed, including a u ap ti wave- vector up-shifted and ilown-shiftes upper

Non-invasive photo acoustic approach for human bone diagnosis.

PubMed

Thella, Ashok Kumar; Rizkalla, James; Helmy, Ahdy; Suryadevara, Vinay Kumar; Salama, Paul; Rizkalla, Maher

2016-12-01

The existing modalities of bone diagnosis including X-ray and ultrasound may cite drawback in some cases related to health issues and penetration depth, while the ultrasound modality may lack image quality. Photo acoustic approach however, provides light energy to the acoustic wave, enabling it to activate and respond according to the propagating media (which is type of bones in this case). At the same time, a differential temperature change may result in the bio heat response, resulting from the heat absorbed across the multiple materials under study. In this work, we have demonstrated the features of using photo acoustic modality in order to non-invasively diagnose the type of human bones based on their electrical, thermal, and acoustic properties that differentiate the output response of each type. COMSOL software was utilized to combine both acoustic equations and bio heat equations, in order to study both the thermal and acoustic responses through which the differential diagnosis can be obtained. In this study, we solved both the acoustic equation and bio heat equations for four types of bones, bone (cancellous), bone (cortical), bone marrow (red), and bone marrow (yellow). 1 MHz acoustic source frequency was chosen and 10(5) W/m(2) power source was used in the simulation. The simulation tested the dynamic response of the wave over a distance of 5 cm from each side for the source. Near 2.4 cm was detected from simulation from each side of the source with a temperature change of within 0.5 K for various types of bones, citing a promising technique for a practical model to detect the type of bones via the differential temperature as well as the acoustic was response via the multiple materials associated with the human bones (skin and blood). The simulation results suggest that the PA technique may be applied to non-invasive diagnosis for the different types of bones, including cancerous bones. A practical model for detecting both the temperature change via IR sensors, and acoustic wave signals may be detected via sensitive pressure transducer, which is reserved for future realization.

Three-dimensional coupled thermoelastodynamic stress and flux induced wave propagation for isotropic half-space with scalar potential functions

NASA Astrophysics Data System (ADS)

Hayati, Yazdan; Eskandari-Ghadi, Morteza

2018-02-01

An asymmetric three-dimensional thermoelastodynamic wave propagation with scalar potential functions is presented for an isotropic half-space, in such a way that the wave may be originated from an arbitrary either traction or heat flux applied on a patch at the free surface of the half-space. The displacements, stresses and temperature are presented within the framework of Biot's coupled thermoelasticity formulations. By employing a complete representation for the displacement and temperature fields in terms of two scalar potential functions, the governing equations of coupled thermoelasticity are uncoupled into a sixth- and a second-order partial differential equation in cylindrical coordinate system. By virtue of Fourier expansion and Hankel integral transforms, the angular and radial variables are suppressed respectively, and a 6{th}- and a 2{nd}-order ordinary differential equation in terms of depth are received, which are solved readily, from which the displacement, stresses and temperature fields are derived in transformed space by satisfying both the regularity and boundary conditions. By applying the inverse Hankel integral transforms, the displacements and temperature are numerically evaluated to determine the solutions in the real space. The numerical evaluations are done for three specific cases of vertical and horizontal time-harmonic patch traction and a constant heat flux passing through a circular disc on the surface of the half-space. It has been previously proved that the potential functions used in this paper are applicable from elastostatics to thermoelastodynamics. Thus, the analytical solutions presented in this paper are verified by comparing the results of this study with two specific problems reported in the literature, which are an elastodynamic problem and an axisymmetric quasi-static thermoelastic problem. To show the accuracy of numerical results, the solution of this study is also compared with the solution for elastodynamics exists in the literature for surface excitation, where a very good agreement is achieved. The formulations presented in this study may be used as benchmark for other related researches and it may be implemented in the related boundary integral equations.

Lump Solitons in Surface Tension Dominated Flows

NASA Astrophysics Data System (ADS)

Milewski, Paul; Berger, Kurt

1999-11-01

The Kadomtsev-Petviashvilli I equation (KPI) which models small-amplitude, weakly three-dimensional surface-tension dominated long waves is integrable and allows for algebraically decaying lump solitary waves. It is not known (theoretically or numerically) whether the full free-surface Euler equations support such solutions. We consider an intermediate model, the generalised Benney-Luke equation (gBL) which is isotropic (not weakly three-dimensional) and contains KPI as a limit. We show numerically that: 1. gBL supports lump solitary waves; 2. These waves collide elastically and are stable; 3. They are generated by resonant flow over an obstacle.

Shock wave equation of state of muscovite

NASA Technical Reports Server (NTRS)

Sekine, Toshimori; Rubin, Allan M.; Ahrens, Thomas J.

1991-01-01

Shock wave data were obtained between 20 and 140 GPa for natural muscovite obtained from Methuen Township (Ontario), in order to provide a shock-wave equation of state for this crustal hydrous mineral. The shock equation of state data could be fit by a linear shock velocity (Us) versus particle velocity (Up) relation Us = 4.62 + 1.27 Up (km/s). Third-order Birch-Murnaghan equation of state parameters were found to be K(OS) = 52 +/-4 GPa and K-prime(OS) = 3.2 +/-0.3 GPa. These parameters are comparable to those of other hydrous minerals such as brucite, serpentine, and tremolite.

Kato Smoothing and Strichartz Estimates for Wave Equations with Magnetic Potentials

NASA Astrophysics Data System (ADS)

D'Ancona, Piero

2015-04-01

Let H be a selfadjoint operator and A a closed operator on a Hilbert space . If A is H-(super)smooth in the sense of Kato-Yajima, we prove that is -(super)smooth. This allows us to include wave and Klein-Gordon equations in the abstract theory at the same level of generality as Schrödinger equations. We give a few applications and in particular, based on the resolvent estimates of Erdogan, Goldberg and Schlag (Forum Mathematicum 21:687-722, 2009), we prove Strichartz estimates for wave equations perturbed with large magnetic potentials on , n ≥ 3.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dallman, Ann Renee; Neary, Vincent Sinclair

Spatial variability of sea states is an important consideration when performing wave resource assessments and wave resource characterization studies for wave energy converter (WEC) test sites and commercial WEC deployments. This report examines the spatial variation of sea states offshore of Humboldt Bay, CA, using the wave model SWAN . The effect of depth and shoaling on bulk wave parameters is well resolved using the model SWAN with a 200 m grid. At this site, the degree of spatial variation of these bulk wave parameters, with shoaling generally perpendicular to the depth contours, is found to depend on the season.more » The variation in wave height , for example, was higher in the summer due to the wind and wave sheltering from the protruding land on the coastline north of the model domain. Ho wever, the spatial variation within an area of a potential Tier 1 WEC test site at 45 m depth and 1 square nautical mile is almost negligible; at most about 0.1 m in both winter and summer. The six wave characterization parameters recommended by the IEC 6 2600 - 101 TS were compared at several points along a line perpendicular to shore from the WEC test site . As expected, these parameters varied based on depth , but showed very similar seasonal trends.« less

An analytical study of M2 tidal waves in the Taiwan Strait using an extended Taylor method

NASA Astrophysics Data System (ADS)

Wu, Di; Fang, Guohong; Cui, Xinmei; Teng, Fei

2018-02-01

The tides in the Taiwan Strait (TS) feature large semidiurnal lunar (M2) amplitudes. An extended Taylor method is employed in this study to provide an analytical model for the M2 tide in the TS. The strait is idealized as a rectangular basin with a uniform depth, and the Coriolis force and bottom friction are retained in the governing equations. The observed tides at the northern and southern openings are used as open boundary conditions. The obtained analytical solution, which consists of a stronger southward propagating Kelvin wave, a weaker northward propagating Kelvin wave, and two families of Poincaré modes trapped at the northern and southern openings, agrees well with the observations in the strait. The superposition of two Kelvin waves basically represents the observed tidal pattern, including an anti-nodal band in the central strait, and the cross-strait asymmetry (greater amplitudes in the west and smaller in the east) of the anti-nodal band. Inclusion of Poincaré modes further improves the model result in that the cross-strait asymmetry can be better reproduced. To explore the formation mechanism of the northward propagating wave in the TS, three experiments are carried out, including the deep basin south of the strait. The results show that the southward incident wave is reflected to form a northward wave by the abruptly deepened topography south of the strait, but the reflected wave is slightly weaker than the northward wave obtained from the above analytical solution, in which the southern open boundary condition is specified with observations. Inclusion of the forcing at the Luzon Strait strengthens the northward Kelvin wave in the TS, and the forcing is thus of some (but lesser) importance to the M2 tide in the TS.

Matter rogue waves for the three-component Gross-Pitaevskii equations in the spinor Bose-Einstein condensates.

PubMed

Sun, Wen-Rong; Wang, Lei

2018-01-01

To show the existence and properties of matter rogue waves in an F =1 spinor Bose-Einstein condensate (BEC), we work on the three-component Gross-Pitaevskii (GP) equations. Via the Darboux-dressing transformation, we obtain a family of rational solutions describing the extreme events, i.e. rogue waves. This family of solutions includes bright-dark-bright and bright-bright-bright rogue waves. The algebraic construction depends on Lax matrices and their Jordan form. The conditions for the existence of rogue wave solutions in an F =1 spinor BEC are discussed. For the three-component GP equations, if there is modulation instability, it is of baseband type only, confirming our analytic conditions. The energy transfers between the waves are discussed.

Matter rogue waves for the three-component Gross-Pitaevskii equations in the spinor Bose-Einstein condensates

NASA Astrophysics Data System (ADS)

Sun, Wen-Rong; Wang, Lei

2018-01-01

To show the existence and properties of matter rogue waves in an F=1 spinor Bose-Einstein condensate (BEC), we work on the three-component Gross-Pitaevskii (GP) equations. Via the Darboux-dressing transformation, we obtain a family of rational solutions describing the extreme events, i.e. rogue waves. This family of solutions includes bright-dark-bright and bright-bright-bright rogue waves. The algebraic construction depends on Lax matrices and their Jordan form. The conditions for the existence of rogue wave solutions in an F=1 spinor BEC are discussed. For the three-component GP equations, if there is modulation instability, it is of baseband type only, confirming our analytic conditions. The energy transfers between the waves are discussed.

Two-dimensional interaction of a shear flow with a free surface in a stratified fluid and its solitary-wave solutions via mathematical methods

NASA Astrophysics Data System (ADS)

Seadawy, Aly R.

2017-12-01

In this study, we presented the problem formulations of models for internal solitary waves in a stratified shear flow with a free surface. The nonlinear higher order of extended KdV equations for the free surface displacement is generated. We derived the coefficients of the nonlinear higher-order extended KdV equation in terms of integrals of the modal function for the linear long-wave theory. The wave amplitude potential and the fluid pressure of the extended KdV equation in the form of solitary-wave solutions are deduced. We discussed and analyzed the stability of the obtained solutions and the movement role of the waves by making graphs of the exact solutions.

Nonlinear interactions between electromagnetic waves and electron plasma oscillations in quantum plasmas.

PubMed

Shukla, P K; Eliasson, B

2007-08-31

We consider nonlinear interactions between intense circularly polarized electromagnetic (CPEM) waves and electron plasma oscillations (EPOs) in a dense quantum plasma, taking into account the electron density response in the presence of the relativistic ponderomotive force and mass increase in the CPEM wave fields. The dynamics of the CPEM waves and EPOs is governed by the two coupled nonlinear Schrödinger equations and Poisson's equation. The nonlinear equations admit the modulational instability of an intense CPEM pump wave against EPOs, leading to the formation and trapping of localized CPEM wave pipes in the electron density hole that is associated with a positive potential distribution in our dense plasma. The relevance of our investigation to the next generation intense laser-solid density plasma interaction experiments is discussed.

A Note on the Wave Action Density of a Viscous Instability Mode on a Laminar Free-shear Flow

NASA Technical Reports Server (NTRS)

Balsa, Thomas F.

1994-01-01

Using the assumptions of an incompressible and viscous flow at large Reynolds number, we derive the evolution equation for the wave action density of an instability wave traveling on top of a laminar free-shear flow. The instability is considered to be viscous; the purpose of the present work is to include the cumulative effect of the (locally) small viscous correction to the wave, over length and time scales on which the underlying base flow appears inhomogeneous owing to its viscous diffusion. As such, we generalize our previous work for inviscid waves. This generalization appears as an additional (but usually non-negligible) term in the equation for the wave action. The basic structure of the equation remains unaltered.

Wave theory in rotating systems: Schrödinger equations bridge the gaps between the equatorial β-plane and the spherical earth

NASA Astrophysics Data System (ADS)

Paldor, N.

2017-12-01

The concise and elegant wave theory developed on the equatorial β-plane by Matsuno (1966, M66 hereafter) is based on the formulation of a Schrödinger equation associated with the governing Linear Rotating Shallow Water Equations (LRSWE). The theory yields explicit expressions for the dispersion relations and meridional amplitude structures of all zonally propagating waves - Rossby, Inertia-Gravity, Kelvin and Yanai. In contrast, the spherical wave theory of Longuet-Higgins (1968) is a collection of asymptotic expansions in many sub-ranges e.g. large, small (and even negative) Lamb Number; high and low frequency; low-latitudes, etc. that rests upon extensive numerical solutions of several Ordinary Differential Equations. The difference between the two theories is highlighted by their lengths. The essential elements of the former planar study are completely revealed in just 3-4 pages including the derivation of explicit formulae for the phase speeds and amplitude meridional structures. In comtrast, the latter spherical theory contains 97 pages and the results of the numerical calculations are summarized in 30 pages of tables filled with numerical values and about 31 figures, each of which containing many separate curves! In my talk I will re-visit the wave problem on a sphere by developing several Schrödinger equations that approximate the governing eigenvalue equation associated with zonally propagating waves. Each of the Schrödinger equations approximates the original second order Ordinary Differential Equation in a different range of the 3 parameters: Lamb-Number, frequency and zonal wavenumber. As in M66, each of the Schrödinger equations yields explicit expressions for the dispersion relations and meridional amplitude structure of Rossby and Inertia-Gravity waves. In addition, the analysis shows that Yanai wave exists on a sphere even tough the zonal velocity is regular everywhere there (in contrast to the β-plane where the zonal velocity is singular everywhere) and that Kelvin waves do not exist as a separate mode (but the eastward propagating n=0 Inertia-Gravity is nearly non-dispersive). References Longuet-Higgins, M. S. Phil. Trans. Roy. Soc. London; 262, 511-607; 1968 Matsuno, T.; J. Met. Soc. Japan. 44(1), 25-43; 1966

Estimating Tsunami Runup with Fault Plane Parameters

NASA Astrophysics Data System (ADS)

Sepulveda, I.; Liu, P. L. F.

2016-12-01

The forecasting of tsunami runup has often been done by solving numerical models. The execution times, however, make them unsuitable for the purpose of warning. We offer an alternative method that provides analytical relationship between the runup height, the fault plane parameters and the characteristic of coastal bathymetry. The method uses the model of Okada (1985) to estimate the coseismic deformation and the corresponding sea surface displacement (η(x,0)). Once the tsunami waves are generated, Carrier & Greenspan (1958) solution (C&G) is adopted to yield analytical expressions for the shoreline elevation and velocity. Two types of problems are investigated. In the first, the bathymetry is modeled as a constant slope that is connected to a constant depth region, where a seismic event occurs. This is a boundary value problem (BVP). In the second, the bathymetry is further simplified as a constant slope, on which a seismic event occurs. This is an initial value problem (IVP). Both problems are depicted in Figure 1. We derive runup solutions in terms of the fault parameters. The earthquake is associated with vertical coseismic seafloor displacements by using Okada's elastic model. In addition to the simplifications considered in Okada's model, we further assume (1) a strike parallel to the shoreline, (2) a very long rupture area and (3) a fast earthquake so surface elevation mimics the seafloor displacements. Then the tsunami origin is modeled in terms of the fault depth (d), fault width (W), fault slip (s) and dip angle (δ). We describe the solution for the BVP. Madsen & Schaeffer (2010) utilized C&G to derive solutions for the shoreline elevation of sinusoidal waves imposed in the offshore boundary. A linear superposition of this solution represents any arbitrary incident wave. Furthermore, we can prescribe the boundary condition at the toe of sloping beach by adopting the linear shallow wave equations in the constant depth area. By means of a dimensional analysis, the runup R is determined by Eq.1. Kanoglu (2004) derived a non-dimensional expression for long wave runup originated over a sloping beach. In our work we determine an analytical expression for a sinusoidal initial condition. Following the same procedure as the BVP, the expression for the runup R in the IVP is given by Eq.2. The curves F1 and F2 are plotted in Figure 2.

Momentum and energy transport by waves in the solar atmosphere and solar wind

NASA Technical Reports Server (NTRS)

Jacques, S. A.

1977-01-01

The fluid equations for the solar wind are presented in a form which includes the momentum and energy flux of waves in a general and consistent way. The concept of conservation of wave action is introduced and is used to derive expressions for the wave energy density as a function of heliocentric distance. The explicit form of the terms due to waves in both the momentum and energy equations are given for radially propagating acoustic, Alfven, and fast mode waves. The effect of waves as a source of momentum is explored by examining the critical points of the momentum equation for isothermal spherically symmetric flow. We find that the principal effect of waves on the solutions is to bring the critical point closer to the sun's surface and to increase the Mach number at the critical point. When a simple model of dissipation is included for acoustic waves, in some cases there are multiple critical points.

Numerical modeling of the interaction of liquid drops and jets with shock waves and gas jets

NASA Astrophysics Data System (ADS)

Surov, V. S.

1993-02-01

The motion of a liquid drop (jet) and of the ambient gas is described, in the general case, by Navier-Stokes equations. An approximate solution to the interaction of a plane shock wave with a single liquid drop is presented. Based on the analysis, the general system of Navier-Stokes equations is reduced to two groups of equations, Euler equations for gas and Navier-Stokes equations for liquid; solutions to these equations are presented. The discussion also covers the modeling of the interaction of a shock wave with a drop screen, interaction of a liquid jet with a counterpropagating supersonic gas flow, and modeling of processes in a shock layer during the impact of a drop against an obstacle in gas flow.

Cross-Shore Exchange on Natural Beaches

DTIC Science & Technology

2014-09-01

87   Figure 2.   Wave conditions measured by the ADCP in 13 m water depth of (a) root- mean-square wave height Hrms...horizontal velocity, Umean, measured in the reference level, ∑Tsig,pulse T3−hour ∑Tsig,pulse T3−hour xi (e) local water depth, h, and (f) local root...mean-square wave height normalized by the local water depth, Hrms/h, measured by ADCPin (blue) and ADCPout (red) during the 3HRLTs. Colored lines

Elastic parabolic equation solutions for oceanic T-wave generation and propagation from deep seismic sources.

PubMed

Frank, Scott D; Collis, Jon M; Odom, Robert I

2015-06-01

Oceanic T-waves are earthquake signals that originate when elastic waves interact with the fluid-elastic interface at the ocean bottom and are converted to acoustic waves in the ocean. These waves propagate long distances in the Sound Fixing and Ranging (SOFAR) channel and tend to be the largest observed arrivals from seismic events. Thus, an understanding of their generation is important for event detection, localization, and source-type discrimination. Recently benchmarked seismic self-starting fields are used to generate elastic parabolic equation solutions that demonstrate generation and propagation of oceanic T-waves in range-dependent underwater acoustic environments. Both downward sloping and abyssal ocean range-dependent environments are considered, and results demonstrate conversion of elastic waves into water-borne oceanic T-waves. Examples demonstrating long-range broadband T-wave propagation in range-dependent environments are shown. These results confirm that elastic parabolic equation solutions are valuable for characterization of the relationships between T-wave propagation and variations in range-dependent bathymetry or elastic material parameters, as well as for modeling T-wave receptions at hydrophone arrays or coastal receiving stations.

Rogue wave spectra of the Kundu-Eckhaus equation.

PubMed

Bayındır, Cihan

2016-06-01

In this paper we analyze the rogue wave spectra of the Kundu-Eckhaus equation (KEE). We compare our findings with their nonlinear Schrödinger equation (NLSE) analogs and show that the spectra of the individual rogue waves significantly differ from their NLSE analogs. A remarkable difference is the one-sided development of the triangular spectrum before the rogue wave becomes evident in time. Also we show that increasing the skewness of the rogue wave results in increased asymmetry in the triangular Fourier spectra. Additionally, the triangular spectra of the rogue waves of the KEE begin to develop at earlier stages of their development compared to their NLSE analogs, especially for larger skew angles. This feature may be used to enhance the early warning times of the rogue waves. However, we show that in a chaotic wave field with many spectral components the triangular spectra remain as the main attribute as a universal feature of the typical wave fields produced through modulation instability and characteristic features of the KEE's analytical rogue wave spectra may be suppressed in a realistic chaotic wave field.

A novel unsplit perfectly matched layer for the second-order acoustic wave equation.

PubMed

Ma, Youneng; Yu, Jinhua; Wang, Yuanyuan

2014-08-01

When solving acoustic field equations by using numerical approximation technique, absorbing boundary conditions (ABCs) are widely used to truncate the simulation to a finite space. The perfectly matched layer (PML) technique has exhibited excellent absorbing efficiency as an ABC for the acoustic wave equation formulated as a first-order system. However, as the PML was originally designed for the first-order equation system, it cannot be applied to the second-order equation system directly. In this article, we aim to extend the unsplit PML to the second-order equation system. We developed an efficient unsplit implementation of PML for the second-order acoustic wave equation based on an auxiliary-differential-equation (ADE) scheme. The proposed method can benefit to the use of PML in simulations based on second-order equations. Compared with the existing PMLs, it has simpler implementation and requires less extra storage. Numerical results from finite-difference time-domain models are provided to illustrate the validity of the approach. Copyright © 2014 Elsevier B.V. All rights reserved.

On the dispersionless Kadomtsev-Petviashvili equation with arbitrary nonlinearity and dimensionality: exact solutions, longtime asymptotics of the Cauchy problem, wave breaking and shocks

NASA Astrophysics Data System (ADS)

Santucci, F.; Santini, P. M.

2016-10-01

We study the generalization of the dispersionless Kadomtsev-Petviashvili (dKP) equation in n+1 dimensions and with nonlinearity of degree m+1, a model equation describing the propagation of weakly nonlinear, quasi one-dimensional waves in the absence of dispersion and dissipation, and arising in several physical contexts, like acoustics, plasma physics, hydrodynamics and nonlinear optics. In 2 + 1 dimensions and with quadratic nonlinearity, this equation is integrable through a novel inverse scattering transform, and it has been recently shown to be a prototype model equation in the description of the two-dimensional wave breaking of localized initial data. In higher dimensions and with higher nonlinearity, the generalized dKP equations are not integrable, but their invariance under motions on the paraboloid allows one to construct in this paper a family of exact solutions describing waves constant on their paraboloidal wave front and breaking simultaneously in all points of it, developing after breaking either multivaluedness or single-valued discontinuous profiles (shocks). Then such exact solutions are used to build the longtime behavior of the solutions of the Cauchy problem, for small and localized initial data, showing that wave breaking of small initial data takes place in the longtime regime if and only if m(n-1)≤slant 2. Lastly, the analytic aspects of such wave breaking are investigated in detail in terms of the small initial data, in both cases in which the solution becomes multivalued after breaking or it develops a shock. These results, contained in the 2012 master’s thesis of one of the authors (FS) [1], generalize those obtained in [2] for the dKP equation in n+1 dimensions with quadratic nonlinearity, and are obtained following the same strategy.

On exact traveling-wave solutions for local fractional Korteweg-de Vries equation.

PubMed

Yang, Xiao-Jun; Tenreiro Machado, J A; Baleanu, Dumitru; Cattani, Carlo

2016-08-01

This paper investigates the Korteweg-de Vries equation within the scope of the local fractional derivative formulation. The exact traveling wave solutions of non-differentiable type with the generalized functions defined on Cantor sets are analyzed. The results for the non-differentiable solutions when fractal dimension is 1 are also discussed. It is shown that the exact solutions for the local fractional Korteweg-de Vries equation characterize the fractal wave on shallow water surfaces.

Perturbed soliton excitations of Rao-dust Alfvén waves in magnetized dusty plasmas

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kavitha, L., E-mail: louiskavitha@yahoo.co.in; The Abdus Salam International Centre for Theoretical Physics, Trieste; Lavanya, C.

We investigate the propagation dynamics of the perturbed soliton excitations in a three component fully ionized dusty magnetoplasma consisting of electrons, ions, and heavy charged dust particulates. We derive the governing equation of motion for the two dimensional Rao-dust magnetohydrodynamic (R-D-MHD) wave by employing the inertialess electron equation of motion, inertial ion equation of motion, the continuity equations in a plasma with immobile charged dust grains, together with the Maxwell's equations, by assuming quasi neutrality and neglecting the displacement current in Ampere's law. Furthermore, we assume the massive dust particles are practically immobile since we are interested in timescales muchmore » shorter than the dusty plasma period, thereby neglecting any damping of the modes due to the grain charge fluctuations. We invoke the reductive perturbation method to represent the governing dynamics by a perturbed cubic nonlinear Schrödinger (pCNLS) equation. We solve the pCNLS, along the lines of Kodama-Ablowitz multiple scale nonlinear perturbation technique and explored the R-D-MHD waves as solitary wave excitations in a magnetized dusty plasma. Since Alfvén waves play an important role in energy transport in driving field-aligned currents, particle acceleration and heating, solar flares, and the solar wind, this representation of R-D-MHD waves as soliton excitations may have extensive applications to study the lower part of the earth's ionosphere.« less

Band gaps and localization of surface water waves over large-scale sand waves with random fluctuations

NASA Astrophysics Data System (ADS)

Zhang, Yu; Li, Yan; Shao, Hao; Zhong, Yaozhao; Zhang, Sai; Zhao, Zongxi

2012-06-01

Band structure and wave localization are investigated for sea surface water waves over large-scale sand wave topography. Sand wave height, sand wave width, water depth, and water width between adjacent sand waves have significant impact on band gaps. Random fluctuations of sand wave height, sand wave width, and water depth induce water wave localization. However, random water width produces a perfect transmission tunnel of water waves at a certain frequency so that localization does not occur no matter how large a disorder level is applied. Together with theoretical results, the field experimental observations in the Taiwan Bank suggest band gap and wave localization as the physical mechanism of sea surface water wave propagating over natural large-scale sand waves.