Properties of Nonlinear Dynamo Waves

NASA Technical Reports Server (NTRS)

Tobias, S. M.

1997-01-01

Dynamo theory offers the most promising explanation of the generation of the sun's magnetic cycle. Mean field electrodynamics has provided the platform for linear and nonlinear models of solar dynamos. However, the nonlinearities included are (necessarily) arbitrarily imposed in these models. This paper conducts a systematic survey of the role of nonlinearities in the dynamo process, by considering the behaviour of dynamo waves in the nonlinear regime. It is demonstrated that only by considering realistic nonlinearities that are non-local in space and time can modulation of the basic dynamo wave he achieved. Moreover, this modulation is greatest when there is a large separation of timescales provided by including a low magnetic Prandtl number in the equation for the velocity perturbations.

Nonlinear modulation of an extraordinary wave under the conditions of parametric decay

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

Dorofeenko, V. G.; Krasovitskiy, V. B.; Turikov, V. A.

2012-06-15

A self-consistent set of Hamilton equations describing nonlinear saturation of the amplitude of oscillations excited under the conditions of parametric decay of an elliptically polarized extraordinary wave in cold plasma is solved analytically and numerically. It is shown that the exponential increase in the amplitude of the secondary wave excited at the half-frequency of the primary wave changes into a reverse process in which energy is returned to the primary wave and nonlinear oscillations propagating across the external magnetic field are generated. The system of 'slow' equations for the amplitudes, obtained by averaging the initial equations over the high-frequency period,more » is used to describe steady-state nonlinear oscillations in plasma.« less

Gaussian variational ansatz in the problem of anomalous sea waves: Comparison with direct numerical simulation

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

Ruban, V. P., E-mail: ruban@itp.ac.ru

2015-05-15

The nonlinear dynamics of an obliquely oriented wave packet on a sea surface is analyzed analytically and numerically for various initial parameters of the packet in relation to the problem of the so-called rogue waves. Within the Gaussian variational ansatz applied to the corresponding (1+2)-dimensional hyperbolic nonlinear Schrödinger equation (NLSE), a simplified Lagrangian system of differential equations is derived that describes the evolution of the coefficients of the real and imaginary quadratic forms appearing in the Gaussian. This model provides a semi-quantitative description of the process of nonlinear spatiotemporal focusing, which is one of the most probable mechanisms of roguemore » wave formation in random wave fields. The system of equations is integrated in quadratures, which allows one to better understand the qualitative differences between linear and nonlinear focusing regimes of a wave packet. Predictions of the Gaussian model are compared with the results of direct numerical simulation of fully nonlinear long-crested waves.« less

Modulation instability, Fermi-Pasta-Ulam recurrence, rogue waves, nonlinear phase shift, and exact solutions of the Ablowitz-Ladik equation.

PubMed

Akhmediev, Nail; Ankiewicz, Adrian

2011-04-01

We study modulation instability (MI) of the discrete constant-background wave of the Ablowitz-Ladik (A-L) equation. We derive exact solutions of the A-L equation which are nonlinear continuations of MI at longer times. These periodic solutions comprise a family of two-parameter solutions with an arbitrary background field and a frequency of initial perturbation. The solutions are recurrent, since they return the field state to the original constant background solution after the process of nonlinear evolution has passed. These solutions can be considered as a complete resolution of the Fermi-Pasta-Ulam paradox for the A-L system. One remarkable consequence of the recurrent evolution is the nonlinear phase shift gained by the constant background wave after the process. A particular case of this family is the rational solution of the first-order or fundamental rogue wave.

TRIADS: A phase-resolving model for nonlinear shoaling of directional wave spectra

NASA Astrophysics Data System (ADS)

Sheremet, Alex; Davis, Justin R.; Tian, Miao; Hanson, Jeffrey L.; Hathaway, Kent K.

2016-03-01

We investigate the performance of TRIADS, a numerical implementation of a phase-resolving, nonlinear, spectral model describing directional wave evolution in intermediate and shallow water. TRIADS simulations of shoaling waves generated by Hurricane Bill, 2009 are compared to directional spectral estimates based on observations collected at the Field Research Facility of the US Army Corps Of Engineers, at Duck, NC. Both the ability of the model to capture the processes essential to the nonlinear wave evolution, and the efficiency of the numerical implementations are analyzed and discussed.

Limitations on the upconversion of ion sound to Langmuir turbulence

NASA Technical Reports Server (NTRS)

Vlahos, L.; Papadopoulos, K.

1982-01-01

The weak turbulence theory of Tsytovich, Stenflo and Wilhelmsson (1981) for evaluation of the nonlinear transfer of ion acoustic waves to Langmuir waves is shown to be limited in its region of validity to the level of ion acoustic waves. It is also demonstrated that, in applying the upconversion of ion sound to Langmuir waves for electron acceleration, nonlinear scattering should be self-consistently included, with a suppression of the upconversion process resulting. The impossibility of accelerating electrons by such a process for any reasonable physical system is thereby reaffirmed.

Covariances and spectra of the kinematics and dynamics of nonlinear waves

NASA Technical Reports Server (NTRS)

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

1985-01-01

Using the Stokes waves as a model of nonlinear waves and considering the linear component as a narrow-band Gaussian process, the covariances and spectra of velocity and acceleration components and pressure for points in the vicinity of still water level were derived taking into consideration the effects of free surface fluctuations. The results are compared with those obtained earlier using linear Gaussian waves.

Breather Rogue Waves in Random Seas

NASA Astrophysics Data System (ADS)

Wang, J.; Ma, Q. W.; Yan, S.; Chabchoub, A.

2018-01-01

Rogue or freak waves are extreme wave events that have heights exceeding 8 times the standard deviation of surrounding waves and emerge, for instance, in the ocean as well as in other physical dispersive wave guides, such as in optical fibers. One effective and convenient way to model such an extreme dynamics in laboratory environments within a controlled framework as well as for short process time and length scales is provided through the breather formalism. Breathers are pulsating localized structures known to model extreme waves in several nonlinear dispersive media in which the initial underlying process is assumed to be narrow banded. On the other hand, several recent studies suggest that breathers can also persist in more complex environments, such as in random seas, beyond the attributed physical limitations. In this work, we study the robustness of the Peregrine breather (PB) embedded in Joint North Sea Wave Project (JONSWAP) configurations using fully nonlinear hydrodynamic numerical simulations in order to validate its practicalness for ocean engineering applications. We provide a specific range for both the spectral bandwidth of the dynamical process as well as the background wave steepness and, thus, quantify the applicability of the PB in modeling rogue waves in realistic oceanic conditions. Our results may motivate analogous studies in fields of physics such as optics and plasma to quantify the limitations of exact weakly nonlinear models, such as solitons and breathers, within the framework of the fully nonlinear governing equations of the corresponding medium.

Investigation of scaling characteristics for defining design environments due to transient ground winds and near-field, nonlinear acoustic fields

NASA Technical Reports Server (NTRS)

Shih, C. C.

1973-01-01

In order to establish a foundation of scaling laws for the highly nonlinear waves associated with the launch vehicle, the basic knowledge of the relationships among the paramaters pertinent to the energy dissipation process associated with the propagation of nonlinear pressure waves in thermoviscous media is required. The problem of interest is to experimentally investigate the temporal and spacial velocity profiles of fluid flow in a 3-inch open-end pipe of various lengths, produced by the propagation of nonlinear pressure waves for various diaphragm burst pressures of a pressure wave generator. As a result, temporal and spacial characteristics of wave propagation for a parametric set of nonlinear pressure waves in the pipe containing air under atmospheric conditions were determined. Velocity measurements at five sections along the pipes of up to 210 ft. in length were made with hot-film anemometers for five pressure waves produced by a piston. The piston was derived with diaphragm burst pressures at 20, 40, 60, 80 and 100 psi in the driver chamber of the pressure wave generator.

Development of attenuation and diffraction corrections for linear and nonlinear Rayleigh surface waves radiating from a uniform line source

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

Jeong, Hyunjo, E-mail: hjjeong@wku.ac.kr; Cho, Sungjong; Zhang, Shuzeng

2016-04-15

In recent studies with nonlinear Rayleigh surface waves, harmonic generation measurements have been successfully employed to characterize material damage and microstructural changes, and found to be sensitive to early stages of damage process. A nonlinearity parameter of Rayleigh surface waves was derived and frequently measured to quantify the level of damage. The accurate measurement of the nonlinearity parameter generally requires making corrections for beam diffraction and medium attenuation. These effects are not generally known for nonlinear Rayleigh waves, and therefore not properly considered in most of previous studies. In this paper, the nonlinearity parameter for a Rayleigh surface wave ismore » defined from the plane wave displacement solutions. We explicitly define the attenuation and diffraction corrections for fundamental and second harmonic Rayleigh wave beams radiated from a uniform line source. Attenuation corrections are obtained from the quasilinear theory of plane Rayleigh wave equations. To obtain closed-form expressions for diffraction corrections, multi-Gaussian beam (MGB) models are employed to represent the integral solutions derived from the quasilinear theory of the full two-dimensional wave equation without parabolic approximation. Diffraction corrections are presented for a couple of transmitter-receiver geometries, and the effects of making attenuation and diffraction corrections are examined through the simulation of nonlinearity parameter determination in a solid sample.« less

Ultrasonic nonlinear guided wave inspection of microscopic damage in a composite structure

NASA Astrophysics Data System (ADS)

Zhang, Li; Borigo, Cody; Owens, Steven; Lissenden, Clifford; Rose, Joseph; Hakoda, Chris

2017-02-01

Sudden structural failure is a severe safety threat to many types of military and industrial composite structures. Because sudden structural failure may occur in a composite structure shortly after macroscale damage initiates, reliable early diagnosis of microdamage formation in the composite structure is critical to ensure safe operation and to reduce maintenance costs. Ultrasonic guided waves have been widely used for long-range defect detection in various structures. When guided waves are generated under certain excitation conditions, in addition to the traditional linear wave mode (known as the fundamental harmonic wave mode), a number of nonlinear higher-order harmonic wave modes are also be generated. Research shows that the nonlinear parameters of a higher-order harmonic wave mode could have excellent sensitivity to microstructural changes in a material. In this work, we successfully employed a nonlinear guided wave structural health monitoring (SHM) method to detect microscopic impact damage in a 32-layer carbon/epoxy fiber-reinforced composite plate. Our effort has demonstrated that, utilizing appropriate transducer design, equipment, excitation signals, and signal processing techniques, nonlinear guided wave parameter measurements can be reliably used to monitor microdamage initiation and growth in composite structures.

Prognostic characteristics of the lowest-mode internal waves in the Sea of Okhotsk

NASA Astrophysics Data System (ADS)

Kurkin, Andrey; Kurkina, Oxana; Zaytsev, Andrey; Rybin, Artem; Talipova, Tatiana

2017-04-01

The nonlinear dynamics of short-period internal waves on ocean shelves is well described by generalized nonlinear evolutionary models of Korteweg - de Vries type. Parameters of these models such as long wave propagation speed, nonlinear and dispersive coefficients can be calculated using hydrological data (sea water density stratification), and therefore have geographical and seasonal variations. The internal wave parameters for the basin of the Sea of Okhotsk are computed on a base of recent version of hydrological data source GDEM V3.0. Geographical and seasonal variability of internal wave characteristics is investigated. It is shown that annually or seasonally averaged data can be used for linear parameters. The nonlinear parameters are more sensitive to temporal averaging of hydrological data and detailed data are preferable to use. The zones for nonlinear parameters to change their signs (so-called "turning points") are selected. Possible internal waveforms appearing in the process of internal tide transformation including the solitary waves changing polarities are simulated for the hydrological conditions in the Sea of Okhotsk shelf to demonstrate different scenarios of internal wave adjustment, transformation, refraction and cylindrical divergence.

Stationary and non-stationary nonlinear optical spectroscopy on surface polaritons

NASA Technical Reports Server (NTRS)

Ponath, H. E.

1984-01-01

A phenomenological theory is given for non-stationary electromagnetic surface waves propagating along the boundary plane between two homogeneous isotropic media. The description of nonlinear optical effects using shortened wave equations is demonstrated for spontaneous and simulated Raman scattering processes on surface polaritons.

All-optical regenerator of multi-channel signals.

PubMed

Li, Lu; Patki, Pallavi G; Kwon, Young B; Stelmakh, Veronika; Campbell, Brandon D; Annamalai, Muthiah; Lakoba, Taras I; Vasilyev, Michael

2017-10-12

One of the main reasons why nonlinear-optical signal processing (regeneration, logic, etc.) has not yet become a practical alternative to electronic processing is that the all-optical elements with nonlinear input-output relationship have remained inherently single-channel devices (just like their electronic counterparts) and, hence, cannot fully utilise the parallel processing potential of optical fibres and amplifiers. The nonlinear input-output transfer function requires strong optical nonlinearity, e.g. self-phase modulation, which, for fundamental reasons, is always accompanied by cross-phase modulation and four-wave mixing. In processing multiple wavelength-division-multiplexing channels, large cross-phase modulation and four-wave mixing crosstalks among the channels destroy signal quality. Here we describe a solution to this problem: an optical signal processor employing a group-delay-managed nonlinear medium where strong self-phase modulation is achieved without such nonlinear crosstalk. We demonstrate, for the first time to our knowledge, simultaneous all-optical regeneration of up to 16 wavelength-division-multiplexing channels by one device. This multi-channel concept can be extended to other nonlinear-optical processing schemes.Nonlinear optical processing devices are not yet fully practical as they are single channel. Here the authors demonstrate all-optical regeneration of up to 16 channels by one device, employing a group-delay-managed nonlinear medium where strong self-phase modulation is achieved without nonlinear inter-channel crosstalk.

Nonlinear Alfvén wave propagating in ideal MHD plasmas

NASA Astrophysics Data System (ADS)

Zheng, Jugao; Chen, Yinhua; Yu, Mingyang

2016-01-01

The behavior of nonlinear Alfvén waves propagating in ideal MHD plasmas is investigated numerically. It is found that in a one-dimensional weakly nonlinear system an Alfvén wave train can excite two longitudinal disturbances, namely an acoustic wave and a ponderomotively driven disturbance, which behave differently for β \\gt 1 and β \\lt 1, where β is the ratio of plasma-to-magnetic pressures. In a strongly nonlinear system, the Alfvén wave train is modulated and can steepen to form shocks, leading to significant dissipation due to appearance of current sheets at magnetic-pressure minima. For periodic boundary condition, we find that the Alfvén wave transfers its energy to the plasma and heats it during the shock formation. In two-dimensional systems, fast magneto-acoustic wave generation due to Alfvén wave phase mixing is considered. It is found that the process depends on the amplitude and frequency of the Alfvén waves, as well as their speed gradients and the pressure of the background plasma.

Reconstruction of nonlinear wave propagation

DOEpatents

Fleischer, Jason W; Barsi, Christopher; Wan, Wenjie

2013-04-23

Disclosed are systems and methods for characterizing a nonlinear propagation environment by numerically propagating a measured output waveform resulting from a known input waveform. The numerical propagation reconstructs the input waveform, and in the process, the nonlinear environment is characterized. In certain embodiments, knowledge of the characterized nonlinear environment facilitates determination of an unknown input based on a measured output. Similarly, knowledge of the characterized nonlinear environment also facilitates formation of a desired output based on a configurable input. In both situations, the input thus characterized and the output thus obtained include features that would normally be lost in linear propagations. Such features can include evanescent waves and peripheral waves, such that an image thus obtained are inherently wide-angle, farfield form of microscopy.

Nonlinear hyperbolic theory of thermal waves in metals

NASA Technical Reports Server (NTRS)

Wilhelm, H. E.; Choi, S. H.

1975-01-01

A closed-form solution for cylindrical thermal waves in metals is given based on the nonlinear hyperbolic system of energy-conservation and heat-flux relaxation equations. It is shown that heat released from a line source propagates radially outward with finite speed in the form of a thermal wave which exhibits a discontinuous wave front. Unique nonlinear thermal-wave solutions exist up to a critical amount of driving energy, i.e., for larger energy releases, the thermal flow becomes multivalued (occurrence of shock waves). By comparison, it is demonstrated that the parabolic thermal-wave theory gives, in general, a misleading picture of the profile and propagation of thermal waves and leads to physical (infinite speed of heat propagation) and mathematical (divergent energy integrals) difficulties. Attention is drawn to the importance of temporal heat-flux relaxation for the physical understanding of fast transient processes such as thermal waves and more general explosions and implosions.

Dynamic of Langmuir and Ion-Sound Waves in Type 3 Solar Radio Sources

NASA Technical Reports Server (NTRS)

Robinson, P. A.; Willes, A. J.; Cairns, I. H.

1993-01-01

The evolution of Langmuir and ion-sound waves in type 3 sources is investigated, incorporating linear growth, linear damping, and nonlinear electrostatic decay. Improved estimates are obtained for the wavenumber range of growing waves and the nonlinear coupling coefficient for the decay process. The resulting prediction for the electrostatic decay threshold is consistent with the observed high-field cutoff in the Langmuir field distribution. It is shown that the conditions in the solar wind do not allow a steady state to be attained; rather, bursty linear and nonlinear interactions take place, consistent with the highly inhomogeneous and impulsive waves actually observed. Nonlinear growth is found to be fast enough to saturate the growth of the parent Langmuir waves in the available interaction time. The resulting levels of product Langmuir and ion-sound waves are estimated theoretically and shown to be consistent with in situ ISEE 3 observations of type 3 events at 1 AU. Nonlinear interactions slave the growth and decay of product sound waves to that of the product Langmuir waves. The resulting probability distribution of ion-sound field strengths is predicted to have a flat tail extending to a high-field cutoff. This prediction is consistent with statistics derived here from ISEE 3 observations. Agreement is also found between the frequencies of the observed waves and predictions for the product S waves. The competing processes of nonlinear wave collapse and quasilinear relaxation are discussed, and it is concluded that neither is responsible for the saturation of Langmuir growth. When wave and beam inhomogeneities are accounted for, arguments from quasi-linear relaxation yield an upper bound on the Langmuir fields that is too high to be relevant. Nor are the criteria for direct wave collapse of the beam-driven waves met, consistent with earlier simulation results that imply that this process is not responsible for saturation of the beam instability. Indeed, even if the highest observed Langmuir fields are assumed to he part of a long-wavelength 'condensate' produced via electrostatic decay, they still fall short of the relevant requirements for wave collapse. The most stringent requirement for collapse is that collapsing wave packets not be disrupted by ambient density fluctuations in the solar wind. Fields of several mV m(exp -1) extending over several hundred km would be needed to satisfy this requirement; at 1 AU such fields are rare at best.

Nonlinear wave interactions in shallow water magnetohydrodynamics of astrophysical plasma

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

Klimachkov, D. A., E-mail: klimachkovdmitry@gmail.com; Petrosyan, A. S., E-mail: apetrosy@iki.rssi.ru

2016-05-15

The rotating magnetohydrodynamic flows of a thin layer of astrophysical and space plasmas with a free surface in a vertical external magnetic field are considered in the shallow water approximation. The presence of a vertical external magnetic field changes significantly the dynamics of wave processes in an astrophysical plasma, in contrast to a neutral fluid and a plasma layer in an external toroidal magnetic field. There are three-wave nonlinear interactions in the case under consideration. Using the asymptotic method of multiscale expansions, we have derived nonlinear equations for the interaction of wave packets: three magneto- Poincare waves, three magnetostrophic waves,more » two magneto-Poincare and one magnetostrophic waves, and two magnetostrophic and one magneto-Poincare waves. The existence of decay instabilities and parametric amplification is predicted. We show that a magneto-Poincare wave decays into two magneto-Poincare waves, a magnetostrophic wave decays into two magnetostrophic waves, a magneto-Poincare wave decays into one magneto-Poincare and one magnetostrophic waves, and a magnetostrophic wave decays into one magnetostrophic and one magneto-Poincare waves. There are the following parametric amplification mechanisms: the parametric amplification of magneto-Poincare waves, the parametric amplification of magnetostrophic waves, the amplification of a magneto-Poincare wave in the field of a magnetostrophic wave, and the amplification of a magnetostrophic wave in the field of a magneto-Poincare wave. The instability growth rates and parametric amplification factors have been found for the corresponding processes.« less

Ion hole formation and nonlinear generation of electromagnetic ion cyclotron waves: THEMIS observations

NASA Astrophysics Data System (ADS)

Shoji, Masafumi; Miyoshi, Yoshizumi; Katoh, Yuto; Keika, Kunihiro; Angelopoulos, Vassilis; Kasahara, Satoshi; Asamura, Kazushi; Nakamura, Satoko; Omura, Yoshiharu

2017-09-01

Electromagnetic plasma waves are thought to be responsible for energy exchange between charged particles in space plasmas. Such an energy exchange process is evidenced by phase space holes identified in the ion distribution function and measurements of the dot product of the plasma wave electric field and the ion velocity. We develop a method to identify ion hole formation, taking into consideration the phase differences between the gyromotion of ions and the electromagnetic ion cyclotron (EMIC) waves. Using this method, we identify ion holes in the distribution function and the resulting nonlinear EMIC wave evolution from Time History of Events and Macroscale Interactions during Substorms (THEMIS) observations. These ion holes are key to wave growth and frequency drift by the ion currents through nonlinear wave-particle interactions, which are identified by a computer simulation in this study.

Rapid decay of nonlinear whistler waves in two dimensions: Full particle simulation

NASA Astrophysics Data System (ADS)

Umeda, Takayuki; Saito, Shinji; Nariyuki, Yasuhiro

2017-05-01

The decay of a nonlinear, short-wavelength, and monochromatic electromagnetic whistler wave is investigated by utilizing a two-dimensional (2D) fully relativistic electromagnetic particle-in-cell code. The simulation is performed under a low-beta condition in which the plasma pressure is much lower than the magnetic pressure. It has been shown that the nonlinear (large-amplitude) parent whistler wave decays through the parametric instability in a one-dimensional (1D) system. The present study shows that there is another channel for the decay of the parent whistler wave in 2D, which is much faster than in the timescale of the parametric decay in 1D. The parent whistler wave decays into two sideband daughter whistlers propagating obliquely with respect to the ambient magnetic field with a frequency close to the parent wave and two quasi-perpendicular electromagnetic modes with a frequency close to zero via a 2D decay instability. The two sideband daughter oblique whistlers also enhance a nonlinear longitudinal electrostatic wave via a three-wave interaction as a secondary process.

Optical Wave Turbulence and Wave Condensation in a Nonlinear Optical Experiment

NASA Astrophysics Data System (ADS)

Laurie, Jason; Bortolozzo, Umberto; Nazarenko, Sergey; Residori, Stefania

We present theory, numerical simulations and experimental observations of a 1D optical wave system. We show that this system is of a dual cascade type, namely, the energy cascading directly to small scales, and the photons or wave action cascading to large scales. In the optical context the inverse cascade is particularly interesting because it means the condensation of photons. We show that the cascades are induced by a six-wave resonant interaction process described by weak turbulence theory. We show that by starting with weakly nonlinear randomized waves as an initial condition, there exists an inverse cascade of photons towards the lowest wavenumbers. During the cascade nonlinearity becomes strong at low wavenumbers and, due to the focusing nature of the nonlinearity, it leads to modulational instability resulting in the formation of solitons. Further interaction of the solitons among themselves and with incoherent waves leads to the final condensate state dominated by a single strong soliton. In addition, we show the existence of the direct energy cascade numerically and that it agrees with the wave turbulence prediction.

Distributed source model for the full-wave electromagnetic simulation of nonlinear terahertz generation.

PubMed

Fumeaux, Christophe; Lin, Hungyen; Serita, Kazunori; Withayachumnankul, Withawat; Kaufmann, Thomas; Tonouchi, Masayoshi; Abbott, Derek

2012-07-30

The process of terahertz generation through optical rectification in a nonlinear crystal is modeled using discretized equivalent current sources. The equivalent terahertz sources are distributed in the active volume and computed based on a separately modeled near-infrared pump beam. This approach can be used to define an appropriate excitation for full-wave electromagnetic numerical simulations of the generated terahertz radiation. This enables predictive modeling of the near-field interactions of the terahertz beam with micro-structured samples, e.g. in a near-field time-resolved microscopy system. The distributed source model is described in detail, and an implementation in a particular full-wave simulation tool is presented. The numerical results are then validated through a series of measurements on square apertures. The general principle can be applied to other nonlinear processes with possible implementation in any full-wave numerical electromagnetic solver.

Computational process to study the wave propagation In a non-linear medium by quasi- linearization

NASA Astrophysics Data System (ADS)

Sharath Babu, K.; Venkata Brammam, J.; Baby Rani, CH

2018-03-01

Two objects having distinct velocities come into contact an impact can occur. The impact study i.e., in the displacement of the objects after the impact, the impact force is function of time‘t’ which is behaves similar to compression force. The impact tenure is very short so impulses must be generated subsequently high stresses are generated. In this work we are examined the wave propagation inside the object after collision and measured the object non-linear behavior in the one-dimensional case. Wave transmission is studied by means of material acoustic parameter value. The objective of this paper is to present a computational study of propagating pulsation and harmonic waves in nonlinear media using quasi-linearization and subsequently utilized the central difference scheme. This study gives focus on longitudinal, one- dimensional wave propagation. In the finite difference scheme Non-linear system is reduced to a linear system by applying quasi-linearization method. The computed results exhibit good agreement on par with the selected non-liner wave propagation.

Wave processes in the human cardiovascular system: The measuring complex, computing models, and diagnostic analysis

NASA Astrophysics Data System (ADS)

Ganiev, R. F.; Reviznikov, D. L.; Rogoza, A. N.; Slastushenskiy, Yu. V.; Ukrainskiy, L. E.

2017-03-01

A description of a complex approach to investigation of nonlinear wave processes in the human cardiovascular system based on a combination of high-precision methods of measuring a pulse wave, mathematical methods of processing the empirical data, and methods of direct numerical modeling of hemodynamic processes in an arterial tree is given.

Studies of the linear and nonlinear properties of Alfvén waves in LAPD

NASA Astrophysics Data System (ADS)

Carter, Troy; Dorfman, Seth; Gekelman, Walter; Tripathi, Shreekrishna; van Compernolle, Bart; Vincena, Steve; Rossi, Giovanni; Jenko, Frank

2015-11-01

An overview will be given of recent experimental research into linear and nonlinear properties of Alfvén waves in the Large Plasma Device (LAPD). The nonlinear three-wave interaction process at the heart of the parametric decay instability is studied by launching counter-propagating Alfvén waves from antennas placed at either end of LAPD, producing a damped ion acoustic mode. The decay of a lone, large amplitude Alfvén wave has been observed, producing co-propagating daughter waves with characteristics consistent with kinetic Alfvén waves. The process has an amplitude threshold and the frequency of the daughter modes varies with the amplitude of the pump. A new plasma source based on LaB6 cathode has been added to LAPD, enabling much higher density (x50), electron temperature (x2) and ion temperature (x6). This provides the opportunity to study the physics of waves and instabilities with space and astrophysically relevant β. Topics under investigation include the physics of Alfvén waves in increased β plasmas, electromagnetic effects in drift-Alfvén wave turbulence and the excitation of ion-temperature-anisotropy driven modes such as the mirror and firehose. Supported by NSF and DOE.

Coherent nonlinear optical studies of elementary processes in biological complexes: diagrammatic techniques based on the wave function versus the density matrix

PubMed Central

Biggs, Jason D.; Voll, Judith A.; Mukamel, Shaul

2012-01-01

Two types of diagrammatic approaches for the design and simulation of nonlinear optical experiments (closed-time path loops based on the wave function and double-sided Feynman diagrams for the density matrix) are presented and compared. We give guidelines for the assignment of relevant pathways and provide rules for the interpretation of existing nonlinear experiments in carotenoids. PMID:22753822

Nonlinear Internal Waves on the Inner Shelf: Observations Using a Distributed Temperature Sensing (DTS) System.

NASA Astrophysics Data System (ADS)

Davis, K. A.; Reid, E. C.; Cohen, A. L.

2016-02-01

Internal waves propagating across the continental slope and shelf are transformed by the competing effects of nonlinear steepening and dispersive spreading, forming nonlinear internal waves (NLIWs) that can penetrate onto the shallow inner shelf, often appearing in the form of bottom-propagating nonlinear internal bores or boluses. NLIWs play a significant role in nearshore dynamics with baroclinic current amplitudes on the order of that of wind- and surface wave-driven flows and rapid temperature changes on the order of annual ranges. In June 2014 we used a Distributed Temperature Sensing (DTS) system to give a continuous cross-shelf view of nonlinear internal wave dynamics on the forereef of Dongsha Atoll, a coral reef in the northern South China Sea. A DTS system measures temperature continuously along the length of an optical fiber, resolving meter-to-kilometer spatial scales. This unique view of cross-shelf temperature structure made it possible to observe internal wave reflection, variable propagation speed across the shelf, bolus formation and dissipation. Additionally, we used the DTS data to track internal waves across the shallow fore reef and onto the reef flat and to quantify spatial patterns in temperature variability. Shoaling internal waves are an important process affecting physical variability and water properties on the reef.

Nonlinear Whistler Wave Physics in the Radiation Belts

NASA Astrophysics Data System (ADS)

Crabtree, Chris

2016-10-01

Wave particle interactions between electrons and whistler waves are a dominant mechanism for controlling the dynamics of energetic electrons in the radiation belts. They are responsible for loss, via pitch-angle scattering of electrons into the loss cone, and energization to millions of electron volts. It has previously been theorized that large amplitude waves on the whistler branch may scatter their wave-vector nonlinearly via nonlinear Landau damping leading to important consequences for the global distribution of whistler wave energy density and hence the energetic electrons. It can dramatically reduce the lifetime of energetic electrons in the radiation belts by increasing the pitch angle scattering rate. The fundamental building block of this theory has now been confirmed through laboratory experiments. Here we report on in situ observations of wave electro-magnetic fields from the EMFISIS instrument on board NASA's Van Allen Probes that show the signatures of nonlinear scattering of whistler waves in the inner radiation belts. In the outer radiation belts, whistler mode chorus is believed to be responsible for the energization of electrons from 10s of Kev to MeV energies. Chorus is characterized by bursty large amplitude whistler mode waves with frequencies that change as a function of time on timescales corresponding to their growth. Theories explaining the chirping have been developed for decades based on electron trapping dynamics in a coherent wave. New high time resolution wave data from the Van Allen probes and advanced spectral techniques are revealing that the wave dynamics is highly structured, with sub-elements consisting of multiple chirping waves with discrete frequency hops between sub-elements. Laboratory experiments with energetic electron beams are currently reproducing the complex frequency vs time dynamics of whistler waves and in addition revealing signatures of wave-wave and beat-wave nonlinear wave-particle interactions. These new data suggest that these weak turbulence processes may be playing a role in saturating the nonlinear instability.

Coexisting rogue waves within the (2+1)-component long-wave-short-wave resonance.

PubMed

Chen, Shihua; Soto-Crespo, Jose M; Grelu, Philippe

2014-09-01

The coexistence of two different types of fundamental rogue waves is unveiled, based on the coupled equations describing the (2+1)-component long-wave-short-wave resonance. For a wide range of asymptotic background fields, each family of three rogue wave components can be triggered by using a slight deterministic alteration to the otherwise identical background field. The ability to trigger markedly different rogue wave profiles from similar initial conditions is confirmed by numerical simulations. This remarkable feature, which is absent in the scalar nonlinear Schrödinger equation, is attributed to the specific three-wave interaction process and may be universal for a variety of multicomponent wave dynamics spanning from oceanography to nonlinear optics.

Nonlinear ring resonator: spatial pattern generation

NASA Astrophysics Data System (ADS)

Ivanov, Vladimir Y.; Lachinova, Svetlana L.; Irochnikov, Nikita G.

2000-03-01

We consider theoretically spatial pattern formation processes in a unidirectional ring cavity with thin layer of Kerr-type nonlinear medium. Our method is based on studying of two coupled equations. The first is a partial differential equation for temporal dynamics of phase modulation of light wave in the medium. It describes nonlinear interaction in the Kerr-type lice. The second is a free propagation equation for the intracavity field complex amplitude. It involves diffraction effects of light wave in the cavity.

Single-cycle high-intensity electromagnetic pulse generation in the interaction of a plasma wakefield with regular nonlinear structures.

PubMed

Bulanov, S S; Esirkepov, T Zh; Kamenets, F F; Pegoraro, F

2006-03-01

The interaction of regular nonlinear structures (such as subcycle solitons, electron vortices, and wake Langmuir waves) with a strong wake wave in a collisionless plasma can be exploited in order to produce ultrashort electromagnetic pulses. The electromagnetic field of the nonlinear structure is partially reflected by the electron density modulations of the incident wake wave and a single-cycle high-intensity electromagnetic pulse is formed. Due to the Doppler effect the length of this pulse is much shorter than that of the nonlinear structure. This process is illustrated with two-dimensional particle-in-cell simulations. The considered laser-plasma interaction regimes can be achieved in present day experiments and can be used for plasma diagnostics.

Nonlinear processes generated by supercritical tidal flow in shallow straits

NASA Astrophysics Data System (ADS)

Bordois, Lucie; Auclair, Francis; Paci, Alexandre; Dossmann, Yvan; Nguyen, Cyril

2017-06-01

Numerical experiments have been carried out using a nonhydrostatic and non-Boussinesq regional oceanic circulation model to investigate the nonlinear processes generated by supercritical tidal flow in shallow straits. Our approach relies on idealized direct numerical simulations inspired by oceanic observations. By analyzing a large set of simulations, a regime diagram is proposed for the nonlinear processes generated in the lee of these straits. The results show that the topography shape of the strait plays a crucial role in the formation of internal solitary waves (ISWs) and in the occurrence of local breaking events. Both of these nonlinear processes are important turbulence producing phenomena. The topographic control, observed in mode 1 ISW formation in previous studies [Y. Dossmann, F. Auclair, and A. Paci, "Topographically induced internal solitary waves in a pycnocline: Primary generation and topographic control," Phys. Fluids 25, 066601 (2013) and Y. Dossmann et al., "Topographically induced internal solitary waves in a pycnocline: Ultrasonic probes and stereo-correlation measurements," Phys. Fluids 26, 056601 (2014)], is clearly reproducible for mode-2 ISW above shallow straits. Strong plunging breaking events are observed above "narrow" straits (straits with a width less than mode 1 wavelength) when the fluid velocity exceeds the local mode 1 wave speed. These results are a step towards future works on vertical mixing quantification and localization around complex strait areas.

Nonlinear Acoustic Propagation into the Seafloor

NASA Astrophysics Data System (ADS)

McDonald, B. Edward

2006-05-01

Explosions near the seafloor result in shock waves entering a much more complicated medium than water or air. Nonlinearities may be increased by two processes inherent to granular media: (1) a poroelastic nonlinearity comparable to the addition of bubbles to water, and (2) the Hertz force resulting from elastic deformation of grains, proportional to the Youngs modulus of the grains times the strain rate to the power 3/2. These two types of nonlinearity for shock propagation into the seafloor are investigated using a variant of the NPE model. The traditional Taylor series expansion of the equation of state (pressure as a function of density) is not appropriate to the Hertz force in the limit of small strain. We present a simple nonlinear wave equation model for compressional waves in marine sediments that retains the Hertz force explicitly with overdensity to the power 3/2. Numerical results for shock propagation are compared with similarity solutions for quadratic nonlinearity and for the fractional nonlinearity of the Hertz force.

One-dimensional optical wave turbulence: Experiment and theory

NASA Astrophysics Data System (ADS)

Laurie, Jason; Bortolozzo, Umberto; Nazarenko, Sergey; Residori, Stefania

2012-05-01

We present a review of the latest developments in one-dimensional (1D) optical wave turbulence (OWT). Based on an original experimental setup that allows for the implementation of 1D OWT, we are able to show that an inverse cascade occurs through the spontaneous evolution of the nonlinear field up to the point when modulational instability leads to soliton formation. After solitons are formed, further interaction of the solitons among themselves and with incoherent waves leads to a final condensate state dominated by a single strong soliton. Motivated by the observations, we develop a theoretical description, showing that the inverse cascade develops through six-wave interaction, and that this is the basic mechanism of nonlinear wave coupling for 1D OWT. We describe theory, numerics and experimental observations while trying to incorporate all the different aspects into a consistent context. The experimental system is described by two coupled nonlinear equations, which we explore within two wave limits allowing for the expression of the evolution of the complex amplitude in a single dynamical equation. The long-wave limit corresponds to waves with wave numbers smaller than the electrical coherence length of the liquid crystal, and the opposite limit, when wave numbers are larger. We show that both of these systems are of a dual cascade type, analogous to two-dimensional (2D) turbulence, which can be described by wave turbulence (WT) theory, and conclude that the cascades are induced by a six-wave resonant interaction process. WT theory predicts several stationary solutions (non-equilibrium and thermodynamic) to both the long- and short-wave systems, and we investigate the necessary conditions required for their realization. Interestingly, the long-wave system is close to the integrable 1D nonlinear Schrödinger equation (NLSE) (which contains exact nonlinear soliton solutions), and as a result during the inverse cascade, nonlinearity of the system at low wave numbers becomes strong. Subsequently, due to the focusing nature of the nonlinearity, this leads to modulational instability (MI) of the condensate and the formation of solitons. Finally, with the aid of the probability density function (PDF) description of WT theory, we explain the coexistence and mutual interactions between solitons and the weakly nonlinear random wave background in the form of a wave turbulence life cycle (WTLC).

Turbulence and wave particle interactions in solar-terrestrial plasmas

NASA Technical Reports Server (NTRS)

Dulk, G. A.; Goldman, M. V.; Toomre, J.

1985-01-01

Activities in the following study areas are reported: (1) particle and wave processes in solar flares; (2) solar convection zone turbulence; and (3) solar radiation emission. To investigate the amplification of cyclotron maser radiation in solar flares, a radio frequency. (RF) heating model was developed for the corona surrounding the energy release site. Then nonlinear simulations of compressible convection display prominent penetration by plumes into regions of stable stratification at the base of the solar convection zone, leading to the excitation of internal gravity waves there. Lastly, linear saturation of electron-beam-driven Langmuir waves by ambient density fluctuations, nonlinear saturation by strong turbulence processes, and radiation emission mechanisms are examined. An additional section discusses solar magnetic fields and hydromagnetic waves in inhomogeneous media, and the effect of magnetic fields on stellar oscillation.

The evolution of a localized nonlinear wave of the Kelvin-Helmholtz instability with gravity

NASA Astrophysics Data System (ADS)

Orazzo, Annagrazia; Hoepffner, Jérôme

2012-11-01

At the interface between two fluids of different density and in the presence of gravity, there are well known periodic surface waves which can propagate for long distances with little attenuation, as it is for instance the case at the surface of the sea. If wind is present, these waves progressively accumulate energy as they propagate and grow to large sizes—this is the Kelvin-Helmholtz instability. On the other hand, we show in this paper that for a given wind strength, there is potential for the growth of a localized nonlinear wave. This wave can reach a size such that the hydrostatic pressure drop from top to bottom equals the stagnation pressure of the wind. This process for the disruption of the flat interface is localized and nonlinear. We study the properties of this wave using numerical simulations of the Navier-Stokes equations.

Turbulence of Weak Gravitational Waves in the Early Universe.

PubMed

Galtier, Sébastien; Nazarenko, Sergey V

2017-12-01

We study the statistical properties of an ensemble of weak gravitational waves interacting nonlinearly in a flat space-time. We show that the resonant three-wave interactions are absent and develop a theory for four-wave interactions in the reduced case of a 2.5+1 diagonal metric tensor. In this limit, where only plus-polarized gravitational waves are present, we derive the interaction Hamiltonian and consider the asymptotic regime of weak gravitational wave turbulence. Both direct and inverse cascades are found for the energy and the wave action, respectively, and the corresponding wave spectra are derived. The inverse cascade is characterized by a finite-time propagation of the metric excitations-a process similar to an explosive nonequilibrium Bose-Einstein condensation, which provides an efficient mechanism to ironing out small-scale inhomogeneities. The direct cascade leads to an accumulation of the radiation energy in the system. These processes might be important for understanding the early Universe where a background of weak nonlinear gravitational waves is expected.

Electron-acoustic Instability Simulated By Modified Zakharov Equations

NASA Astrophysics Data System (ADS)

Jásenský, V.; Fiala, V.; Vána, O.; Trávnícek, P.; Hellinger, P.

We present non-linear equations describing processes in plasma when electron - acoustic waves are excited. These waves are present for instance in the vicinity of Earth's bow shock and in the polar ionosphere. Frequently they are excited by an elec- tron beam in a plasma with two electron populations, a cold and hot one. We derive modified Zakharov equations from kinetic theory for such a case together with numer- ical method for solving of this type of equations. Bispectral analysis is used to show which non-linear wave processes are of importance in course of the instability. Finally, we compare these results with similar simulations using Vlasov approach.

All-Optical Control of Linear and Nonlinear Energy Transfer via the Zeno Effect

NASA Astrophysics Data System (ADS)

Guo, Xiang; Zou, Chang-Ling; Jiang, Liang; Tang, Hong X.

2018-05-01

Microresonator-based nonlinear processes are fundamental to applications including microcomb generation, parametric frequency conversion, and harmonics generation. While nonlinear processes involving either second- (χ(2 )) or third- (χ(3 )) order nonlinearity have been extensively studied, the interaction between these two basic nonlinear processes has seldom been reported. In this paper we demonstrate a coherent interplay between second- and third- order nonlinear processes. The parametric (χ(2 ) ) coupling to a lossy ancillary mode shortens the lifetime of the target photonic mode and suppresses its density of states, preventing the photon emissions into the target photonic mode via the Zeno effect. Such an effect is then used to control the stimulated four-wave mixing process and realize a suppression ratio of 34.5.

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

Dechant, Lawrence J.

Wave packet analysis provides a connection between linear small disturbance theory and subsequent nonlinear turbulent spot flow behavior. The traditional association between linear stability analysis and nonlinear wave form is developed via the method of stationary phase whereby asymptotic (simplified) mean flow solutions are used to estimate dispersion behavior and stationary phase approximation are used to invert the associated Fourier transform. The resulting process typically requires nonlinear algebraic equations inversions that can be best performed numerically, which partially mitigates the value of the approximation as compared to a more complete, e.g. DNS or linear/nonlinear adjoint methods. To obtain a simpler,more » closed-form analytical result, the complete packet solution is modeled via approximate amplitude (linear convected kinematic wave initial value problem) and local sinusoidal (wave equation) expressions. Significantly, the initial value for the kinematic wave transport expression follows from a separable variable coefficient approximation to the linearized pressure fluctuation Poisson expression. The resulting amplitude solution, while approximate in nature, nonetheless, appears to mimic many of the global features, e.g. transitional flow intermittency and pressure fluctuation magnitude behavior. A low wave number wave packet models also recover meaningful auto-correlation and low frequency spectral behaviors.« less

Proof of Concept for an Ultrasensitive Technique to Detect and Localize Sources of Elastic Nonlinearity Using Phononic Crystals.

PubMed

Miniaci, M; Gliozzi, A S; Morvan, B; Krushynska, A; Bosia, F; Scalerandi, M; Pugno, N M

2017-05-26

The appearance of nonlinear effects in elastic wave propagation is one of the most reliable and sensitive indicators of the onset of material damage. However, these effects are usually very small and can be detected only using cumbersome digital signal processing techniques. Here, we propose and experimentally validate an alternative approach, using the filtering and focusing properties of phononic crystals to naturally select and reflect the higher harmonics generated by nonlinear effects, enabling the realization of time-reversal procedures for nonlinear elastic source detection. The proposed device demonstrates its potential as an efficient, compact, portable, passive apparatus for nonlinear elastic wave sensing and damage detection.

Harmonic generation of Lamb waves

NASA Astrophysics Data System (ADS)

Ing, Ros Kiri

2002-11-01

Lamb waves are dispersive waves that propagate following a number of distinct modes that depend on the values of the central frequency and frequency band. According to such properties and using the time-reversal process, it is shown that the hyperfocusing effect may be experienced [R. K. Ing and M. Fink, IEEE Trans. Ultrason. Ferroelectr. Freq. Control 45, 1032-1043 (1998)]. Such a focusing effect both relates the time recompression of the dispersive Lamb waves and constructive interference on the focus point of the modes involved. The hyperfocusing effect is interesting because it allows the amplitude of the Lamb waves to reach huge values on the focus point. In our experiments, Lamb waves with normal amplitudes of micrometer values have been achieved on the free surface of a Duralumin plate of 3 mm thickness. By analyzing the Lamb waves in the neighborhood of the focus point using the 2-D Fourier transform technique, a nonlinear process of harmonic generation is then observed--the fundamental frequency component is centered at 1.5 MHz. This nonlinear process is under study and quantified.

Waves at Navigation Structures

DTIC Science & Technology

2014-10-27

upgrades the Coastal Modeling System’s (CMS) wave model CMS-Wave, a phase-averaged spectral wave model, and BOUSS-2D, a Boussinesq -type nonlinear wave...nearshore wave processes in practical applications. These capabilities facilitate optimization of innovative infrastructure for navigation systems to...navigation systems . The advanced models develop probabilistic engineering design estimates for rehabilitation of coastal structures to evaluate the

Gordon Research Conference on Nonlinear Optics and Lasers

NASA Astrophysics Data System (ADS)

Haus, Hermann

1992-02-01

The topics chosen were production of X rays with high power lasers, generation of millimeter waves with femtosecond pulses, microcavities and microlasers, second harmonic generation in fibers and advances in photorefractivity and parallel optical processing. It introduces ways of thinking and scientific methods in fields that are related, but would not generally appear in specialized conferences. There were three such examples: the methods of nonlinear optics as applied to electronic signal processing, the concept of squeezing (special quantum states of the electromagnetic field) as used to explain the generation of gravitational waves in the expanding universe, and particle interferometers with particle- instead of wave-gratings. By asking Nobel laureate Bloembergen one year in advance to give the traditional after dinner speech, we were privileged to hear him speak of the history of optics over the centuries resulting in the various principles of linear optics, and the highly accelerated pace of discovery of the analogous principles in nonlinear optics.

Jet formation at the interaction of localized waves on the free surface of dielectric liquid in a tangential electric field

NASA Astrophysics Data System (ADS)

Kochurin, E. A.; Zubarev, N. M.

2018-01-01

Nonlinear dynamics of the free surface of finite depth non-conducting fluid with high dielectric constant subjected to a strong horizontal electric field is considered. Using the conformal transformation of the region occupied by the fluid into a strip, the process of interaction of counter-propagating waves is numerically simulated. The nonlinear solitary waves on the surface can separately propagate along or against the direction of electric field without distortion. At the same time, the shape of the oppositely traveling waves can be distorted as the result of their interaction. In the problem under study, the nonlinearity leads to increasing the wave amplitudes and the duration of their interaction. This effect is inversely proportional to the fluid depth. In the shallow water limit, the tendency to the formation of a vertical liquid jet is observed.

Nonreciprocal acoustics and dynamics in the in-plane oscillations of a geometrically nonlinear lattice.

PubMed

Zhang, Zhen; Koroleva, I; Manevitch, L I; Bergman, L A; Vakakis, A F

2016-09-01

We study the dynamics and acoustics of a nonlinear lattice with fixed boundary conditions composed of a finite number of particles coupled by linear springs, undergoing in-plane oscillations. The source of the strongly nonlinearity of this lattice is geometric effects generated by the in-plane stretching of the coupling linear springs. It has been shown that in the limit of low energy the lattice gives rise to a strongly nonlinear acoustic vacuum, which is a medium with zero speed of sound as defined in classical acoustics. The acoustic vacuum possesses strongly nonlocal coupling effects and an orthogonal set of nonlinear standing waves [or nonlinear normal modes (NNMs)] with mode shapes identical to those of the corresponding linear lattice; in contrast to the linear case, however, all NNMs except the one with the highest wavelength are unstable. In addition, the lattice supports two types of waves, namely, nearly linear sound waves (termed "L waves") corresponding to predominantly axial oscillations of the particles and strongly nonlinear localized propagating pulses (termed "NL pulses") corresponding to predominantly transverse oscillating wave packets of the particles with localized envelopes. We show the existence of nonlinear nonreciprocity phenomena in the dynamics and acoustics of the lattice. Two opposite cases are examined in the limit of low energy. The first gives rise to nonreciprocal dynamics and corresponds to collective, spatially extended transverse loading of the lattice leading to the excitation of individual, predominantly transverse NNMs, whereas the second case gives rise to nonreciprocal acoutics by considering the response of the lattice to spatially localized, transverse impulse or displacement excitations. We demonstrate intense and recurring energy exchanges between a directly excited NNM and other NNMs with higher wave numbers, so that nonreciprocal energy exchanges from small-to-large wave numbers are established. Moreover, we show the existence of nonreciprocal wave interaction phenomena in the form of irreversible targeted energy transfers from L waves to NL pulses during collisions of these two types of waves. Additional nonreciprocal acoustics are found in the form of complex "cascading processes, as well as nonreciprocal interactions between L waves and stationary discrete breathers. The computational studies confirm the theoretically predicted transition of the lattice dynamics to a low-energy state of nonlinear acoustic vacum with strong nonlocality.

Nonlinear interaction of near-planar TS waves and longitudinal vortices in boundary-layer transition

NASA Technical Reports Server (NTRS)

Smith, F. T.

1988-01-01

The nonlinear interactions that evolve between a planar or nearly planar Tollmien-Schlichting (TS) wave and the associated longitudinal vortices are considered theoretically for a boundary layer at high Reynolds number. The vortex flow is either induced by the TS nonlinear forcing or is input upstream, and similarly for the nonlinear wave development. Three major kinds of nonlinear spatial evolution, Types 1-3, are found. Each can start from secondary instability and then become nonlinear, Type 1 proving to be relatively benign but able to act as a pre-cursor to the Types 2, 3 which turn out to be very powerful nonlinear interactions. Type 2 involves faster stream-wise dependence and leads to a finite-distance blow-up in the amplitudes, which then triggers the full nonlinear 3-D triple-deck response, thus entirely altering the mean-flow profile locally. In contrast, Type 3 involves slower streamwise dependence but a faster spanwise response, with a small TS amplitude thereby causing an enhanced vortex effect which, again, is substantial enough to entirely alter the meanflow profile, on a more global scale. Streak-like formations in which there is localized concentration of streamwise vorticity and/or wave amplitude can appear, and certain of the nonlinear features also suggest by-pass processes for transition and significant changes in the flow structure downstream. The powerful nonlinear 3-D interactions 2, 3 are potentially very relevant to experimental findings in transition.

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.

A coupled "AB" system: Rogue waves and modulation instabilities.

PubMed

Wu, C F; Grimshaw, R H J; Chow, K W; Chan, H N

2015-10-01

Rogue waves are unexpectedly large and localized displacements from an equilibrium position or an otherwise calm background. For the nonlinear Schrödinger (NLS) model widely used in fluid mechanics and optics, these waves can occur only when dispersion and nonlinearity are of the same sign, a regime of modulation instability. For coupled NLS equations, rogue waves will arise even if dispersion and nonlinearity are of opposite signs in each component as new regimes of modulation instability will appear in the coupled system. The same phenomenon will be demonstrated here for a coupled "AB" system, a wave-current interaction model describing baroclinic instability processes in geophysical flows. Indeed, the onset of modulation instability correlates precisely with the existence criterion for rogue waves for this system. Transitions from "elevation" rogue waves to "depression" rogue waves are elucidated analytically. The dispersion relation as a polynomial of the fourth order may possess double pairs of complex roots, leading to multiple configurations of rogue waves for a given set of input parameters. For special parameter regimes, the dispersion relation reduces to a cubic polynomial, allowing the existence criterion for rogue waves to be computed explicitly. Numerical tests correlating modulation instability and evolution of rogue waves were conducted.

WaveAR: A software tool for calculating parameters for water waves with incident and reflected components

NASA Astrophysics Data System (ADS)

Landry, Blake J.; Hancock, Matthew J.; Mei, Chiang C.; García, Marcelo H.

2012-09-01

The ability to determine wave heights and phases along a spatial domain is vital to understanding a wide range of littoral processes. The software tool presented here employs established Stokes wave theory and sampling methods to calculate parameters for the incident and reflected components of a field of weakly nonlinear waves, monochromatic at first order in wave slope and propagating in one horizontal dimension. The software calculates wave parameters over an entire wave tank and accounts for reflection, weak nonlinearity, and a free second harmonic. Currently, no publicly available program has such functionality. The included MATLAB®-based open source code has also been compiled for Windows®, Mac® and Linux® operating systems. An additional companion program, VirtualWave, is included to generate virtual wave fields for WaveAR. Together, the programs serve as ideal analysis and teaching tools for laboratory water wave systems.

System and method for generating 3D images of non-linear properties of rock formation using surface seismic or surface to borehole seismic or both

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

Vu, Cung Khac; Nihei, Kurt Toshimi; Johnson, Paul A.

A system and method of characterizing properties of a medium from a non-linear interaction are include generating, by first and second acoustic sources disposed on a surface of the medium on a first line, first and second acoustic waves. The first and second acoustic sources are controllable such that trajectories of the first and second acoustic waves intersect in a mixing zone within the medium. The method further includes receiving, by a receiver positioned in a plane containing the first and second acoustic sources, a third acoustic wave generated by a non-linear mixing process from the first and second acousticmore » waves in the mixing zone; and creating a first two-dimensional image of non-linear properties or a first ratio of compressional velocity and shear velocity, or both, of the medium in a first plane generally perpendicular to the surface and containing the first line, based on the received third acoustic wave.« less

Optical rogue waves generation in a nonlinear metamaterial

NASA Astrophysics Data System (ADS)

Onana Essama, Bedel Giscard; Atangana, Jacques; Biya-Motto, Frederick; Mokhtari, Bouchra; Cherkaoui Eddeqaqi, Noureddine; Kofane, Timoleon Crepin

2014-11-01

We investigate the behavior of electromagnetic wave which propagates in a metamaterial for negative index regime. The optical pulse propagation is described by the nonlinear Schrödinger equation with cubic-quintic nonlinearities, second- and third-order dispersion effects. The behavior obtained for negative index regime is compared to that observed for positive index regime. The characterization of electromagnetic wave uses some pulse parameters obtained analytically and called collective coordinates such as amplitude, temporal position, width, chirp, frequency shift and phase. Six frequency ranges have been pointed out where a numerical evolution of collective coordinates and their stability are studied under a typical example to verify our analysis. It appears that a robust soliton due to a perfect compensation process between second-order dispersion and cubic-nonlinearity is presented at each frequency range for both negative and positive index regimes. Thereafter, the stability of the soliton pulse and physical conditions leading to optical rogue waves generation are discussed at each frequency range for both regimes, when third-order dispersion and quintic-nonlinearity come into play. We have demonstrated that collective coordinates give much useful information on external and internal behavior of rogue events. Firstly, we determine at what distance begins the internal excitation leading to rogue waves. Secondly, what kind of internal modification and how it modifies the system in order to build-up rogue events. These results lead to a best comprehension of the mechanism of rogue waves generation. So, it clearly appears that the rogue wave behavior strongly depends on nonlinearity strength of distortion, frequency and regime considered.

Temporal evolution of circularly polarized dispersive Alfvén wave and effect on solar wind turbulence

NASA Astrophysics Data System (ADS)

Sharma, Swati; Sharma, R. P.; Gaur, Nidhi

2016-01-01

Space provides a vast medium to study turbulence and is accessible to detailed in situ measurements. Alfvén waves (AW) are ubiquitous in space and a main component of magnetohydrodynamic turbulence in heliosphere. The wave interaction with the density fluctuations is considered to be an important driver of nonlinear processes in space plasmas. Present study involves the nonlinear coupling, on the account of the ponderomotive nonlinearity, of the parallel propagating circularly polarized dispersive Alfvén wave (DAW) with the density fluctuations associated with magnetosonic wave propagating in the direction perpendicular to ambient magnetic field. The localization of DAW electric field intensity and the corresponding power spectra has been studied for the case of solar wind at 1 A.U. A breakpoint in power spectrum is seen around ion inertial length and spectra goes steeper at smaller scales which is consistent with the observations reported by CLUSTER in context of solar wind turbulence. Thus nonlinear interaction of DAW with transverse fluctuations causes the transfer of wave energy from larger scales to the smaller scales and may contribute in providing the energy needed to accelerate the solar wind.

Nonlinear Evolution of Counter-Propagating Whistler Mode Waves Excited by Anisotropic Electrons Within the Equatorial Source Region: 1-D PIC Simulations

NASA Astrophysics Data System (ADS)

Chen, Huayue; Gao, Xinliang; Lu, Quanming; Sun, Jicheng; Wang, Shui

2018-02-01

Nonlinear physical processes related to whistler mode waves are attracting more and more attention for their significant role in reshaping whistler mode spectra in the Earth's magnetosphere. Using a 1-D particle-in-cell simulation model, we have investigated the nonlinear evolution of parallel counter-propagating whistler mode waves excited by anisotropic electrons within the equatorial source region. In our simulations, after the linear phase of whistler mode instability, the strong electrostatic standing structures along the background magnetic field will be formed, resulting from the coupling between excited counter-propagating whistler mode waves. The wave numbers of electrostatic standing structures are about twice those of whistler mode waves generated by anisotropic hot electrons. Moreover, these electrostatic standing structures can further be coupled with either parallel or antiparallel propagating whistler mode waves to excite high-k modes in this plasma system. Compared with excited whistler mode waves, these high-k modes typically have 3 times wave number, same frequency, and about 2 orders of magnitude smaller amplitude. Our study may provide a fresh view on the evolution of whistler mode waves within their equatorial source regions in the Earth's magnetosphere.

Experimental evidence of phase coherence of magnetohydrodynamic turbulence in the solar wind: GEOTAIL satellite data.

PubMed

Koga, D; Chian, A C-L; Hada, T; Rempel, E L

2008-02-13

Magnetohydrodynamic (MHD) turbulence is commonly observed in the solar wind. Nonlinear interactions among MHD waves are likely to produce finite correlation of the wave phases. For discussions of various transport processes of energetic particles, it is fundamentally important to determine whether the wave phases are randomly distributed (as assumed in the quasi-linear theory) or have a finite coherence. Using a method based on the surrogate data technique, we analysed the GEOTAIL magnetic field data to evaluate the phase coherence in MHD turbulence in the Earth's foreshock region. The results demonstrate the existence of finite phase correlation, indicating that nonlinear wave-wave interactions are in progress.

Waves at Navigation Structures

DTIC Science & Technology

2015-10-30

upgrades the Coastal Modeling System (CMS) wave models CMS-Wave, a phase- averaged spectral wave model, and BOUSS-2D, a Boussinesq type nonlinear wave...developing WaveNet and TideNet, two Web-based tool systems for wind and wave data access and processing, which provide critical data for USACE project...practical applications, resulting in optimization of navigation system to improve safety, reliability and operations with innovative infrastructures

Time and space analysis of turbulence of gravity surface waves

NASA Astrophysics Data System (ADS)

Mordant, Nicolas; Aubourg, Quentin; Viboud, Samuel; Sommeria, Joel

2016-11-01

Wave turbulence is a statistical state made of a very large number of nonlinearly interacting waves. The Weak Turbulence Theory was developed to describe such a situation in the weakly nonlinear regime. Although, oceanic data tend to be compatible with the theory, laboratory data fail to fulfill the theoretical predictions. A space-time resolved measurement of the waves have proven to be especially fruitful to identify the mechanism at play in turbulence of gravity-capillary waves. We developed an image processing algorithm to measure the motion of the surface of water with both space and time resolution. We first seed the surface with slightly buoyant polystyrene particles and use 3 cameras to reconstruct the surface. Our stereoscopic algorithm is coupled to PIV so that to obtain both the surface deformation and the velocity of the water surface. Such a coupling is shown to improve the sensitivity of the measurement by one order of magnitude. We use this technique to probe the existence of weakly nonlinear turbulence excited by two small wedge wavemakers in a 13-m diameter wave flume. We observe a truly weakly nonlinear regime of isotropic wave turbulence. This project has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (Grant Agreement No 647018-WATU).

Harmonic generation and parametric decay in the ion cyclotron frequency range

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

Skiff, F.N.; Wong, K.L.; Ono, M.

1984-06-01

Harmonic generation and parametric decay are examined in a toroidal ACT-I plasma using electrostatic plate antennas. The harmonic generation, which is consistent with sheath rectification, is sufficiently strong that the nonlinearly generated harmonic modes themselves decay parametrically. Resonant and nonresonant parametric decay of the second harmonic are observed and compared with uniform pump theory. Resonant decay of lower hybrid waves into lower hybrid waves and slow ion cyclotron waves is seen for the first time. Surprisingly, the decay processes are nonlinearly saturated, indicating absolute instability.

Higher-order modulation instability in nonlinear fiber optics.

PubMed

Erkintalo, Miro; Hammani, Kamal; Kibler, Bertrand; Finot, Christophe; Akhmediev, Nail; Dudley, John M; Genty, Goëry

2011-12-16

We report theoretical, numerical, and experimental studies of higher-order modulation instability in the focusing nonlinear Schrödinger equation. This higher-order instability arises from the nonlinear superposition of elementary instabilities, associated with initial single breather evolution followed by a regime of complex, yet deterministic, pulse splitting. We analytically describe the process using the Darboux transformation and compare with experiments in optical fiber. We show how a suitably low frequency modulation on a continuous wave field induces higher-order modulation instability splitting with the pulse characteristics at different phases of evolution related by a simple scaling relationship. We anticipate that similar processes are likely to be observed in many other systems including plasmas, Bose-Einstein condensates, and deep water waves. © 2011 American Physical Society

FOREWORD: Workshop on Large Amplitude Waves and Fields in Plasmas, sponsored by the Commission of the European Communities

NASA Astrophysics Data System (ADS)

Bingham, R.; De Angelis, U.; Shukla, P. K.; Stenflo, L.

1990-01-01

During the last decade considerable progress has been made in the area of nonlinear plasma wave phenomena and their applications. In order to exhibit the present state-of-art in this field, a one-week (22-26 May) workshop on Large Amplitude Waves and Fields was organized at the International Centre for Theoretical Physics (ICTP), Trieste, Italy, during the bi-yearly activity of the Spring College on Plasma Physics (15 May-9 June, 1989). Most of the invited lectures are published in this Topical Issue of Physica Scripta so that scientists working, or who want to enter the field of nonlinear plasma wave theory, can find out what has been achieved and what are the current research trends in this area. The material included here consists of general plasma wave theory, results of computer simulations, and experimental verifications. Without going into any detail, we shall just highlight the topics and the general features of the lectures contained in these proceedings. Various aspects of the excitation, propagation and interaction of nonlinear waves in plasmas are reviewed. Their relevance to plasma-based beat wave accelerators, short pulse laser and particle beam wake-field accelerators, plasma lenses, laser fusion and ionospheric modification experiments is discussed. Some introductory lectures present the general physics of nonlinear plasma waves including the saturation mechanisms and wave breaking conditions for both non-relativistic and relativistic nonlinearities. Three wave and four wave processes which include stimulated Raman, Brillouin and Compton scattering, modulational instabilities, self-focusing and collapse of the waves are discussed, emphasizing the important effects due to the relativistic electron mass variation and ponderomotive force. Detailed numerical studies of the interaction of high frequency plasma waves with low frequency density fluctuations described by the Zakharov equations show the localization of the high frequency field in density cavities and their burn-out resulting in very strong turbulence. Remarkable agreement between the simulations and ionospheric modification experiments have been demonstrated. The articles presented also attempted to correlate the theories of parametric instabilities with experimental observations. The properties of plasma lenses used for focusing of high energy particle beams is also presented as part of the uses of the nonlinear plasmas. Self-organisation of plasmas resulting in coherent nonlinear structures and particle diffusion processes are reported. On the experimental side the nonlinear optics of plasmas as a new area of research has been reviewed. This is becoming an important area for research since it treats the plasma from the outset as a nonlinear medium. Experimental observations of phase conjugation of electromagnetic signals demonstrate once again the importance of the nonlinearities inherent in the interaction of large amplitude waves with plasmas. Finally the importance of turbulence in space plasmas is emphasized in a discussion of the auroral phenomenon, presenting the plasma physicists point of view on this topic. The workshop, attended by scientists from all over the world, stimulated a great deal of lively discussions about the theoretical foundations, experimental observations and interpretations together with computer simulation results on the physics of nonlinear plasma wave phenomena. The workshop was made possible by the kind support of Professors A Salam, L Bertocchi and M Hassan. We are grateful to them for giving us the opportunity to organize the workshop within the activities of the Spring College on Plasma Physics. Thanks are also due to the ICTP and the European Economic Community (EEC) for providing partial financial support. Finally, our most cordial thanks are extended to the invited speakers for coming to Trieste delivering excellent talks and enhancing the activity of the Spring College.

A k-Space Method for Moderately Nonlinear Wave Propagation

PubMed Central

Jing, Yun; Wang, Tianren; Clement, Greg T.

2013-01-01

A k-space method for moderately nonlinear wave propagation in absorptive media is presented. The Westervelt equation is first transferred into k-space via Fourier transformation, and is solved by a modified wave-vector time-domain scheme. The present approach is not limited to forward propagation or parabolic approximation. One- and two-dimensional problems are investigated to verify the method by comparing results to analytic solutions and finite-difference time-domain (FDTD) method. It is found that to obtain accurate results in homogeneous media, the grid size can be as little as two points per wavelength, and for a moderately nonlinear problem, the Courant–Friedrichs–Lewy number can be as large as 0.4. Through comparisons with the conventional FDTD method, the k-space method for nonlinear wave propagation is shown here to be computationally more efficient and accurate. The k-space method is then employed to study three-dimensional nonlinear wave propagation through the skull, which shows that a relatively accurate focusing can be achieved in the brain at a high frequency by sending a low frequency from the transducer. Finally, implementations of the k-space method using a single graphics processing unit shows that it required about one-seventh the computation time of a single-core CPU calculation. PMID:22899114

Local numerical modelling of ultrasonic guided waves in linear and nonlinear media

NASA Astrophysics Data System (ADS)

Packo, Pawel; Radecki, Rafal; Kijanka, Piotr; Staszewski, Wieslaw J.; Uhl, Tadeusz; Leamy, Michael J.

2017-04-01

Nonlinear ultrasonic techniques provide improved damage sensitivity compared to linear approaches. The combination of attractive properties of guided waves, such as Lamb waves, with unique features of higher harmonic generation provides great potential for characterization of incipient damage, particularly in plate-like structures. Nonlinear ultrasonic structural health monitoring techniques use interrogation signals at frequencies other than the excitation frequency to detect changes in structural integrity. Signal processing techniques used in non-destructive evaluation are frequently supported by modeling and numerical simulations in order to facilitate problem solution. This paper discusses known and newly-developed local computational strategies for simulating elastic waves, and attempts characterization of their numerical properties in the context of linear and nonlinear media. A hybrid numerical approach combining advantages of the Local Interaction Simulation Approach (LISA) and Cellular Automata for Elastodynamics (CAFE) is proposed for unique treatment of arbitrary strain-stress relations. The iteration equations of the method are derived directly from physical principles employing stress and displacement continuity, leading to an accurate description of the propagation in arbitrarily complex media. Numerical analysis of guided wave propagation, based on the newly developed hybrid approach, is presented and discussed in the paper for linear and nonlinear media. Comparisons to Finite Elements (FE) are also discussed.

Consistent nonlinear deterministic and stochastic evolution equations for deep to shallow water wave shoaling

NASA Astrophysics Data System (ADS)

Vrecica, Teodor; Toledo, Yaron

2015-04-01

One-dimensional deterministic and stochastic evolution equations are derived for the dispersive nonlinear waves while taking dissipation of energy into account. The deterministic nonlinear evolution equations are formulated using operational calculus by following the approach of Bredmose et al. (2005). Their formulation is extended to include the linear and nonlinear effects of wave dissipation due to friction and breaking. The resulting equation set describes the linear evolution of the velocity potential for each wave harmonic coupled by quadratic nonlinear terms. These terms describe the nonlinear interactions between triads of waves, which represent the leading-order nonlinear effects in the near-shore region. The equations are translated to the amplitudes of the surface elevation by using the approach of Agnon and Sheremet (1997) with the correction of Eldeberky and Madsen (1999). The only current possibility for calculating the surface gravity wave field over large domains is by using stochastic wave evolution models. Hence, the above deterministic model is formulated as a stochastic one using the method of Agnon and Sheremet (1997) with two types of stochastic closure relations (Benney and Saffman's, 1966, and Hollway's, 1980). These formulations cannot be applied to the common wave forecasting models without further manipulation, as they include a non-local wave shoaling coefficients (i.e., ones that require integration along the wave rays). Therefore, a localization method was applied (see Stiassnie and Drimer, 2006, and Toledo and Agnon, 2012). This process essentially extracts the local terms that constitute the mean nonlinear energy transfer while discarding the remaining oscillatory terms, which transfer energy back and forth. One of the main findings of this work is the understanding that the approximated non-local coefficients behave in two essentially different manners. In intermediate water depths these coefficients indeed consist of rapidly oscillating terms, but as the water depth becomes shallow they change to an exponential growth (or decay) behavior. Hence, the formerly used localization technique cannot be justified for the shallow water region. A new formulation is devised for the localization in shallow water, it approximates the nonlinear non-local shoaling coefficient in shallow water and matches it to the one fitting to the intermediate water region. This allows the model behavior to be consistent from deep water to intermediate depths and up to the shallow water regime. Various simulations of the model were performed for the cases of intermediate, and shallow water, overall the model was found to give good results in both shallow and intermediate water depths. The essential difference between the shallow and intermediate nonlinear shoaling physics is explained via the dominating class III Bragg resonances phenomenon. By inspecting the resonance conditions and the nature of the dispersion relation, it is shown that unlike in the intermediate water regime, in shallow water depths the formation of resonant interactions is possible without taking into account bottom components. References Agnon, Y. & Sheremet, A. 1997 Stochastic nonlinear shoaling of directional spectra. J. Fluid Mech. 345, 79-99. Benney, D. J. & Saffman, P. G. 1966 Nonlinear interactions of random waves. Proc. R. Soc. Lond. A 289, 301-321. Bredmose, H., Agnon, Y., Madsen, P.A. & Schaffer, H.A. 2005 Wave transformation models with exact second-order transfer. European J. of Mech. - B/Fluids 24 (6), 659-682. Eldeberky, Y. & Madsen, P. A. 1999 Deterministic and stochastic evolution equations for fully dispersive and weakly nonlinear waves. Coastal Engineering 38, 1-24. Kaihatu, J. M. & Kirby, J. T. 1995 Nonlinear transformation of waves in infinite water depth. Phys. Fluids 8, 175-188. Holloway, G. 1980 Oceanic internal waves are not weak waves. J. Phys. Oceanogr. 10, 906-914. Stiassnie, M. & Drimer, N. 2006 Prediction of long forcing waves for harbor agitation studies. J. of waterways, port, coastal and ocean engineering 132(3), 166-171. Toledo, Y. & Agnon, Y. 2012 Stochastic evolution equations with localized nonlinear shoaling coefficients. European J. of Mech. - B/Fluids 34, 13-18.

Shoaling of nonlinear internal waves in Massachusetts Bay

USGS Publications Warehouse

Scotti, A.; Beardsley, R.C.; Butman, B.; Pineda, J.

2008-01-01

The shoaling of the nonlinear internal tide in Massachusetts Bay is studied with a fully nonlinear and nonhydrostatic model. The results are compared with current and temperature observations obtained during the August 1998 Massachusetts Bay Internal Wave Experiment and observations from a shorter experiment which took place in September 2001. The model shows how the approaching nonlinear undular bore interacts strongly with a shoaling bottom, offshore of where KdV theory predicts polarity switching should occur. It is shown that the shoaling process is dominated by nonlinearity, and the model results are interpreted with the aid of a two-layer nonlinear but hydrostatic model. After interacting with the shoaling bottom, the undular bore emerges on the shallow shelf inshore of the 30-m isobath as a nonlinear internal tide with a range of possible shapes, all of which are found in the available observational record. Copyright 2008 by the American Geophysical Union.

Modeling of Nonlinear Hydrodynamics of the Coastal Areas of the Black Sea by the Chain of the Proprietary and Open Source Models

NASA Astrophysics Data System (ADS)

Kantardgi, Igor; Zheleznyak, Mark; Demchenko, Raisa; Dykyi, Pavlo; Kivva, Sergei; Kolomiets, Pavlo; Sorokin, Maxim

2014-05-01

The nearshore hydrodynamic fields are produced by the nonlinear interactions of the shoaling waves of different time scales and currents. To simulate the wind wave and swells propagated to the coasts, wave generated near shore currents, nonlinear-dispersive wave transformation and wave diffraction in interaction with coastal and port structure, sediment transport and coastal erosion the chains of the models should be used. The objective of this presentation is to provide an overview of the results of the application of the model chains for the assessment of the wave impacts on new construction designed at the Black Sea coasts and the impacts of these constructions on the coastal erosion/ accretion processes to demonstrate needs for further development of the nonlinear models for the coastal engineering applications. The open source models Wave Watch III and SWAN has been used to simulate wave statistics of the dedicated areas of the Black Sea in high resolution to calculated the statistical parameters of the extreme wave approaching coastal zone construction in accordance with coastal engineering standards. As the main tool for the costal hydrodynamic simulations the modeling system COASTOX-MORPHO has been used, that includes the following models. HWAVE -code based on hyperbolic version of mild slope equations., HWAVE-S - spectral version of HWAVE., BOUSS-FNL - fully nonlinear system of Boussinesq equations for simulation wave nonlinear -dispersive wave transformation in coastal areas. COASTOX-CUR - the code provided the numerical solution of the Nonlinear Shallow Water Equations (NLSWE) by finite-volume methods on the unstructured grid describing the long wave transformation in the coastal zone with the efficient drying -wetting algorithms to simulate the inundation of the coastal areas including tsunami wave runup. Coastox -Cur equations with the radiation stress term calculated via near shore wave fields simulate the wave generated nearhore currents. COASTOX-SED - the module of the simulation of the sediment transport in which the suspended sediments are simulated on the basis of the solution of 2-D advection -diffusion equation and the bottom sediment transport calculations are provided the basis of a library of the most popular semi-empirical formulas. MORPH - the module of the simulation of the morphological transformation of coastal zone based on the mass balance equation, on the basis of the sediment fluxes, calculated in the SED module. MORPH management submodel is responsible for the execution of the model chain "waves- current- sediments - morphodynamics- waves". The open source model SWASH has been used to simulate nonlinear resonance phenomena in coastal waters. The model chain was applied to simulate the potential impact of the designed shore protection structures at the Sochi Olympic Park on coastal morphodynamics, the wave parameters and nonlinear oscillations in the new ports designed in Gelenddjik and Taman at North-East coast of the Black Sea. The modeling results are compared with the results of the physical modeling in the hydraulic flumes of Moscow University of Civil Engineering.

Microphysics of Waves and Instabilities in the Solar Wind and their Macro Manifestations in the Corona and Interplanetary Space

NASA Technical Reports Server (NTRS)

Habbal, Shadia R.; Gurman, Joseph (Technical Monitor)

2003-01-01

Investigations of the physical processes responsible for the acceleration of the solar wind were pursued with the development of two new solar wind codes: a hybrid code and a 2-D MHD code. Hybrid simulations were performed to investigate the interaction between ions and parallel propagating low frequency ion cyclotron waves in a homogeneous plasma. In a low-beta plasma such as the solar wind plasma in the inner corona, the proton thermal speed is much smaller than the Alfven speed. Vlasov linear theory predicts that protons are not in resonance with low frequency ion cyclotron waves. However, non-linear effect makes it possible that these waves can strongly heat and accelerate protons. This study has important implications for study of the corona and the solar wind. Low frequency ion cyclotron waves or Alfven waves are commonly observed in the solar wind. Until now, it is believed that these waves are not able to heat the solar wind plasma unless some cascading processes transfer the energy of these waves to high frequency part. However, this study shows that these waves may directly heat and accelerate protons non-linearly. This process may play an important role in the coronal heating and the solar wind acceleration, at least in some parameter space.

New Observation of Wave Excitation and Inverse Cascade in the Foreshock Region

NASA Astrophysics Data System (ADS)

He, Jiansen; Duan, Die; Yan, Limei; Huang, Shiyong; Tu, Chuanyi; Marsch, Eckart; Wang, Linghua; Tian, Hui

2016-04-01

Foreshock with nascent plasma turbulence is regarded as a fascinating region to understand the basic plasma physical processes, e.g., wave-particle interactions as well as wave-wave couplings. Although there have been a bunch of intensive studies on this topic, some key clues about the chain of the physical processes still lacks from observations, e.g., the co-existence of upstream energetic particles as the free energy source, excited pump waves as the wave seed, inverse cascaded daughter waves, and scattered energetic particles as the end of nonlinear processes. A relatively comprehensive case study with some new observations is presented in this work. In our case, upstream energetic protons drifting at tens of Alfvén speed with respect to the background plasma protons is observed from 3DP/PESA-High onboard the WIND spacecraft. When looking at the wave magnetic activities, we are surprised to find the co-existence of high-frequency (0.1-0.5 Hz) large-amplitude right-hand polarized (RHP) waves and low-frequency (0.02-0.1 Hz) small-amplitude left-hand polarized (LHP) waves in the spacecraft (SC) frame. The anti-correlation between magnetic and velocity fluctuations along with the sunward magnetic field direction indicates the low-frequency LHP waves in the SC frame is in fact the sunward upstream RHP waves in the solar wind frame. This new observation lays solid foundation for the applicability of plasma non-resonance instability theory and inverse cascade theory to the foreshock region, in which the downstream high-frequency RHP pump waves are excited by the upstream reflected energetic protons through non-resonance instability and low-frequency RHP daughter waves are generated by the pump waves due to nonlinear parametric decay. The weak signal of alpha particle flux in the foreshock region concerned is also favorable to the occurrence of nonlinear decay process. Furthermore, enhanced downstream energetic proton fluxes are found and inferred to be scattered by the nascent turbulent fluctuations. Therefore, some key clues about the newborn turbulence in the foreshock are supplemented in this work. Nevertheless, the more complete scenario about the fundamental plasma physical processes in the foreshock is left for the newly launched MMS project and the proposed THOR mission.

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

LANGMUIR WAVE DECAY IN INHOMOGENEOUS SOLAR WIND PLASMAS: SIMULATION RESULTS

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

Krafft, C.; Volokitin, A. S.; Krasnoselskikh, V. V., E-mail: catherine.krafft@u-psud.fr

2015-08-20

Langmuir turbulence excited by electron flows in solar wind plasmas is studied on the basis of numerical simulations. In particular, nonlinear wave decay processes involving ion-sound (IS) waves are considered in order to understand their dependence on external long-wavelength plasma density fluctuations. In the presence of inhomogeneities, it is shown that the decay processes are localized in space and, due to the differences between the group velocities of Langmuir and IS waves, their duration is limited so that a full nonlinear saturation cannot be achieved. The reflection and the scattering of Langmuir wave packets on the ambient and randomly varying density fluctuationsmore » lead to crucial effects impacting the development of the IS wave spectrum. Notably, beatings between forward propagating Langmuir waves and reflected ones result in the parametric generation of waves of noticeable amplitudes and in the amplification of IS waves. These processes, repeated at different space locations, form a series of cascades of wave energy transfer, similar to those studied in the frame of weak turbulence theory. The dynamics of such a cascading mechanism and its influence on the acceleration of the most energetic part of the electron beam are studied. Finally, the role of the decay processes in the shaping of the profiles of the Langmuir wave packets is discussed, and the waveforms calculated are compared with those observed recently on board the spacecraft Solar TErrestrial RElations Observatory and WIND.« less

Experimental implementation of phase locking in a nonlinear interferometer

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

Wang, Hailong; Jing, Jietai, E-mail: jtjing@phy.ecnu.edu.cn; Marino, A. M.

2015-09-21

Based upon two cascade four-wave mixing processes in two identical hot rubidium vapor cells, a nonlinear interferometer has been experimentally realized [Jing et al., Appl. Phys. Lett. 99, 011110 (2011); Hudelist et al., Nat. Commun. 5, 3049 (2014)]. It has a higher degree of phase sensitivity than a traditional linear interferometer and has many potential applications in quantum metrology. Phase locking of the nonlinear interferometer is needed before it can find its way into applications. In this letter, we investigate the experimental implementation of phase locking of the relative phase between the three beams at different frequencies involved in suchmore » a nonlinear interferometer. We have utilized two different methods, namely, beat note locking and coherent modulation locking. We find that coherent modulation locking can achieve much better phase stability than beat note locking in our system. Our results pave the way for real applications of a nonlinear interferometer in precision measurement and quantum manipulation, for example, phase control in phase-sensitive N-wave mixing process, N-port nonlinear interferometer and quantum-enhanced real-time phase tracking.« less

Nonlinear plasma wave models in 3D fluid simulations of laser-plasma interaction

NASA Astrophysics Data System (ADS)

Chapman, Thomas; Berger, Richard; Arrighi, Bill; Langer, Steve; Banks, Jeffrey; Brunner, Stephan

2017-10-01

Simulations of laser-plasma interaction (LPI) in inertial confinement fusion (ICF) conditions require multi-mm spatial scales due to the typical laser beam size and durations of order 100 ps in order for numerical laser reflectivities to converge. To be computationally achievable, these scales necessitate a fluid-like treatment of light and plasma waves with a spatial grid size on the order of the light wave length. Plasma waves experience many nonlinear phenomena not naturally described by a fluid treatment, such as frequency shifts induced by trapping, a nonlinear (typically suppressed) Landau damping, and mode couplings leading to instabilities that can cause the plasma wave to decay rapidly. These processes affect the onset and saturation of stimulated Raman and Brillouin scattering, and are of direct interest to the modeling and prediction of deleterious LPI in ICF. It is not currently computationally feasible to simulate these Debye length-scale phenomena in 3D across experimental scales. Analytically-derived and/or numerically benchmarked models of processes occurring at scales finer than the fluid simulation grid offer a path forward. We demonstrate the impact of a range of kinetic processes on plasma reflectivity via models included in the LPI simulation code pF3D. This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344.

Semiclassical limit of the focusing NLS: Whitham equations and the Riemann-Hilbert Problem approach

NASA Astrophysics Data System (ADS)

Tovbis, Alexander; El, Gennady A.

2016-10-01

The main goal of this paper is to put together: a) the Whitham theory applicable to slowly modulated N-phase nonlinear wave solutions to the focusing nonlinear Schrödinger (fNLS) equation, and b) the Riemann-Hilbert Problem approach to particular solutions of the fNLS in the semiclassical (small dispersion) limit that develop slowly modulated N-phase nonlinear wave in the process of evolution. Both approaches have their own merits and limitations. Understanding of the interrelations between them could prove beneficial for a broad range of problems involving the semiclassical fNLS.

Giant nonlinear response at a plasmonic nanofocus drives efficient four-wave mixing

NASA Astrophysics Data System (ADS)

Nielsen, Michael P.; Shi, Xingyuan; Dichtl, Paul; Maier, Stefan A.; Oulton, Rupert F.

2017-12-01

Efficient optical frequency mixing typically must accumulate over large interaction lengths because nonlinear responses in natural materials are inherently weak. This limits the efficiency of mixing processes owing to the requirement of phase matching. Here, we report efficient four-wave mixing (FWM) over micrometer-scale interaction lengths at telecommunications wavelengths on silicon. We used an integrated plasmonic gap waveguide that strongly confines light within a nonlinear organic polymer. The gap waveguide intensifies light by nanofocusing it to a mode cross-section of a few tens of nanometers, thus generating a nonlinear response so strong that efficient FWM accumulates over wavelength-scale distances. This technique opens up nonlinear optics to a regime of relaxed phase matching, with the possibility of compact, broadband, and efficient frequency mixing integrated with silicon photonics.

On Holo-Hilbert Spectral Analysis: A Full Informational Spectral Representation for Nonlinear and Non-Stationary Data

NASA Technical Reports Server (NTRS)

Huang, Norden E.; Hu, Kun; Yang, Albert C. C.; Chang, Hsing-Chih; Jia, Deng; Liang, Wei-Kuang; Yeh, Jia Rong; Kao, Chu-Lan; Juan, Chi-Huang; Peng, Chung Kang;

On Holo-Hilbert spectral analysis: a full informational spectral representation for nonlinear and non-stationary data

PubMed Central

Huang, Norden E.; Hu, Kun; Yang, Albert C. C.; Chang, Hsing-Chih; Jia, Deng; Liang, Wei-Kuang; Yeh, Jia Rong; Kao, Chu-Lan; Juan, Chi-Hung; Peng, Chung Kang; Meijer, Johanna H.; Wang, Yung-Hung; Long, Steven R.; Wu, Zhauhua

2016-01-01

The Holo-Hilbert spectral analysis (HHSA) method is introduced to cure the deficiencies of traditional spectral analysis and to give a full informational representation of nonlinear and non-stationary data. It uses a nested empirical mode decomposition and Hilbert–Huang transform (HHT) approach to identify intrinsic amplitude and frequency modulations often present in nonlinear systems. Comparisons are first made with traditional spectrum analysis, which usually achieved its results through convolutional integral transforms based on additive expansions of an a priori determined basis, mostly under linear and stationary assumptions. Thus, for non-stationary processes, the best one could do historically was to use the time–frequency representations, in which the amplitude (or energy density) variation is still represented in terms of time. For nonlinear processes, the data can have both amplitude and frequency modulations (intra-mode and inter-mode) generated by two different mechanisms: linear additive or nonlinear multiplicative processes. As all existing spectral analysis methods are based on additive expansions, either a priori or adaptive, none of them could possibly represent the multiplicative processes. While the earlier adaptive HHT spectral analysis approach could accommodate the intra-wave nonlinearity quite remarkably, it remained that any inter-wave nonlinear multiplicative mechanisms that include cross-scale coupling and phase-lock modulations were left untreated. To resolve the multiplicative processes issue, additional dimensions in the spectrum result are needed to account for the variations in both the amplitude and frequency modulations simultaneously. HHSA accommodates all the processes: additive and multiplicative, intra-mode and inter-mode, stationary and non-stationary, linear and nonlinear interactions. The Holo prefix in HHSA denotes a multiple dimensional representation with both additive and multiplicative capabilities. PMID:26953180

Synchronism of nonlinear internal waves in a three-layer fluid

NASA Astrophysics Data System (ADS)

Talipova, Tatiana; Kurkina, Oxana; Terletska, Katerina; Rouvinskaya, Ekaterina

2017-04-01

In a three layer fluid with arbitrary layer widths and densities the existence of long internal solitons and breathers is proven theoretically and numerically, see for example (Pelinovsky et al., 2007; Lamb et al., 2007). The existence of breather-like waves of the intermediate length is also shown in numerical simulations (Terletska et al., 2016). For such waves conditions of synchronism are valid when a breather of the first mode and a soliton of the second mode move together with the same speed and form an asymmetric solitary wave of the second mode. The process of strong interaction of long nonlinear internal waves in the framework of three-layer Camassa-Choi model demonstrates the same effect (Jo&Choi, 2014; Barros, 2016). We analyze possible synchronism conditions for steady-state internal waves in a three-layer fluid analytically the framework of the Gardner equation, which is valid for long weakly nonlinear internal waves. The equations for synchronism conditions are derived and considered in terms of wave amplitudes, layer widths and density jumps. The configurations of three-layer fluid are found for which such a synchronism is possible. References: Barros R. Large amplitude internal waves in three-layer flows. The forth international conference "Nonlinear Waves - Theory and Applications", MS7, Beijing, China, June 25 - 28, 2016 Pelinovsky E., Polukhina O., Slunyaev A., Talipova T. Internal solitary waves // Chapter 4 in the book "Solitary Waves in Fluids". WIT Press. Southampton, Boston. 2007. P. 85 - 110. K. Terletska., K. T. Jung, T. Talipova, V. Maderich, I. Brovchenko and R. Grimshaw Internal breather-like wave generation by the second mode solitary wave interaction with a step// Physics of Fluids, 2016, accepted

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.

Numerical studies of nonlinear ultrasonic guided waves in uniform waveguides with arbitrary cross sections

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

Zuo, Peng; Fan, Zheng, E-mail: ZFAN@ntu.edu.sg; Zhou, Yu

2016-07-15

Nonlinear guided waves have been investigated widely in simple geometries, such as plates, pipe and shells, where analytical solutions have been developed. This paper extends the application of nonlinear guided waves to waveguides with arbitrary cross sections. The criteria for the existence of nonlinear guided waves were summarized based on the finite deformation theory and nonlinear material properties. Numerical models were developed for the analysis of nonlinear guided waves in complex geometries, including nonlinear Semi-Analytical Finite Element (SAFE) method to identify internal resonant modes in complex waveguides, and Finite Element (FE) models to simulate the nonlinear wave propagation at resonantmore » frequencies. Two examples, an aluminum plate and a steel rectangular bar, were studied using the proposed numerical model, demonstrating the existence of nonlinear guided waves in such structures and the energy transfer from primary to secondary modes.« less

The nonlinear gyroresonance interaction between energetic electrons and coherent VLF waves propagating at an arbitrary angle with respect to the earth's magnetic field

NASA Technical Reports Server (NTRS)

Bell, T. F.

1984-01-01

A theory is presented of the nonlinear gyroresonance interaction that takes place in the magnetosphere between energetic electrons and coherent VLF waves propagating in the whistler mode at an arbitrary angle psi with respect to the earth's magnetic field B-sub-0. Particularly examined is the phase trapping (PT) mechanism believed to be responsible for the generation of VLF emissions. It is concluded that near the magnetic equatorial plane gradients of psi may play a very important part in the PT process for nonducted waves. Predictions of a higher threshold value for PT for nonducted waves generally agree with experimental data concerning VLF emission triggering by nonducted waves.

Toward nonlinear magnonics: Intensity-dependent spin-wave switching in insulating side-coupled magnetic stripes

NASA Astrophysics Data System (ADS)

Sadovnikov, A. V.; Odintsov, S. A.; Beginin, E. N.; Sheshukova, S. E.; Sharaevskii, Yu. P.; Nikitov, S. A.

2017-10-01

We demonstrate that the nonlinear spin-wave transport in two laterally parallel magnetic stripes exhibit the intensity-dependent power exchange between the adjacent spin-wave channels. By the means of Brillouin light scattering technique, we investigate collective nonlinear spin-wave dynamics in the presence of magnetodipolar coupling. The nonlinear intensity-dependent effect reveals itself in the spin-wave mode transformation and differential nonlinear spin-wave phase shift in each adjacent magnetic stripe. The proposed analytical theory, based on the coupled Ginzburg-Landau equations, predicts the geometry design involving the reduction of power requirement to the all-magnonic switching. A very good agreement between calculation and experiment was found. In addition, a micromagnetic and finite-element approach has been independently used to study the nonlinear behavior of spin waves in adjacent stripes and the nonlinear transformation of spatial profiles of spin-wave modes. Our results show that the proposed spin-wave coupling mechanism provides the basis for nonlinear magnonic circuits and opens the perspectives for all-magnonic computing architecture.

Nonlinear Interactions Between Shear Alfvén waves on LaPD

NASA Astrophysics Data System (ADS)

Brugman, B.; Carter, T. A.; Pribyl, P.; Dorland, W.; Quataert, E.

2003-10-01

Turbulent energy cascades may play a major role in many astrophysical phenomenon, such as accretion disks, as well as in terrestrial plasmas, as related to turbulent cross field transport. Existing theories have yet to be rigorously compared with experimental results and instead have relied on indirect measurements from astrophysics and solar probes. The turbulent interaction between counter propagating shear Alfvén waves and the interaction of Alfvén waves launched into a reflecting cavity represent two practical experiments relevant to the study of such cascades. These experiments will be conducted on the LaPD and the results compared to those calculated using the GS2 code, which makes use of the gyrokinetic approximation. Due to the effects of Landau damping it is believed that high amplitude Alfvén waves must be launched in order for nonlinear processes to be measurable; several means of launching such waves will be employed. The first method will employ the use of antenna launched Alfvén waves and the second will make use of waves launched by a source instability native to LaPD (J. E. Maggs, G. Morales, PRL, In Press). It is believed that both of these schemes will be capable of generating waves of sufficient magnitude to probe the nonlinear interactions of interest. Initial measurements show signs of nonlinear effects when shear Alfvén waves, generated by instabilities in the LaPD source, are launched into a closed cavity. These effects are manifested as coupling between a low frequency wave and the launched wave, as indicated by the creation of side bands centered on the frequency of the launched wave. Further measurements of this effect and wave sources will be presented.

Efficient non-linear two-photon effects from the Cesium 6D manifold

NASA Astrophysics Data System (ADS)

Haluska, Nathan D.; Perram, Glen P.; Rice, Christopher A.

2018-02-01

We report several non-linear process that occur when two-photon pumping the cesium 6D states. Cesium vapor possess some of the largest two-photon pump cross sections in nature. Pumping these cross sections leads to strong amplified spontaneous emission that we observe on over 17 lasing lines. These new fields are strong enough to couple with the pump to create additional tunable lines. We use a heat pipe with cesium densities of 1014 to 1016 cm-3 and 0 to 5 Torr of helium buffer gas. The cesium 6D States are interrogated by both high energy pulses and low power CW sources. We observe four-wave mixing, six-wave mixing, potential two-photon lasing, other unknown nonlinear processes, and the persistence of some processes at low thresholds. This system is also uniquely qualified to support two-photon lasing under the proper conditions.

Nonlinear Excitation of Acoustic Modes by Large Amplitude Alfvén waves in the Large Plasma Device (LAPD)

NASA Astrophysics Data System (ADS)

Dorfman, S.; Carter, T.; Pribyl, P.; Tripathi, S. K. P.; van Compernolle, B.; Vincena, S.; Sydora, R.

2013-10-01

Alfvén waves, a fundamental mode of magnetized plasmas, are ubiquitous in lab and space. While the linear behavior of these waves has been extensively studied, non-linear effects are important in many real systems, including the solar wind and solar corona. In particular, a parametric decay process in which a large amplitude Alfvén wave decays into an ion acoustic wave and backward propagating Alfvén wave may play an important role in coronal heating and/or in establishing the spectrum of solar wind turbulence. Recent counter-propagating Alfvén wave experiments have recorded the first laboratory observation of the Alfvén-acoustic mode coupling at the heart of this parametric decay instability. The resonance in the observed beat process has several features consistent with ponderomotive coupling to an ion acoustic mode, including the measured dispersion relation and spatial profile. Strong damping observed after the pump Alfvén waves are turned off is under investigation. New experiments and simulations also aim to identify decay instabilities from a single large-amplitude Alfvén wave. Supported by DOE and NSF.

Nonlinear mechanism for the generation of electromagnetic fields in a magnetized plasma by the beatings of waves

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

Aburjania, G. D.; Machabeli, G. Z.; Kharshiladze, O. A.

2006-07-15

The modulational instability in a plasma in a strong constant external magnetic field is considered. The plasmon condensate is modulated not by conventional low-frequency ion sound but by the beatings of two high-frequency transverse electromagnetic waves propagating along the magnetic field. The instability reduces the spatial scales of Langmuir turbulence along the external magnetic field and generates electromagnetic fields. It is shown that, for a pump wave with a sufficiently large amplitude, the effect described in the present paper can be a dominant nonlinear process.

Ultralow power continuous-wave frequency conversion in hydrogenated amorphous silicon waveguides.

PubMed

Wang, Ke-Yao; Foster, Amy C

2012-04-15

We demonstrate wavelength conversion through nonlinear parametric processes in hydrogenated amorphous silicon (a-Si:H) with maximum conversion efficiency of -13 dB at telecommunication data rates (10 GHz) using only 15 mW of pump peak power. Conversion bandwidths as large as 150 nm (20 THz) are measured in continuous-wave regime at telecommunication wavelengths. The nonlinear refractive index of the material is determined by four-wave mixing (FWM) to be n(2)=7.43×10(-13) cm(2)/W, approximately an order of magnitude larger than that of single crystal silicon. © 2012 Optical Society of America

Nonlinear ultrasonic wave modulation for online fatigue crack detection

NASA Astrophysics Data System (ADS)

Sohn, Hoon; Lim, Hyung Jin; DeSimio, Martin P.; Brown, Kevin; Derriso, Mark

2014-02-01

This study presents a fatigue crack detection technique using nonlinear ultrasonic wave modulation. Ultrasonic waves at two distinctive driving frequencies are generated and corresponding ultrasonic responses are measured using permanently installed lead zirconate titanate (PZT) transducers with a potential for continuous monitoring. Here, the input signal at the lower driving frequency is often referred to as a 'pumping' signal, and the higher frequency input is referred to as a 'probing' signal. The presence of a system nonlinearity, such as a crack formation, can provide a mechanism for nonlinear wave modulation, and create spectral sidebands around the frequency of the probing signal. A signal processing technique combining linear response subtraction (LRS) and synchronous demodulation (SD) is developed specifically to extract the crack-induced spectral sidebands. The proposed crack detection method is successfully applied to identify actual fatigue cracks grown in metallic plate and complex fitting-lug specimens. Finally, the effect of pumping and probing frequencies on the amplitude of the first spectral sideband is investigated using the first sideband spectrogram (FSS) obtained by sweeping both pumping and probing signals over specified frequency ranges.

Feedback loop compensates for rectifier nonlinearity

NASA Technical Reports Server (NTRS)

1966-01-01

Signal processing circuit with two negative feedback loops rectifies two sinusoidal signals which are 180 degrees out of phase and produces a single full-wave rectified output signal. Each feedback loop incorporates a feedback rectifier to compensate for the nonlinearity of the circuit.

Nonlinear magnetoacoustic wave propagation with chemical reactions

NASA Astrophysics Data System (ADS)

Margulies, Timothy Scott

2002-11-01

The magnetoacoustic problem with an application to sound wave propagation through electrically conducting fluids such as the ocean in the Earth's magnetic field, liquid metals, or plasmas has been addressed taking into account several simultaneous chemical reactions. Using continuum balance equations for the total mass, linear momentum, energy; as well as Maxwell's electrodynamic equations, a nonlinear beam equation has been developed to generalize the Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation for a fluid with linear viscosity but nonlinear and diffraction effects. Thermodynamic parameters are used and not tailored to only an adiabatic fluid case. The chemical kinetic equations build on a relaxing media approach presented, for example, by K. Naugolnukh and L. Ostrovsky [Nonlinear Wave Processes in Acoustics (Cambridge Univ. Press, Cambridge, 1998)] for a linearized single reaction and thermodynamic pressure equation of state. Approximations for large and small relaxation times and for magnetohydrodynamic parameters [Korsunskii, Sov. Phys. Acoust. 36 (1990)] are examined. Additionally, Cattaneo's equation for heat conduction and its generalization for a memory process rather than a Fourier's law are taken into account. It was introduced for the heat flux depends on the temperature gradient at an earlier time to generate heat pulses of finite speed.

Fate and Contribution of Internal Wave-Forced Barnacle Settlers to Community Structure in Northern Baja California, a Year after Settlement

NASA Astrophysics Data System (ADS)

Lievana, A.; Ladah, L. B.; Lavin, M. F.; Filonov, A. E.; Tapia, F. J.; Leichter, J.; Valencia Gasti, J. A.

2016-02-01

Physical transport processes, such as nonlinear internal waves, operating within the coastal ocean of Baja California, Mexico, are diverse, variable and operate on a variety of temporal and spatial scales. Understanding the influence of nonlinear internal waves, in part responsible for the exchange of water properties between coastal and offshore environments, on the structure of intertidal communities is important for the generation of working ecological models. The relationship between the supply of ecological subsidies associated with physical transport processes that operate on relatively short spatial and temporal scales, such as the internal tide, and intertidal community structure must be understood as processes that operate on distinct spatial and temporal scales may be prone to react uniquely as the climate changes. We designed an experiment to quantify recruitment and adult survivorship of Chthamalus sp. whose settlement was associated with internal wave activity in the nearby ocean and found that the number of settlers was a robust predictor of the number of adults observed, indicating that post-settlement processes such as competition and predation are not likely to significantly affect the structure of the intertidal barnacle community resulting from internal-wave forced settlement.

Specific Features of Destabilization of the Wave Profile During Reflection of an Intense Acoustic Beam from a Soft Boundary

NASA Astrophysics Data System (ADS)

Deryabin, M. S.; Kasyanov, D. A.; Kurin, V. V.; Garasyov, M. A.

2016-05-01

We show that a significant energy redistribution occurs in the spectrum of reflected nonlinear waves, when an intense acoustic beam is reflected from an acoustically soft boundary, which manifests itself at short wave distances from a reflecting boundary. This effect leads to the appearance of extrema in the distributions of the amplitude and intensity of the field of the reflected acoustic beam near the reflecting boundary. The results of physical experiments are confirmed by numerical modeling of the process of transformation of nonlinear waves reflected from an acoustically soft boundary. Numerical modeling was performed by means of the Khokhlov—Zabolotskaya—Kuznetsov (KZK) equation.

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.

Nonlinear and linear bottom interaction effects in shallow water

NASA Technical Reports Server (NTRS)

Shemdin, O.; Hsiao, S. V.; Hasselmann, K.; Herterich, K.

1978-01-01

The paper examines wave-energy dissipation rates in shallow water calculated from measured wave spectra at different distances from the shore. Different linear and nonlinear transfer and dissipation mechanisms are discussed. The various data sets are interpreted in terms of prevailing mechanisms at the respective sites. The incorporation of different processes in a predictive shallow-water model is outlined. The analysis suggests that bottom motion is primarily responsible for wave-energy dissipation in the Delta Region of the Gulf of Mexico, that friction is mainly responsible for wave-energy dissipation in Marineland, Panama City and Melkbosstrand, and that percolation is probably the dominant mechanism in the JONSWAP area of the North Sea.

Future Reef Growth Can Mitigate Physical Impacts of Sea-Level Rise on Atoll Islands

NASA Astrophysics Data System (ADS)

Beetham, Edward; Kench, Paul S.; Popinet, Stéphane

2017-10-01

We present new detail on how future sea-level rise (SLR) will modify nonlinear wave transformation processes, shoreline wave energy, and wave driven flooding on atoll islands. Frequent and destructive wave inundation is a primary climate-change hazard that may render atoll islands uninhabitable in the near future. However, limited research has examined the physical vulnerability of atoll islands to future SLR and sparse information are available to implement process-based coastal management on coral reef environments. We utilize a field-verified numerical model capable of resolving all nonlinear wave transformation processes to simulate how future SLR will modify wave dissipation and overtopping on Funafuti Atoll, Tuvalu, accounting for static and accretionary reef adjustment morphologies. Results show that future SLR coupled with a static reef morphology will not only increase shoreline wave energy and overtopping but will fundamentally alter the spectral composition of shoreline energy by decreasing the contemporary influence of low-frequency infragravity waves. "Business-as-usual" emissions (RCP 8.5) will result in annual wave overtopping on Funafuti Atoll by 2030, with overtopping at high tide under mean wave conditions occurring from 2090. Comparatively, vertical reef accretion in response to SLR will prevent any significant increase in shoreline wave energy and mitigate wave driven flooding volume by 72%. Our results provide the first quantitative assessment of how effective future reef accretion can be at mitigating SLR-associated flooding on atoll islands and endorse active reef conservation and restoration for future coastal protection.

Nonlinear optical memory for manipulation of orbital angular momentum of light.

PubMed

de Oliveira, R A; Borba, G C; Martins, W S; Barreiro, S; Felinto, D; Tabosa, J W R

2015-11-01

We report on the demonstration of a nonlinear optical memory (NOM) for storage and on-demand manipulation of orbital angular momentum (OAM) of light via higher-order nonlinear processes in cold cesium atoms. A spatially resolved phase-matching technique is used to select each order of the nonlinear susceptibility associated, respectively, with time-delayed four-, six-, and eight-wave mixing processes. For a specific configuration of the stored OAM of the incident beams, we demonstrated that the OAM of the retrieved beam can be manipulated according to the order of the nonlinear process chosen by the operator for reading out the NOM. This demonstration indicates new pathways for applications in classical and quantum information processing where OAM of light is used to encode optical information.

Phase Domain Walls in Weakly Nonlinear Deep Water Surface Gravity Waves.

PubMed

Tsitoura, F; Gietz, U; Chabchoub, A; Hoffmann, N

2018-06-01

We report a theoretical derivation, an experimental observation and a numerical validation of nonlinear phase domain walls in weakly nonlinear deep water surface gravity waves. The domain walls presented are connecting homogeneous zones of weakly nonlinear plane Stokes waves of identical amplitude and wave vector but differences in phase. By exploiting symmetry transformations within the framework of the nonlinear Schrödinger equation we demonstrate the existence of exact analytical solutions representing such domain walls in the weakly nonlinear limit. The walls are in general oblique to the direction of the wave vector and stationary in moving reference frames. Experimental and numerical studies confirm and visualize the findings. Our present results demonstrate that nonlinear domain walls do exist in the weakly nonlinear regime of general systems exhibiting dispersive waves.

Phase Domain Walls in Weakly Nonlinear Deep Water Surface Gravity Waves

NASA Astrophysics Data System (ADS)

Tsitoura, F.; Gietz, U.; Chabchoub, A.; Hoffmann, N.

2018-06-01

We report a theoretical derivation, an experimental observation and a numerical validation of nonlinear phase domain walls in weakly nonlinear deep water surface gravity waves. The domain walls presented are connecting homogeneous zones of weakly nonlinear plane Stokes waves of identical amplitude and wave vector but differences in phase. By exploiting symmetry transformations within the framework of the nonlinear Schrödinger equation we demonstrate the existence of exact analytical solutions representing such domain walls in the weakly nonlinear limit. The walls are in general oblique to the direction of the wave vector and stationary in moving reference frames. Experimental and numerical studies confirm and visualize the findings. Our present results demonstrate that nonlinear domain walls do exist in the weakly nonlinear regime of general systems exhibiting dispersive waves.

Relativistically strong electromagnetic radiation in a plasma

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

Bulanov, S. V., E-mail: svbulanov@gmail.com, E-mail: bulanov.sergei@jaea.go.jp; Esirkepov, T. Zh.; Kando, M.

Physical processes in a plasma under the action of relativistically strong electromagnetic waves generated by high-power lasers have been briefly reviewed. These processes are of interest in view of the development of new methods for acceleration of charged particles, creation of sources of bright hard electromagnetic radiation, and investigation of macroscopic quantum-electrodynamical processes. Attention is focused on nonlinear waves in a laser plasma for the creation of compact electron accelerators. The acceleration of plasma bunches by the radiation pressure of light is the most efficient regime of ion acceleration. Coherent hard electromagnetic radiation in the relativistic plasma is generated inmore » the form of higher harmonics and/or electromagnetic pulses, which are compressed and intensified after reflection from relativistic mirrors created by nonlinear waves. In the limit of extremely strong electromagnetic waves, radiation friction, which accompanies the conversion of radiation from the optical range to the gamma range, fundamentally changes the behavior of the plasma. This process is accompanied by the production of electron–positron pairs, which is described within quantum electrodynamics theory.« less

Nonlinear ion-acoustic cnoidal waves in a dense relativistic degenerate magnetoplasma.

PubMed

El-Shamy, E F

2015-03-01

The complex pattern and propagation characteristics of nonlinear periodic ion-acoustic waves, namely, ion-acoustic cnoidal waves, in a dense relativistic degenerate magnetoplasma consisting of relativistic degenerate electrons and nondegenerate cold ions are investigated. By means of the reductive perturbation method and appropriate boundary conditions for nonlinear periodic waves, a nonlinear modified Korteweg-de Vries (KdV) equation is derived and its cnoidal wave is analyzed. The various solutions of nonlinear ion-acoustic cnoidal and solitary waves are presented numerically with the Sagdeev potential approach. The analytical solution and numerical simulation of nonlinear ion-acoustic cnoidal waves of the nonlinear modified KdV equation are studied. Clearly, it is found that the features (amplitude and width) of nonlinear ion-acoustic cnoidal waves are proportional to plasma number density, ion cyclotron frequency, and direction cosines. The numerical results are applied to high density astrophysical situations, such as in superdense white dwarfs. This research will be helpful in understanding the properties of compact astrophysical objects containing cold ions with relativistic degenerate electrons.

Frequency sweep rates of rising tone electromagnetic ion cyclotron waves: Comparison between nonlinear theory and Cluster observation

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

He, Zhaoguo; University of Chinese Academy of Sciences, Beijing 100049; Zong, Qiugang, E-mail: qgzong@gmail.com

2014-12-15

Resonant pitch angle scattering by electromagnetic ion cyclotron (EMIC) waves has been suggested to account for the rapid loss of ring current ions and radiation belt electrons. For the rising tone EMIC wave (classified as triggered EMIC emission), its frequency sweep rate strongly affects the efficiency of pitch-angle scattering. Based on the Cluster observations, we analyze three typical cases of rising tone EMIC waves. Two cases locate at the nightside (22.3 and 22.6 magnetic local time (MLT)) equatorial region and one case locates at the duskside (18MLT) higher magnetic latitude (λ = –9.3°) region. For the three cases, the time-dependent wave amplitude,more » cold electron density, and cold ion density ratio are derived from satellite data; while the ambient magnetic field, thermal proton perpendicular temperature, and the wave spectral can be directly provided by observation. These parameters are input into the nonlinear wave growth model to simulate the time-frequency evolutions of the rising tones. The simulated results show good agreements with the observations of the rising tones, providing further support for the previous finding that the rising tone EMIC wave is excited through the nonlinear wave growth process.« less

Experimental quantification of nonlinear time scales in inertial wave rotating turbulence

NASA Astrophysics Data System (ADS)

Yarom, Ehud; Salhov, Alon; Sharon, Eran

2017-12-01

We study nonlinearities of inertial waves in rotating turbulence. At small Rossby numbers the kinetic energy in the system is contained in helical inertial waves with time dependence amplitudes. In this regime the amplitude variations time scales are slow compared to wave periods, and the spectrum is concentrated along the dispersion relation of the waves. A nonlinear time scale was extracted from the width of the spectrum, which reflects the intensity of nonlinear wave interactions. This nonlinear time scale is found to be proportional to (U.k ) -1, where k is the wave vector and U is the root-mean-square horizontal velocity, which is dominated by large scales. This correlation, which indicates the existence of turbulence in which inertial waves undergo weak nonlinear interactions, persists only for small Rossby numbers.

A Finite-Difference Time-Domain Model of Artificial Ionospheric Modification

NASA Astrophysics Data System (ADS)

Cannon, Patrick; Honary, Farideh; Borisov, Nikolay

Experiments in the artificial modification of the ionosphere via a radio frequency pump wave have observed a wide range of non-linear phenomena near the reflection height of an O-mode wave. These effects exhibit a strong aspect-angle dependence thought to be associated with the process by which, for a narrow range of off-vertical launch angles, the O-mode pump wave can propagate beyond the standard reflection height at X=1 as a Z-mode wave and excite additional plasma activity. A numerical model based on Finite-Difference Time-Domain method has been developed to simulate the interaction of the pump wave with an ionospheric plasma and investigate different non-linear processes involved in modification experiments. The effects on wave propagation due to plasma inhomogeneity and anisotropy are introduced through coupling of the Lorentz equation of motion for electrons and ions to Maxwell’s wave equations in the FDTD formulation, leading to a model that is capable of exciting a variety of plasma waves including Langmuir and upper-hybrid waves. Additionally, discretized equations describing the time-dependent evolution of the plasma fluid temperature and density are included in the FDTD update scheme. This model is used to calculate the aspect angle dependence and angular size of the radio window for which Z-mode excitation occurs, and the results compared favourably with both theoretical predictions and experimental observations. The simulation results are found to reproduce the angular dependence on electron density and temperature enhancement observed experimentally. The model is used to investigate the effect of different initial plasma density conditions on the evolution of non-linear effects, and demonstrates that the inclusion of features such as small field-aligned density perturbations can have a significant influence on wave propagation and the magnitude of temperature and density enhancements.

Stabilization of the Peregrine soliton and Kuznetsov-Ma breathers by means of nonlinearity and dispersion management

NASA Astrophysics Data System (ADS)

Cuevas-Maraver, J.; Malomed, Boris A.; Kevrekidis, P. G.; Frantzeskakis, D. J.

2018-04-01

We demonstrate a possibility to make rogue waves (RWs) in the form of the Peregrine soliton (PS) and Kuznetsov-Ma breathers (KMBs) effectively stable objects, with the help of properly defined dispersion or nonlinearity management applied to the continuous-wave (CW) background supporting the RWs. In particular, it is found that either management scheme, if applied along the longitudinal coordinate, making the underlying nonlinear Schrödinger equation (NLSE) self-defocusing in the course of disappearance of the PS, indeed stabilizes the global solution with respect to the modulational instability of the background. In the process, additional excitations are generated, namely, dispersive shock waves and, in some cases, also a pair of slowly separating dark solitons. Further, the nonlinearity-management format, which makes the NLSE defocusing outside of a finite domain in the transverse direction, enables the stabilization of the KMBs, in the form of confined oscillating states. On the other hand, a nonlinearity-management format applied periodically along the propagation direction, creates expanding patterns featuring multiplication of KMBs through their cascading fission.

A conservative numerical scheme for modeling nonlinear acoustic propagation in thermoviscous homogeneous media

NASA Astrophysics Data System (ADS)

Diaz, Manuel A.; Solovchuk, Maxim A.; Sheu, Tony W. H.

2018-06-01

A nonlinear system of partial differential equations capable of describing the nonlinear propagation and attenuation of finite amplitude perturbations in thermoviscous media is presented. This system constitutes a full nonlinear wave model that has been formulated in the conservation form. Initially, this model is investigated analytically in the inviscid limit where it has been found that the resulting flux function fulfills the Lax-Wendroff theorem, and the scheme can match the solutions of the Westervelt and Burgers equations numerically. Here, high-order numerical descriptions of strongly nonlinear wave propagations become of great interest. For that matter we consider finite difference formulations of the weighted essentially non-oscillatory (WENO) schemes associated with explicit strong stability preserving Runge-Kutta (SSP-RK) time integration methods. Although this strategy is known to be computationally demanding, it is found to be effective when implemented to be solved in graphical processing units (GPUs). As we consider wave propagations in unbounded domains, perfectly matching layers (PML) have been also considered in this work. The proposed system model is validated and illustrated by using one- and two-dimensional benchmark test cases proposed in the literature for nonlinear acoustic propagation in homogeneous thermoviscous media.

Multidimensional nonlinear ion-acoustic waves in a plasma in view of relativistic effects

NASA Astrophysics Data System (ADS)

Belashov, V. Yu.

2017-05-01

The structure and dynamics of ion-acoustic waves in an unmagnetized plasma, including the case of weakly relativistic collisional plasma (when it is necessary to take into account the high energy particle flows which are observed in the magnetospheric plasma), are studied analytically and numerically on the basis of a model of the Kadomtsev-Petviashvili (KP) equation. It is shown that, if the velocity of plasma particles approaches the speed of light, the relativistic effects start to strongly influence on the wave characteristics, such as its phase velocity, amplitude, and characteristic wavelength, with the propagation of the twodimensional solitary ion-acoustic wave. The results can be used in the study of nonlinear wave processes in the magnetosphere and in laser and astrophysical plasma.

Detectability of electrostatic decay products in Ulysses and Galileo observations of type 3 solar radio sources

NASA Technical Reports Server (NTRS)

Cairns, Iver H.

1995-01-01

Recent in situ Ulysses and Galileo observations of the source regions of type 3 solar radio bursts appear to show an absence of ion acoustic waves S produced by nonlinear Langmuir wave processes such as the electrostatic (ES) decay, in contradiction with earlier ISEE 3 observations and analytic theory. This letter resolves these apparent contradictions. Refined analyses of the maximum S-wave electric fields produced by ES decay and of the characteristics of the Ulysses Wave Form Analyzer (WFA) instrument show that the bursty S waves observed by the ISEE 3 should be essentially undetectable by the Ulysses WFA. It is also shown that the maximum S-wave levels predicted for the Galileo event are approximately less than the instrumental noise level, thereby confirming an earlier suggestion. Thus, no contradictions exist between the ISEE 3 and Ulysses/Galileo observation, and no evidence exists against ES decay in the published Ulysses and Galileo data. All available data are consistent with, or at worst not inconsistent with, the ES decay proceeding and being the dominant nonlinear process in type 3 bursts.

Coherent generation of the auroral kilometric radiation by nonlinear beatings between electrostatic waves

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

Pellat, R.; Roux, A.

1979-09-01

The propagation of electrostatic plasma waves in an inhomogeneous and magnetized plasma is studied analytically. These waves, which are driven unstable by auroral beams of electrons, are shown to suffer a further geometrical amplification while they propagate toward cut-off. Simultaneously their group velocities tend to be aligned with the geomagnetic field. Then it is shown that the electrostatic energy tends to accumulate at or near ..omega../sub L/H and ..omega../sub U/H, the local lower and upper hybrid frequencies. Due to this process, large amplitude electrostatic waves with very narrow spectra should be observed near these frequencies at any place along themore » auroral field lines where intense beam driven instability takes place. These intense quasi-monochromatic electrostatic waves are then shown to give rise by a coherent nonlinear three wave process to an intense electromagnetic radiation. Provided that the ratio ..omega../sub p/e/..omega../sub c/e tends to be smaller than unity, it is shown that the most intense radiation should be observed at 2..omega../sub U/H in the extraordinary mode.« less

Advances in nonlinear optical materials and devices

NASA Technical Reports Server (NTRS)

Byer, Robert L.

1991-01-01

The recent progress in the application of nonlinear techniques to extend the frequency of laser sources has come from the joint progress in laser sources and in nonlinear materials. A brief summary of the progress in diode pumped solid state lasers is followed by an overview of progress in nonlinear frequency extension by harmonic generation and parametric processes. Improved nonlinear materials including bulk crystals, quasiphasematched interactions, guided wave devices, and quantum well intersubband studies are discussed with the idea of identifying areas of future progress in nonlinear materials and devices.

Nonlinear shallow ocean-wave soliton interactions on flat beaches.

PubMed

Ablowitz, Mark J; Baldwin, Douglas E

2012-09-01

Ocean waves are complex and often turbulent. While most ocean-wave interactions are essentially linear, sometimes two or more waves interact in a nonlinear way. For example, two or more waves can interact and yield waves that are much taller than the sum of the original wave heights. Most of these shallow-water nonlinear interactions look like an X or a Y or two connected Ys; at other times, several lines appear on each side of the interaction region. It was thought that such nonlinear interactions are rare events: they are not. Here we report that such nonlinear interactions occur every day, close to low tide, on two flat beaches that are about 2000 km apart. These interactions are closely related to the analytic, soliton solutions of a widely studied multidimensional nonlinear wave equation. On a much larger scale, tsunami waves can merge in similar ways.

Nonlinear optical magnetometry with accessible in situ optical squeezing

DOE PAGES

Otterstrom, N.; Pooser, R. C.; Lawrie, B. J.

2014-11-14

In this paper, we demonstrate compact and accessible squeezed-light magnetometry using four-wave mixing in a single hot rubidium vapor cell. The strong intrinsic coherence of the four-wave mixing process results in nonlinear magneto-optical rotation (NMOR) on each mode of a two-mode relative-intensity squeezed state. Finally, this framework enables 4.7 dB of quantum noise reduction while the opposing polarization rotation signals of the probe and conjugate fields add to increase the total signal to noise ratio.

Raman-Suppressing Coupling for Optical Parametric Oscillator

NASA Technical Reports Server (NTRS)

Savchenkov, Anatoliy; Maleki, Lute; Matsko, Andrey; Rubiola, Enrico

2007-01-01

A Raman-scattering-suppressing input/ output coupling scheme has been devised for a whispering-gallery-mode optical resonator that is used as a four-wave-mixing device to effect an all-optical parametric oscillator. Raman scattering is undesired in such a device because (1) it is a nonlinear process that competes with the desired nonlinear four-wave conversion process involved in optical parametric oscillation and (2) as such, it reduces the power of the desired oscillation and contributes to output noise. The essence of the present input/output coupling scheme is to reduce output loading of the desired resonator modes while increasing output loading of the undesired ones.

The prediction of nonlinear three dimensional combustion instability in liquid rockets with conventional nozzles

NASA Technical Reports Server (NTRS)

Powell, E. A.; Zinn, B. T.

1973-01-01

An analytical technique is developed to solve nonlinear three-dimensional, transverse and axial combustion instability problems associated with liquid-propellant rocket motors. The Method of Weighted Residuals is used to determine the nonlinear stability characteristics of a cylindrical combustor with uniform injection of propellants at one end and a conventional DeLaval nozzle at the other end. Crocco's pressure sensitive time-lag model is used to describe the unsteady combustion process. The developed model predicts the transient behavior and nonlinear wave shapes as well as limit-cycle amplitudes and frequencies typical of unstable motor operation. The limit-cycle amplitude increases with increasing sensitivity of the combustion process to pressure oscillations. For transverse instabilities, calculated pressure waveforms exhibit sharp peaks and shallow minima, and the frequency of oscillation is within a few percent of the pure acoustic mode frequency. For axial instabilities, the theory predicts a steep-fronted wave moving back and forth along the combustor.

Using field-particle correlations to study auroral electron acceleration in the LAPD

NASA Astrophysics Data System (ADS)

Schroeder, J. W. R.; Howes, G. G.; Skiff, F.; Kletzing, C. A.; Carter, T. A.; Vincena, S.; Dorfman, S.

2017-10-01

Resonant nonlinear Alfvén wave-particle interactions are believed to contribute to the acceleration of auroral electrons. Experiments in the Large Plasma Device (LAPD) at UCLA have been performed with the goal of providing the first direct measurement of this nonlinear process. Recent progress includes a measurement of linear fluctuations of the electron distribution function associated with the production of inertial Alfvén waves in the LAPD. These linear measurements have been analyzed using the field-particle correlation technique to study the nonlinear transfer of energy between the Alfvén wave electric fields and the electron distribution function. Results of this analysis indicate collisions alter the resonant signature of the field-particle correlation, and implications for resonant Alfvénic electron acceleration in the LAPD are considered. This work was supported by NSF, DOE, and NASA.

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.

Controllable optical rogue waves via nonlinearity management.

PubMed

Yang, Zhengping; Zhong, Wei-Ping; Belić, Milivoj; Zhang, Yiqi

2018-03-19

Using a similarity transformation, we obtain analytical solutions to a class of nonlinear Schrödinger (NLS) equations with variable coefficients in inhomogeneous Kerr media, which are related to the optical rogue waves of the standard NLS equation. We discuss the dynamics of such optical rogue waves via nonlinearity management, i.e., by selecting the appropriate nonlinearity coefficients and integration constants, and presenting the solutions. In addition, we investigate higher-order rogue waves by suitably adjusting the nonlinearity coefficient and the rogue wave parameters, which could help in realizing complex but controllable optical rogue waves in properly engineered fibers and other photonic materials.

Nonlinear wavenumber shift of large amplitude Langmuir waves

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

Li, Dehui, E-mail: dhli@ipp.ac.cn; Wang, Shaojie

2016-07-15

Nonlinear particle-in-cell simulation is carried out to investigate the nonlinear behavior of the Langmuir wave launched with a fixed frequency in a uniform plasma. It is found that in the strong driving case, the launched wave propagates in a phase velocity larger than that predicted by the linear theory; there appears a nonlinear down-shift of wavenumber. The phase velocity of the nonlinear wave and the down-shift of the wavenumber are demonstrated to be determined by the velocity of nonlinearly accelerated resonant electrons.

Study of nonlinear electron-acoustic solitary and shock waves in a dissipative, nonplanar space plasma with superthermal hot electrons

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

Han, Jiu-Ning, E-mail: hanjiuning@126.com; He, Yong-Lin; Luo, Jun-Hua

2014-01-15

With the consideration of the superthermal electron distribution, we present a theoretical investigation about the nonlinear propagation of electron-acoustic solitary and shock waves in a dissipative, nonplanar non-Maxwellian plasma comprised of cold electrons, superthermal hot electrons, and stationary ions. The reductive perturbation technique is used to obtain a modified Korteweg-de Vries Burgers equation for nonlinear waves in this plasma. We discuss the effects of various plasma parameters on the time evolution of nonplanar solitary waves, the profile of shock waves, and the nonlinear structure induced by the collision between planar solitary waves. It is found that these parameters have significantmore » effects on the properties of nonlinear waves and collision-induced nonlinear structure.« less

Nonlinear interaction of strong S-waves with the rupture front in the shallow subsurface

NASA Astrophysics Data System (ADS)

Sleep, N. H.

2017-12-01

Shallow deformation in moderate to large earthquakes is sometimes distributed rather than being concentrated on a single fault plane. Strong high-frequency S-waves interact with the rupture front to produce this effect. For strike-slip faults, the rupture propagation velocity is a fraction of the S-wave velocity. The rupture propagation vector refracts essentially vertically in the low (S-wave) velocity shallow subsurface. So does the propagation direction of S-waves. The shallow rupture front is essentially mode 3 near the surface. Strong S-waves arrive before the rupture front. They continue to arrive for several seconds in a large event. There are simple scaling relationships. The dynamic Coulomb stress ratio of horizontal stress on horizontal planes from S-waves is the normalized acceleration in g's. For fractured rock and gravel, frictional failure occurs when the normalized acceleration exceeds the effective coefficient of friction. Acceleration tends to saturate at that level as the anelastic strain rate increases rapidly with stress. For muddy materials, failure begins at a low normalized acceleration but increases slowly with dynamic stress. Dynamic accelerations sometimes exceed 1 g. In both cases, the rupture tip finds the shallow subsurface already in nonlinear failure down to a few to tens of meters depth. The material does not distinguish between S-wave and rupture tip stresses. Both stresses add to the stress invariant and hence to the anelastic strain rate tensor. Surface anelastic strain from fault slip is thus distributed laterally over a distance scaling to the depth of nonlinearity from S-waves. The environs of the fault anelastically accommodate the fault slip at depth. This process differs from blind faults where the shallow coseismic strain is mostly elastic and interseismic anelastic processes accommodate the long-term shallow deformation.

Time reversal of arbitrary photonic temporal modes via nonlinear optical frequency conversion

NASA Astrophysics Data System (ADS)

Raymer, Michael G.; Reddy, Dileep V.; van Enk, Steven J.; McKinstrie, Colin J.

2018-05-01

Single-photon wave packets can carry quantum information between nodes of a quantum network. An important general operation in photon-based quantum information systems is ‘blind’ reversal of a photon’s temporal wave packet envelope, that is, the ability to reverse an envelope without knowing the temporal state of the photon. We present an all-optical means for doing so, using nonlinear-optical frequency conversion driven by a short pump pulse. The process used may be sum-frequency generation or four-wave Bragg scattering. This scheme allows for quantum operations such as a temporal-mode parity sorter. We also verify that the scheme works for arbitrary states (not only single-photon ones) of an unknown wave packet.

Nonlinear VLF Wave Physics in the Radiation Belts

NASA Astrophysics Data System (ADS)

Crabtree, C. E.; Tejero, E. M.; Ganguli, G.; Mithaiwala, M.; Rudakov, L.; Hospodarsky, G. B.; Kletzing, C.

2014-12-01

Electromagnetic VLF waves, such as whistler mode waves, both control the lifetime of trapped electrons in the radiation belts by pitch-angle scattering and are responsible for the energization of electrons during storms. Traditional approaches to understanding the influence of waves on trapped electrons have assumed that the wave characteristics (frequency spectrum, wave-normal angle distribution, etc.) were both stationary in time and amplitude independent from event to event. In situ data from modern satellite missions, such as the Van Allen probes, are showing that this assumption may not be justified. In addition, recent theoretical results [Crabtree et al. 2012] show that the threshold for nonlinear wave scattering can often be met by naturally occurring VLF waves in the magnetosphere, with wave magnetic fields of the order of 50-100 pT inside the plasmapause. Nonlinear wave scattering (Nonlinear Landau Damping) is an amplitude dependent mechanism that can strongly alter VLF wave propagation [Ganguli et al. 2010], primarily by altering the direction of propagation. Laboratory results have confirmed the dramatic change in propagation direction when the pump wave has sufficient amplitude to exceed the nonlinear threshold [Tejero et al. 2014]. Nonlinear scattering can alter the macroscopic dynamics of waves in the radiation belts leading to the formation of a long-lasting wave-cavity [Crabtree et al. 2012] and, when amplification is present, a multi-pass amplifier [Ganguli et al., 2012]. Such nonlinear wave effects can dramatically reduce electron lifetimes. Nonlinear wave dynamics such as these occur when there are more than one wave present, such a condition necessarily violates the assumption of traditional wave-normal analysis [Santolik et al., 2003] which rely on the plane wave assumption. To investigate nonlinear wave dynamics using modern in situ data we apply the maximum entropy method [Skilling and Bryan, 1984] to solve for the wave distribution function [Storey and Lefeuvre, 1979] to yield the power distribution as a function of wave-normal angle and local azimuthal angle. We have validated this technique in the NRL space chamber and applied this methodology to Van Allen probe data to demonstrate that traditional wave-normal analaysis can give misleading results when multiple waves are present.

Peculiarities of evolutions of elastic-plastic shock compression waves in different materials

NASA Astrophysics Data System (ADS)

Kanel, G. I.; Savinykh, A. S.; Garkushin, G. V.; Razorenov, S. V.; Ashitkov, S. I.; Zaretsky, E. B.

2016-11-01

In the paper, we discuss such unexpected features in the wave evolution in solids as strongly nonlinear uniaxial elastic compression in a picosecond time range, a departure from self-similar development of the wave process which is accompanied with apparent sub-sonic wave propagation, changes of shape of elastic precursor wave as a result of variations in the material structure and the temperature, unexpected peculiarities of reflection of elastic-plastic waves from free surface.

Linear and nonlinear Biot waves in a noncohesive granular medium slab: transfer function, self-action, second harmonic generation.

PubMed

Legland, J-B; Tournat, V; Dazel, O; Novak, A; Gusev, V

2012-06-01

Experimental results are reported on second harmonic generation and self-action in a noncohesive granular medium supporting wave energy propagation both in the solid frame and in the saturating fluid. The acoustic transfer function of the probed granular slab can be separated into two main frequency regions: a low frequency region where the wave propagation is controlled by the solid skeleton elastic properties, and a higher frequency region where the behavior is dominantly due to the air saturating the beads. Experimental results agree well with a recently developed nonlinear Biot wave model applied to granular media. The linear transfer function, second harmonic generation, and self-action effect are studied as a function of bead diameter, compaction step, excitation amplitude, and frequency. This parametric study allows one to isolate different propagation regimes involving a range of described and interpreted linear and nonlinear processes that are encountered in granular media experiments. In particular, a theoretical interpretation is proposed for the observed strong self-action effect.

GEOPHYSICS, ASTRONOMY AND ASTROPHYSICS: Numerical method of studying nonlinear interactions between long waves and multiple short waves

NASA Astrophysics Data System (ADS)

Xie, Tao; Kuang, Hai-Lan; William, Perrie; Zou, Guang-Hui; Nan, Cheng-Feng; He, Chao; Shen, Tao; Chen, Wei

2009-07-01

Although the nonlinear interactions between a single short gravity wave and a long wave can be solved analytically, the solution is less tractable in more general cases involving multiple short waves. In this work we present a numerical method of studying nonlinear interactions between a long wave and multiple short harmonic waves in infinitely deep water. Specifically, this method is applied to the calculation of the temporal and spatial evolutions of the surface elevations in which a given long wave interacts with several short harmonic waves. Another important application of our method is to quantitatively analyse the nonlinear interactions between an arbitrary short wave train and another short wave train. From simulation results, we obtain that the mechanism for the nonlinear interactions between one short wave train and another short wave train (expressed as wave train 2) leads to the energy focusing of the other short wave train (expressed as wave train 3). This mechanism occurs on wave components with a narrow frequency bandwidth, whose frequencies are near that of wave train 3.

Rogue Wave Modes for the Long Wave-Short Wave Resonance and the Derivative Nonlinear Schrödinger Models

NASA Astrophysics Data System (ADS)

Chan, Hiu Ning; Chow, Kwok Wing; Kedziora, David Jacob; Grimshaw, Roger Hamilton James; Ding, Edwin

2014-11-01

Rogue waves are unexpectedly large displacements of the water surface and will obviously pose threat to maritime activities. Recently, the formation of rogue waves is correlated with the onset of modulation instabilities of plane waves of the system. The long wave-short wave resonance and the derivative nonlinear Schrödinger models are considered. They are relevant in a two-layer fluid and a fourth order perturbation expansion of free surface waves respectively. Analytical solutions of rogue wave modes for the two models are derived by the Hirota bilinear method. Properties and amplitudes of these rogue wave modes are investigated. Conditions for modulation instability of the plane waves are shown to be precisely the requirements for the occurrence of rogue waves. In contrast with the nonlinear Schrödinger equation, rogue wave modes for the derivative nonlinear Schrödinger model exist even if the dispersion and cubic nonlinearity are of the opposite signs, provided that a sufficiently strong self-steepening nonlinearity is present. Extensions to the coupled case (multiple waveguides) will be discussed. This work is partially supported by the Research Grants Council General Research Fund Contract HKU 711713E.

Rogue wave modes for a derivative nonlinear Schrödinger model.

PubMed

Chan, Hiu Ning; Chow, Kwok Wing; Kedziora, David Jacob; Grimshaw, Roger Hamilton James; Ding, Edwin

2014-03-01

Rogue waves in fluid dynamics and optical waveguides are unexpectedly large displacements from a background state, and occur in the nonlinear Schrödinger equation with positive linear dispersion in the regime of positive cubic nonlinearity. Rogue waves of a derivative nonlinear Schrödinger equation are calculated in this work as a long-wave limit of a breather (a pulsating mode), and can occur in the regime of negative cubic nonlinearity if a sufficiently strong self-steepening nonlinearity is also present. This critical magnitude is shown to be precisely the threshold for the onset of modulation instabilities of the background plane wave, providing a strong piece of evidence regarding the connection between a rogue wave and modulation instability. The maximum amplitude of the rogue wave is three times that of the background plane wave, a result identical to that of the Peregrine breather in the classical nonlinear Schrödinger equation model. This amplification ratio and the resulting spectral broadening arising from modulation instability correlate with recent experimental results of water waves. Numerical simulations in the regime of marginal stability are described.

Effect of P T symmetry on nonlinear waves for three-wave interaction models in the quadratic nonlinear media

NASA Astrophysics Data System (ADS)

Shen, Yujia; Wen, Zichao; Yan, Zhenya; Hang, Chao

2018-04-01

We study the three-wave interaction that couples an electromagnetic pump wave to two frequency down-converted daughter waves in a quadratic optical crystal and P T -symmetric potentials. P T symmetric potentials are shown to modulate stably nonlinear modes in two kinds of three-wave interaction models. The first one is a spatially extended three-wave interaction system with odd gain-and-loss distribution in the channel. Modulated by the P T -symmetric single-well or multi-well Scarf-II potentials, the system is numerically shown to possess stable soliton solutions. Via adiabatical change of system parameters, numerical simulations for the excitation and evolution of nonlinear modes are also performed. The second one is a combination of P T -symmetric models which are coupled via three-wave interactions. Families of nonlinear modes are found with some particular choices of parameters. Stable and unstable nonlinear modes are shown in distinct families by means of numerical simulations. These results will be useful to further investigate nonlinear modes in three-wave interaction models.

A novel method for predicting the power outputs of wave energy converters

NASA Astrophysics Data System (ADS)

Wang, Yingguang

2018-03-01

This paper focuses on realistically predicting the power outputs of wave energy converters operating in shallow water nonlinear waves. A heaving two-body point absorber is utilized as a specific calculation example, and the generated power of the point absorber has been predicted by using a novel method (a nonlinear simulation method) that incorporates a second order random wave model into a nonlinear dynamic filter. It is demonstrated that the second order random wave model in this article can be utilized to generate irregular waves with realistic crest-trough asymmetries, and consequently, more accurate generated power can be predicted by subsequently solving the nonlinear dynamic filter equation with the nonlinearly simulated second order waves as inputs. The research findings demonstrate that the novel nonlinear simulation method in this article can be utilized as a robust tool for ocean engineers in their design, analysis and optimization of wave energy converters.

Parametric array technique for microbubble excitation.

PubMed

Vos, Hendrik J; Goertz, David E; van der Steen, Antonius F W; de Jong, Nico

2011-05-01

This study investigates the use of an acoustic parametric array as a means for microbubble excitation. The excitation wave is generated during propagation in a nonlinear medium of two high-frequency carrier waves, whereby the frequency of the excitation wave is the difference frequency of the carrier waves. Carrier waves of around 10 and 25 MHz are used to generate low-frequency waves between 0.5 and 3.5 MHz at amplitudes in the range of 25 to 80 kPa in water. We demonstrate with high-speed camera observations that it is possible to induce microbubble oscillations with the low frequency signal arising from the nonlinear propagation process. As an application, we determined the resonance frequency of Definity contrast agent microbubbles with radius ranging from 1.5 to 5 μm by sweeping the difference frequency in the range from 0.5 to 3.5 MHz.

Single-mode dispersive waves and soliton microcomb dynamics

PubMed Central

Yi, Xu; Yang, Qi-Fan; Zhang, Xueyue; Yang, Ki Youl; Li, Xinbai; Vahala, Kerry

2017-01-01

Dissipative Kerr solitons are self-sustaining optical wavepackets in resonators. They use the Kerr nonlinearity to both compensate dispersion and offset optical loss. Besides providing insights into nonlinear resonator physics, they can be applied in frequency metrology, precision clocks, and spectroscopy. Like other optical solitons, the dissipative Kerr soliton can radiate power as a dispersive wave through a process that is the optical analogue of Cherenkov radiation. Dispersive waves typically consist of an ensemble of optical modes. Here, a limiting case is studied in which the dispersive wave is concentrated into a single cavity mode. In this limit, its interaction with the soliton induces hysteresis behaviour in the soliton's spectral and temporal properties. Also, an operating point of enhanced repetition-rate stability occurs through balance of dispersive-wave recoil and Raman-induced soliton-self-frequency shift. The single-mode dispersive wave can therefore provide quiet states of soliton comb operation useful in many applications. PMID:28332495

Four-wave mixing in an asymmetric double quantum dot molecule

NASA Astrophysics Data System (ADS)

Kosionis, Spyridon G.

2018-06-01

The four-wave mixing (FWM) effect of a weak probe field, in an asymmetric semiconductor double quantum dot (QD) structure driven by a strong pump field is theoretically studied. Similarly to the case of examining several other nonlinear optical processes, the nonlinear differential equations of the density matrix elements are used, under the rotating wave approximation. By suitably tuning the intensity and the frequency of the pump field as well as by changing the value of the applied bias voltage, a procedure used to properly adjust the electron tunneling coupling, we control the FWM in the same way as several other nonlinear optical processes of the system. While in the weak electron tunneling regime, the impact of the pump field intensity on the FWM is proven to be of crucial importance, for even higher rates of the electron tunneling it is evident that the intensity of the pump field has only a slight impact on the form of the FWM spectrum. The number of the spectral peaks, depends on the relation between specific parameters of the system.

The influence of compressibility on nonlinear spectral energy transfer - Part 1: Fundamental mechanisms

NASA Astrophysics Data System (ADS)

Praturi, Divya Sri; Girimaji, Sharath

2017-11-01

Nonlinear spectral energy transfer by triadic interactions is one of the foundational processes in fluid turbulence. Much of our current knowledge of this process is contingent upon pressure being a Lagrange multiplier with the only function of re-orienting the velocity wave vector. In this study, we examine how the nonlinear spectral transfer is affected in compressible turbulence when pressure is a true thermodynamic variable with a wave character. We perform direct numerical simulations of multi-mode evolution at different turbulent Mach numbers of Mt = 0.03 , 0.6 . Simulations are performed with initial modes that are fully solenoidal, fully dilatational and mixed solenoidal-dilatational. It is shown that solenoidal-solenoidal interactions behave in canonical manner at all Mach numbers. However, dilatational and mixed mode interactions are profoundly different. This is due to the fact that wave-pressure leads to kinetic-internal energy exchange via the pressure-dilatation mechanism. An important consequence of this exchange is that the triple correlation term, responsible for spectral transfer, experiences non-monotonic behavior resulting in inefficient energy transfer to other modes.

Nonlinear generation of kinetic-scale waves by magnetohydrodynamic Alfvén waves and nonlocal spectral transport in the solar wind

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

Zhao, J. S.; Wu, D. J.; Voitenko, Y.

We study the nonlocal nonlinear coupling and generation of kinetic Alfvén waves (KAWs) and kinetic slow waves (KSWs) by magnetohydrodynamic Alfvén waves (MHD AWs) in conditions typical for the solar wind in the inner heliosphere. This cross-scale process provides an alternative to the turbulent energy cascade passing through many intermediate scales. The nonlinearities we study are proportional to the scalar products of wave vectors and hence are called 'scalar' ones. Despite the strong Landau damping of kinetic waves, we found fast growing KAWs and KSWs at perpendicular wavelengths close to the ion gyroradius. Using the parametric decay formalism, we investigatemore » two independent decay channels for the pump AW: forward decay (involving co-propagating product waves) and backward decay (involving counter-propagating product waves). The growth rate of the forward decay is typically 0.05 but can exceed 0.1 of the pump wave frequency. The resulting spectral transport is nonlocal and anisotropic, sharply increasing perpendicular wavenumbers but not parallel ones. AWs and KAWs propagating against the pump AW grow with about the same rate and contribute to the sunward wave flux in the solar wind. Our results suggest that the nonlocal decay of MHD AWs into KAWs and KSWs is a robust mechanism for the cross-scale spectral transport of the wave energy from MHD to dissipative kinetic scales in the solar wind and similar media.« less

Development of Electric Field and Plasma Wave Investigations for Future Space Weather Missions: ERG, SCOPE, and beyond

NASA Astrophysics Data System (ADS)

Kasaba, Y.; Kumamoto, A.; Ono, T.; Misawa, H.; Kojima, H.; Yagitani, S.; Kasahara, Y.; Ishisaka, K.

2009-04-01

The electric field and plasma wave investigation is important for the clarification of global plasma dynamics and energetic processes in the planetary Magnetospheric studies. We have several missions which will contribute those objectives. the small-sized radiation belt mission, ERG (Energization and Radiation in Geospace), the cross-scale formation flight mission, SCOPE, the BepiColombo mission to Mercury, and the small-sized and full-scale Jovian mission in future. Those will prevail the universal plasma mechanism and processes in the space laboratory. The main purposes of electric field and plasma wave observation for those missions are: (1) Examination of the theories of high-energy particle acceleration by plasma waves, (2) identification of the origin of electric fields in the magnetosphere associated with cross-scale coupling processes, (3) diagnosis of plasma density, temperature and composition, and (4) investigation of wave-particle interaction and mode conversion processes. Simultaneous observation of plasma waves and energetic particles with high resolution will enable us to investigate the wave-particle interaction based on quasi-linear theory and non-linear models. In this paper, we will summarize the current plan and efforts for those future activities. In order to achieve those objectives, the instrument including sensitive sensors (the long wire / stem antennae, the search-coil / loop antennae) and integrated receiver systems are now in development, including the direct identification of nonlinear wave-particle interactions associated will be tried by Wave-particle Correlator. And, as applications of those development, we will mention to the space interferometer and the radar sounder technologies.

Generation Process of Large-Amplitude Upper-Band Chorus Emissions Observed by Van Allen Probes

DOE PAGES

Kubota, Yuko; Omura, Yoshiharu; Kletzing, Craig; ...

2018-04-19

In this paper, we analyze large-amplitude upper-band chorus emissions measured near the magnetic equator by the Electric and Magnetic Field Instrument Suite and Integrated Science instrument package on board the Van Allen Probes. In setting up the parameters of source electrons exciting the emissions based on theoretical analyses and observational results measured by the Helium Oxygen Proton Electron instrument, we calculate threshold and optimum amplitudes with the nonlinear wave growth theory. We find that the optimum amplitude is larger than the threshold amplitude obtained in the frequency range of the chorus emissions and that the wave amplitudes grow between themore » threshold and optimum amplitudes. Finally, in the frame of the wave growth process, the nonlinear growth rates are much greater than the linear growth rates.« less

Generation Process of Large-Amplitude Upper-Band Chorus Emissions Observed by Van Allen Probes

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

Kubota, Yuko; Omura, Yoshiharu; Kletzing, Craig

In this paper, we analyze large-amplitude upper-band chorus emissions measured near the magnetic equator by the Electric and Magnetic Field Instrument Suite and Integrated Science instrument package on board the Van Allen Probes. In setting up the parameters of source electrons exciting the emissions based on theoretical analyses and observational results measured by the Helium Oxygen Proton Electron instrument, we calculate threshold and optimum amplitudes with the nonlinear wave growth theory. We find that the optimum amplitude is larger than the threshold amplitude obtained in the frequency range of the chorus emissions and that the wave amplitudes grow between themore » threshold and optimum amplitudes. Finally, in the frame of the wave growth process, the nonlinear growth rates are much greater than the linear growth rates.« less

Study of Linear and Nonlinear Waves in Plasma Crystals Using the Box_Tree Code

NASA Astrophysics Data System (ADS)

Qiao, K.; Hyde, T.; Barge, L.

Dusty plasma systems play an important role in both astrophysical and planetary environments (protostellar clouds, planetary ring systems and magnetospheres, cometary environments) and laboratory settings (plasma processing or nanofabrication). Recent research has focussed on defining (both theoretically and experimentally) the different types of wave mode propagations, which are possible within plasma crystals. This is an important topic since several of the fundamental quantities for characterizing such crystals can be obtained directly from an analysis of the wave propagation/dispersion. This paper will discuss a num rical model fore 2D-monolayer plasma crystals, which was established using a modified box tree code. Different wave modes were examined by adding a time dependent potential to the code designed to simulate a laser radiation perturbation as has been applied in many experiments. Both linear waves (for example, longitudinal and transverse dust lattice waves) and nonlinear waves (solitary waves) are examined. The output data will also be compared with the results of corresponding experiments and discussed.

Continuous-wave optical parametric oscillators on their way to the terahertz range

NASA Astrophysics Data System (ADS)

Sowade, Rosita; Breunig, Ingo; Kiessling, Jens; Buse, Karsten

2010-02-01

Continuous-wave optical parametric oscillators (OPOs) are known to be working horses for spectroscopy in the near- and mid-infrared. However, strong absorption in nonlinear media like lithium niobate complicates the generation of far-infrared light. This absorption leads to pump thresholds vastly exceeding the power of standard pump lasers. Our first approach was, therefore, to combine the established technique of photomixing with optical parametric oscillators. Here, two OPOs provide one wave each, with a tunable difference frequency. These waves are combined to a beat signal as a source for photomixers. Terahertz radiation between 0.065 and 1.018 THz is generated with powers in the order of nanowatts. To overcome the upper frequency limit of the opto-electronic photomixers, terahertz generation has to rely entirely on optical methods. Our all-optical approach, getting around the high thresholds for terahertz generation, is based on cascaded nonlinear processes: the resonantly enhanced signal field, generated in the primary parametric process, is intense enough to act as the pump for a secondary process, creating idler waves with frequencies in the terahertz regime. The latter ones are monochromatic and tunable with detected powers of more than 2 μW at 1.35 THz. Thus, continuous-wave optical parametric oscillators have entered the field of terahertz photonics.

Analytic descriptions of cylindrical electromagnetic waves in a nonlinear medium

PubMed Central

Xiong, Hao; Si, Liu-Gang; Yang, Xiaoxue; Wu, Ying

2015-01-01

A simple but highly efficient approach for dealing with the problem of cylindrical electromagnetic waves propagation in a nonlinear medium is proposed based on an exact solution proposed recently. We derive an analytical explicit formula, which exhibiting rich interesting nonlinear effects, to describe the propagation of any amount of cylindrical electromagnetic waves in a nonlinear medium. The results obtained by using the present method are accurately concordant with the results of using traditional coupled-wave equations. As an example of application, we discuss how a third wave affects the sum- and difference-frequency generation of two waves propagation in the nonlinear medium. PMID:26073066

On the interaction of small-scale linear waves with nonlinear solitary waves

NASA Astrophysics Data System (ADS)

Xu, Chengzhu; Stastna, Marek

2017-04-01

In the study of environmental and geophysical fluid flows, linear wave theory is well developed and its application has been considered for phenomena of various length and time scales. However, due to the nonlinear nature of fluid flows, in many cases results predicted by linear theory do not agree with observations. One of such cases is internal wave dynamics. While small-amplitude wave motion may be approximated by linear theory, large amplitude waves tend to be solitary-like. In some cases, when the wave is highly nonlinear, even weakly nonlinear theories fail to predict the wave properties correctly. We study the interaction of small-scale linear waves with nonlinear solitary waves using highly accurate pseudo spectral simulations that begin with a fully nonlinear solitary wave and a train of small-amplitude waves initialized from linear waves. The solitary wave then interacts with the linear waves through either an overtaking collision or a head-on collision. During the collision, there is a net energy transfer from the linear wave train to the solitary wave, resulting in an increase in the kinetic energy carried by the solitary wave and a phase shift of the solitary wave with respect to a freely propagating solitary wave. At the same time the linear waves are greatly reduced in amplitude. The percentage of energy transferred depends primarily on the wavelength of the linear waves. We found that after one full collision cycle, the longest waves may retain as much as 90% of the kinetic energy they had initially, while the shortest waves lose almost all of their initial energy. We also found that a head-on collision is more efficient in destroying the linear waves than an overtaking collision. On the other hand, the initial amplitude of the linear waves has very little impact on the percentage of energy that can be transferred to the solitary wave. Because of the nonlinearity of the solitary wave, these results provide us some insight into wave-mean flow interaction in a fully nonlinear framework.

An oscillating wave energy converter with nonlinear snap-through Power-Take-Off systems in regular waves

NASA Astrophysics Data System (ADS)

Zhang, Xian-tao; Yang, Jian-min; Xiao, Long-fei

2016-07-01

Floating oscillating bodies constitute a large class of wave energy converters, especially for offshore deployment. Usually the Power-Take-Off (PTO) system is a directly linear electric generator or a hydraulic motor that drives an electric generator. The PTO system is simplified as a linear spring and a linear damper. However the conversion is less powerful with wave periods off resonance. Thus, a nonlinear snap-through mechanism with two symmetrically oblique springs and a linear damper is applied in the PTO system. The nonlinear snap-through mechanism is characteristics of negative stiffness and double-well potential. An important nonlinear parameter γ is defined as the ratio of half of the horizontal distance between the two springs to the original length of both springs. Time domain method is applied to the dynamics of wave energy converter in regular waves. And the state space model is used to replace the convolution terms in the time domain equation. The results show that the energy harvested by the nonlinear PTO system is larger than that by linear system for low frequency input. While the power captured by nonlinear converters is slightly smaller than that by linear converters for high frequency input. The wave amplitude, damping coefficient of PTO systems and the nonlinear parameter γ affect power capture performance of nonlinear converters. The oscillation of nonlinear wave energy converters may be local or periodically inter well for certain values of the incident wave frequency and the nonlinear parameter γ, which is different from linear converters characteristics of sinusoidal response in regular waves.

Resonant triad in boundary-layer stability. Part 1: Fully nonlinear interaction

NASA Technical Reports Server (NTRS)

Mankbadi, Reda R.

1991-01-01

A first principles theory is developed to study the nonlinear spatial evolution of a near-resonance triad of instability waves in boundary layer transition. This triad consists of a plane wave at fundamental frequency and a pair of symmetrical, oblique waves at the subharmonic frequency. A low frequency, high Reynolds number asymptotic scaling leads to a distinct critical layer where nonlinearity first becomes important; the development of the triad's waves is determined by the critical layer's nonlinear, viscous dynamics. The resulting theory is fully nonlinear in that all nonlinearly generated oscillatory and nonoscillatory components are accounted for. The presence of the plane wave initially causes exponential of exponential growth of the oblique waves. However, the plane wave continues to follow the linear theory, even when the oblique waves' amplitude attains the same order of magnitude as that of the plane wave. A fully interactive stage then comes into effect when the oblique waves exceed a certain level compared to that of the plane wave. The oblique waves react back on the fundamental, slowing its growth rate. The oblique waves' saturation results from their self-interaction - a mechanism that does not require the presence of the plane wave. The oblique waves' saturation level is independent of their initial level, but decreases as the obliqueness angle increases.

Experimental investigation of material nonlinearity using the Rayleigh surface waves excited and detected by angle beam wedge transducers.

PubMed

Zhang, Shuzeng; Li, Xiongbing; Jeong, Hyunjo; Hu, Hongwei

2018-05-12

Angle beam wedge transducers are widely used in nonlinear Rayleigh wave experiments as they can generate Rayleigh wave easily and produce high intensity nonlinear waves for detection. When such a transducer is used, the spurious harmonics (source nonlinearity) and wave diffraction may occur and will affect the measurement results, so it is essential to fully understand its acoustic nature. This paper experimentally investigates the nonlinear Rayleigh wave beam fields generated and received by angle beam wedge transducers, in which the theoretical predictions are based on the acoustic model developed previously for angle beam wedge transducers [S. Zhang, et al., Wave Motion, 67, 141-159, (2016)]. The source of the spurious harmonics is fully characterized by scrutinizing the nonlinear Rayleigh wave behavior in various materials with different driving voltages. Furthermore, it is shown that the attenuation coefficients for both fundamental and second harmonic Rayleigh waves can be extracted by comparing the measurements with the predictions when the experiments are conducted at many locations along the propagation path. A technique is developed to evaluate the material nonlinearity by making appropriate corrections for source nonlinearity, diffraction and attenuation. The nonlinear parameters of three aluminum alloy specimens - Al 2024, Al 6061 and Al 7075 - are measured, and the results indicate that the measurement results can be significantly improved using the proposed method. Copyright © 2018. Published by Elsevier B.V.

Cubic nonlinearity in shear wave beams with different polarizations

PubMed Central

Wochner, Mark S.; Hamilton, Mark F.; Ilinskii, Yurii A.; Zabolotskaya, Evgenia A.

2008-01-01

A coupled pair of nonlinear parabolic equations is derived for the two components of the particle motion perpendicular to the axis of a shear wave beam in an isotropic elastic medium. The equations account for both quadratic and cubic nonlinearity. The present paper investigates, analytically and numerically, effects of cubic nonlinearity in shear wave beams for several polarizations: linear, elliptical, circular, and azimuthal. Comparisons are made with effects of quadratic nonlinearity in compressional wave beams. PMID:18529167

Linear and nonlinear 2D finite element analysis of sloshing modes and pressures in rectangular tanks subject to horizontal harmonic motions

NASA Astrophysics Data System (ADS)

Virella, Juan C.; Prato, Carlos A.; Godoy, Luis A.

2008-05-01

The influence of nonlinear wave theory on the sloshing natural periods and their modal pressure distributions are investigated for rectangular tanks under the assumption of two-dimensional behavior. Natural periods and mode shapes are computed and compared for both linear wave theory (LWT) and nonlinear wave theory (NLWT) models, using the finite element package ABAQUS. Linear wave theory is implemented in an acoustic model, whereas a plane strain problem with large displacements is used in NLWT. Pressure distributions acting on the tank walls are obtained for the first three sloshing modes using both linear and nonlinear wave theory. It is found that the nonlinearity does not have significant effects on the natural sloshing periods. For the sloshing pressures on the tank walls, different distributions were found using linear and nonlinear wave theory models. However, in all cases studied, the linear wave theory conservatively estimated the magnitude of the pressure distribution, whereas larger pressures resultant heights were obtained when using the nonlinear theory. It is concluded that the nonlinearity of the surface wave does not have major effects in the pressure distribution on the walls for rectangular tanks.

Pitch Angle Scattering of Energetic Electrons by Plasmaspheric Hiss Emissions

NASA Astrophysics Data System (ADS)

Tobita, M.; Omura, Y.; Summers, D.

2017-12-01

We study scattering of energetic electrons in pitch angles and kinetic energies through their resonance with plasmaspheric hiss emissions consisting of many coherent discrete whistler-mode wave packets with rising and falling frequencies [1,2,3]. Using test particle simulations, we evaluate the efficiency of scattering, which depends on the inhomogeneity ratio S of whistler mode wave-particle interaction [4]. The value of S is determined by the wave amplitude, frequency sweep rate, and the gradient of the background magnetic field. We first modulate those parameters and observe variations of pitch angles and kinetic energies of electrons with a single wave under various S values so as to obtain basic understanding. We then include many waves into the system to simulate plasmaspheric hiss emissions. As the wave packets propagate away from the magnetic equator, the nonlinear trapping potential at the resonance velocity is deformed, making a channel of gyrophase for untrapped electrons to cross the resonance velocity, and causing modulations in their pitch angles and kinetic energies. We find efficient scattering of pitch angles and kinetic energies because of coherent nonlinear wave-particle interaction, resulting in electron precipitations into the polar atmosphere. We compare the results with the bounce averaged pitch angle diffusion coefficient based on quasi-linear theory, and show that the nonlinear wave model with many coherent packets can cause scattering of resonant electrons much faster than the quasi-linear diffusion process. [1] Summers, D., Omura, Y., Nakamura, S., and C. A. Kletzing (2014), Fine structure of plasmaspheric hiss, J. Geophys. Res., 119, 9134-9149. [2] Omura, Y., Y. Miyashita, M. Yoshikawa, D. Summers, M. Hikishima, Y. Ebihara, and Y. Kubota (2015), Formation process of relativistic electron flux through interaction with chorus emissions in the Earth's inner magnetosphere, J. Geophys. Res. Space Physics, 120, 9545-9562. [3] Nakamura, S., Y. Omura, D. Summers, and C. A. Kletzing (2016), Observational evidence of the nonlinear wave growth theory of plasmaspheric hiss, Geophys. Res. Lett., 43, 10,040-10,049. [4] Omura, Y., Katoh, Y., and Summers, D., Theory and simulation of the generation of whistler-mode chorus (2008), J. Geophys. Res., 113, A04223.

A Multiscale Nested Modeling Framework to Simulate the Interaction of Surface Gravity Waves with Nonlinear Internal Gravity Waves

DTIC Science & Technology

2015-09-30

We aim at understanding the impact of tidal , seasonal, and mesoscale variability of the internal wave field and how it influences the surface waves ...Interaction of Surface Gravity Waves with Nonlinear Internal Gravity Waves Lian Shen St. Anthony Falls Laboratory and Department of Mechanical...on studying surface gravity wave evolution and spectrum in the presence of surface currents caused by strongly nonlinear internal solitary waves

Real-time measurements of spontaneous breathers and rogue wave events in optical fibre modulation instability

PubMed Central

Närhi, Mikko; Wetzel, Benjamin; Billet, Cyril; Toenger, Shanti; Sylvestre, Thibaut; Merolla, Jean-Marc; Morandotti, Roberto; Dias, Frederic; Genty, Goëry; Dudley, John M.

2016-01-01

Modulation instability is a fundamental process of nonlinear science, leading to the unstable breakup of a constant amplitude solution of a physical system. There has been particular interest in studying modulation instability in the cubic nonlinear Schrödinger equation, a generic model for a host of nonlinear systems including superfluids, fibre optics, plasmas and Bose–Einstein condensates. Modulation instability is also a significant area of study in the context of understanding the emergence of high amplitude events that satisfy rogue wave statistical criteria. Here, exploiting advances in ultrafast optical metrology, we perform real-time measurements in an optical fibre system of the unstable breakup of a continuous wave field, simultaneously characterizing emergent modulation instability breather pulses and their associated statistics. Our results allow quantitative comparison between experiment, modelling and theory, and are expected to open new perspectives on studies of instability dynamics in physics. PMID:27991513

Nonlinear optimization method of ship floating condition calculation in wave based on vector

NASA Astrophysics Data System (ADS)

Ding, Ning; Yu, Jian-xing

2014-08-01

Ship floating condition in regular waves is calculated. New equations controlling any ship's floating condition are proposed by use of the vector operation. This form is a nonlinear optimization problem which can be solved using the penalty function method with constant coefficients. And the solving process is accelerated by dichotomy. During the solving process, the ship's displacement and buoyant centre have been calculated by the integration of the ship surface according to the waterline. The ship surface is described using an accumulative chord length theory in order to determine the displacement, the buoyancy center and the waterline. The draught forming the waterline at each station can be found out by calculating the intersection of the ship surface and the wave surface. The results of an example indicate that this method is exact and efficient. It can calculate the ship floating condition in regular waves as well as simplify the calculation and improve the computational efficiency and the precision of results.

Nonlinear Evolution of Short-wavelength Torsional Alfvén Waves

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

Shestov, S. V.; Nakariakov, V. M.; Ulyanov, A. S.

2017-05-10

We analyze nonlinear evolution of torsional Alfvén waves in a straight magnetic flux tube filled in with a low- β plasma, and surrounded with a plasma of lower density. Such magnetic tubes model, in particular, a segment of a coronal loop or a polar plume. The wavelength is taken comparable to the tube radius. We perform a numerical simulation of the wave propagation using ideal magnetohydrodynamics. We find that a torsional wave nonlinearly induces three kinds of compressive flows: the parallel flow at the Alfvén speed, which constitutes a bulk plasma motion along the magnetic field, the tube wave, andmore » also transverse flows in the radial direction, associated with sausage fast magnetoacoustic modes. In addition, the nonlinear torsional wave steepens and its propagation speed increases. The latter effect leads to the progressive distortion of the torsional wave front, i.e., nonlinear phase mixing. Because of the intrinsic non-uniformity of the torsional wave amplitude across the tube radius, the nonlinear effects are more pronounced in regions with higher wave amplitudes. They are always absent at the axes of the flux tube. In the case of a linear radial profile of the wave amplitude, the nonlinear effects are localized in an annulus region near the tube boundary. Thus, the parallel compressive flows driven by torsional Alfvén waves in the solar and stellar coronae, are essentially non-uniform in the perpendicular direction. The presence of additional sinks for the wave energy reduces the efficiency of the nonlinear parallel cascade in torsional Alfvén waves.« less

Nonlinear Evolution of Short-wavelength Torsional Alfvén Waves

NASA Astrophysics Data System (ADS)

Shestov, S. V.; Nakariakov, V. M.; Ulyanov, A. S.; Reva, A. A.; Kuzin, S. V.

2017-05-01

We analyze nonlinear evolution of torsional Alfvén waves in a straight magnetic flux tube filled in with a low-β plasma, and surrounded with a plasma of lower density. Such magnetic tubes model, in particular, a segment of a coronal loop or a polar plume. The wavelength is taken comparable to the tube radius. We perform a numerical simulation of the wave propagation using ideal magnetohydrodynamics. We find that a torsional wave nonlinearly induces three kinds of compressive flows: the parallel flow at the Alfvén speed, which constitutes a bulk plasma motion along the magnetic field, the tube wave, and also transverse flows in the radial direction, associated with sausage fast magnetoacoustic modes. In addition, the nonlinear torsional wave steepens and its propagation speed increases. The latter effect leads to the progressive distortion of the torsional wave front, I.e., nonlinear phase mixing. Because of the intrinsic non-uniformity of the torsional wave amplitude across the tube radius, the nonlinear effects are more pronounced in regions with higher wave amplitudes. They are always absent at the axes of the flux tube. In the case of a linear radial profile of the wave amplitude, the nonlinear effects are localized in an annulus region near the tube boundary. Thus, the parallel compressive flows driven by torsional Alfvén waves in the solar and stellar coronae, are essentially non-uniform in the perpendicular direction. The presence of additional sinks for the wave energy reduces the efficiency of the nonlinear parallel cascade in torsional Alfvén waves.

Asymmetric nonlinear system is not sufficient for a nonreciprocal wave diode

NASA Astrophysics Data System (ADS)

Wu, Gaomin; Long, Yang; Ren, Jie

2018-05-01

We demonstrate symmetric wave propagations in asymmetric nonlinear systems. By solving the nonlinear Schördinger equation, we first analytically prove the existence of symmetric transmission in asymmetric systems with a single nonlinear delta-function interface. We then point out that a finite width of the nonlinear interface region is necessary to produce nonreciprocity in asymmetric systems. However, a geometrical resonant condition for breaking nonreciprocal propagation is then identified theoretically and verified numerically. With such a resonant condition, the nonlinear interface region of finite width behaves like a single nonlinear delta-barrier so that wave propagations in the forward and backward directions are identical under arbitrary incident wave intensity. As such, reciprocity reemerges periodically in the asymmetric nonlinear system when changing the width of interface region. Finally, similar resonant conditions of discrete nonlinear Schördinger equation are discussed. Therefore, we have identified instances of reciprocity that breaking spatial symmetry in nonlinear interface systems is not sufficient to produce nonreciprocal wave propagation.

Book review: Nonlinear ocean waves and the inverse scattering transform

USGS Publications Warehouse

Geist, Eric L.

2011-01-01

Nonlinear Ocean Waves and the Inverse Scattering Transform is a comprehensive examination of ocean waves built upon the theory of nonlinear Fourier analysis. The renowned author, Alfred R. Osborne, is perhaps best known for the discovery of internal solitons in the Andaman Sea during the 1970s. In this book, he provides an extensive treatment of nonlinear water waves based on a nonlinear spectral theory known as the inverse scattering transform. The writing is exceptional throughout the book, which is particularly useful in explaining some of the more difficult mathematical concepts.  Review info: Nonlinear Ocean Waves and the Inverse Scattering Transform. By Alfred R. Osborne, 2010. ISBN: 978-125286299, 917 pp.

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.

Experimental and numerical investigations of temporally and spatially periodic modulated wave trains

NASA Astrophysics Data System (ADS)

Houtani, H.; Waseda, T.; Tanizawa, K.

2018-03-01

A number of studies on steep nonlinear waves were conducted experimentally with the temporally periodic and spatially evolving (TPSE) wave trains and numerically with the spatially periodic and temporally evolving (SPTE) ones. The present study revealed that, in the vicinity of their maximum crest height, the wave profiles of TPSE and SPTE modulated wave trains resemble each other. From the investigation of the Akhmediev-breather solution of the nonlinear Schrödinger equation (NLSE), it is revealed that the dispersion relation deviated from the quadratic dependence of frequency on wavenumber and became linearly dependent instead. Accordingly, the wave profiles of TPSE and SPTE breathers agree. The range of this agreement is within the order of one wave group of the maximum crest height and persists during the long-term evolution. The findings extend well beyond the NLSE regime and can be applied to modulated wave trains that are highly nonlinear and broad-banded. This was demonstrated from the numerical wave tank simulations with a fully nonlinear potential flow solver based on the boundary element method, in combination with the nonlinear wave generation method based on the prior simulation with the higher-order spectral model. The numerical wave tank results were confirmed experimentally in a physical wave tank. The findings of this study unravel the fundamental nature of the nonlinear wave evolution. The deviation of the dispersion relation of the modulated wave trains occurs because of the nonlinear phase variation due to quasi-resonant interaction, and consequently, the wave geometry of temporally and spatially periodic modulated wave trains coincides.

A numerical and experimental study on the nonlinear evolution of long-crested irregular waves

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

Goullet, Arnaud; Choi, Wooyoung; Division of Ocean Systems Engineering, Korea Advanced Institute of Science and Technology, Daejeon 305-701

2011-01-15

The spatial evolution of nonlinear long-crested irregular waves characterized by the JONSWAP spectrum is studied numerically using a nonlinear wave model based on a pseudospectral (PS) method and the modified nonlinear Schroedinger (MNLS) equation. In addition, new laboratory experiments with two different spectral bandwidths are carried out and a number of wave probe measurements are made to validate these two wave models. Strongly nonlinear wave groups are observed experimentally and their propagation and interaction are studied in detail. For the comparison with experimental measurements, the two models need to be initialized with care and the initialization procedures are described. Themore » MNLS equation is found to approximate reasonably well for the wave fields with a relatively smaller Benjamin-Feir index, but the phase error increases as the propagation distance increases. The PS model with different orders of nonlinear approximation is solved numerically, and it is shown that the fifth-order model agrees well with our measurements prior to wave breaking for both spectral bandwidths.« less

Theoretical Investigation of Dual Tuning of Solitonic Processes in Multiferroic Structures

NASA Astrophysics Data System (ADS)

Cherkasskii, M. A.; Nikitin, A. A.; Ustinov, A. B.; Stashkevich, A.; Kalinikos, B. A.

2016-11-01

. The solitonic wave processes in a multiferroic structure based on ferroelectric and ferrite layers are studied. The influence of external electric and magnetic fields on frequency and wave-number ranges, where bright and dark solitons can exist, are analysed. The investigation was carried out with the nonlinear Schrodinger equation. Results show that an increase of the electric field shifts the boundary between bright and dark solitons to long-wave region. An increase in magnetic field results in the opposite effect.

Solar coronal loop heating by cross-field wave transport

NASA Technical Reports Server (NTRS)

Amendt, Peter; Benford, Gregory

1989-01-01

Solar coronal arches heated by turbulent ion-cyclotron waves may suffer significant cross-field transport by these waves. Nonlinear processes fix the wave-propagation speed at about a tenth of the ion thermal velocity, which seems sufficient to spread heat from a central core into a large cool surrounding cocoon. Waves heat cocoon ions both through classical ion-electron collisions and by turbulent stochastic ion motions. Plausible cocoon sizes set by wave damping are in roughly kilometers, although the wave-emitting core may be only 100 m wide. Detailed study of nonlinear stabilization and energy-deposition rates predicts that nearby regions can heat to values intermediate between the roughly electron volt foot-point temperatures and the about 100 eV core, which is heated by anomalous Ohmic losses. A volume of 100 times the core volume may be affected. This qualitative result may solve a persistent problem with current-driven coronal heating; that it affects only small volumes and provides no way to produce the extended warm structures perceptible to existing instruments.

Deterministic quantum nonlinear optics with single atoms and virtual photons

NASA Astrophysics Data System (ADS)

Kockum, Anton Frisk; Miranowicz, Adam; Macrı, Vincenzo; Savasta, Salvatore; Nori, Franco

2017-06-01

We show how analogs of a large number of well-known nonlinear-optics phenomena can be realized with one or more two-level atoms coupled to one or more resonator modes. Through higher-order processes, where virtual photons are created and annihilated, an effective deterministic coupling between two states of such a system can be created. In this way, analogs of three-wave mixing, four-wave mixing, higher-harmonic and -subharmonic generation (i.e., up- and down-conversion), multiphoton absorption, parametric amplification, Raman and hyper-Raman scattering, the Kerr effect, and other nonlinear processes can be realized. In contrast to most conventional implementations of nonlinear optics, these analogs can reach unit efficiency, only use a minimal number of photons (they do not require any strong external drive), and do not require more than two atomic levels. The strength of the effective coupling in our proposed setups becomes weaker the more intermediate transition steps are needed. However, given the recent experimental progress in ultrastrong light-matter coupling and improvement of coherence times for engineered quantum systems, especially in the field of circuit quantum electrodynamics, we estimate that many of these nonlinear-optics analogs can be realized with currently available technology.

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.

HAARP-based Investigations of Lightning-induced Nonlinearities within the D-Region Ionosphere

NASA Astrophysics Data System (ADS)

Moore, R. C.

2015-12-01

It is well-documented that energetic lightning can produce fantastical events with the lower ionosphere. Although the High-frequency Active Auroral Research Program (HAARP) transmitter is not as powerful as lightning, it can be used to investigate the nonlinear interactions that occur within the lower ionosphere, many of which also occur during lightning-induced ionospheric events. This paper presents the best experimental results obtained during D-region modification experiments performed by the University of Florida at the HAARP observatory between 2007 and 2014, including ELF/VLF wave generation experiments, wave-wave mixing experiments, and cross-modulation experiments. We emphasize the physical processes important for lightning-ionosphere interactions that can be directly investigated using HAARP.

Pressure fluctuations beneath turbulent spots and instability wave packets in a hypersonic boundary layer.

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

Beresh, Steven Jay; Casper, Katya M.; Schneider, Steven P.

2010-12-01

The development of turbulent spots in a hypersonic boundary layer was studied on the nozzle wall of the Boeing/AFOSR Mach-6 Quiet Tunnel. Under quiet flow conditions, the nozzle wall boundary layer remains laminar and grows very thick over the long nozzle length. This allows the development of large turbulent spots that can be readily measured with pressure transducers. Measurements of naturally occurring wave packets and developing turbulent spots were made. The peak frequencies of these natural wave packets were in agreement with second-mode computations. For a controlled study, the breakdown of disturbances created by spark and glow perturbations were studiedmore » at similar freestream conditions. The spark perturbations were the most effective at creating large wave packets that broke down into turbulent spots. The flow disturbances created by the controlled perturbations were analyzed to obtain amplitude criteria for nonlinearity and breakdown as well as the convection velocities of the turbulent spots. Disturbances first grew into linear instability waves and then quickly became nonlinear. Throughout the nonlinear growth of the wave packets, large harmonics are visible in the power spectra. As breakdown begins, the peak amplitudes of the instability waves and harmonics decrease into the rising broad-band frequencies. Instability waves are still visible on either side of the growing turbulent spots during this breakdown process.« less

Nonlinear ionospheric responses to large-amplitude infrasonic-acoustic waves generated by undersea earthquakes

NASA Astrophysics Data System (ADS)

Zettergren, M. D.; Snively, J. B.; Komjathy, A.; Verkhoglyadova, O. P.

2017-02-01

Numerical models of ionospheric coupling with the neutral atmosphere are used to investigate perturbations of plasma density, vertically integrated total electron content (TEC), neutral velocity, and neutral temperature associated with large-amplitude acoustic waves generated by the initial ocean surface displacements from strong undersea earthquakes. A simplified source model for the 2011 Tohoku earthquake is constructed from estimates of initial ocean surface responses to approximate the vertical motions over realistic spatial and temporal scales. Resulting TEC perturbations from modeling case studies appear consistent with observational data, reproducing pronounced TEC depletions which are shown to be a consequence of the impacts of nonlinear, dissipating acoustic waves. Thermospheric acoustic compressional velocities are ˜±250-300 m/s, superposed with downward flows of similar amplitudes, and temperature perturbations are ˜300 K, while the dominant wave periodicity in the thermosphere is ˜3-4 min. Results capture acoustic wave processes including reflection, onset of resonance, and nonlinear steepening and dissipation—ultimately leading to the formation of ionospheric TEC depletions "holes"—that are consistent with reported observations. Three additional simulations illustrate the dependence of atmospheric acoustic wave and subsequent ionospheric responses on the surface displacement amplitude, which is varied from the Tohoku case study by factors of 1/100, 1/10, and 2. Collectively, results suggest that TEC depletions may only accompany very-large amplitude thermospheric acoustic waves necessary to induce a nonlinear response, here with saturated compressional velocities ˜200-250 m/s generated by sea surface displacements exceeding ˜1 m occurring over a 3 min time period.

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.

A comparative numerical analysis of linear and nonlinear aerodynamic sound generation by vortex disturbances in homentropic constant shear flows

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

Hau, Jan-Niklas, E-mail: hau@fdy.tu-darmstadt.de; Oberlack, Martin; GSC CE, Technische Universität Darmstadt, Dolivostraße 15, 64293 Darmstadt

2015-12-15

Aerodynamic sound generation in shear flows is investigated in the light of the breakthrough in hydrodynamics stability theory in the 1990s, where generic phenomena of non-normal shear flow systems were understood. By applying the thereby emerged short-time/non-modal approach, the sole linear mechanism of wave generation by vortices in shear flows was captured [G. D. Chagelishvili, A. Tevzadze, G. Bodo, and S. S. Moiseev, “Linear mechanism of wave emergence from vortices in smooth shear flows,” Phys. Rev. Lett. 79, 3178-3181 (1997); B. F. Farrell and P. J. Ioannou, “Transient and asymptotic growth of two-dimensional perturbations in viscous compressible shear flow,” Phys.more » Fluids 12, 3021-3028 (2000); N. A. Bakas, “Mechanism underlying transient growth of planar perturbations in unbounded compressible shear flow,” J. Fluid Mech. 639, 479-507 (2009); and G. Favraud and V. Pagneux, “Superadiabatic evolution of acoustic and vorticity perturbations in Couette flow,” Phys. Rev. E 89, 033012 (2014)]. Its source is the non-normality induced linear mode-coupling, which becomes efficient at moderate Mach numbers that is defined for each perturbation harmonic as the ratio of the shear rate to its characteristic frequency. Based on the results by the non-modal approach, we investigate a two-dimensional homentropic constant shear flow and focus on the dynamical characteristics in the wavenumber plane. This allows to separate from each other the participants of the dynamical processes — vortex and wave modes — and to estimate the efficacy of the process of linear wave-generation. This process is analyzed and visualized on the example of a packet of vortex modes, localized in both, spectral and physical, planes. Further, by employing direct numerical simulations, the wave generation by chaotically distributed vortex modes is analyzed and the involved linear and nonlinear processes are identified. The generated acoustic field is anisotropic in the wavenumber plane, which results in highly directional linear sound radiation, whereas the nonlinearly generated waves are almost omni-directional. As part of this analysis, we compare the effectiveness of the linear and nonlinear mechanisms of wave generation within the range of validity of the rapid distortion theory and show the dominance of the linear aerodynamic sound generation. Finally, topological differences between the linear source term of the acoustic analogy equation and of the anisotropic non-normality induced linear mechanism of wave generation are found.« less

System and method for investigating sub-surface features of a rock formation using compressional acoustic sources

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

Vu, Cung Khac; Skelt, Christopher; Nihei, Kurt

A system and method for investigating rock formations outside a borehole are provided. The method includes generating a first compressional acoustic wave at a first frequency by a first acoustic source; and generating a second compressional acoustic wave at a second frequency by a second acoustic source. The first and the second acoustic sources are arranged within a localized area of the borehole. The first and the second acoustic waves intersect in an intersection volume outside the borehole. The method further includes receiving a third shear acoustic wave at a third frequency, the third shear acoustic wave returning to themore » borehole due to a non-linear mixing process in a non-linear mixing zone within the intersection volume at a receiver arranged in the borehole. The third frequency is equal to a difference between the first frequency and the second frequency.« less

A discontinuous Galerkin approach for conservative modeling of fully nonlinear and weakly dispersive wave transformations

NASA Astrophysics Data System (ADS)

Sharifian, Mohammad Kazem; Kesserwani, Georges; Hassanzadeh, Yousef

2018-05-01

This work extends a robust second-order Runge-Kutta Discontinuous Galerkin (RKDG2) method to solve the fully nonlinear and weakly dispersive flows, within a scope to simultaneously address accuracy, conservativeness, cost-efficiency and practical needs. The mathematical model governing such flows is based on a variant form of the Green-Naghdi (GN) equations decomposed as a hyperbolic shallow water system with an elliptic source term. Practical features of relevance (i.e. conservative modeling over irregular terrain with wetting and drying and local slope limiting) have been restored from an RKDG2 solver to the Nonlinear Shallow Water (NSW) equations, alongside new considerations to integrate elliptic source terms (i.e. via a fourth-order local discretization of the topography) and to enable local capturing of breaking waves (i.e. via adding a detector for switching off the dispersive terms). Numerical results are presented, demonstrating the overall capability of the proposed approach in achieving realistic prediction of nearshore wave processes involving both nonlinearity and dispersion effects within a single model.

X-ray plane-wave diffraction effects in a crystal with third-order nonlinearity

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

Balyan, M. K., E-mail: mbalyan@ysu.am

The two-wave dynamical diffraction in the Laue geometry has been theoretically considered for a plane X-ray wave in a crystal with a third-order nonlinear response to the external field. An analytical solution to the problem stated is found for certain diffraction conditions. A nonlinear pendulum effect is analyzed. The nonlinear extinction length is found to depend on the incident-wave intensity. A pendulum effect of a new type is revealed: the intensities of the transmitted and diffracted waves periodically depend on the incidentwave intensity at a fixed crystal thickness. The rocking curves and Borrmann nonlinear effect are numerically calculated.

Four-Wave Mixing of Gigawatt Power, Long-Wave Infrared Radiation in Gases and Semiconductors

NASA Astrophysics Data System (ADS)

Pigeon, Jeremy James

The nonlinear optics of gigawatt power, 10 microm, 3 and 200 ps long pulses propagating in gases and semiconductors has been studied experimentally and numerically. In this work, the development of a high-repetition rate, picosecond, CO2 laser system has enabled experiments using peak intensities in the range of 1-10 GW/cm2, approximately one thousand times greater than previous nonlinear optics experiments in the long-wave infrared (LWIR) spectral region. The first measurements of the nonlinear refractive index of the atomic and molecular gases Kr, Xe, N2, O2 and the air at a wavelength near 10 microm were accomplished by studying the four-wave mixing (FWM) of dual-wavelength, 200 ps CO2 laser pulses. These measurements indicate that the nonlinearities of the diatomic molecules N2, O2 and the air are dominated by the molecular contribution to the nonlinear refractive index. Supercontinuum (SC) generation covering the infrared spectral range, from 2-20 microm, was realized by propagating 3 ps, 10 microm pulses in an approximately 7 cm long, Cr-doped GaAs crystal. Temporal measurements of the SC radiation show that pulse splitting accompanies the generation of such broadband light in GaAs. The propagation of 3 ps, 10 microm pulses in GaAs was studied numerically by solving the Generalized Nonlinear Schrodinger Equation (GNLSE). These simulations, combined with analytic estimates, were used to determine that stimulated Raman scattering combined with a modulational instability caused by the propagation of intense LWIR radiation in the negative group velocity dispersion region of GaAs are responsible for the SC generation process. The multiple FWM of a 106 GHz, 200 ps CO2 laser beat-wave propagating in GaAs was used to generate a broadband FWM spectrum that was compressed by the negative group velocity dispersion of GaAs and NaCl crystals to form trains of high-power, picosecond pulses at a wavelength near 10 microm. Experimental FWM spectra obtained using 165 and 882 GHz beat-waves revealed an unexpected and rapid decrease in the FWM yield that was not predicted by the GNLSE model that accounts for third-order nonlinearities alone. These results suggest that the effective nonlinear refractive index of GaAs, having formidable second- and third-order susceptibilities, may be altered by quadratic nonlinearities.

Introduction to Plasma Physics

NASA Astrophysics Data System (ADS)

Gurnett, Donald A.; Bhattacharjee, Amitava

2017-03-01

Preface; 1. Introduction; 2. Characteristic parameters of a plasma; 3. Single particle motions; 4. Waves in a cold plasma; 5. Kinetic theory and the moment equations; 6. Magnetohydrodynamics; 7. MHD equilibria and stability; 8. Discontinuities and shock waves; 9. Electrostatic waves in a hot unmagnetized plasma; 10. Waves in a hot magnetized plasma; 11. Nonlinear effects; 12. Collisional processes; Appendix A. Symbols; Appendix B. Useful trigonometric identities; Appendix C. Vector differential operators; Appendix D. Vector calculus identities; Index.

On the physics of waves in the solar atmosphere: Wave heating and wind acceleration

NASA Technical Reports Server (NTRS)

Musielak, Z. E.

1992-01-01

In the area of solar physics, new calculations of the acoustic wave energy fluxes generated in the solar convective zone was performed. The original theory developed was corrected by including a new frequency factor describing temporal variations of the turbulent energy spectrum. We have modified the original Stein code by including this new frequency factor, and tested the code extensively. Another possible source of the mechanical energy generated in the solar convective zone is the excitation of magnetic flux tube waves which can carry energy along the tubes far away from the region. The problem as to how efficiently those waves are generated in the Sun was recently solved. The propagation of nonlinear magnetic tube waves in the solar atmosphere was calculated, and mode coupling, shock formation, and heating of the local medium was studied. The wave trapping problems and evaluation of critical frequencies for wave reflection in the solar atmosphere was studied. It was shown that the role played by Alfven waves in the wind accelerations and the coronal hole heating is dominant. Presently, we are performing calculations of wave energy fluxes generated in late-type dwarf stars and studying physical processes responsible for the heating of stellar chromospheres and coronae. In the area of physics of waves, a new analytical approach for studying linear Alfven waves in smoothly nonuniform media was recently developed. This approach is presently being extended to study the propagation of linear and nonlinear magnetohydrodynamic (MHD) waves in stratified, nonisothermal and solar atmosphere. The Lighthill theory of sound generation to nonisothermal media (with a special temperature distribution) was extended. Energy cascade by nonlinear MHD waves and possible chaos driven by these waves are presently considered.

Fatigue crack detection by nonlinear spectral correlation with a wideband input

NASA Astrophysics Data System (ADS)

Liu, Peipei; Sohn, Hoon

2017-04-01

Due to crack-induced nonlinearity, ultrasonic wave can distort, create accompanying harmonics, multiply waves of different frequencies, and, under resonance conditions, change resonance frequencies as a function of driving amplitude. All these nonlinear ultrasonic features have been widely studied and proved capable of detecting fatigue crack at its very early stage. However, in noisy environment, the nonlinear features might be drown in the noise, therefore it is difficult to extract those features using a conventional spectral density function. In this study, nonlinear spectral correlation is defined as a new nonlinear feature, which considers not only nonlinear modulations in ultrasonic waves but also spectral correlation between the nonlinear modulations. The proposed nonlinear feature is associated with the following two advantages: (1) stationary noise in the ultrasonic waves has little effect on nonlinear spectral correlation; and (2) the contrast of nonlinear spectral correlation between damage and intact conditions can be enhanced simply by using a wideband input. To validate the proposed nonlinear feature, micro fatigue cracks are introduced to aluminum plates by repeated tensile loading, and the experiment is conducted using surface-mounted piezoelectric transducers for ultrasonic wave generation and measurement. The experimental results confirm that the nonlinear spectral correlation can successfully detect fatigue crack with a higher sensitivity than the classical nonlinear coefficient.

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

Parameterization of planetary wave breaking in the middle atmosphere

NASA Technical Reports Server (NTRS)

Garcia, Rolando R.

1991-01-01

A parameterization of planetary wave breaking in the middle atmosphere has been developed and tested in a numerical model which includes governing equations for a single wave and the zonal-mean state. The parameterization is based on the assumption that wave breaking represents a steady-state equilibrium between the flux of wave activity and its dissipation by nonlinear processes, and that the latter can be represented as linear damping of the primary wave. With this and the additional assumption that the effect of breaking is to prevent further amplitude growth, the required dissipation rate is readily obtained from the steady-state equation for wave activity; diffusivity coefficients then follow from the dissipation rate. The assumptions made in the derivation are equivalent to those commonly used in parameterizations for gravity wave breaking, but the formulation in terms of wave activity helps highlight the central role of the wave group velocity in determining the dissipation rate. Comparison of model results with nonlinear calculations of wave breaking and with diagnostic determinations of stratospheric diffusion coefficients reveals remarkably good agreement, and suggests that the parameterization could be useful for simulating inexpensively, but realistically, the effects of planetary wave transport.

Simulating energy cascade of shock wave formation process in a resonator by gas kinetic scheme

NASA Astrophysics Data System (ADS)

Qu, Chengwu; Zhang, Xiaoqing; Feng, Heying

2017-12-01

The temporal-spatial evolution of gas oscillation was simulated by gas kinetic scheme (GKS) in a cylindrical resonator, driven by a piston at one end and rigidly closed at the other end. Periodic shock waves propagating back and forth were observed in the resonator under finite amplitude of gas oscillation. The studied results demonstrated that the acoustic pressure is a saw-tooth waveform and the oscillatory velocity is a square waveform at the central position of the resonant tube. Moreover, it was found by harmonic analysis that there was no presence of obvious feature for pressure node in such a typical standing wave resonator, and the distribution of acoustic fields displayed a one-dimensional feature for the acoustic pressure while a quasi-one-dimensional form for oscillatory velocity, which demonstrated the nonlinear effects. The simulation results for axial distribution of acoustic intensity showed a good consistency with the published experimental data in the open literature domain, which provides a verification for the effectiveness of the GKS model proposed. The influence of displacement amplitude of the driving piston on the formation of shock wave was numerically investigated, and the simulated results revealed the cascade process of harmonic wave energy from the fundamental wave to higher harmonics. In addition, this study found that the acoustic intensity at the driving end of the resonant tube would increase linearly with the displacement amplitude of the piston due to nonlinear effects, rather than the exponential variation by linear theory. This research demonstrates that the GKS model is strongly capable of simulating nonlinear acoustic problems.

A Multiscale Nested Modeling Framework to Simulate the Interaction of Surface Gravity Waves with Nonlinear Internal Gravity Waves

DTIC Science & Technology

2015-09-30

Meneveau, C., and L. Shen (2014), Large-eddy simulation of offshore wind farm , Physics of Fluids, 26, 025101. Zhang, Z., Fringer, O.B., and S.R...being centimeter scale, surface mixed layer processes arising from the combined actions of tides, winds and mesoscale currents. Issues related to...the internal wave field and how it impacts the surface waves. APPROACH We are focusing on the problem of modification of the wind -wave field

Numerical tools to predict the environmental loads for offshore structures under extreme weather conditions

NASA Astrophysics Data System (ADS)

Wu, Yanling

2018-05-01

In this paper, the extreme waves were generated using the open source computational fluid dynamic (CFD) tools — OpenFOAM and Waves2FOAM — using linear and nonlinear NewWave input. They were used to conduct the numerical simulation of the wave impact process. Numerical tools based on first-order (with and without stretching) and second-order NewWave are investigated. The simulation to predict force loading for the offshore platform under the extreme weather condition is implemented and compared.

Coupling nonlinear optical waves to photoreactive and phase-separating soft matter: Current status and perspectives

NASA Astrophysics Data System (ADS)

Biria, Saeid; Morim, Derek R.; An Tsao, Fu; Saravanamuttu, Kalaichelvi; Hosein, Ian D.

2017-10-01

Nonlinear optics and polymer systems are distinct fields that have been studied for decades. These two fields intersect with the observation of nonlinear wave propagation in photoreactive polymer systems. This has led to studies on the nonlinear dynamics of transmitted light in polymer media, particularly for optical self-trapping and optical modulation instability. The irreversibility of polymerization leads to permanent capture of nonlinear optical patterns in the polymer structure, which is a new synthetic route to complex structured soft materials. Over time more intricate polymer systems are employed, whereby nonlinear optical dynamics can couple to nonlinear chemical dynamics, opening opportunities for self-organization. This paper discusses the work to date on nonlinear optical pattern formation processes in polymers. A brief overview of nonlinear optical phenomenon is provided to set the stage for understanding their effects. We review the accomplishments of the field on studying nonlinear waveform propagation in photopolymerizable systems, then discuss our most recent progress in coupling nonlinear optical pattern formation to polymer blends and phase separation. To this end, perspectives on future directions and areas of sustained inquiry are provided. This review highlights the significant opportunity in exploiting nonlinear optical pattern formation in soft matter for the discovery of new light-directed and light-stimulated materials phenomenon, and in turn, soft matter provides a platform by which new nonlinear optical phenomenon may be discovered.

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.

Quasi-phase-matching of the dual-band nonlinear left-handed metamaterial

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

Liu, Yahong, E-mail: yhliu@nwpu.edu.cn; Song, Kun; Gu, Shuai

2014-11-17

We demonstrate a type of nonlinear meta-atom creating a dual-band nonlinear left-handed metamaterial (DNLHM). The DNLHM operates at two distinct left-handed frequency bands where there is an interval of one octave between the two center frequencies. Under the illumination of a high-power signal at the first left-handed frequency band corresponding to fundamental frequency (FF), second-harmonic generation (SHG) is observed at the second left-handed band. This means that our DNLHM supports backward-propagating waves both at FF and second-harmonic (SH) frequency. We also experimentally demonstrate quasi-phase-matching configurations for the backward SHG. This fancy parametric process can significantly transmits the SH generated bymore » an incident FF wave.« less

Self-modulational formation of pulsar microstructures

NASA Technical Reports Server (NTRS)

Kennel, C. F.; Chian, A. C.-L.

1987-01-01

A nonlinear plasma theory for self modulation of pulsar radio pulses is discussed. A nonlinear Schroedinger equation is derived for strong electromagnetic waves propagating in an electron positron plasma. The nonlinearities arising from wave intensity induced particle mass variation may excite the modulational instability of circularly and linearly polarized pulsar radiation. The resulting wave envelopes can take the form of periodic wave trains or solitons. These nonlinear stationary waveforms may account for the formation of pulsar microstructures.

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.

Emergent rogue wave structures and statistics in spontaneous modulation instability.

PubMed

Toenger, Shanti; Godin, Thomas; Billet, Cyril; Dias, Frédéric; Erkintalo, Miro; Genty, Goëry; Dudley, John M

2015-05-20

The nonlinear Schrödinger equation (NLSE) is a seminal equation of nonlinear physics describing wave packet evolution in weakly-nonlinear dispersive media. The NLSE is especially important in understanding how high amplitude "rogue waves" emerge from noise through the process of modulation instability (MI) whereby a perturbation on an initial plane wave can evolve into strongly-localised "breather" or "soliton on finite background (SFB)" structures. Although there has been much study of such structures excited under controlled conditions, there remains the open question of how closely the analytic solutions of the NLSE actually model localised structures emerging in noise-seeded MI. We address this question here using numerical simulations to compare the properties of a large ensemble of emergent peaks in noise-seeded MI with the known analytic solutions of the NLSE. Our results show that both elementary breather and higher-order SFB structures are observed in chaotic MI, with the characteristics of the noise-induced peaks clustering closely around analytic NLSE predictions. A significant conclusion of our work is to suggest that the widely-held view that the Peregrine soliton forms a rogue wave prototype must be revisited. Rather, we confirm earlier suggestions that NLSE rogue waves are most appropriately identified as collisions between elementary SFB solutions.

Method to improve optical parametric oscillator beam quality

DOEpatents

Smith, Arlee V.; Alford, William J.; Bowers, Mark S.

2003-11-11

A method to improving optical parametric oscillator (OPO) beam quality having an optical pump, which generates a pump beam at a pump frequency greater than a desired signal frequency, a nonlinear optical medium oriented so that a signal wave at the desired signal frequency and a corresponding idler wave are produced when the pump beam (wave) propagates through the nonlinear optical medium, resulting in beam walk off of the signal and idler waves, and an optical cavity which directs the signal wave to repeatedly pass through the nonlinear optical medium, said optical cavity comprising an equivalently even number of non-planar mirrors that produce image rotation on each pass through the nonlinear optical medium. Utilizing beam walk off where the signal wave and said idler wave have nonparallel Poynting vectors in the nonlinear medium and image rotation, a correlation zone of distance equal to approximately .rho.L.sub.crystal is created which, through multiple passes through the nonlinear medium, improves the beam quality of the OPO output.

Optical parametric osicllators with improved beam quality

DOEpatents

Smith, Arlee V.; Alford, William J.

2003-11-11

An optical parametric oscillator (OPO) having an optical pump, which generates a pump beam at a pump frequency greater than a desired signal frequency, a nonlinear optical medium oriented so that a signal wave at the desired signal frequency and a corresponding idler wave are produced when the pump beam (wave) propagates through the nonlinear optical medium, resulting in beam walk off of the signal and idler waves, and an optical cavity which directs the signal wave to repeatedly pass through the nonlinear optical medium, said optical cavity comprising an equivalently even number of non-planar mirrors that produce image rotation on each pass through the nonlinear optical medium. Utilizing beam walk off where the signal wave and said idler wave have nonparallel Poynting vectors in the nonlinear medium and image rotation, a correlation zone of distance equal to approximately .rho.L.sub.crystal is created which, through multiple passes through the nonlinear medium, improves the beam quality of the OPO output.

Glimpses of Kolmogorov's spectral energy dynamics in nonlinear acoustic waves

NASA Astrophysics Data System (ADS)

Gupta, Prateek; Scalo, Carlo

2017-11-01

Gupta, Lodato, and Scalo (AIAA 2017) have demonstrated the existence of an equilibrium spectral energy cascade in shock waves formed as a result of continued modal thermoacoustic amplification consistent with Kolmogorov's theory for high-Reynolds-number hydrodynamic turbulence. In this talk we discuss the derivation of a perturbation energy density norm that guarantees energy conservation during the nonlinear wave steepening process, analogous to inertial subrange turbulent energy cascade dynamics. The energy cascade is investigated via a bi-spectral analysis limited to wave-numbers and frequencies lower than the ones associated with the shock, analogous to the viscous dissipation length scale in turbulence. The proposed norm is derived by recombining second-order nonlinear acoustic equations and is positive definite; moreover, it decays to zero in the presence of viscous dissipation and is hence classifiable as a Lyapunov function of acoustic perturbation variables. The cumulative energy spectrum wavenumber distribution demonstrates a -3/2 decay law in the inertial range. The governing equation for the thus-derived energy norm highlights terms responsible for energy cascade towards higher harmonics, analogous to vortex stretching terms in hydrodynamic turbulence.

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).

Stationary states of extended nonlinear Schrödinger equation with a source

NASA Astrophysics Data System (ADS)

Borich, M. A.; Smagin, V. V.; Tankeev, A. P.

2007-02-01

Structure of nonlinear stationary states of the extended nonlinear Schrödinger equation (ENSE) with a source has been analyzed with allowance for both third-order and nonlinearity dispersion. A new class of particular solutions (solitary waves) of the ENSe has been obtained. The scenario of the destruction of these states under the effect of an external perturbation has been investigated analytically and numerically. The results obtained can be used to interpret experimental data on the weakly nonlinear dynamics of the magnetostatic envelope in heterophase ferromagnet-insulator-metal, metal-insulator-ferromagnet-insulator-metal, and other similar structures and upon the simulation of nonlinear processes in optical systems.

Nonlinear Scattering of VLF Waves in the Radiation Belts

NASA Astrophysics Data System (ADS)

Crabtree, Chris; Rudakov, Leonid; Ganguli, Guru; Mithaiwala, Manish

2014-10-01

Electromagnetic VLF waves, such as whistler mode waves, control the lifetime of trapped electrons in the radiation belts by pitch-angle scattering. Since the pitch-angle scattering rate is a strong function of the wave properties, a solid understanding of VLF wave sources and propagation in the magnetosphere is critical to accurately calculate electron lifetimes. Nonlinear scattering (Nonlinear Landau Damping) is a mechanism that can strongly alter VLF wave propagation [Ganguli et al. 2010], primarily by altering the direction of propagation, and has not been accounted for in previous models of radiation belt dynamics. Laboratory results have confirmed the dramatic change in propagation direction when the pump wave has sufficient amplitude to exceed the nonlinear threshold [Tejero et al. 2014]. Recent results show that the threshold for nonlinear scattering can often be met by naturally occurring VLF waves in the magnetosphere, with wave magnetic fields of the order of 50-100 pT inside the plasmapause. Nonlinear scattering can then dramatically alter the macroscopic dynamics of waves in the radiation belts leading to the formation of a long-lasting wave-cavity [Crabtree et al. 2012] and, when amplification is present, a multi-pass amplifier [Ganguli et al. 2012]. By considering these effects, the lifetimes of electrons can be dramatically reduced. This work is supported by the Naval Research Laboratory base program.

Nonlinear optical detection of terahertz-wave radiation from resonant tunneling diodes.

PubMed

Takida, Yuma; Nawata, Kouji; Suzuki, Safumi; Asada, Masahiro; Minamide, Hiroaki

2017-03-06

The sensitive detection of terahertz (THz)-wave radiation from compact sources at room temperature is crucial for real-world THz-wave applications. Here, we demonstrate the nonlinear optical detection of THz-wave radiation from continuous-wave (CW) resonant tunneling diodes (RTDs) at 0.58, 0.78, and 1.14 THz. The up-conversion process in a MgO:LiNbO₃ crystal under the noncollinear phase-matching condition offers efficient wavelength conversion from a THz wave to a near-infrared (NIR) wave that is detected using a commercial NIR photodetector. The minimum detection limit of CW THz-wave power is as low as 5 nW at 1.14 THz, corresponding to 2-aJ energy and 2.7 × 10³ photons within the time window of a 0.31-ns pump pulse. Our results show that the input frequency and power of RTD devices can be calibrated by measuring the output wavelength and energy of up-converted waves, respectively. This optical detection technique for compact electronic THz-wave sources will open up a new opportunity for the realization of real-world THz-wave applications.

Free-carrier-induced soliton fission unveiled by in situ measurements in nanophotonic waveguides

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

Husko, Chad; Wulf, Matthias; Lefrancois, Simon

Solitons are localized waves formed by a balance of focusing and defocusing effects. These nonlinear waves exist in diverse forms of matter yet exhibit similar properties including stability, periodic recurrence and particle-like trajectories. One important property is soliton fission, a process by which an energetic higher-order soliton breaks apart due to dispersive or nonlinear perturbations. Here we demonstrate through both experiment and theory that nonlinear photocarrier generation can induce soliton fission. Using near-field measurements, we directly observe the nonlinear spatial and temporal evolution of optical pulses in situ in a nanophotonic semiconductor waveguide. We develop an analytic formalism describing themore » free-carrier dispersion (FCD) perturbation and show the experiment exceeds the minimum threshold by an order of magnitude. We confirm these observations with a numerical nonlinear Schrodinger equation model. Finally, these results provide a fundamental explanation and physical scaling of optical pulse evolution in free-carrier media and could enable improved supercontinuum sources in gas based and integrated semiconductor waveguides.« less

Nonlinear oscillations and waves in multi-species cold plasmas

NASA Astrophysics Data System (ADS)

Verma, Prabal Singh

2016-12-01

The spatio-temporal evolution of nonlinear oscillations in multi-species plasma is revisited to provide more insight into the physics of phase mixing by constructing two sets of nonlinear solutions up to the second order. The first solution exhibits perfect oscillations in the linear regime and phase mixing appears only nonlinearly in the second order as a response to the ponderomotive forces. This response can be both direct and indirect. The indirect contribution of the ponderomotive forces appears through self-consistently generated low frequency fields. Furthermore, the direct and indirect contributions of the ponderomotive forces on the phase mixing process is explored and it is found that the indirect contribution is negligible in an electron-ion plasma and it disappears in the case of electron-positron plasma, yet represents an equal contribution in the electron-positron-ion plasma. However, the second solution does not exhibit any phase mixing due to the absence of ponderomotive forces but results in an undistorted nonlinear traveling wave. These investigations have relevance for laboratory/astrophysical multi-species plasma.

Free-carrier-induced soliton fission unveiled by in situ measurements in nanophotonic waveguides

DOE PAGES

Husko, Chad; Wulf, Matthias; Lefrancois, Simon; ...

2016-04-15

Solitons are localized waves formed by a balance of focusing and defocusing effects. These nonlinear waves exist in diverse forms of matter yet exhibit similar properties including stability, periodic recurrence and particle-like trajectories. One important property is soliton fission, a process by which an energetic higher-order soliton breaks apart due to dispersive or nonlinear perturbations. Here we demonstrate through both experiment and theory that nonlinear photocarrier generation can induce soliton fission. Using near-field measurements, we directly observe the nonlinear spatial and temporal evolution of optical pulses in situ in a nanophotonic semiconductor waveguide. We develop an analytic formalism describing themore » free-carrier dispersion (FCD) perturbation and show the experiment exceeds the minimum threshold by an order of magnitude. We confirm these observations with a numerical nonlinear Schrodinger equation model. Finally, these results provide a fundamental explanation and physical scaling of optical pulse evolution in free-carrier media and could enable improved supercontinuum sources in gas based and integrated semiconductor waveguides.« less

The Harp probe - An in situ Bragg scattering sensor

NASA Technical Reports Server (NTRS)

Mollo-Christensen, E.; Huang, N. E.; Long, S. R.; Bliven, L. F.

1984-01-01

A wave sensor, consisting of parallel, evenly spaced capacitance wires, whose output is the sum of the water surface deflections at the wires, has been built and tested in a wave tank. The probe output simulates Bragg scattering of electromagnetic waves from a water surface with waves; it can be used to simulate electromagnetic probing of the sea surface by radar. The study establishes that the wave probe, called the 'Harp' for short, will simulate Bragg scattering and that it can also be used to study nonlinear wave processes.

Phonon-assisted nonlinear optical processes in ultrashort-pulse pumped optical parametric amplifiers

NASA Astrophysics Data System (ADS)

Isaienko, Oleksandr; Robel, István

2016-03-01

Optically active phonon modes in ferroelectrics such as potassium titanyl phosphate (KTP) and potassium titanyl arsenate (KTA) in the ~7-20 THz range play an important role in applications of these materials in Raman lasing and terahertz wave generation. Previous studies with picosecond pulse excitation demonstrated that the interaction of pump pulses with phonons can lead to efficient stimulated Raman scattering (SRS) accompanying optical parametric oscillation or amplification processes (OPO/OPA), and to efficient polariton-phonon scattering. In this work, we investigate the behavior of infrared OPAs employing KTP or KTA crystals when pumped with ~800-nm ultrashort pulses of duration comparable to the oscillation period of the optical phonons. We demonstrate that under conditions of coherent impulsive Raman excitation of the phonons, when the effective χ(2) nonlinearity cannot be considered instantaneous, the parametrically amplified waves (most notably, signal) undergo significant spectral modulations leading to an overall redshift of the OPA output. The pump intensity dependence of the redshifted OPA output, the temporal evolution of the parametric gain, as well as the pump spectral modulations suggest the presence of coupling between the nonlinear optical polarizations PNL of the impulsively excited phonons and those of parametrically amplified waves.

Nonlinear optical waves with the second Painleve transcendent shape of envelope in Kerr media

NASA Astrophysics Data System (ADS)

Shcherbakov, Alexandre S.; Tepichin Rodriguez, Eduardo; Sanchez Sanchez, Mauro

2004-05-01

Nonlinear optical wave packets with the second Painleve transcendent shape of envelope are revealed in Kerr media, manifesting weakly focusing cubic nonlinearity, square-law dispersion, and linear losses. When the state of nonlinear optical transmission is realized, two possible types of boundary conditions turn out to be satisfied for these wave packets. The propagation of initially unchirped optical wave packets under consideration could be supported by lossless medium in both normal and anomalous dispersion regimes. At the same time initially chirped optical waves with the second Painleve transcendent shape in low-loss medium and need matching the magnitude of optical losses by the dispersion and nonlinear properties of that medium.

Influence of nonlinear detuning at plasma wavebreaking threshold on backward Raman compression of non-relativistic laser pulses

NASA Astrophysics Data System (ADS)

Balakin, A. A.; Fraiman, G. M.; Jia, Q.; Fisch, N. J.

2018-06-01

Taking into account the nonlinear dispersion of the plasma wave, the fluid equations for the three-wave (Raman) interaction in plasmas are derived. It is found that, in some parameter regimes, the nonlinear detuning resulting from the plasma wave dispersion during Raman compression limits the plasma wave amplitude to noticeably below the generally recognized wavebreaking threshold. Particle-in-cell simulations confirm the theoretical estimates. For weakly nonlinear dispersion, the detuning effect can be counteracted by pump chirping or, equivalently, by upshifting slightly the pump frequency, so that the frequency-upshifted pump interacts with the seed at the point where the plasma wave enters the nonlinear stage.

Hollow Gaussian beam generation through nonlinear interaction of photons with orbital angular momentum

PubMed Central

Chaitanya, N. Apurv; Jabir, M. V.; Banerji, J.; Samanta, G. K.

2016-01-01

Hollow Gaussian beams (HGB) are a special class of doughnut shaped beams that do not carry orbital angular momentum (OAM). Such beams have a wide range of applications in many fields including atomic optics, bio-photonics, atmospheric science, and plasma physics. Till date, these beams have been generated using linear optical elements. Here, we show a new way of generating HGBs by three-wave mixing in a nonlinear crystal. Based on nonlinear interaction of photons having OAM and conservation of OAM in nonlinear processes, we experimentally generated ultrafast HGBs of order as high as 6 and power >180 mW at 355 nm. This generic concept can be extended to any wavelength, timescales (continuous-wave and ultrafast) and any orders. We show that the removal of azimuthal phase of vortices does not produce Gaussian beam. We also propose a new and only method to characterize the order of the HGBs. PMID:27581625

Nonlinear Propagation of Planet-Generated Tidal Waves

NASA Technical Reports Server (NTRS)

Rafikov, R. R.

2002-01-01

The propagation and evolution of planet-generated density waves in protoplanetary disks is considered. The evolution of waves, leading to shock formation and wake dissipation, is followed in the weakly nonlinear regime. The 2001 local approach of Goodman and Rafikov is extended to include the effects of surface density and temperature variations in the disk as well as the disk cylindrical geometry and nonuniform shear. Wave damping due to shocks is demonstrated to be a nonlocal process spanning a significant fraction of the disk. Torques induced by the planet could be significant drivers of disk evolution on timescales of approx. 10(exp 6)-10(exp 7) yr, even in the absence of strong background viscosity. A global prescription for angular momentum deposition is developed that could be incorporated into the study of gap formation in a gaseous disk around the planet.

Generation of Caustics and Rogue Waves from Nonlinear Instability.

PubMed

Safari, Akbar; Fickler, Robert; Padgett, Miles J; Boyd, Robert W

2017-11-17

Caustics are phenomena in which nature concentrates the energy of waves and may exhibit rogue-type behavior. Although they are known mostly in optics, caustics are intrinsic to all wave phenomena. As we demonstrate in this Letter, the formation of caustics and consequently rogue events in linear systems requires strong phase fluctuations. We show that nonlinear phase shifts can generate sharp caustics from even small fluctuations. Moreover, in that the wave amplitude increases dramatically in caustics, nonlinearity is usually inevitable. We perform an experiment in an optical system with Kerr nonlinearity, simulate the results based on the nonlinear Schrödinger equation, and achieve perfect agreement. As the same theoretical framework is used to describe other wave systems such as large-scale water waves, our results may also aid the understanding of ocean phenomena.

Generation of Caustics and Rogue Waves from Nonlinear Instability

NASA Astrophysics Data System (ADS)

Safari, Akbar; Fickler, Robert; Padgett, Miles J.; Boyd, Robert W.

2017-11-01

Caustics are phenomena in which nature concentrates the energy of waves and may exhibit rogue-type behavior. Although they are known mostly in optics, caustics are intrinsic to all wave phenomena. As we demonstrate in this Letter, the formation of caustics and consequently rogue events in linear systems requires strong phase fluctuations. We show that nonlinear phase shifts can generate sharp caustics from even small fluctuations. Moreover, in that the wave amplitude increases dramatically in caustics, nonlinearity is usually inevitable. We perform an experiment in an optical system with Kerr nonlinearity, simulate the results based on the nonlinear Schrödinger equation, and achieve perfect agreement. As the same theoretical framework is used to describe other wave systems such as large-scale water waves, our results may also aid the understanding of ocean phenomena.

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

Interactions of large amplitude solitary waves in viscous fluid conduits

NASA Astrophysics Data System (ADS)

Lowman, Nicholas K.; Hoefer, M. A.; El, G. A.

2014-07-01

The free interface separating an exterior, viscous fluid from an intrusive conduit of buoyant, less viscous fluid is known to support strongly nonlinear solitary waves due to a balance between viscosity-induced dispersion and buoyancy-induced nonlinearity. The overtaking, pairwise interaction of weakly nonlinear solitary waves has been classified theoretically for the Korteweg-de Vries equation and experimentally in the context of shallow water waves, but a theoretical and experimental classification of strongly nonlinear solitary wave interactions is lacking. The interactions of large amplitude solitary waves in viscous fluid conduits, a model physical system for the study of one-dimensional, truly dissipationless, dispersive nonlinear waves, are classified. Using a combined numerical and experimental approach, three classes of nonlinear interaction behavior are identified: purely bimodal, purely unimodal, and a mixed type. The magnitude of the dispersive radiation due to solitary wave interactions is quantified numerically and observed to be beyond the sensitivity of our experiments, suggesting that conduit solitary waves behave as "physical solitons." Experimental data are shown to be in excellent agreement with numerical simulations of the reduced model. Experimental movies are available with the online version of the paper.

Quantum information processing with a travelling wave of light

NASA Astrophysics Data System (ADS)

Serikawa, Takahiro; Shiozawa, Yu; Ogawa, Hisashi; Takanashi, Naoto; Takeda, Shuntaro; Yoshikawa, Jun-ichi; Furusawa, Akira

2018-02-01

We exploit quantum information processing on a traveling wave of light, expecting emancipation from thermal noise, easy coupling to fiber communication, and potentially high operation speed. Although optical memories are technically challenging, we have an alternative approach to apply multi-step operations on traveling light, that is, continuous-variable one-way computation. So far our achievement includes generation of a one-million-mode entangled chain in time-domain, mode engineering of nonlinear resource states, and real-time nonlinear feedforward. Although they are implemented with free space optics, we are also investigating photonic integration and performed quantum teleportation with a passive liner waveguide chip as a demonstration of entangling, measurement, and feedforward. We also suggest a loop-based architecture as another model of continuous-variable computing.

Evaluating the role of higher order nonlinearity in water of finite and shallow depth with a direct numerical simulation method of Euler equations

NASA Astrophysics Data System (ADS)

Fernandez, L.; Toffoli, A.; Monbaliu, J.

2012-04-01

In deep water, the dynamics of surface gravity waves is dominated by the instability of wave packets to side band perturbations. This mechanism, which is a nonlinear third order in wave steepness effect, can lead to a particularly strong focusing of wave energy, which in turn results in the formation of waves of very large amplitude also known as freak or rogue waves [1]. In finite water depth, however, the interaction between waves and the ocean floor induces a mean current. This subtracts energy from wave instability and causes it to cease for relative water depth , where k is the wavenumber and h the water depth [2]. Yet, this contradicts field observations of extreme waves such as the infamous 26-m "New Year" wave that have mainly been recorded in regions of relatively shallow water . In this respect, recent studies [3] seem to suggest that higher order nonlinearity in water of finite depth may sustain instability. In order to assess the role of higher order nonlinearity in water of finite and shallow depth, here we use a Higher Order Spectral Method [4] to simulate the evolution of surface gravity waves according to the Euler equations of motion. This method is based on an expansion of the vertical velocity about the surface elevation under the assumption of weak nonlinearity and has a great advantage of allowing the activation or deactivation of different orders of nonlinearity. The model is constructed to deal with an arbitrary order of nonlinearity and water depths so that finite and shallow water regimes can be analyzed. Several wave configurations are considered with oblique and collinear with the primary waves disturbances and different water depths. The analysis confirms that nonlinearity higher than third order play a substantial role in the destabilization of a primary wave train and subsequent growth of side band perturbations.

Energy dynamics in a simulation of LAPD turbulence

NASA Astrophysics Data System (ADS)

Friedman, B.; Carter, T. A.; Umansky, M. V.; Schaffner, D.; Dudson, B.

2012-10-01

Energy dynamics calculations in a 3D fluid simulation of drift wave turbulence in the linear Large Plasma Device [W. Gekelman et al., Rev. Sci. Instrum. 62, 2875 (1991)] illuminate processes that drive and dissipate the turbulence. These calculations reveal that a nonlinear instability dominates the injection of energy into the turbulence by overtaking the linear drift wave instability that dominates when fluctuations about the equilibrium are small. The nonlinear instability drives flute-like (k∥=0) density fluctuations using free energy from the background density gradient. Through nonlinear axial wavenumber transfer to k∥≠0 fluctuations, the nonlinear instability accesses the adiabatic response, which provides the requisite energy transfer channel from density to potential fluctuations as well as the phase shift that causes instability. The turbulence characteristics in the simulations agree remarkably well with experiment. When the nonlinear instability is artificially removed from the system through suppressing k∥=0 modes, the turbulence develops a coherent frequency spectrum which is inconsistent with experimental data. This indicates the importance of the nonlinear instability in producing experimentally consistent turbulence.

Tsunami Wave Run-up on a Vertical Wall in Tidal Environment

NASA Astrophysics Data System (ADS)

Didenkulova, Ira; Pelinovsky, Efim

2018-04-01

We solve analytically a nonlinear problem of shallow water theory for the tsunami wave run-up on a vertical wall in tidal environment. Shown that the tide can be considered static in the process of tsunami wave run-up. In this approximation, it is possible to obtain the exact solution for the run-up height as a function of the incident wave height. This allows us to investigate the tide influence on the run-up characteristics.

Nonlinear Landau damping in the ionosphere

NASA Technical Reports Server (NTRS)

Kiwamoto, Y.; Benson, R. F.

1978-01-01

A model is presented to explain the non-resonant waves which give rise to the diffuse resonance observed near 3/2 f sub H by the Alouette and ISIS topside sounders, where f sub H is the ambient electron cyclotron frequency. In a strictly linear analysis, these instability driven waves will decay due to Landau damping on a time scale much shorter than the observed time duration of the diffuse resonance. Calculations of the nonlinear wave particle coupling coefficients, however, indicate that the diffuse resonance wave can be maintained by the nonlinear Landau damping of the sounder stimulated 2f sub H wave. The time duration of the diffuse resonance is determined by the transit time of the instability generated and nonlinearly maintained diffuse resonance wave from the remote short lived hot region back to the antenna. The model is consistent with the Alouette/ISIS observations, and clearly demonstrates the existence of nonlinear wave-particle interactions in the ionosphere.

Nonlinear electrostatic solitary waves in electron-positron plasmas

NASA Astrophysics Data System (ADS)

Lazarus, I. J.; Bharuthram, R.; Moolla, S.; Singh, S. V.; Lakhina, G. S.

2016-02-01

The generation of nonlinear electrostatic solitary waves (ESWs) is explored in a magnetized four component two-temperature electron-positron plasma. Fluid theory is used to derive a set of nonlinear equations for the ESWs, which propagate obliquely to an external magnetic field. The electric field structures are examined for various plasma parameters and are shown to yield sinusoidal, sawtooth and bipolar waveforms. It is found that an increase in the densities of the electrons and positrons strengthen the nonlinearity while the periodicity and nonlinearity of the wave increases as the cool-to-hot temperature ratio increases. Our results could be useful in understanding nonlinear propagation of waves in astrophysical environments and related laboratory experiments.

Second order harmonic guided wave mutual interactions in plate: Vector analysis, numerical simulation, and experimental results

NASA Astrophysics Data System (ADS)

Hasanian, Mostafa; Lissenden, Cliff J.

2017-08-01

The extraordinary sensitivity of nonlinear ultrasonic waves to the early stages of material degradation makes them excellent candidates for nondestructive material characterization. However, distinguishing weak material nonlinearity from instrumentation nonlinearity remains problematic for second harmonic generation approaches. A solution to this problem is to mix waves having different frequencies and to let their mutual interaction generate sum and difference harmonics at frequencies far from those of the instrumentation. Mixing of bulk waves and surface waves has been researched for some time, but mixing of guided waves has not yet been investigated in depth. A unique aspect of guided waves is their dispersive nature, which means we need to assure that a wave can propagate at the sum or difference frequency. A wave vector analysis is conducted that enables selection of primary waves traveling in any direction that generate phase matched secondary waves. We have tabulated many sets of primary waves and phase matched sum and difference harmonics. An example wave mode triplet of two counter-propagating collinear shear horizontal waves that interact to generate a symmetric Lamb wave at the sum frequency is simulated using finite element analysis and then laboratory experiments are conducted. The finite element simulation eliminates issues associated with instrumentation nonlinearities and signal-to-noise ratio. A straightforward subtraction method is used in the experiments to identify the material nonlinearity induced mutual interaction and show that the generated Lamb wave propagates on its own and is large enough to measure. Since the Lamb wave has different polarity than the shear horizontal waves the material nonlinearity is clearly identifiable. Thus, the mutual interactions of shear horizontal waves in plates could enable volumetric characterization of material in remote regions from transducers mounted on just one side of the plate.

Generation and propagation of nonlinear internal waves in Massachusetts Bay

USGS Publications Warehouse

Scotti, A.; Beardsley, R.C.; Butman, B.

2007-01-01

During the summer, nonlinear internal waves (NLIWs) are commonly observed propagating in Massachusetts Bay. The topography of the area is unique in the sense that the generation area (over Stellwagen Bank) is only 25 km away from the shoaling area, and thus it represents an excellent natural laboratory to study the life cycle of NLIWs. To assist in the interpretation of the data collected during the 1998 Massachusetts Bay Internal Wave Experiment (MBIWE98), a fully nonlinear and nonhydrostatic model covering the generation/shoaling region was developed, to investigate the response of the system to the range of background and driving conditions observed. Simplified models were also used to elucidate the role of nonlinearity and dispersion in shaping the NLIW field. This paper concentrates on the generation process and the subsequent evolution in the basin. The model was found to reproduce well the range of propagation characteristics observed (arrival time, propagation speed, amplitude), and provided a coherent framework to interpret the observations. Comparison with a fully nonlinear hydrostatic model shows that during the generation and initial evolution of the waves as they move away from Stellwagen Bank, dispersive effects play a negligible role. Thus the problem can be well understood considering the geometry of the characteristics along which the Riemann invariants of the hydrostatic problem propagate. Dispersion plays a role only during the evolution of the undular bore in the middle of Stellwagen Basin. The consequences for modeling NLIWs within hydrostatic models are briefly discussed at the end.

From solitons to rogue waves in nonlinear left-handed metamaterials.

PubMed

Shen, Yannan; Kevrekidis, P G; Veldes, G P; Frantzeskakis, D J; DiMarzio, D; Lan, X; Radisic, V

2017-03-01

In the present work, we explore soliton and roguelike wave solutions in the transmission line analog of a nonlinear left-handed metamaterial. The nonlinearity is expressed through a voltage-dependent, symmetric capacitance motivated by recently developed ferroelectric barium strontium titanate thin-film capacitor designs. We develop both the corresponding nonlinear dynamical lattice and its reduction via a multiple scales expansion to a nonlinear Schrödinger (NLS) model for the envelope of a given carrier wave. The reduced model can feature either a focusing or a defocusing nonlinearity depending on the frequency (wave number) of the carrier. We then consider the robustness of different types of solitary waves of the reduced model within the original nonlinear left-handed medium. We find that both bright and dark solitons persist in a suitable parametric regime, where the reduction to the NLS model is valid. Additionally, for suitable initial conditions, we observe a rogue wave type of behavior that differs significantly from the classic Peregrine rogue wave evolution, including most notably the breakup of a single Peregrine-like pattern into solutions with multiple wave peaks. Finally, we touch upon the behavior of generalized members of the family of the Peregrine solitons, namely, Akhmediev breathers and Kuznetsov-Ma solitons, and explore how these evolve in the left-handed transmission line.

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

Non-reciprocal geometric wave diode by engineering asymmetric shapes of nonlinear materials.

PubMed

Li, Nianbei; Ren, Jie

2014-08-29

Unidirectional nonreciprocal transport is at the heart of many fundamental problems and applications in both science and technology. Here we study the novel design of wave diode devices by engineering asymmetric shapes of nonlinear materials to realize the function of non-reciprocal wave propagations. We first show analytical results revealing that both nonlinearity and asymmetry are necessary to induce such non-reciprocal (asymmetric) wave propagations. Detailed numerical simulations are further performed for a more realistic geometric wave diode model with typical asymmetric shape, where good non-reciprocal wave diode effect is demonstrated. Finally, we discuss the scalability of geometric wave diodes. The results open a flexible way for designing wave diodes efficiently simply through shape engineering of nonlinear materials, which may find broad implications in controlling energy, mass and information transports.

Energetic mid-IR femtosecond pulse generation by self-defocusing soliton-induced dispersive waves in a bulk quadratic nonlinear crystal.

PubMed

Zhou, Binbin; Guo, Hairun; Bache, Morten

2015-03-09

Generating energetic femtosecond mid-IR pulses is crucial for ultrafast spectroscopy, and currently relies on parametric processes that, while efficient, are also complex. Here we experimentally show a simple alternative that uses a single pump wavelength without any pump synchronization and without critical phase-matching requirements. Pumping a bulk quadratic nonlinear crystal (unpoled LiNbO(3) cut for noncritical phase-mismatched interaction) with sub-mJ near-IR 50-fs pulses, tunable and broadband (∼ 1,000 cm(-1)) mid-IR pulses around 3.0 μm are generated with excellent spatio-temporal pulse quality, having up to 10.5 μJ energy (6.3% conversion). The mid-IR pulses are dispersive waves phase-matched to near-IR self-defocusing solitons created by the induced self-defocusing cascaded nonlinearity. This process is filament-free and the input pulse energy can therefore be scaled arbitrarily by using large-aperture crystals. The technique can readily be implemented with other crystals and laser wavelengths, and can therefore potentially replace current ultrafast frequency-conversion processes to the mid-IR.

Direct Harmonic Linear Navier-Stokes Methods for Efficient Simulation of Wave Packets

NASA Technical Reports Server (NTRS)

Streett, C. L.

1998-01-01

Wave packets produced by localized disturbances play an important role in transition in three-dimensional boundary layers, such as that on a swept wing. Starting with the receptivity process, we show the effects of wave-space energy distribution on the development of packets and other three-dimensional disturbance patterns. Nonlinearity in the receptivity process is specifically addressed, including demonstration of an effect which can enhance receptivity of traveling crossflow disturbances. An efficient spatial numerical simulation method is allowing most of the simulations presented to be carried out on a workstation.

Rogue waves generation in a left-handed nonlinear transmission line with series varactor diodes

NASA Astrophysics Data System (ADS)

Onana Essama, B. G.; Atangana, J.; Biya Motto, F.; Mokhtari, B.; Cherkaoui Eddeqaqi, N.; Kofane, Timoleon C.

2014-07-01

We investigate the electromagnetic wave behavior and its characterization using collective variables technique. Second-order dispersion, first- and second-order nonlinearities, which strongly act in a left-handed nonlinear transmission line with series varactor diodes, are taken into account. Four frequency ranges have been found. The first one gives the so-called energetic soliton due to a perfect combination of second-order dispersion and first-order nonlinearity. The second frequency range presents a dispersive soliton leading to the collapse of the electromagnetic wave at the third frequency range. But the fourth one shows physical conditions which are able to provoke the appearance of wave trains generation with some particular waves, the rogue waves. Moreover, we demonstrate that the number of rogue waves increases with frequency. The soliton, thereafter, gains a relative stability when second-order nonlinearity comes into play with some specific values in the fourth frequency range. Furthermore, the stability conditions of the electromagnetic wave at high frequencies have been also discussed.

Spectro-spatial analysis of wave packet propagation in nonlinear acoustic metamaterials

NASA Astrophysics Data System (ADS)

Zhou, W. J.; Li, X. P.; Wang, Y. S.; Chen, W. Q.; Huang, G. L.

2018-01-01

The objective of this work is to analyze wave packet propagation in weakly nonlinear acoustic metamaterials and reveal the interior nonlinear wave mechanism through spectro-spatial analysis. The spectro-spatial analysis is based on full-scale transient analysis of the finite system, by which dispersion curves are generated from the transmitted waves and also verified by the perturbation method (the L-P method). We found that the spectro-spatial analysis can provide detailed information about the solitary wave in short-wavelength region which cannot be captured by the L-P method. It is also found that the optical wave modes in the nonlinear metamaterial are sensitive to the parameters of the nonlinear constitutive relation. Specifically, a significant frequency shift phenomenon is found in the middle-wavelength region of the optical wave branch, which makes this frequency region behave like a band gap for transient waves. This special frequency shift is then used to design a direction-biased waveguide device, and its efficiency is shown by numerical simulations.

Controllable rogue waves in the nonautonomous nonlinear system with a linear potential

NASA Astrophysics Data System (ADS)

Dai, C. Q.; Zheng, C. L.; Zhu, H. P.

2012-04-01

Based on the similarity transformation connected the nonautonomous nonlinear Schrödinger equation with the autonomous nonlinear Schrödinger equation, we firstly derive self-similar rogue wave solutions (rational solutions) for the nonautonomous nonlinear system with a linear potential. Then, we investigate the controllable behaviors of one-rogue wave, two-rogue wave and rogue wave triplets in a soliton control system. Our results demonstrate that the propagation behaviors of rogue waves, including postpone, sustainment, recurrence and annihilation, can be manipulated by choosing the relation between the maximum value of the effective propagation distance Z m and the parameter Z 0. Moreover, the excitation time of controllable rogue waves is decided by the parameter T 0.

Nonlinear fractional waves at elastic interfaces

NASA Astrophysics Data System (ADS)

Kappler, Julian; Shrivastava, Shamit; Schneider, Matthias F.; Netz, Roland R.

2017-11-01

We derive the nonlinear fractional surface wave equation that governs compression waves at an elastic interface that is coupled to a viscous bulk medium. The fractional character of the differential equation comes from the fact that the effective thickness of the bulk layer that is coupled to the interface is frequency dependent. The nonlinearity arises from the nonlinear dependence of the interface compressibility on the local compression, which is obtained from experimental measurements and reflects a phase transition at the interface. Numerical solutions of our nonlinear fractional theory reproduce several experimental key features of surface waves in phospholipid monolayers at the air-water interface without freely adjustable fitting parameters. In particular, the propagation distance of the surface wave abruptly increases at a threshold excitation amplitude. The wave velocity is found to be of the order of 40 cm/s in both experiments and theory and slightly increases as a function of the excitation amplitude. Nonlinear acoustic switching effects in membranes are thus shown to arise purely based on intrinsic membrane properties, namely, the presence of compressibility nonlinearities that accompany phase transitions at the interface.

Dissipation of ionospheric irregularities by wave-particle and collisional interactions

NASA Technical Reports Server (NTRS)

Bernhardt, P. A.; Pongratz, M. B.; Gray, S. P.; Thomsen, M. F.

1982-01-01

The nonlinear dissipation of plasma irregularities aligned parallel to an ambient magnetic field is studied numerically using a model which employs both wave-particle and collisional diffusion. A wave-particle diffusion coefficient derived from a local theory of the universal drift instability is used. This coefficient is effective in regions of nonzero plasma gradients and produces triangular-shaped irregularities with spectra which vary as f to the -4th, where f is the spatial frequency. Collisional diffusion acts rapidly on the vertices of the irregularities to reduce their amplitude. The simultaneous action of the two dissipative processes is more efficient than collisions acting alone. In this model, wave-particle diffusion mimics the forward cascade process of wave-wave coupling.

Optical measurement of the weak non-linearity in the eardrum vibration response to auditory stimuli

NASA Astrophysics Data System (ADS)

Aerts, Johan

The mammalian hearing organ consists of the external ear (auricle and ear canal) followed by the middle ear (eardrum and ossicles) and the inner ear (cochlea). Its function is to convert the incoming sound waves and convert them into nerve pulses which are processed in the final stage by the brain. The main task of the external and middle ear is to concentrate the incoming sound waves on a smaller surface to reduce the loss that would normally occur in transmission from air to inner ear fluid. In the past it has been shown that this is a linear process, thus without serious distortions, for sound waves going up to pressures of 130 dB SPL (˜90 Pa). However, at large pressure changes up to several kPa, the middle ear movement clearly shows non-linear behaviour. Thus, it is possible that some small non-linear distortions are also present in the middle ear vibration at lower sound pressures. In this thesis a sensitive measurement set-up is presented to detect this weak non-linear behaviour. Essentially, this set-up consists of a loud-speaker which excites the middle ear, and the resulting vibration is measured with an heterodyne vibrometer. The use of specially designed acoustic excitation signals (odd random phase multisines) enables the separation of the linear and non-linear response. The application of this technique on the middle ear demonstrates that there are already non-linear distortions present in the vibration of the middle ear at a sound pressure of 93 dB SPL. This non-linear component also grows strongly with increasing sound pressure. Knowledge of this non-linear component can contribute to the improvement of modern hearing aids, which operate at higher sound pressures where the non-linearities could distort the signal considerably. It is also important to know the contribution of middle ear non-linearity to otoacoustic emissions. This are non-linearities caused by the active feedback amplifier in the inner ear, and can be detected in the external and middle ear. These signals are used for diagnostic purposes, and therefore it is important to have an estimate the non-linear middle ear contribution to these emissions.

Two-dimensional solitary waves and periodic waves on coupled nonlinear electrical transmission lines

NASA Astrophysics Data System (ADS)

Wang, Heng; Zheng, Shuhua

2017-06-01

By using the dynamical system approach, the exact travelling wave solutions for a system of coupled nonlinear electrical transmission lines are studied. Based on this method, the bifurcations of phase portraits of a dynamical system are given. The two-dimensional solitary wave solutions and periodic wave solutions on coupled nonlinear transmission lines are obtained. With the aid of Maple, the numerical simulations are conducted for solitary wave solutions and periodic wave solutions to the model equation. The results presented in this paper improve upon previous studies.

Nonlinear low frequency (LF) waves - Comets and foreshock phenomena

NASA Technical Reports Server (NTRS)

Tsurutani, Bruce T.

1991-01-01

A review is conducted of LF wave nonlinear properties at comets and in the earth's foreshock, engaging such compelling questions as why there are no cometary cyclotron waves, the physical mechanism responsible for 'dispersive whiskers', and the character of a general description of linear waves. Attention is given to the nonlinear properties of LF waves, whose development is illustrated by examples of waves and their features at different distances from the comet, as well as by computer simulation results. Also discussed is a curious wave mode detected from Comet Giacobini-Zinner, both at and upstream of the bow shock/wave.

Asymmetry of wind waves studied in a laboratory tank

NASA Astrophysics Data System (ADS)

Ileykin, L. A.; Donelan, M. A.; Mellen, R. H.; McLaughlin, D. J.

1995-03-01

Asymmetry of wind waves was studied in laboratory tank tinder varied wind and fetch conditions using both bispectral analysis of wave records and third-order statistics of the surface elevation. It is found skewness S (the normalized third-order moment of surface elevation describing the horizontal asymmetry waves) varies only slightly with the inverse wave u*/Cm (where u* is the air friction velocity and Cm is phase speed of the dominant waves). At the same time asymmetry A, which is determined from the Hilbert transform of the wave record and characterizes the skewness of the rate of change of surface elevation, increase consistently in magnitude with the ratio u*/Cm. This suggests that nonlinear distortion of the wave profile determined by the degree of wind forcing and is a sensitive indicator of wind-wave interaction processes. It is shown that the asymmetric profile of waves can described within the frameworks of the nonlinear nonspectral concept (Plate, 1972; Lake and Yuen, 197 according to which the wind-wave field can be represented as a coherent bound-wave system consisting mainly of dominant component w. and its harmonics propagating with the same speed C. , as observed by Ramamonjiaris and Coantic (1976). The phase shift between o). harmonics is found and shown to increase with the asymmetry of the waves.

Asymmetry of wind waves studied in a laboratory tank

NASA Astrophysics Data System (ADS)

Leykin, I. A.; Donelan, M. A.; Mellen, R. H.; McLaughlin, D. J.

Asymmetry of wind waves was studied in laboratory tank tinder varied wind and fetch conditions using both bispectral analysis of wave records and third-order statistics of the surface elevation. It is found skewness S (the normalized third-order moment of surface elevation describing the horizontal asymmetry waves) varies only slightly with the inverse wave u*/Cm (where u* is the air friction velocity and Cm is phase speed of the dominant waves). At the same time asymmetry A, which is determined from the Hilbert transform of the wave record and characterizes the skewness of the rate of change of surface elevation, increase consistently in magnitude with the ratio u*/Cm. This suggests that nonlinear distortion of the wave profile determined by the degree of wind forcing and is a sensitive indicator of wind-wave interaction processes. It is shown that the asymmetric profile of waves can described within the frameworks of the nonlinear nonspectral concept (Plate, 1972; Lake and Yuen, 197 according to which the wind-wave field can be represented as a coherent bound-wave system consisting mainly of dominant component w. and its harmonics propagating with the same speed C. , as observed by Ramamonjiaris and Coantic (1976). The phase shift between o). harmonics is found and shown to increase with the asymmetry of the waves.

Laboratory modeling of edge wave generation over a plane beach by breaking waves

NASA Astrophysics Data System (ADS)

Abcha, Nizar; Ezersky, Alexander; Pelinovsky, Efim

2015-04-01

Edge waves play an important role in coastal hydrodynamics: in sediment transport, in formation of coastline structure and coastal bottom topography. Investigation of physical mechanisms leading to the edge waves generation allows us to determine their effect on the characteristics of spatially periodic patterns like crescent submarine bars and cusps observed in the coastal zone. In the present paper we investigate parametric excitation of edge wave with frequency two times less than the frequency of surface wave propagating perpendicular to the beach. Such mechanism of edge wave generation has been studied previously in a large number of papers using the assumption of non-breaking waves. This assumption was used in theoretical calculations and such conditions were created in laboratory experiments. In the natural conditions, the wave breaking is typical when edge waves are generated at sea beach. We study features of such processes in laboratory experiments. Experiments were performed in the wave flume of the Laboratory of Continental and Coast Morphodynamics (M2C), Caen. The flume is equipment with a wave maker controlled by computer. To model a plane beach, a PVC plate is placed at small angle to the horizontal bottom. Several resistive probes were used to measure characteristics of waves: one of them was used to measure free surface displacement near the wave maker and two probes were glued on the inclined plate. These probes allowed us to measure run-up due to parametrically excited edge waves. Run-up height is determined by processing a movie shot by high-speed camera. Sub-harmonic generation of standing edge waves is observed for definite control parameters: edge waves represent themselves a spatial mode with wavelength equal to double width of the flume; the frequency of edge wave is equal to half of surface wave frequency. Appearance of sub-harmonic mode instability is studied using probes and movie processing. The dependence of edge wave exponential growth rate index on the amplitude of surface wave is found. On the plane of parameters (amplitude - frequency) of surface wave we have found a region corresponding parametric instability leading to excitation of edge waves. It is shown that for small super criticalities, the amplitude of edge wave grows with amplitude of surface wave. For large amplitude of surface wave, wave breaking appears and parametric instability is suppressed. Such suppression of instability is caused by increasing of turbulent viscosity in near shore zone. It was shown that parametric excitation of edge wave can increase significantly (up to two times) the maximal run-up. Theoretical model is developed to explain suppression of instability due to turbulent viscosity. This theoretical model is based on nonlinear mode amplitude equation including terms responsible for parametric forcing, frequency detuning, nonlinear detuning, linear and nonlinear edge wave damping. Dependence of coefficients on turbulent viscosity is discussed.

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.

Mixing of ultrasonic Lamb waves in thin plates with quadratic nonlinearity.

PubMed

Li, Feilong; Zhao, Youxuan; Cao, Peng; Hu, Ning

2018-07-01

This paper investigates the propagation of Lamb waves in thin plates with quadratic nonlinearity by one-way mixing method using numerical simulations. It is shown that an A 0 -mode wave can be generated by a pair of S 0 and A 0 mode waves only when mixing condition is satisfied, and mixing wave signals are capable of locating the damage zone. Additionally, it is manifested that the acoustic nonlinear parameter increases linearly with quadratic nonlinearity but monotonously with the size of mixing zone. Furthermore, because of frequency deviation, the waveform of the mixing wave changes significantly from a regular diamond shape to toneburst trains. Copyright © 2018 Elsevier B.V. All rights reserved.

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.

The dissipation of electromagnetic waves in plasmas

NASA Astrophysics Data System (ADS)

Basov, N. G.

The present anthology includes articles concerning the experimental study of the interaction of high power electromagnetic waves with collisionless plasmas and with electrons. Among the topics covered are the nonlinear dissipation of electromagnetic waves in inhomogeneous collisionless plasmas, the collisionless absorption of electromagnetic waves in plasmas and 'slow' nonlinear phenomena, the nonlinear effects of electron plasma waves propagating in an inhomogeneous plasma layer, and secondary-emission microwave discharges having large electron transit angles.

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.

Achieving nonlinear optical modulation via four-wave mixing in a four-level atomic system

NASA Astrophysics Data System (ADS)

Li, Hai-Chao; Ge, Guo-Qin; Zubairy, M. Suhail

2018-05-01

We propose an accessible scheme for implementing tunable nonlinear optical amplification and attenuation via a synergetic mechanism of four-wave mixing (FWM) and optical interference in a four-level ladder-type atomic system. By constructing a cyclic atom-field interaction, we show that two reverse FWM processes can coexist via optical transitions in different branches. In the suitable input-field conditions, strong interference effects between the input fields and the generated FWM fields can be induced and result in large amplification and deep attenuation of the output fields. Moreover, such an optical modulation from enhancement to suppression can be controlled by tuning the relative phase. The quantum system can be served as a switchable optical modulator with potential applications in quantum nonlinear optics.

The Alfvénic nature of energy transfer mediation in localized, strongly nonlinear Alfvén wavepacket collisions

NASA Astrophysics Data System (ADS)

Verniero, J. L.; Howes, G. G.

2018-02-01

In space and astrophysical plasmas, violent events or instabilities inject energy into turbulent motions at large scales. Nonlinear interactions among the turbulent fluctuations drive a cascade of energy to small perpendicular scales at which the energy is ultimately converted into plasma heat. Previous work with the incompressible magnetohydrodynamic (MHD) equations has shown that this turbulent energy cascade is driven by the nonlinear interaction between counterpropagating Alfvén waves - also known as Alfvén wave collisions. Direct numerical simulations of weakly collisional plasma turbulence enables deeper insight into the nature of the nonlinear interactions underlying the turbulent cascade of energy. In this paper, we directly compare four cases: both periodic and localized Alfvén wave collisions in the weakly and strongly nonlinear limits. Our results reveal that in the more realistic case of localized Alfvén wave collisions (rather than the periodic case), all nonlinearly generated fluctuations are Alfvén waves, which mediates nonlinear energy transfer to smaller perpendicular scales.

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.

Laser-based linear and nonlinear guided elastic waves at surfaces (2D) and wedges (1D).

PubMed

Hess, Peter; Lomonosov, Alexey M; Mayer, Andreas P

2014-01-01

The characteristic features and applications of linear and nonlinear guided elastic waves propagating along surfaces (2D) and wedges (1D) are discussed. Laser-based excitation, detection, or contact-free analysis of these guided waves with pump-probe methods are reviewed. Determination of material parameters by broadband surface acoustic waves (SAWs) and other applications in nondestructive evaluation (NDE) are considered. The realization of nonlinear SAWs in the form of solitary waves and as shock waves, used for the determination of the fracture strength, is described. The unique properties of dispersion-free wedge waves (WWs) propagating along homogeneous wedges and of dispersive wedge waves observed in the presence of wedge modifications such as tip truncation or coatings are outlined. Theoretical and experimental results on nonlinear wedge waves in isotropic and anisotropic solids are presented. Copyright © 2013 Elsevier B.V. All rights reserved.

Nonlinear evolution of energetic-particles-driven waves in collisionless plasmas

NASA Astrophysics Data System (ADS)

Li, Shuhan; Liu, Jinyuan; Wang, Feng; Shen, Wei; Li, Dong

2018-06-01

A one-dimensional electrostatic collisionless particle-in-cell code has been developed to study the nonlinear interaction between electrostatic waves and energetic particles (EPs). For a single wave, the results are clear and agree well with the existing theories. For coexisting two waves, although the mode nonlinear coupling between two wave fields is ignored, the second-order phase space islands can still exist between first-order islands generated by the two waves. However, the second-order phase islands are not formed by the superposed wave fields and the perturbed motions of EPs induced by the combined effect of two main resonances make these structures in phase space. Owing to these second-order islands, energy can be transferred between waves, even if the overlap of two main resonances never occurs. Depending on the distance between the main resonance islands in velocity space, the second-order island can affect the nonlinear dynamics and saturations of waves.

Non-Reciprocal Geometric Wave Diode by Engineering Asymmetric Shapes of Nonlinear Materials

PubMed Central

Li, Nianbei; Ren, Jie

2014-01-01

Unidirectional nonreciprocal transport is at the heart of many fundamental problems and applications in both science and technology. Here we study the novel design of wave diode devices by engineering asymmetric shapes of nonlinear materials to realize the function of non-reciprocal wave propagations. We first show analytical results revealing that both nonlinearity and asymmetry are necessary to induce such non-reciprocal (asymmetric) wave propagations. Detailed numerical simulations are further performed for a more realistic geometric wave diode model with typical asymmetric shape, where good non-reciprocal wave diode effect is demonstrated. Finally, we discuss the scalability of geometric wave diodes. The results open a flexible way for designing wave diodes efficiently simply through shape engineering of nonlinear materials, which may find broad implications in controlling energy, mass and information transports. PMID:25169668

Extremely frequency-widened terahertz wave generation using Cherenkov-type radiation.

PubMed

Suizu, Koji; Koketsu, Kaoru; Shibuya, Takayuki; Tsutsui, Toshihiro; Akiba, Takuya; Kawase, Kodo

2009-04-13

Terahertz (THz) wave generation based on nonlinear frequency conversion is promising way for realizing a tunable monochromatic bright THz-wave source. Such a development of efficient and wide tunable THz-wave source depends on discovery of novel brilliant nonlinear crystal. Important factors of a nonlinear crystal for THz-wave generation are, 1. High nonlinearity and 2. Good transparency at THz frequency region. Unfortunately, many nonlinear crystals have strong absorption at THz frequency region. The fact limits efficient and wide tunable THz-wave generation. Here, we show that Cherenkov radiation with waveguide structure is an effective strategy for achieving efficient and extremely wide tunable THz-wave source. We fabricated MgO-doped lithium niobate slab waveguide with 3.8 microm of thickness and demonstrated difference frequency generation of THz-wave generation with Cherenkov phase matching. Extremely frequency-widened THz-wave generation, from 0.1 to 7.2 THz, without no structural dips successfully obtained. The tuning frequency range of waveguided Cherenkov radiation source was extremely widened compare to that of injection seeded-Terahertz Parametric Generator. The tuning range obtained in this work for THz-wave generation using lithium niobate crystal was the widest value in our knowledge. The highest THz-wave energy obtained was about 3.2 pJ, and the energy conversion efficiency was about 10(-5) %. The method can be easily applied for many conventional nonlinear crystals, results in realizing simple, reasonable, compact, high efficient and ultra broad band THz-wave sources.

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

DTIC Science & Technology

2009-01-01

attenuation and mass transport of a water -mud system due to a solitary wave on the free surface has been modeled by using the Chebyshev-Chebyshev...in Lagrangian coordinates and perturbation equations for shallow water waves were 3 derived. An iteration-by-subdomain technique was introduced to...found. Although the model is focused on solitary waves and Newtonian fluid-mud, the methodology can be extended to oscillatory, nonlinear water waves

Stationary Shock Waves with Oscillating Front in Dislocation Systems of Semiconductors

NASA Astrophysics Data System (ADS)

Gestrin, S. G.; Shchukina, E. V.

2018-05-01

The paper presents a study of weakly nonlinear wave processes in the cylindrical region of a hole gas surrounding a negatively charged dislocation in an n-type semiconductor crystal. It is shown that shock waves propagating along the dislocation are the solutions of the Korteweg-de Vries-Burgers equation when the dispersion and dissipation of medium are taken into account. Estimates are obtained for the basic physical parameters characterizing the shock wave and the region inside the Reed cylinder.

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.

Solitary wave for a nonintegrable discrete nonlinear Schrödinger equation in nonlinear optical waveguide arrays

NASA Astrophysics Data System (ADS)

Ma, Li-Yuan; Ji, Jia-Liang; Xu, Zong-Wei; Zhu, Zuo-Nong

2018-03-01

We study a nonintegrable discrete nonlinear Schrödinger (dNLS) equation with the term of nonlinear nearest-neighbor interaction occurred in nonlinear optical waveguide arrays. By using discrete Fourier transformation, we obtain numerical approximations of stationary and travelling solitary wave solutions of the nonintegrable dNLS equation. The analysis of stability of stationary solitary waves is performed. It is shown that the nonlinear nearest-neighbor interaction term has great influence on the form of solitary wave. The shape of solitary wave is important in the electric field propagating. If we neglect the nonlinear nearest-neighbor interaction term, much important information in the electric field propagating may be missed. Our numerical simulation also demonstrates the difference of chaos phenomenon between the nonintegrable dNLS equation with nonlinear nearest-neighbor interaction and another nonintegrable dNLS equation without the term. Project supported by the National Natural Science Foundation of China (Grant Nos. 11671255 and 11701510), the Ministry of Economy and Competitiveness of Spain (Grant No. MTM2016-80276-P (AEI/FEDER, EU)), and the China Postdoctoral Science Foundation (Grant No. 2017M621964).

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.

Wave-Kinetic Simulations of the Nonlinear Generation of Electromagnetic VLF Waves through Velocity Ring Instabilities

NASA Astrophysics Data System (ADS)

Ganguli, G.; Crabtree, C. E.; Rudakov, L.; Mithaiwala, M.

2014-12-01

Velocity ring instabilities are a common naturally occuring magnetospheric phenomenon that can also be generated by man made ionospheric experiments. These instabilities are known to generate lower-hybrid waves, which generally cannot propagte out of the source region. However, nonlinear wave physics can convert these linearly driven electrostatic lower-hybrid waves into electromagnetic waves that can escape the source region. These nonlinearly generated waves can be an important source of VLF turbulence that controls the trapped electron lifetime in the radiation belts. We develop numerical solutions to the wave-kinetic equation in a periodic box including the effects of nonlinear (NL) scattering (nonlinear Landau damping) of Lower-hybrid waves giving the evolution of the wave-spectra in wavenumber space. Simultaneously we solve the particle diffusion equation of both the background plasma particles and the ring ions, due to both linear and nonlinear Landau resonances. At initial times for cold ring ions, an electrostatic beam mode is excited, while the kinetic mode is stable. As the instability progresses the ring ions heat, the beam mode is stabilized, and the kinetic mode destabilizes. When the amplitude of the waves becomes sufficient the lower-hybrid waves are scattered (by either nearly unmagnetized ions or magnetized electrons) into electromagnetic magnetosonic waves [Ganguli et al 2010]. The effect of NL scattering is to limit the amplitude of the waves, slowing down the quasilinear relaxation time and ultimately allowing more energy from the ring to be liberated into waves [Mithaiwala et al. 2011]. The effects of convection out of the instability region are modeled, additionally limiting the amplitude of the waves, allowing further energy to be liberated from the ring [Scales et al., 2012]. Results are compared to recent 3D PIC simulations [Winske and Duaghton 2012].

Statistics for long irregular wave run-up on a plane beach from direct numerical simulations

NASA Astrophysics Data System (ADS)

Didenkulova, Ira; Senichev, Dmitry; Dutykh, Denys

2017-04-01

Very often for global and transoceanic events, due to the initial wave transformation, refraction, diffraction and multiple reflections from coastal topography and underwater bathymetry, the tsunami approaches the beach as a very long wave train, which can be considered as an irregular wave field. The prediction of possible flooding and properties of the water flow on the coast in this case should be done statistically taking into account the formation of extreme (rogue) tsunami wave on a beach. When it comes to tsunami run-up on a beach, the most used mathematical model is the nonlinear shallow water model. For a beach of constant slope, the nonlinear shallow water equations have rigorous analytical solution, which substantially simplifies the mathematical formulation. In (Didenkulova et al. 2011) we used this solution to study statistical characteristics of the vertical displacement of the moving shoreline and its horizontal velocity. The influence of the wave nonlinearity was approached by considering modifications of probability distribution of the moving shoreline and its horizontal velocity for waves of different amplitudes. It was shown that wave nonlinearity did not affect the probability distribution of the velocity of the moving shoreline, while the vertical displacement of the moving shoreline was affected substantially demonstrating the longer duration of coastal floods with an increase in the wave nonlinearity. However, this analysis did not take into account the actual transformation of irregular wave field offshore to oscillations of the moving shoreline on a slopping beach. In this study we would like to cover this gap by means of extensive numerical simulations. The modeling is performed in the framework of nonlinear shallow water equations, which are solved using a modern shock-capturing finite volume method. Although the shallow water model does not pursue the wave breaking and bore formation in a general sense (including the water surface overturning), it allows shock-wave formation and propagation with the speed given by Rankine-Hugoniot jump conditions, which to some extent approximates wave breaking. The scheme is second order accurate thanks to the UNO2 special reconstruction. It was described and validated in (Dutykh et al. 2011a) and has already been successfully used to simulate wave run-up on random beaches (Dutykh et al. 2011b). For simplicity the incident wave field offshore is taken Gaussian in the present study, however, this distribution can be easily changed in the numerical code. Similar to (Didenkulova et al. 2011), in order to study influence of wave nonlinearity during wave propagation to the coast we consider waves of different amplitudes and the corresponding modifications of statistics of the moving shoreline. We also consider wave fields with a different bandwidth, so that we can see the influence of the bandwidth of the incoming wave field on statistics of wave run-up on a beach. In order to validate the numerical results we use the available experimental data of irregular wave run-up on a beach (Denissenko et al. 2011; 2013). For this in our simulations we use the corresponding bathymetry set-up: the flat part of the flume with a water depth of 3.5 m is matched with the beach of constant slope 1:6. The significant wave heights Hs are chosen according to (Denissenko et al. 2013) and are equal to 0.1m, 0.2m, 0.3m, 0.4m and 0.5m, while the bandwidth is selected as 0.1, 0.4 and 0.8, which allows comparison of the behavior of wide-band and narrow-band wave fields on the beach. The characteristic wave period is 20s, as in (Denissenko et al. 2013) that provides long wave condition. All time records contain several weeks of simulations that provides significant amount of data for extreme value statistics. [1] P. Denissenko, I. Didenkulova, E. Pelinovsky, J. Pearson. Influence of the nonlinearity on statistical characteristics of long wave runup. Nonlinear Processes in Geophysics 18, 967-975 (2011). [2] P. Denissenko, I. Didenkulova, A. Rodin, M. Listak, E. Pelinovsky. Experimental statistics of long wave runup on a plane beach. Journal of Coastal Research 65, 195-200 (2013). [3] I. Didenkulova, E. Pelinovsky, A. Sergeeva. Statistical characteristics of long waves nearshore. Coastal Engineering 58, 94-102 (2011). [4] D. Dutykh, T. Katsaounis, D. Mitsotakis. Finite volume schemes for dispersive wave propagation and runup. J. Comput. Phys. 230 (8), 3035-3061 (2011a). [5] D. Dutykh, C. Labart, D. Mitsotakis. Long wave run-up on random beaches. Phys. Rev. Lett. 107, 184504 (2011b).

Directional nonlinear guided wave mixing: Case study of counter-propagating shear horizontal waves

NASA Astrophysics Data System (ADS)

Hasanian, Mostafa; Lissenden, Cliff J.

2018-04-01

While much nonlinear ultrasonics research has been conducted on higher harmonic generation, wave mixing provides the potential for sensitive measurements of incipient damage unencumbered by instrumentation nonlinearity. Studies of nonlinear ultrasonic wave mixing, both collinear and noncollinear, for bulk waves have shown the robust capability of wave mixing for early damage detection. One merit of bulk wave mixing lies in their non-dispersive nature, but guided waves enable inspection of otherwise inaccessible material and a variety of mixing options. Co-directional guided wave mixing was studied previously, but arbitrary direction guided wave mixing has not been addressed until recently. Wave vector analysis is applied to study variable mixing angles to find wave mode triplets (two primary waves and a secondary wave) resulting in the phase matching condition. As a case study, counter-propagating Shear Horizontal (SH) guided wave mixing is analyzed. SH wave interactions generate a secondary Lamb wave mode that is readily receivable. Reception of the secondary Lamb wave mode is compared for an angle beam transducer, an air coupled transducer, and a laser Doppler vibrometer (LDV). Results from the angle beam and air coupled transducers are quite consistent, while the LDV measurement is plagued by variability issues.

Ultrasound shear wave simulation based on nonlinear wave propagation and Wigner-Ville Distribution analysis

NASA Astrophysics Data System (ADS)

Bidari, Pooya Sobhe; Alirezaie, Javad; Tavakkoli, Jahan

2017-03-01

This paper presents a method for modeling and simulation of shear wave generation from a nonlinear Acoustic Radiation Force Impulse (ARFI) that is considered as a distributed force applied at the focal region of a HIFU transducer radiating in nonlinear regime. The shear wave propagation is simulated by solving the Navier's equation from the distributed nonlinear ARFI as the source of the shear wave. Then, the Wigner-Ville Distribution (WVD) as a time-frequency analysis method is used to detect the shear wave at different local points in the region of interest. The WVD results in an estimation of the shear wave time of arrival, its mean frequency and local attenuation which can be utilized to estimate medium's shear modulus and shear viscosity using the Voigt model.

Generation mechanisms of fundamental rogue wave spatial-temporal structure.

PubMed

Ling, Liming; Zhao, Li-Chen; Yang, Zhan-Ying; Guo, Boling

2017-08-01

We discuss the generation mechanism of fundamental rogue wave structures in N-component coupled systems, based on analytical solutions of the nonlinear Schrödinger equation and modulational instability analysis. Our analysis discloses that the pattern of a fundamental rogue wave is determined by the evolution energy and growth rate of the resonant perturbation that is responsible for forming the rogue wave. This finding allows one to predict the rogue wave pattern without the need to solve the N-component coupled nonlinear Schrödinger equation. Furthermore, our results show that N-component coupled nonlinear Schrödinger systems may possess N different fundamental rogue wave patterns at most. These results can be extended to evaluate the type and number of fundamental rogue wave structure in other coupled nonlinear systems.

Signatures of Nonlinear Waves in Coronal Plumes and Holes

NASA Technical Reports Server (NTRS)

Ofman, Leon

1999-01-01

In recent Ultraviolet Coronagraph Spectrometer/Solar and Heliospheric Observatory (UVCS/SOHO) White Light Channel (WLC) observations we found quasi-periodic variations in the polarized brightness (pB) in the polar coronal holes at heliocentric distances of 1.9-2.45 solar radii. The motivation for the observation is the 2.5D Magnetohydrodynamics (MHD) model of solar wind acceleration by nonlinear waves, that predicts compressive fluctuations in coronal holes. To help identify the waves observed with the UVCS/WLC we model the propagation and dissipation of slow magnetosonic waves in polar plumes using 1D MHD code in spherical geometry, We find that the slow waves nonlinearly steepen in the gravitationally stratified plumes. The nonlinear steepening of the waves leads to enhanced dissipation due to compressive viscosity at the wave-fronts.

Free-surface tracking of submerged features to infer hydrodynamic flow characteristics

NASA Astrophysics Data System (ADS)

Mandel, Tracy; Rosenzweig, Itay; Koseff, Jeffrey

2016-11-01

As sea level rise and stronger storm events threaten our coastlines, increased attention has been focused on coastal vegetation as a potentially resilient, financially viable tool to mitigate flooding and erosion. However, the actual effect of this "green infrastructure" on near-shore wave fields and flow patterns is not fully understood. For example, how do wave setup, wave nonlinearity, and canopy-generated instabilities change due to complex bottom roughness? Answering this question requires detailed knowledge of the free surface. We develop easy-to-use laboratory techniques to remotely measure physical processes by imaging the apparent distortion of the fixed features of a submerged cylinder array. Measurements of surface turbulence from a canopy-generated Kelvin-Helmholtz instability are possible with a single camera. A stereoscopic approach similar to Morris (2004) and Gomit et al. (2013) allows for measurement of waveform evolution and the effect of vegetation on wave steepness and nonlinearity.

MJO: Asymptotically-Nondivergent Nonlinear Wave?: A Review

NASA Astrophysics Data System (ADS)

Yano, J. I.

2014-12-01

MJO is often considered a convectively-coupled wave. The present talk is going to argue that it is best understood primarily as a nonlinear solitary wave dominated by vorticity. Role of convection is secondary,though likely catalytic. According to Charney's (1963) scale analysis, the large-scale tropical circulations are nondivergent to the leading order, i.e., dominated by rotational flows. Yano et al (2009) demonstrate indeed that is the case for a period dominated by three MJO events. The scale analysis of Yano and Bonazzola (2009, JAS) demonstrates such an asymptotically nondivergent regime is a viable alternative to the traditionally-believed equatorial-wave regime. Wedi and Smolarkiewicz (2010, JAS) in turn, show by numerical computations of a dry system that a MJO-like oscillation for a similar period can indeed be generated by free solitary nonlinear equatorial Rossby-wave dynamicswithout any convective forcing to a system. Unfortunately, this perspective is slow to be accepted with people's mind so much fixed on the role of convection. This situation may be compared to a slow historical process of acceptance of Eady and Charney's baroclinicinstability simply because it does not invoke any convection Ironically, once the nonlinear free-wave view for MJO is accepted, interpretations can more easily be developed for a recent series of numerical model experiments under a global channel configuration overthe tropics with a high-resolution of 5-50 km with or without convection parameterization. All those experiments tend to reproduce observed large-scale circulations associated with MJO rather well, though most of time, they fail to reproduce convective coherency associated with MJO.These large-scale circulations appear to be generated by lateral forcing imposed at the latitudinal walls. These lateral boundaries are reasonably far enough (30NS) to induce any direct influence to the tropics. There is no linear dry equatorial wave that supports this period either. In Wedi and Smolarkiewicz's analysis, such a lateral forcing is essential in order to obtain their nonlinear solitary wave solution. Thus is the leading-order solution for MJO in the same sense as the linear baroclinic instability is a leading-order solution to the midlatitude synoptic-scale storm.

Higher-order rogue wave-like solutions for a nonautonomous nonlinear Schrödinger equation with external potentials

NASA Astrophysics Data System (ADS)

Liu, Lei; Tian, Bo; Wu, Xiao-Yu; Sun, Yan

2018-02-01

Under investigation in this paper is the higher-order rogue wave-like solutions for a nonautonomous nonlinear Schrödinger equation with external potentials which can be applied in the nonlinear optics, hydrodynamics, plasma physics and Bose-Einstein condensation. Based on the Kadomtsev-Petviashvili hierarchy reduction, we construct the Nth order rogue wave-like solutions in terms of the Gramian under the integrable constraint. With the help of the analytic and graphic analysis, we exhibit the first-, second- and third-order rogue wave-like solutions through the different dispersion, nonlinearity and linear potential coefficients. We find that only if the dispersion and nonlinearity coefficients are proportional to each other, heights of the background of those rogue waves maintain unchanged with time increasing. Due to the existence of complex parameters, such nonautonomous rogue waves in the higher-order cases have more complex features than those in the lower.

Measurement of attenuation coefficients of the fundamental and second harmonic waves in water

NASA Astrophysics Data System (ADS)

Zhang, Shuzeng; Jeong, Hyunjo; Cho, Sungjong; Li, Xiongbing

2016-02-01

Attenuation corrections in nonlinear acoustics play an important role in the study of nonlinear fluids, biomedical imaging, or solid material characterization. The measurement of attenuation coefficients in a nonlinear regime is not easy because they depend on the source pressure and requires accurate diffraction corrections. In this work, the attenuation coefficients of the fundamental and second harmonic waves which come from the absorption of water are measured in nonlinear ultrasonic experiments. Based on the quasilinear theory of the KZK equation, the nonlinear sound field equations are derived and the diffraction correction terms are extracted. The measured sound pressure amplitudes are adjusted first for diffraction corrections in order to reduce the impact on the measurement of attenuation coefficients from diffractions. The attenuation coefficients of the fundamental and second harmonics are calculated precisely from a nonlinear least squares curve-fitting process of the experiment data. The results show that attenuation coefficients in a nonlinear condition depend on both frequency and source pressure, which are much different from a linear regime. In a relatively lower drive pressure, the attenuation coefficients increase linearly with frequency. However, they present the characteristic of nonlinear growth in a high drive pressure. As the diffraction corrections are obtained based on the quasilinear theory, it is important to use an appropriate source pressure for accurate attenuation measurements.

Emergent rogue wave structures and statistics in spontaneous modulation instability

PubMed Central

Toenger, Shanti; Godin, Thomas; Billet, Cyril; Dias, Frédéric; Erkintalo, Miro; Genty, Goëry; Dudley, John M.

2015-01-01

The nonlinear Schrödinger equation (NLSE) is a seminal equation of nonlinear physics describing wave packet evolution in weakly-nonlinear dispersive media. The NLSE is especially important in understanding how high amplitude “rogue waves” emerge from noise through the process of modulation instability (MI) whereby a perturbation on an initial plane wave can evolve into strongly-localised “breather” or “soliton on finite background (SFB)” structures. Although there has been much study of such structures excited under controlled conditions, there remains the open question of how closely the analytic solutions of the NLSE actually model localised structures emerging in noise-seeded MI. We address this question here using numerical simulations to compare the properties of a large ensemble of emergent peaks in noise-seeded MI with the known analytic solutions of the NLSE. Our results show that both elementary breather and higher-order SFB structures are observed in chaotic MI, with the characteristics of the noise-induced peaks clustering closely around analytic NLSE predictions. A significant conclusion of our work is to suggest that the widely-held view that the Peregrine soliton forms a rogue wave prototype must be revisited. Rather, we confirm earlier suggestions that NLSE rogue waves are most appropriately identified as collisions between elementary SFB solutions. PMID:25993126

Shapes, spectra and new methods in nonlinear spatial optics

NASA Astrophysics Data System (ADS)

Sun, Can

For a myriad of optical applications, the quality of the light source is poor and the beam is inherently spatially partially-coherent. For this broad class of systems, wave dynamics depends not only on the wave intensity, but also on its distribution of spatial frequencies. Unfortunately, this entire spectrum of problems has often been overlooked - for reasons of theoretical ease or experimental difficulties. Here, we remedy this by demonstrating a novel experimental setup which, for the first time, allows arbitrarily modulation of the spatial spectra of light to obtain any distribution of interest. Using modulation instability as an example, we isolate the effect of different spectral shapes and observe distinct beam dynamics. Next, we turn to a thermodynamic description of the long-term evolution of statistical fields. For quantum systems, a major consequence is Bose-Einstein Condensation. However, recent theoretical studies have suggested that quantum mechanics is not necessary for the condensation process: classical waves with random phases can also self-organize into a coherent state. Starting from a random ensemble, nonlinear interactions can lead to a turbulent energy cascade towards longer spatial scales. In complete analogy with the kinetics of a gas system, there is a statistical dynamics of waves in which particle velocities map to wavepacket k-vectors while collisions are mimicked by four-wave mixing. As with collisions, each wave interaction is formally reversible, yet entropy principles mandate that the ensemble evolves towards an equilibrium state of maximum disorder. The result is an equipartition of energy, in the form of a Rayleigh-Jeans spectrum, with information about the condensation process recorded in small-scale fluctuations. Here, we give the first experimental observation of the condensation of classical waves in any media. Using classical light in a self-defocusing photorefractive, we observe all aspects of the condensation process, including the population of a coherent state, spectral redistribution towards the Rayleigh-Jeans spectrum, and formal reversibility of the interactions. The latter is proved experimentally by introducing a digital "Maxwell's Demon" to reverse (phase-conjugate) the momentum of each wavepacket and recover the original "thermal cloud". The results integrate digital and physical methods of nonlinear processing, confirm fundamental ideas in wave turbulence, and greatly extend the range of Bose-Einstein theory.

Multi-fluid Approach to High-frequency Waves in Plasmas. III. Nonlinear Regime and Plasma Heating

NASA Astrophysics Data System (ADS)

Martínez-Gómez, David; Soler, Roberto; Terradas, Jaume

2018-03-01

The multi-fluid modeling of high-frequency waves in partially ionized plasmas has shown that the behavior of magnetohydrodynamic waves in the linear regime is heavily influenced by the collisional interaction between the different species that form the plasma. Here, we go beyond linear theory and study large-amplitude waves in partially ionized plasmas using a nonlinear multi-fluid code. It is known that in fully ionized plasmas, nonlinear Alfvén waves generate density and pressure perturbations. Those nonlinear effects are more pronounced for standing oscillations than for propagating waves. By means of numerical simulations and analytical approximations, we examine how the collisional interaction between ions and neutrals affects the nonlinear evolution. The friction due to collisions dissipates a fraction of the wave energy, which is transformed into heat and consequently raises the temperature of the plasma. As an application, we investigate frictional heating in a plasma with physical conditions akin to those in a quiescent solar prominence.

Wave excitation by nonlinear coupling among shear Alfvén waves in a mirror-confined plasma

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

Ikezoe, R., E-mail: ikezoe@prc.tsukuba.ac.jp; Ichimura, M.; Okada, T.

2015-09-15

A shear Alfvén wave at slightly below the ion-cyclotron frequency overcomes the ion-cyclotron damping and grows because of the strong anisotropy of the ion temperature in the magnetic mirror configuration, and is called the Alfvén ion-cyclotron (AIC) wave. Density fluctuations caused by the AIC waves and the ion-cyclotron range of frequencies (ICRF) waves used for ion heating have been detected using a reflectometer in a wide radial region of the GAMMA 10 tandem mirror plasma. Various wave-wave couplings are clearly observed in the density fluctuations in the interior of the plasma, but these couplings are not so clear in themore » magnetic fluctuations at the plasma edge when measured using a pick-up coil. A radial dependence of the nonlinearity is found, particularly in waves with the difference frequencies of the AIC waves; bispectral analysis shows that such wave-wave coupling is significant near the core, but is not so evident at the periphery. In contrast, nonlinear coupling with the low-frequency background turbulence is quite distinct at the periphery. Nonlinear coupling associated with the AIC waves may play a significant role in the beta- and anisotropy-limits of a mirror-confined plasma through decay of the ICRF heating power and degradation of the plasma confinement by nonlinearly generated waves.« less

Transverse effects in nonlinear optics: Toward the photon superfluid

NASA Astrophysics Data System (ADS)

McCormick, Colin Fraser

Nonlinear optics displays a wealth of transverse effects. These effects are particularly rich in the presence of an optical cavity. Many considerations suggest that in a Kerr nonlinear cavity a new state of light known as a "photon superfluid" can form, with strong analogies to atomic superfluids. The conditions for the formation of the photon superfluid include requirements on the cavity, input light fields and the nonlinear medium as well as various timescales. The most favorable candidate nonlinear medium for observing the photon super-fluid is an atomic vapor. With a strong and fast Kerr effect, atomic vapors also have the advantage of a Kerr coefficient that is tunable in both magnitude and sign. A series of z-scan experiments in far-detuned atomic rubidium vapor is reported, measuring the Kerr coefficient and determining its functional dependence on detuning to be that of a Doppler-broadened two-level model with adiabatic following of the electric field by the atom pseudomoment. Saturation effects are found to be important. Z-scan measurements for detunings within the Doppler profile are shown to agree well with numerical simulations based on the Doppler-broadened model. Agreement between absorptive and refractive non-linear coefficients is evidence of the Kramers-Kronig relations at work, even in this nonlinear system. The formation of the photon superfluid is discussed and the calculation of a new process, nearly collinear four-wave mixing, is presented. This process is essentially an inverse beam filamentation that is likely to be the underlying physical mechanism for transverse cooling and condensation of photons in a nonlinear optical cavity. Nearly collinear four-wave mixing may also be related to phenomena in general nonlinear physics, including modulation instability and Fermi-Pasta-Ulam recurrence.

Resonant Triad in Boundary-Layer Stability. Part 2; Composite Solution and Comparison with Observations

NASA Technical Reports Server (NTRS)

Mankbadi, Reda R.

1991-01-01

Here, numerical results are computed from an asymptotic near-resonance triad analysis. The analysis considers a resonant triad of instability waves consisting of a plane fundamental wave and a pair of symmetrical oblique subharmonic waves. The relevant scaling ensures that nonlinearity is confined to a distinct critical layer. The analysis is first used to form a composite solution that accounts for both the flow divergence and nonlinear effects. It is shown that the backreaction on the plane Tollmien Schlichting (TS) fundamental wave, although fully accounted for, is of little significance. The observed enhancement at the fundamental frequency disturbance is not in the plane TS wave, but is caused by nonlinearly generated waves at the fundamental frequency that result from nonlinear interactions in the critical layer. The saturation of the oblique waves is caused by their self-interaction. The nonlinear phase-locking phenomenon, the location of resonance with respect to the neutral stability curve, low frequency effects, detuning in the streamwise wave numbers, and nonlinear distortion of the mode shapes are discussed. Nonlinearity modifies the initially two dimensional Blasius profile into a fuller one with spanwise periodicity. The interactions at a wide range of unstable spanwise wave numbers are considered, and the existence of a preferred spanwise wave number is explained by means of the vorticity distribution in the critical layer. Besides presenting novel features of the phenomena and explaining the delicate mechanisms of the interactions, the results of the theory are in excellent agreement with experimental and numerical observations for all stages of the development and for various input parameters.

Nonlinear Wave Process Hierarchies and the Cyclic Development of Quasi-Ordered Structures in Turbulent Shear Flows.

DTIC Science & Technology

1979-11-01

can be evaluated semi- analitically in both the strongly nonlinear inner (critical layer) region and the weakly nonlinear outer region, reproduce the...experimental evidence of Ref. 8 (Figure 3, stage 3). Whereas the exact s~lutions of the Schridinger equation (Ref. 13) predict that an arbitrary smooth...peaks and valleys, different from the comon rate predicted by linear theory) arise suddenly and at surpris- ingly low disturbance levels [(u’/U 10-2] as

Concatenons as the solutions for non-linear partial differential equations

NASA Astrophysics Data System (ADS)

Kudryashov, N. A.; Volkov, A. K.

2017-07-01

New class of solutions for nonlinear partial differential equations is introduced. We call them the concaten solutions. As an example we consider equations for the description of wave processes in the Fermi-Pasta-Ulam mass chain and construct the concatenon solutions for these equation. Stability of the concatenon-type solutions is investigated numerically. Interaction between the concatenon and solitons is discussed.

Theory of ITG turbulent saturation in stellarators: identifying mechanisms to reduce turbulent transport

DOE PAGES

Hegna, Chris C.; Terry, Paul W.; Faber, Ben J.

2018-02-01

A three-field fluid model that allows for general three-dimensional equilibrium geometry is developed to describe ion temperature gradient turbulent saturation processes in stellarators. The theory relies on the paradigm of nonlinear transfer of energy from unstable to damped modes at comparable wavelength as the dominant saturation mechanism. The unstable-to-damped mode interaction is enabled by a third mode that for dominant energy transfer channels primarily serves as a regulator of the nonlinear energy transfer rate. The identity of the third wave in the interaction defines different scenarios for turbulent saturation with the dominant scenario depending upon the properties of the 3Dmore » geometry. The nonlinear energy transfer physics is quantified by the product of a turbulent correlation lifetime and a geometric coupling coefficient. The turbulent correlation time is determined by a three-wave frequency mismatch, which at long wavelength can be calculated from the sum of the linear eigenfrequencies of the three modes. Larger turbulent correlation times denote larger levels of nonlinear energy transfer and hence smaller turbulent transport. The theory provides an analytic prediction for how 3D shaping can be tuned to lower turbulent transport through saturation processes.« less

Theory of ITG turbulent saturation in stellarators: identifying mechanisms to reduce turbulent transport

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

Hegna, Chris C.; Terry, Paul W.; Faber, Ben J.

A three-field fluid model that allows for general three-dimensional equilibrium geometry is developed to describe ion temperature gradient turbulent saturation processes in stellarators. The theory relies on the paradigm of nonlinear transfer of energy from unstable to damped modes at comparable wavelength as the dominant saturation mechanism. The unstable-to-damped mode interaction is enabled by a third mode that for dominant energy transfer channels primarily serves as a regulator of the nonlinear energy transfer rate. The identity of the third wave in the interaction defines different scenarios for turbulent saturation with the dominant scenario depending upon the properties of the 3Dmore » geometry. The nonlinear energy transfer physics is quantified by the product of a turbulent correlation lifetime and a geometric coupling coefficient. The turbulent correlation time is determined by a three-wave frequency mismatch, which at long wavelength can be calculated from the sum of the linear eigenfrequencies of the three modes. Larger turbulent correlation times denote larger levels of nonlinear energy transfer and hence smaller turbulent transport. The theory provides an analytic prediction for how 3D shaping can be tuned to lower turbulent transport through saturation processes.« less

Nonlinear ship waves and computational fluid dynamics

PubMed Central

MIYATA, Hideaki; ORIHARA, Hideo; SATO, Yohei

2014-01-01

Research works undertaken in the first author’s laboratory at the University of Tokyo over the past 30 years are highlighted. Finding of the occurrence of nonlinear waves (named Free-Surface Shock Waves) in the vicinity of a ship advancing at constant speed provided the start-line for the progress of innovative technologies in the ship hull-form design. Based on these findings, a multitude of the Computational Fluid Dynamic (CFD) techniques have been developed over this period, and are highlighted in this paper. The TUMMAC code has been developed for wave problems, based on a rectangular grid system, while the WISDAM code treats both wave and viscous flow problems in the framework of a boundary-fitted grid system. These two techniques are able to cope with almost all fluid dynamical problems relating to ships, including the resistance, ship’s motion and ride-comfort issues. Consequently, the two codes have contributed significantly to the progress in the technology of ship design, and now form an integral part of the ship-designing process. PMID:25311139

Omnidirectional spin-wave nanograting coupler

PubMed Central

Yu, Haiming; Duerr, G.; Huber, R.; Bahr, M.; Schwarze, T.; Brandl, F.; Grundler, D.

2013-01-01

Magnonics as an emerging nanotechnology offers functionalities beyond current semiconductor technology. Spin waves used in cellular nonlinear networks are expected to speed up technologically, demanding tasks such as image processing and speech recognition at low power consumption. However, efficient coupling to microelectronics poses a vital challenge. Previously developed techniques for spin-wave excitation (for example, by using parametric pumping in a cavity) may not allow for the relevant downscaling or provide only individual point-like sources. Here we demonstrate that a grating coupler of periodically nanostructured magnets provokes multidirectional emission of short-wavelength spin waves with giantly enhanced amplitude compared with a bare microwave antenna. Exploring the dependence on ferromagnetic materials, lattice constants and the applied magnetic field, we find the magnonic grating coupler to be more versatile compared with gratings in photonics and plasmonics. Our results allow one to convert, in particular, straight microwave antennas into omnidirectional emitters for short-wavelength spin waves, which are key to cellular nonlinear networks and integrated magnonics. PMID:24189978

Global Simulation of Electromagnetic Ion Cyclotron Waves

NASA Technical Reports Server (NTRS)

Khazanov, George V.; Gallagher, D. L.; Kozyra, J. U.

2007-01-01

It is very well known that the effects of electromagnetic ion cyclotron (EMIC) waves on ring current (RC) ion and radiation belt (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. The consequence is that accurate modeling of EMIC waves and RC particles requires robust inclusion of the interdependent dynamics of wave growth/damping, wave propagation, and particles. Such a self-consistent model is being progressively developed by Khazanov et al. This model is based on a system of coupled kinetic equations for the RC and EMIC wave power spectral density along with the ray tracing equations. We will discuss the recent progress in understanding EMIC waves formation mechanisms in the inner magnetosphere. This problem remains unsettled in spite of many years of experimental and theoretical studies. Modern satellite observations by CRRES, Polar and Cluster still do not reveal the whole picture experimentally since they do not stay long enough in the generation region to give a full account of all the spatio-temporal structure of EMIC waves. The complete self-consistent theory taking into account all factors significant for EMIC waves generation remains to be developed. Several mechanisms are discussed with respect to formation of EMIC waves, among them are nonlinear modification of the ionospheric reflection by precipitating energetic protons, modulation of ion-cyclotron instability by long-period (Pc3/4) pulsations, reflection of waves from layers of heavy-ion gyroresonances, and nonlinearities of wave generation process. We show that each of these mechanisms have their attractive features and explains certain part experimental data but any of them, if taken alone, meets some difficulties when compared to observations. We conclude that development of a refined nonlinear theory and further correlated analysis of modern satellite and ground-based data is needed to solve this very intriguing problem.

Global Simulation of Electromagnetic Ion Cyclotron Waves

NASA Technical Reports Server (NTRS)

Khazanov, G. V.; Gamayunov, K.; Gallagher, D. L.; Kozyra, J. U.

2007-01-01

It is well known that the effects of electromagnetic ion cyclotron (EMIC) waves on ring current (RC) ion and radiation belt (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. The consequence is that accurate modeling of EMIC waves and RC particles requires robust inclusion of the interdependent dynamics of wave growth/damping, wave propagation, and particles. Such a self-consistent model is being progressively developed by Khazanov et al. [2002 - 2007]. This model is based on a system of coupled kinetic equations for the RC and EMIC wave power spectral density along with the ray tracing equations. We will discuss the recent progress in understanding EMIC waves formation mechanisms in the inner magnetosphere. This problem remains unsettled in spite of many years of experimental and theoretical studies. Modern satellite observations by CRRES, Polar and Cluster still do not reveal the whole picture experimentally since they do not stay long enough in the generation region to give a full account of all the spatio-temporal structure of EMIC waves. The complete self-consistent theory taking into account all factors significant for EMIC waves generation remains to be developed. Several mechanisms are discussed with respect to formation of EMIC waves, among them are nonlinear modification of the ionospheric reflection by precipitating energetic protons, modulation of ion-cyclotron instability by long-period (Pc3/4) pulsations, reflection of waves from layers of heavy-ion gyroresonances, and nonlinearities of wave generation process. We show that each of these mechanisms have their attractive features and explains certain part experimental data but any of them, if taken alone, meets some difficulties when compared to observations. We conclude that development of a refined nonlinear theory and further correlated analysis of modern satellite and ground-based data is needed to solve this very intriguing problem.

Non-linear Frequency Shifts, Mode Couplings, and Decay Instability of Plasma Waves

NASA Astrophysics Data System (ADS)

Affolter, Mathew; Anderegg, F.; Driscoll, C. F.; Valentini, F.

2015-11-01

We present experiments and theory for non-linear plasma wave decay to longer wavelengths, in both the oscillatory coupling and exponential decay regimes. The experiments are conducted on non-neutral plasmas in cylindrical Penning-Malmberg traps, θ-symmetric standing plasma waves have near acoustic dispersion ω (kz) ~kz - αkz2 , discretized by kz =mz (π /Lp) . Large amplitude waves exhibit non-linear frequency shifts δf / f ~A2 and Fourier harmonic content, both of which are increased as the plasma dispersion is reduced. Non-linear coupling rates are measured between large amplitude mz = 2 waves and small amplitude mz = 1 waves, which have a small detuning Δω = 2ω1 -ω2 . At small excitation amplitudes, this detuning causes the mz = 1 mode amplitude to ``bounce'' at rate Δω , with amplitude excursions ΔA1 ~ δn2 /n0 consistent with cold fluid theory and Vlasov simulations. At larger excitation amplitudes, where the non-linear coupling exceeds the dispersion, phase-locked exponential growth of the mz = 1 mode is observed, in qualitative agreement with simple 3-wave instability theory. However, significant variations are observed experimentally, and N-wave theory gives stunningly divergent predictions that depend sensitively on the dispersion-moderated harmonic content. Measurements on higher temperature Langmuir waves and the unusual ``EAW'' (KEEN) waves are being conducted to investigate the effects of wave-particle kinetics on the non-linear coupling rates. Department of Energy Grants DE-SC0002451and DE-SC0008693.

Nonlinear dynamics of global atmospheric and Earth system processes

NASA Technical Reports Server (NTRS)

Saltzman, Barry

1993-01-01

During the past eight years, we have been engaged in a NASA-supported program of research aimed at establishing the connection between satellite signatures of the earth's environmental state and the nonlinear dynamics of the global weather and climate system. Thirty-five publications and four theses have resulted from this work, which included contributions in five main areas of study: (1) cloud and latent heat processes in finite-amplitude baroclinic waves; (2) application of satellite radiation data in global weather analysis; (3) studies of planetary waves and low-frequency weather variability; (4) GCM studies of the atmospheric response to variable boundary conditions measurable from satellites; and (5) dynamics of long-term earth system changes. Significant accomplishments from the three main lines of investigation pursued during the past year are presented and include the following: (1) planetary atmospheric waves and low frequency variability; (2) GCM studies of the atmospheric response to changed boundary conditions; and (3) dynamics of long-term changes in the global earth system.

Parabolic equation for nonlinear acoustic wave propagation in inhomogeneous moving media

NASA Astrophysics Data System (ADS)

Aver'yanov, M. V.; Khokhlova, V. A.; Sapozhnikov, O. A.; Blanc-Benon, Ph.; Cleveland, R. O.

2006-12-01

A new parabolic equation is derived to describe the propagation of nonlinear sound waves in inhomogeneous moving media. The equation accounts for diffraction, nonlinearity, absorption, scalar inhomogeneities (density and sound speed), and vectorial inhomogeneities (flow). A numerical algorithm employed earlier to solve the KZK equation is adapted to this more general case. A two-dimensional version of the algorithm is used to investigate the propagation of nonlinear periodic waves in media with random inhomogeneities. For the case of scalar inhomogeneities, including the case of a flow parallel to the wave propagation direction, a complex acoustic field structure with multiple caustics is obtained. Inclusion of the transverse component of vectorial random inhomogeneities has little effect on the acoustic field. However, when a uniform transverse flow is present, the field structure is shifted without changing its morphology. The impact of nonlinearity is twofold: it produces strong shock waves in focal regions, while, outside the caustics, it produces higher harmonics without any shocks. When the intensity is averaged across the beam propagating through a random medium, it evolves similarly to the intensity of a plane nonlinear wave, indicating that the transverse redistribution of acoustic energy gives no considerable contribution to nonlinear absorption.

Study on acceleration processes of the radiation belt electrons through interaction with sub-packet chorus waves in parallel propagation

NASA Astrophysics Data System (ADS)

Hiraga, R.; Omura, Y.

2017-12-01

By recent observations, chorus waves include fine structures such as amplitude fluctuations (i.e. sub-packet structure), and it has not been verified in detail yet how energetic electrons are efficiently accelerated under the wave features. In this study, we firstly focus on the acceleration process of a single electron: how it experiences the efficient energy increase by interaction with sub-packet chorus waves in parallel propagation along the Earth's magnetic field. In order to reproduce the chorus waves as seen by the latest observations by Van Allen Probes (Foster et al. 2017), the wave model amplitude in our simulation is structured such that when the wave amplitude nonlinearly grows to reach the optimum amplitude, it starts decreasing until crossing the threshold. Once it crosses the threshold, the wave dissipates and a new wave rises to repeat the nonlinear growth and damping in the same manner. The multiple occurrence of this growth-damping cycle forms a saw tooth-like amplitude variation called sub-packet. This amplitude variation also affects the wave frequency behavior which is derived by the chorus wave equations as a function of the wave amplitude (Omura et al. 2009). It is also reasonable to assume that when a wave packet diminishes and the next wave rises, it has a random phase independent of the previous wave. This randomness (discontinuity) in phase variation is included in the simulation. Through interaction with such waves, dynamics of energetic electrons were tracked. As a result, some electrons underwent an efficient acceleration process defined as successive entrapping, in which an electron successfully continues to surf the trapping potential generated by consecutive wave packets. When successive entrapping occurs, an electron trapped and de-trapped (escape the trapping potential) by a single wave packet falls into another trapping potential generated by the next wave sub-packet and continuously accelerated. The occurrence of successive entrapping is influenced by some factors such as the magnitude of wave amplitude or inhomogeneity of the Earth's dipole magnetic field. In addition, an energy range of electrons is also a major factor. In this way, it has been examined in detail how and under which conditions electrons are efficiently accelerated in the formation process of the radiation belts.

Mid-IR femtosecond frequency conversion by soliton-probe collision in phase-mismatched quadratic nonlinear crystals.

PubMed

Liu, Xing; Zhou, Binbin; Guo, Hairun; Bache, Morten

2015-08-15

We show numerically that ultrashort self-defocusing temporal solitons colliding with a weak pulsed probe in the near-IR can convert the probe to the mid-IR. A near-perfect conversion efficiency is possible for a high effective soliton order. The near-IR self-defocusing soliton can form in a quadratic nonlinear crystal (beta-barium borate) in the normal dispersion regime due to cascaded (phase-mismatched) second-harmonic generation, and the mid-IR converted wave is formed in the anomalous dispersion regime between λ=2.2-2.4  μm as a resonant dispersive wave. This process relies on nondegenerate four-wave mixing mediated by an effective negative cross-phase modulation term caused by cascaded soliton-probe sum-frequency generation.

All-optical simultaneous multichannel quadrature phase shift keying signal regeneration based on phase-sensitive amplification

NASA Astrophysics Data System (ADS)

Wang, Hongxiang; Wang, Qi; Bai, Lin; Ji, Yuefeng

2018-01-01

A scheme is proposed to realize the all-optical phase regeneration of four-channel quadrature phase shift keying (QPSK) signal based on phase-sensitive amplification. By utilizing conjugate pump and common pump in a highly nonlinear optical fiber, degenerate four-wave mixing process is observed, and QPSK signals are regenerated. The number of waves is reduced to decrease the cross talk caused by undesired nonlinear interaction during the coherent superposition process. In addition, to avoid the effect of overlapping frequency, frequency spans between pumps and signals are set to be nonintegral multiples. Optical signal-to-noise ratio improvement is validated by bit error rate measurements. Compared with single-channel regeneration, multichannel regeneration brings 0.4-dB OSNR penalty when the value of BER is 10-3, which shows the cross talk in regeneration process is negligible.

Interactions of localized wave structures and dynamics in the defocusing coupled nonlinear Schrödinger equations.

PubMed

Zhang, Guoqiang; Yan, Zhenya; Wen, Xiao-Yong; Chen, Yong

2017-04-01

We investigate the defocusing coupled nonlinear Schrödinger equations from a 3×3 Lax pair. The Darboux transformations with the nonzero plane-wave solutions are presented to derive the newly localized wave solutions including dark-dark and bright-dark solitons, breather-breather solutions, and different types of new vector rogue wave solutions, as well as interactions between distinct types of localized wave solutions. Moreover, we analyze these solutions by means of parameters modulation. Finally, the perturbed wave propagations of some obtained solutions are explored by means of systematic simulations, which demonstrates that nearly stable and strongly unstable solutions. Our research results could constitute a significant contribution to explore the distinct nonlinear waves (e.g., dark solitons, breather solutions, and rogue wave solutions) dynamics of the coupled system in related fields such as nonlinear optics, plasma physics, oceanography, and Bose-Einstein condensates.

Rogue wave solutions for the infinite integrable nonlinear Schrödinger equation hierarchy.

PubMed

Ankiewicz, A; Akhmediev, N

2017-07-01

We present rogue wave solutions of the integrable nonlinear Schrödinger equation hierarchy with an infinite number of higher-order terms. The latter include higher-order dispersion and higher-order nonlinear terms. In particular, we derive the fundamental rogue wave solutions for all orders of the hierarchy, with exact expressions for velocities, phase, and "stretching factors" in the solutions. We also present several examples of exact solutions of second-order rogue waves, including rogue wave triplets.

Optical rogue waves for the inhomogeneous generalized nonlinear Schrödinger equation.

PubMed

Loomba, Shally; Kaur, Harleen

2013-12-01

We present optical rogue wave solutions for a generalized nonlinear Schrodinger equation by using similarity transformation. We have predicted the propagation of rogue waves through a nonlinear optical fiber for three cases: (i) dispersion increasing (decreasing) fiber, (ii) periodic dispersion parameter, and (iii) hyperbolic dispersion parameter. We found that the rogue waves and their interactions can be tuned by properly choosing the parameters. We expect that our results can be used to realize improved signal transmission through optical rogue waves.

Design of materials configurations for enhanced phononic and electronic properties

NASA Astrophysics Data System (ADS)

Daraio, Chiara

The discovery of novel nonlinear dynamic and electronic phenomena is presented for the specific cases of granular materials and carbon nanotubes. This research was conducted for designing and constructing optimized macro-, micro- and nano-scale structural configurations of materials, and for studying their phononic and electronic behavior. Variation of composite arrangements of granular elements with different elastic properties in a linear chain-of-sphere, Y-junction or 3-D configurations led to a variety of novel phononic phenomena and interesting physical properties, which can be potentially useful for security, communications, mechanical and biomedical engineering applications. Mechanical and electronic properties of carbon nanotubes with different atomic arrangements and microstructures were also investigated. Electronic properties of Y-junction configured carbon nanotubes exhibit an exciting transistor switch behavior which is not seen in linear configuration nanotubes. Strongly nonlinear materials were designed and fabricated using novel and innovative concepts. Due to their unique strongly nonlinear and anisotropic nature, novel wave phenomena have been discovered. Specifically, violations of Snell's law were detected and a new mechanism of wave interaction with interfaces between NTPCs (Nonlinear Tunable Phononic Crystals) was established. Polymer-based systems were tested for the first time, and the tunability of the solitary waves speed was demonstrated. New materials with transformed signal propagation speed in the manageable range of 10-100 m/s and signal amplitude typical for audible speech have been developed. The enhancing of the mitigation of solitary and shock waves in 1-D chains were demonstrated and a new protective medium was designed for practical applications. 1-D, 2-D and 3-D strongly nonlinear system have been investigated providing a broad impact on the whole area of strongly nonlinear wave dynamics and creating experimental basis for new theories and models. Potential applications include (1) designing of a sound scrambler/decoder for secure voice communications, (2) improving invisibility of submarine to acoustic detection signal, (3) noise and shock wave mitigation for protection of vibration sensitive devices such as head mounted vision devices, (4) drastic compression of acoustic signals into centimeter regime impulses for artificial ear implants, hearing aid and devices for ease of conversion to electronic signals and processing, and acoustic delay lines for communication applications.

Evaluation of a wave-vector-frequency-domain method for nonlinear wave propagation

PubMed Central

Jing, Yun; Tao, Molei; Clement, Greg T.

2011-01-01

A wave-vector-frequency-domain method is presented to describe one-directional forward or backward acoustic wave propagation in a nonlinear homogeneous medium. Starting from a frequency-domain representation of the second-order nonlinear acoustic wave equation, an implicit solution for the nonlinear term is proposed by employing the Green’s function. Its approximation, which is more suitable for numerical implementation, is used. An error study is carried out to test the efficiency of the model by comparing the results with the Fubini solution. It is shown that the error grows as the propagation distance and step-size increase. However, for the specific case tested, even at a step size as large as one wavelength, sufficient accuracy for plane-wave propagation is observed. A two-dimensional steered transducer problem is explored to verify the nonlinear acoustic field directional independence of the model. A three-dimensional single-element transducer problem is solved to verify the forward model by comparing it with an existing nonlinear wave propagation code. Finally, backward-projection behavior is examined. The sound field over a plane in an absorptive medium is backward projected to the source and compared with the initial field, where good agreement is observed. PMID:21302985

The Effect of Crack Orientation on the Nonlinear Interaction of a P-wave with an S-wave

DOE PAGES

TenCate, J. A.; Malcolm, A. E.; Feng, X.; ...

2016-06-06

Cracks, joints, fluids, and other pore-scale structures have long been hypothesized to be the cause of the large elastic nonlinearity observed in rocks. It is difficult to definitively say which pore-scale features are most important, however, because of the difficulty in isolating the source of the nonlinear interaction. In this work, we focus on the influence of cracks on the recorded nonlinear signal and in particular on how the orientation of microcracks changes the strength of the nonlinear interaction. We do this by studying the effect of orientation on the measurements in a rock with anisotropy correlated with the presencemore » and alignment of microcracks. We measure the nonlinear response via the traveltime delay induced in a low-amplitude P wave probe by a high-amplitude S wave pump. We find evidence that crack orientation has a significant effect on the nonlinear signal.« less

Electron-acoustic rogue waves in a plasma with Tribeche–Tsallis–Cairns distributed electrons

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

Merriche, Abderrzak; Tribeche, Mouloud, E-mail: mouloudtribeche@yahoo.fr; Algerian Academy of Sciences and Technologies, Algiers

2017-01-15

The problem of electron-acoustic (EA) rogue waves in a plasma consisting of fluid cold electrons, nonthermal nonextensive electrons and stationary ions, is addressed. A standard multiple scale method has been carried out to derive a nonlinear Schrödinger-like equation. The coefficients of dispersion and nonlinearity depend on the nonextensive and nonthermal parameters. The EA wave stability is analyzed. Interestingly, it is found that the wave number threshold, above which the EA wave modulational instability (MI) sets in, increases as the nonextensive parameter increases. As the nonthermal character of the electrons increases, the MI occurs at large wavelength. Moreover, it is shownmore » that as the nonextensive parameter increases, the EA rogue wave pulse grows while its width is narrowed. The amplitude of the EA rogue wave decreases with an increase of the number of energetic electrons. In the absence of nonthermal electrons, the nonextensive effects are more perceptible and more noticeable. In view of the crucial importance of rogue waves, our results can contribute to the understanding of localized electrostatic envelope excitations and underlying physical processes, that may occur in space as well as in laboratory plasmas.« less

Nonlinear spin waves in magnetic thin films - foldover, dispersive shock waves, and spin pumping

NASA Astrophysics Data System (ADS)

Janantha, Pasdunkorale Arachchige Praveen

Three nonlinear phenomena of spin waves and the spin Seebeck effect in yttrium iron garnet (YIG)/Pt bi-layer structures are studied in this thesis and are reported in detail in Chapters 4-7. In the fourth chapter, the first observation of foldover effect of nonlinear eigenmodes in feedback ring systems is reported. The experiments made use of a system that consisted of a YIG thin film strip, which supported the propagation of forward volume spin waves, and a microwave amplifier, which amplified the signal from the output of the YIG strip and then fed it back to the input of the strip. The signal amplitude vs. frequency response in this ring system showed resonant peaks which resulted from ring eigenmodes. With an increase in the resonance amplitude, those resonant peaks evolved from symmetric peaks to asymmetric ones and then folded over to higher frequencies. The experimental observations were reproduced by theoretical calculations that took into account the nonlinearity-produced frequency shift of the traveling spin waves. The fifth chapter presents the first experimental observation of the formation of envelope dispersive shock wave (DSW) excitations from repulsive nonlinear spin waves. The experiments used a microwave step pulse to excite a spin-wave step pulse in a YIG thin film strip, in which the spin-wave amplitude increases rapidly. Under certain conditions, the spin-wave pulse evolved into a DSW excitation that consisted of a train of dark soliton-like dips with both the dip width and depth increasing from the front to the back and was terminated by a black soliton that had an almost zero intensity and a nearly 180° phase jump at its center. The sixth chapter reports on the spin pumping due to traveling spin waves. The experiment used a micron-thick YIG strip capped by a nanometer-thick Pt layer. The YIG film was biased by an in-plane magnetic field. The spin waves pumped spin currents into the Pt layer, and the later produced electrical voltages across the length of the Pt strip through the inverse spin Hall effect (ISHE). Several distinct pumping regimes were observed and were interpreted in the frame work of the nonlinear three-wave splitting processes of the spin waves. The seventh chapter presents the first experimental work on the roles of damping in the spin Seebeck effect (SSE). The experiments used YIG/Pt bi-layered structures where the YIG films exhibited very similar structural and static magnetic properties but very different damping. The data indicate that a decrease in the damping of the YIG film gives rise to an increase in the SSE coefficient, and this response shows quasi-linear behavior. The data also indicate that the SSE coefficient shows no notable dependences on the enhanced damping due to spin pumping.

Second-harmonic generation in shear wave beams with different polarizations

NASA Astrophysics Data System (ADS)

Spratt, Kyle S.; Ilinskii, Yurii A.; Zabolotskaya, Evgenia A.; Hamilton, Mark F.

2015-10-01

A coupled pair of nonlinear parabolic equations was derived by Zabolotskaya [1] that model the transverse components of the particle motion in a collimated shear wave beam propagating in an isotropic elastic solid. Like the KZK equation, the parabolic equation for shear wave beams accounts consistently for the leading order effects of diffraction, viscosity and nonlinearity. The nonlinearity includes a cubic nonlinear term that is equivalent to that present in plane shear waves, as well as a quadratic nonlinear term that is unique to diffracting beams. The work by Wochner et al. [2] considered shear wave beams with translational polarizations (linear, circular and elliptical), wherein second-order nonlinear effects vanish and the leading order nonlinear effect is third-harmonic generation by the cubic nonlinearity. The purpose of the current work is to investigate the quadratic nonlinear term present in the parabolic equation for shear wave beams by considering second-harmonic generation in Gaussian beams as a second-order nonlinear effect using standard perturbation theory. In order for second-order nonlinear effects to be present, a broader class of source polarizations must be considered that includes not only the familiar translational polarizations, but also polarizations accounting for stretching, shearing and rotation of the source plane. It is found that the polarization of the second harmonic generated by the quadratic nonlinearity is not necessarily the same as the polarization of the source-frequency beam, and we are able to derive a general analytic solution for second-harmonic generation from a Gaussian source condition that gives explicitly the relationship between the polarization of the source-frequency beam and the polarization of the second harmonic.

3D DNS and LES of Breaking Inertia-Gravity Waves

NASA Astrophysics Data System (ADS)

Remmler, S.; Fruman, M. D.; Hickel, S.; Achatz, U.

2012-04-01

As inertia-gravity waves we refer to gravity waves that have a sufficiently low frequency and correspondingly large horizontal wavelength to be strongly influenced by the Coriolis force. Inertia-gravity waves are very active in the middle atmosphere and their breaking is potentially an important influence on the circulation in this region. The parametrization of this process requires a good theoretical understanding, which we want to enhance with the present study. Primary linear instabilities of an inertia-gravity wave and "2.5-dimensional" nonlinear simulations (where the spatial dependence is two dimensional but the velocity and vorticity fields are three-dimensional) with the wave perturbed by its leading primary instabilities by Achatz [1] have shown that the breaking differs significantly from that of high-frequency gravity waves due to the strongly sheared component of velocity perpendicular to the plane of wave-propagation. Fruman & Achatz [2] investigated the three-dimensionalization of the breaking by computing the secondary linear instabilities of the same waves using singular vector analysis. These secondary instabilities are variations perpendicular to the direction of the primary perturbation and the wave itself, and their wavelengths are an order of magnitude shorter than both. In continuation of this work, we carried out fully three-dimensional nonlinear simulations of inertia-gravity waves perturbed by their leading primary and secondary instabilities. The direct numerical simulation (DNS) was made tractable by restricting the domain size to the dominant scales selected by the linear analyses. The study includes both convectively stable and unstable waves. To the best of our knowledge, this is the first fully three-dimensional nonlinear direct numerical simulation of inertia-gravity waves at realistic Reynolds numbers with complete resolution of the smallest turbulence scales. Previous simulations either were restricted to high frequency gravity waves (e. g. Fritts et al. [3]), or the ratio N/f was artificially reduced (e. g. Lelong & Dunkerton [4]). The present simulations give us insight into the three-dimensional breaking process as well as the emerging turbulence. We assess the possibility of reducing the computational costs of three-dimensional simulations by using an implicit turbulence subgrid-scale parametrization based on the Adaptive Local Deconvolution Method (ALDM) for stratified turbulence [5]. In addition, we have performed ensembles of nonlinear 2.5-dimensional DNS, like those in Achatz [1] but with a small amount of noise superposed to the initial state, and compared the results with coarse-resolution simulations using either ALDM as well as with standard LES schemes. We found that the results of the models with parametrized turbulence, which are orders of magnitude more computationally economical than the DNS, compare favorably with the DNS in terms of the decay of the wave amplitude with time (the quantity most important for application to gravity-wave drag parametrization) suggesting that they may be trusted in future simulations of gravity wave breaking.

Modelling of Resonantly Forced Density Waves in Dense Planetary Rings

NASA Astrophysics Data System (ADS)

Lehmann, M.; Schmidt, J.; Salo, H.

2014-04-01

Density wave theory, originally proposed to explain the spiral structure of galactic disks, has been applied to explain parts of the complex sub-structure in Saturn's rings, such as the wavetrains excited at the inner Lindblad resonances (ILR) of various satellites. The linear theory for the excitation and damping of density waves in Saturn's rings is fairly well developed (e.g. Goldreich & Tremaine [1979]; Shu [1984]). However, it fails to describe certain aspects of the observed waves. The non-applicability of the linear theory is already indicated by the "cusplike" shape of many of the observed wave profiles. This is a typical nonlinear feature which is also present in overstability wavetrains (Schmidt & Salo [2003]; Latter & Ogilvie [2010]). In particular, it turns out that the detailed damping mechanism, as well as the role of different nonlinear effects on the propagation of density waves remain intransparent. First attemps are being made to investigate the excitation and propagation of nonlinear density waves within a hydrodynamical formalism, which is also the natural formalism for describing linear density waves. A simple weakly nonlinear model, derived from a multiple-scale expansion of the hydrodynamic equations, is presented. This model describes the damping of "free" spiral density waves in a vertically integrated fluid disk with density dependent transport coefficients, where the effects of the hydrodynamic nonlinearities are included. The model predicts that density waves are linearly unstable in a ring region where the conditions for viscous overstability are met, which translates to a steep dependence of the shear viscosity with respect to the disk's surface density. The possibility that this dependence could lead to a growth of density waves with increasing distance from the resonance, was already mentioned in Goldreich & Tremaine [1978]. Sufficiently far away from the ILR, the surface density perturbation caused by the wave, is predicted to saturate to a constant value due to the effects of nonlinear viscous damping. A qualitatively similar behaviour has also been predicted for the damping of nonlinear density waves, as described within a streamline formalism (Borderies, Goldreich & Tremaine [1985]). The damping lengths which follow from the weakly nonlinear model depend more or less strongly on a set of different input parameters, such as the viscosity and the surface density of the unperturbed ring state. Further, they depend on the wave's amplitude at resonance. For a real wave, which has been excited by an external satellite, this amplitude can be deduced from the magnitude of the satellite's forcing potential. Appart from that, hydrodynamical simulations are being developed to study the nonlinear damping of resonantly forced density waves.

Phonon-assisted nonlinear optical processes in ultrashort-pulse pumped optical parametric amplifiers

DOE PAGES

Isaienko, Oleksandr; Robel, Istvan

2016-03-15

Optically active phonon modes in ferroelectrics such as potassium titanyl phosphate (KTP) and potassium titanyl arsenate (KTA) in the ~7–20 THz range play an important role in applications of these materials in Raman lasing and terahertz wave generation. Previous studies with picosecond pulse excitation demonstrated that the interaction of pump pulses with phonons can lead to efficient stimulated Raman scattering (SRS) accompanying optical parametric oscillation or amplification processes (OPO/OPA), and to efficient polariton-phonon scattering. In this work, we investigate the behavior of infrared OPAs employing KTP or KTA crystals when pumped with ~800-nm ultrashort pulses of duration comparable to themore » oscillation period of the optical phonons. We demonstrate that under conditions of coherent impulsive Raman excitation of the phonons, when the effective χ (2) nonlinearity cannot be considered instantaneous, the parametrically amplified waves (most notably, signal) undergo significant spectral modulations leading to an overall redshift of the OPA output. Furthermore, the pump intensity dependence of the redshifted OPA output, the temporal evolution of the parametric gain, as well as the pump spectral modulations suggest the presence of coupling between the nonlinear optical polarizations P NL of the impulsively excited phonons and those of parametrically amplified waves.« less

Onset and saturation of backward stimulated Raman scattering of laser in trapping regime in three spatial dimensions

NASA Astrophysics Data System (ADS)

Yin, L.; Albright, B. J.; Rose, H. A.; Bowers, K. J.; Bergen, B.; Montgomery, D. S.; Kline, J. L.; Fernández, J. C.

2009-11-01

A suite of three-dimensional (3D) VPIC [K. J. Bowers et al., Phys. Plasmas 15, 055703 (2008)] particle-in-cell simulations of backward stimulated Raman scattering (SRS) in inertial confinement fusion hohlraum plasma has been performed on the heterogeneous multicore supercomputer, Roadrunner, presently the world's most powerful supercomputer. These calculations reveal the complex nonlinear behavior of SRS and point to a new era of "at scale" 3D modeling of SRS in solitary and multiple laser speckles. The physics governing nonlinear saturation of SRS in a laser speckle in 3D is consistent with that of prior two-dimensional (2D) studies [L. Yin et al., Phys. Rev. Lett. 99, 265004 (2007)], but with important differences arising from enhanced diffraction and side loss in 3D compared with 2D. In addition to wave front bowing of electron plasma waves (EPWs) due to trapped electron nonlinear frequency shift and amplitude-dependent damping, we find for the first time that EPW self-focusing, which evolved from trapped particle modulational instability [H. A. Rose and L. Yin, Phys. Plasmas 15, 042311 (2008)], also exhibits loss of angular coherence by formation of a filament necklace, a process not available in 2D. These processes in 2D and 3D increase the side-loss rate of trapped electrons, increase wave damping, decrease source coherence for backscattered light, and fundamentally limit how much backscatter can occur from a laser speckle. For both SRS onset and saturation, the nonlinear trapping induced physics is not captured in linear gain modeling of SRS. A simple metric is described for using single-speckle reflectivities obtained from VPIC simulations to infer the total reflectivity from the population of laser speckles of amplitude sufficient for significant trapping-induced nonlinearity to arise.

Josephson Metamaterial with a Widely Tunable Positive or Negative Kerr Constant

NASA Astrophysics Data System (ADS)

Zhang, Wenyuan; Huang, W.; Gershenson, M. E.; Bell, M. T.

2017-11-01

We report on the microwave characterization of a novel one-dimensional Josephson metamaterial composed of a chain of asymmetric superconducting quantum interference devices with nearest-neighbor coupling through common Josephson junctions. This metamaterial demonstrates a strong Kerr nonlinearity, with a Kerr constant tunable over a wide range, from positive to negative values, by a magnetic flux threading the superconducting quantum interference devices. The experimental results are in good agreement with the theory of nonlinear effects in Josephson chains. The metamaterial is very promising as an active medium for Josephson traveling-wave parametric amplifiers; its use facilitates phase matching in a four-wave-mixing process for efficient parametric gain.

Nonlinear surface waves at ferrite-metamaterial waveguide structure

NASA Astrophysics Data System (ADS)

Hissi, Nour El Houda; Mokhtari, Bouchra; Eddeqaqi, Noureddine Cherkaoui; Shabat, Mohammed Musa; Atangana, Jacques

2016-09-01

A new ferrite slab made of a metamaterial (MTM), surrounded by a nonlinear cover cladding and a ferrite substrate, was shown to support unusual types of electromagnetic surface waves. We impose the boundary conditions to derive the dispersion relation and others necessary to formulate the proposed structure. We analyse the dispersion properties of the nonlinear surface waves and we calculate the associated propagation index and the film-cover interface nonlinearity. In the calculation, several sets of the permeability of the MTM are considered. Results show that the waves behaviour depends on the values of the permeability of the MTM, the thickness of the waveguide and the film-cover interface nonlinearity. It is also shown that the use of the singular solutions to the electric field equation allows to identify several new properties of surface waves which do not exist in conventional waveguide.

Time-Reversal Generation of Rogue Waves

NASA Astrophysics Data System (ADS)

Chabchoub, Amin; Fink, Mathias

2014-03-01

The formation of extreme localizations in nonlinear dispersive media can be explained and described within the framework of nonlinear evolution equations, such as the nonlinear Schrödinger equation (NLS). Within the class of exact NLS breather solutions on a finite background, which describe the modulational instability of monochromatic wave trains, the hierarchy of rational solutions localized in both time and space is considered to provide appropriate prototypes to model rogue wave dynamics. Here, we use the time-reversal invariance of the NLS to propose and experimentally demonstrate a new approach to constructing strongly nonlinear localized waves focused in both time and space. The potential applications of this time-reversal approach include remote sensing and motivated analogous experimental analysis in other nonlinear dispersive media, such as optics, Bose-Einstein condensates, and plasma, where the wave motion dynamics is governed by the NLS.

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.

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

Lee, Wonjung; Kovacic, Gregor; Cai, David

Using the (1+1)D Majda-McLaughlin-Tabak model as an example, we present an extension of the wave turbulence (WT) theory to systems with strong nonlinearities. We demonstrate that nonlinear wave interactions renormalize the dynamics, leading to (i) a possible destruction of scaling structures in the bare wave systems and a drastic deformation of the resonant manifold even at weak nonlinearities, and (ii) creation of nonlinear resonance quartets in wave systems for which there would be no resonances as predicted by the linear dispersion relation. Finally, we derive an effective WT kinetic equation and show that our prediction of the renormalized Rayleigh-Jeans distributionmore » is in excellent agreement with the simulation of the full wave system in equilibrium.« less

Nonlinear layered lattice model and generalized solitary waves in imperfectly bonded structures.

PubMed

Khusnutdinova, Karima R; Samsonov, Alexander M; Zakharov, Alexey S

2009-05-01

We study nonlinear waves in a two-layered imperfectly bonded structure using a nonlinear lattice model. The key element of the model is an anharmonic chain of oscillating dipoles, which can be viewed as a basic lattice analog of a one-dimensional macroscopic waveguide. Long nonlinear longitudinal waves in a layered lattice with a soft middle (or bonding) layer are governed by a system of coupled Boussinesq-type equations. For this system we find conservation laws and show that pure solitary waves, which exist in a single equation and can exist in the coupled system in the symmetric case, are structurally unstable and are replaced with generalized solitary waves.

Propagation of flexural waves in inhomogeneous plates exhibiting hysteretic nonlinearity: Nonlinear acoustic black holes.

PubMed

Gusev, Vitalyi E; Ni, Chenyin; Lomonosov, Alexey; Shen, Zhonghua

2015-08-01

Theory accounting for the influence of hysteretic nonlinearity of micro-inhomogeneous material on flexural wave in the plates of continuously varying thickness is developed. For the wedges with thickness increasing as a power law of distance from its edge strong modifications of the wave dynamics with propagation distance are predicted. It is found that nonlinear absorption progressively disappearing with diminishing wave amplitude leads to complete attenuation of acoustic waves in most of the wedges exhibiting black hole phenomenon. It is also demonstrated that black holes exist beyond the geometrical acoustic approximation. Applications include nondestructive evaluation of micro-inhomogeneous materials and vibrations damping. Copyright © 2015 Elsevier B.V. All rights reserved.

Nonlinear Wave-Particle Interaction: Implications for Newborn Planetary and Backstreaming Proton Velocity Distribution Functions

NASA Astrophysics Data System (ADS)

Romanelli, N.; Mazelle, C.; Meziane, K.

2018-02-01

Seen from the solar wind (SW) reference frame, the presence of newborn planetary protons upstream from the Martian and Venusian bow shocks and SW protons reflected from each of them constitutes two sources of nonthermal proton populations. In both cases, the resulting proton velocity distribution function is highly unstable and capable of giving rise to ultralow frequency quasi-monochromatic electromagnetic plasma waves. When these instabilities take place, the resulting nonlinear waves are convected by the SW and interact with nonthermal protons located downstream from the wave generation region (upstream from the bow shock), playing a predominant role in their dynamics. To improve our understanding of these phenomena, we study the interaction between a charged particle and a large-amplitude monochromatic circularly polarized electromagnetic wave propagating parallel to a background magnetic field, from first principles. We determine the number of fix points in velocity space, their stability, and their dependence on different wave-particle parameters. Particularly, we determine the temporal evolution of a charged particle in the pitch angle-gyrophase velocity plane under nominal conditions expected for backstreaming protons in planetary foreshocks and for newborn planetary protons in the upstream regions of Venus and Mars. In addition, the inclusion of wave ellipticity effects provides an explanation for pitch angle distributions of suprathermal protons observed at the Earth's foreshock, reported in previous studies. These analyses constitute a mean to evaluate if nonthermal proton velocity distribution functions observed at these plasma environments present signatures that can be understood in terms of nonlinear wave-particle processes.

A novel nonlinear damage resonance intermodulation effect for structural health monitoring

NASA Astrophysics Data System (ADS)

Ciampa, Francesco; Scarselli, Gennaro; Meo, Michele

2017-04-01

This paper is aimed at developing a theoretical model able to predict the generation of nonlinear elastic effects associated to the interaction of ultrasonic waves with the steady-state nonlinear response of local defect resonance (LDR). The LDR effect is used in nonlinear elastic wave spectroscopy to enhance the excitation of the material damage at its local resonance, thus to dramatically increase the vibrational amplitude of material nonlinear phenomena. The main result of this work is to prove both analytically and experimentally the generation of novel nonlinear elastic wave effects, here named as nonlinear damage resonance intermodulation, which correspond to a nonlinear intermodulation between the driving frequency and the LDR one. Beside this intermodulation effect, other nonlinear elastic wave phenomena such as higher harmonics of the input frequency and superharmonics of LDR frequency were found. The analytical model relies on solving the nonlinear equation of motion governing bending displacement under the assumption of both quadratic and cubic nonlinear defect approximation. Experimental tests on a damaged composite laminate confirmed and validated these predictions and showed that using continuous periodic excitation, the nonlinear structural phenomena associated to LDR could also be featured at locations different from the damage resonance. These findings will provide new opportunities for material damage detection using nonlinear ultrasounds.

Growth of ring ripple in a collisionless plasma in relativistic-ponderomotive regime and its effect on stimulated Raman backscattering process

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

Rawat, Priyanka; Purohit, Gunjan, E-mail: gunjan75@gmail.com; Gauniyal, Rakhi

A theoretical and numerical study has been made of the propagation of a ring rippled laser beam in collisionless plasma with dominant relativistic ponderomotive nonlinearity and its effect on the excitation of electron plasma wave and stimulated Raman backscattering process. The growth of ring ripple, riding on an intense Gaussian laser beam in plasma has also been studied. A paraxial-ray and WKB approximation has been invoked to understand the nature of propagation of the ring rippled Gaussian laser beam in plasma, electron plasma wave and back reflectivity under the influence of both nonlinearities. The growth rate and focusing of amore » ring rippled beam is found to be considerably affected by the power of the main beam and the phase angle between the electric vectors of the main beam and the ring ripple. It has also been observed that the focusing is released by the coupling of relativistic and ponderomotive nonlinearities, which significantly affected the dynamics of the excitation of electron plasma wave and back reflectivity of stimulated Raman scattering (SRS). Due to the strong coupling between ring rippled laser beam and the excited electron plasma wave, back reflectivity of SRS is enhanced. It has been observed from the computational results that the effect of the increased intensity leads to suppression of SRS back reflectivity. The results have been presented for established laser and plasma parameters.« less

Evaluation of crack status in a meter-size concrete structure using the ultrasonic nonlinear coda wave interferometry.

PubMed

Legland, Jean-Baptiste; Zhang, Yuxiang; Abraham, Odile; Durand, Olivier; Tournat, Vincent

2017-10-01

The field of civil engineering is in need of new methods of non-destructive testing, especially in order to prevent and monitor the serious deterioration of concrete structures. In this work, experimental results are reported on fault detection and characterization in a meter-scale concrete structure using an ultrasonic nonlinear coda wave interferometry (NCWI) method. This method entails the nonlinear mixing of strong pump waves with multiple scattered probe (coda) waves, along with analysis of the net effect using coda wave interferometry. A controlled damage protocol is implemented on a post-tensioned, meter-scale concrete structure in order to generate cracking within a specific area being monitored by NCWI. The nonlinear acoustic response due to the high amplitude of acoustic modulation yields information on the elastic nonlinearities of concrete, as evaluated by two specific nonlinear observables. The increase in nonlinearity level corresponds to the creation of a crack with a network of microcracks localized at its base. In addition, once the crack closes as a result of post-tensioning, the residual nonlinearities confirm the presence of the closed crack. Last, the benefits and applicability of this NCWI method to the characterization and monitoring of large structures are discussed.

An Improved Spectral Analysis Method for Fatigue Damage Assessment of Details in Liquid Cargo Tanks

NASA Astrophysics Data System (ADS)

Zhao, Peng-yuan; Huang, Xiao-ping

2018-03-01

Errors will be caused in calculating the fatigue damages of details in liquid cargo tanks by using the traditional spectral analysis method which is based on linear system, for the nonlinear relationship between the dynamic stress and the ship acceleration. An improved spectral analysis method for the assessment of the fatigue damage in detail of a liquid cargo tank is proposed in this paper. Based on assumptions that the wave process can be simulated by summing the sinusoidal waves in different frequencies and the stress process can be simulated by summing the stress processes induced by these sinusoidal waves, the stress power spectral density (PSD) is calculated by expanding the stress processes induced by the sinusoidal waves into Fourier series and adding the amplitudes of each harmonic component with the same frequency. This analysis method can take the nonlinear relationship into consideration and the fatigue damage is then calculated based on the PSD of stress. Take an independent tank in an LNG carrier for example, the accuracy of the improved spectral analysis method is proved much better than that of the traditional spectral analysis method by comparing the calculated damage results with the results calculated by the time domain method. The proposed spectral analysis method is more accurate in calculating the fatigue damages in detail of ship liquid cargo tanks.

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.

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.

Planning for coordinated space and ground-based ionospheric modification experiments

NASA Technical Reports Server (NTRS)

Lee, M. C.; Burke, William J.; Carlson, Herbert C.; Heckscher, John L.; Kossey, Paul A.; Weber, E. J.; Kuo, S. P.

1990-01-01

The planning and conduction of coordinated space and ground-based ionospheric modification experiments are discussed. The purpose of these experiments is to discuss: (1) the nonlinear VLF wave interaction with the ionospheric plasmas; and (2) the nonlinear propagation of VLF waves in the HF-modified ionosphere. It is expected that the HF-induced ionospheric density striations can render the nonlinear mode conversion of VLF waved into lower hybrid waves. Lower hybrid waves can also be excited parametrically by the VLF waves in the absence of the density striations if the VLF waves are intense enough. Laboratory experiments are planned for crosschecking the results obtained from the field experiments.

Excitations of breathers and rogue wave in the Heisenberg spin chain

NASA Astrophysics Data System (ADS)

Qi, Jian-Wen; Duan, Liang; Yang, Zhan-Ying; Yang, Wen-Li

2018-01-01

We study the excitations of breathers and rogue wave in a classical Heisenberg spin chain with twist interaction, which is governed by a fourth-order integrable nonlinear Schrödinger equation. The dynamics of these waves have been extracted from an exact solution. In particular, the corresponding existence conditions based on the parameters of perturbation wave number K, magnon number N, background wave vector ks and amplitude c are presented explicitly. Furthermore, the characteristics of magnetic moment distribution corresponding to these nonlinear waves are also investigated in detail. Finally, we discussed the state transition of three types nonlinear localized waves under the different excitation conditions.

NONLINEAR OPTICAL EFFECTS AND FIBER OPTICS: Theory of four-wave mixing in photorefractive media when the response of a medium is nonlinear in respect of the modulation parameter

NASA Astrophysics Data System (ADS)

Zozulya, A. A.

1988-12-01

A theoretical model is constructed for four-wave mixing in a photorefractive crystal where a transmission grating is formed by the drift-diffusion nonlinearity mechanism in the absence of an external electrostatic field and the response of the medium is nonlinear in respect of the modulation parameter. A comparison is made with a model in which the response of the medium is linear in respect of the modulation parameter. Theoretical models of four-wave and two-wave mixing are also compared with experiments.

Gamma-ray vortices from nonlinear inverse Thomson scattering of circularly polarized light.

PubMed

Taira, Yoshitaka; Hayakawa, Takehito; Katoh, Masahiro

2017-07-10

Inverse Thomson scattering is a well-known radiation process that produces high-energy photons both in nature and in the laboratory. Nonlinear inverse Thomson scattering occurring inside an intense light field is a process which generates higher harmonic photons. In this paper, we theoretically show that the higher harmonic gamma-ray produced by nonlinear inverse Thomson scattering of circularly polarized light is a gamma-ray vortex, which means that it possesses a helical wave front and carries orbital angular momentum. Our work explains a recent experimental result regarding nonlinear inverse Thomson scattering that clearly shows an annular intensity distribution as a remarkable feature of a vortex beam. Our work implies that gamma-ray vortices should be produced in various situations in astrophysics in which high-energy electrons and intense circularly polarized light fields coexist. Nonlinear inverse Thomson scattering is a promising radiation process for realizing a gamma-ray vortex source based on currently available laser and accelerator technologies, which would be an indispensable tool for exploring gamma-ray vortex science.

Modeling Boulder Transport by Smooth Particle Hydrodynamics

NASA Astrophysics Data System (ADS)

Karpytchev, M.

2017-12-01

Large coastal boulders are often believed to have been transported by strong tsunami andstorm waves. Understanding and quantifying the boulder transport processes is, therefore,crucial for evaluation of strength and timing of the past tsunamis and storms. Over the last10-15 year, a series of studies have obtained estimates of basic wave parameters neededto set in motion a boulder of given size, shape and mass by using simplified paramaterizationsof fluid-particle interactions. Although, parameterizing the principal hydraulic forces drivingboulder transport was succefull in reproducing effects of several historical tsunamis, someimportant details about initiation of boulder motion and the contribution of coastal wavetransformations as well as of suspended sediment to enhancing coastal currents are still lacking.These essentially non-linear processes can be particularly important for distingushing, in everyparticular case, whether it is a storm wave or a tsunami (or both) that was capable to transportspecific boulder to a given site.In this study, we employ the Smooth Particle Hydrodynamics (SPH) method in orderto get new insights on interaction of waves with boulders in the nearshore area.We first compare the SPH predictions with available laboratory experiments and thenexplore the effects of realistic 3D coastal bathymetry, non-linear behaviour of coastal waves,boulders shape and the impact of bedload and suspended sediment on dislodgement and initiationof boulder transport.

Kuznetsov-Ma waves train generation in a left-handed material

NASA Astrophysics Data System (ADS)

Atangana, Jacques; Giscard Onana Essama, Bedel; Biya-Motto, Frederick; Mokhtari, Bouchra; Cherkaoui Eddeqaqi, Noureddine; Crépin Kofane, Timoléon

2015-03-01

We analyze the behavior of an electromagnetic wave which propagates in a left-handed material. Second-order dispersion and cubic-quintic nonlinearities are considered. This behavior of an electromagnetic wave is modeled by a nonlinear Schrödinger equation which is solved by collective coordinates theory in order to characterize the light pulse intensity profile. More so, a specific frequency range has been outlined where electromagnetic wave behavior will be investigated. The perfect combination of second-order dispersion and cubic nonlinearity leads to a robust soliton. When the quintic nonlinearity comes into play, it provokes strong and long internal perturbations which lead to Benjamin-Feir instability. This phenomenon, also called modulational instability, induces appearance of a Kuznetsov-Ma waves train. We numerically verify the validity of Kuznetsov-Ma theory by presenting physical conditions which lead to Kuznetsov-Ma waves train generation. Thereafter, some properties of such waves train are also verified.

Experimental Measurement of the Nonlinear Interaction between Counterpropagating Alfv'en Waves in the LaPD

NASA Astrophysics Data System (ADS)

Schroeder, J. W. R.; Drake, D. J.; Howes, G. G.; Skiff, F.; Kletzing, C. A.; Carter, T. A.; Dorfman, S.; Auerbach, D.

2012-10-01

Turbulence plays an important role in the transport of mass and energy in many space and astrophysical plasmas ranging from galaxy clusters to Earth's magnetosphere. One active topic of research is the application of idealized Alfv'enic turbulence models to plasma conditions relevant to space and astrophysical plasmas. Alfv'enic turbulence models based on incompressible magnetohydrodynamics (MHD) contain a nonlinear interaction that drives the cascade of energy to smaller scales. We describe experiments at the Large Plasma Device (LaPD) that focus on the interaction of an Alfv'en wave traveling parallel to the mean magnetic field with a counterpropagating Alfv'en wave. Theory predicts the nonlinear interaction of the two primary waves will produce a secondary daughter Alfv'en wave. In this study, we present the first experimental identification of the daughter wave generated by nonlinear interactions between the primary Alfv'en waves.

Effect of Forcing Function on Nonlinear Acoustic Standing Waves

NASA Technical Reports Server (NTRS)

Finkheiner, Joshua R.; Li, Xiao-Fan; Raman, Ganesh; Daniels, Chris; Steinetz, Bruce

2003-01-01

Nonlinear acoustic standing waves of high amplitude have been demonstrated by utilizing the effects of resonator shape to prevent the pressure waves from entering saturation. Experimentally, nonlinear acoustic standing waves have been generated by shaking an entire resonating cavity. While this promotes more efficient energy transfer than a piston-driven resonator, it also introduces complicated structural dynamics into the system. Experiments have shown that these dynamics result in resonator forcing functions comprised of a sum of several Fourier modes. However, previous numerical studies of the acoustics generated within the resonator assumed simple sinusoidal waves as the driving force. Using a previously developed numerical code, this paper demonstrates the effects of using a forcing function constructed with a series of harmonic sinusoidal waves on resonating cavities. From these results, a method will be demonstrated which allows the direct numerical analysis of experimentally generated nonlinear acoustic waves in resonators driven by harmonic forcing functions.

Linear and Nonlinear Coupling of Electrostatic Drift and Acoustic Perturbations in a Nonuniform Bi-Ion Plasma with Non-Maxwellian Electrons

NASA Astrophysics Data System (ADS)

Ali, Gul-e.; Ahmad, Ali; Masood, W.; Mirza, Arshad M.

2017-12-01

Linear and nonlinear coupling of drift and ion acoustic waves are studied in a nonuniform magnetized plasma comprising of Oxygen and Hydrogen ions with nonthermal distribution of electrons. It has been observed that different ratios of ion number densities and kappa and Cairns distributed electrons significantly modify the linear dispersion characteristics of coupled drift-ion acoustic waves. In the nonlinear regime, KdV (for pure drift waves) and KP (for coupled drift-ion acoustic waves) like equations have been derived to study the nonlinear evolution of drift solitary waves in one and two dimensions. The dependence of drift solitary structures on different ratios of ion number densities and nonthermal distribution of electrons has also been explored in detail. It has been found that the ratio of the diamagnetic drift velocity to the velocity of the nonlinear structure determines the existence regimes for the drift solitary waves. The present investigation may be beneficial to understand the formation of solitons in the ionospheric F-region.

The role of nonlinear critical layers in boundary layer transition

NASA Technical Reports Server (NTRS)

Goldstein, M.E.

1995-01-01

Asymptotic methods are used to describe the nonlinear self-interaction between pairs of oblique instability modes that eventually develops when initially linear spatially growing instability waves evolve downstream in nominally two-dimensional laminar boundary layers. The first nonlinear reaction takes place locally within a so-called 'critical layer', with the flow outside this layer consisting of a locally parallel mean flow plus a pair of oblique instability waves - which may or may not be accompanied by an associated plane wave. The amplitudes of these waves, which are completely determined by nonlinear effects within the critical layer, satisfy either a single integro-differential equation or a pair of integro-differential equations with quadratic to quartic-type nonlinearities. The physical implications of these equations are discussed.

Stochastic Growth of Ion Cyclotron And Mirror Waves In Earth's Magnetosheath

NASA Technical Reports Server (NTRS)

Cairns, Iver H.; Grubits, K. A.

2001-01-01

Electromagnetic ion cyclotron and mirror waves in Earth's magnetosheath are bursty, have widely variable fields, and are unexpectedly persistent, properties difficult to reconcile with uniform secular growth. Here it is shown for specific periods that stochastic growth theory (SGT) quantitatively accounts for the functional form of the wave statistics and qualitatively explains the wave properties. The wave statistics are inconsistent with uniform secular growth or self-organized criticality, but nonlinear processes sometimes play a role at high fields. The results show SGT's relevance near marginal stability and suggest that it is widely relevant to space and astrophysical plasmas.

Tailorable stimulated Brillouin scattering in nanoscale silicon waveguides.

PubMed

Shin, Heedeuk; Qiu, Wenjun; Jarecki, Robert; Cox, Jonathan A; Olsson, Roy H; Starbuck, Andrew; Wang, Zheng; Rakich, Peter T

2013-01-01

Nanoscale modal confinement is known to radically enhance the effect of intrinsic Kerr and Raman nonlinearities within nanophotonic silicon waveguides. By contrast, stimulated Brillouin-scattering nonlinearities, which involve coherent coupling between guided photon and phonon modes, are stifled in conventional nanophotonics, preventing the realization of a host of Brillouin-based signal-processing technologies in silicon. Here we demonstrate stimulated Brillouin scattering in silicon waveguides, for the first time, through a new class of hybrid photonic-phononic waveguides. Tailorable travelling-wave forward-stimulated Brillouin scattering is realized-with over 1,000 times larger nonlinearity than reported in previous systems-yielding strong Brillouin coupling to phonons from 1 to 18 GHz. Experiments show that radiation pressures, produced by subwavelength modal confinement, yield enhancement of Brillouin nonlinearity beyond those of material nonlinearity alone. In addition, such enhanced and wideband coherent phonon emission paves the way towards the hybridization of silicon photonics, microelectromechanical systems and CMOS signal-processing technologies on chip.

A Model for the Propagation of Nonlinear Surface Waves over Viscous Muds

DTIC Science & Technology

2007-07-05

grained, cohesive sedimentary 1993; Foda et al., 1993). With the exception of fluidization environments is well known. Extreme dissipation rates have...processes ( Foda et al., 1993; DeWit, 1995), these models focus on a single, well-defined mud phase. Although the models Corresponding author. Tel.: +1...However, surface-interface wave interactions ( Foda , 1989; Hill and Foda , our focus at the present is on a wave model which can be 1998; Jamali et al

Lagrangian methods in nonlinear plasma wave interaction

NASA Technical Reports Server (NTRS)

Crawford, F. W.

1980-01-01

Analysis of nonlinear plasma wave interactions is usually very complicated, and simplifying mathematical approaches are highly desirable. The application of averaged-Lagrangian methods offers a considerable reduction in effort, with improved insight into synchronism and conservation (Manley-Rowe) relations. This chapter indicates how suitable Lagrangian densities have been defined, expanded, and manipulated to describe nonlinear wave-wave and wave-particle interactions in the microscopic, macroscopic and cold plasma models. Recently, further simplifications have been introduced by the use of techniques derived from Lie algebra. These and likely future developments are reviewed briefly.

Study of diffusion of wave packets in a square lattice under external fields along the discrete nonlinear Schrödinger equation

NASA Astrophysics Data System (ADS)

de Brito, P. E.; Nazareno, H. N.

2012-09-01

The object of the present work is to analyze the effect of nonlinearity on wave packet propagation in a square lattice subject to a magnetic and an electric field in the Hall configuration, by using the Discrete Nonlinear Schrödinger Equation (DNLSE). In previous works we have shown that without the nonlinear term, the presence of the magnetic field induces the formation of vortices that remain stationary, while a wave packet is introduced in the system. As for the effect of an applied electric field, it was shown that the vortices propagate in a direction perpendicular to the electric field, similar behavior as presented in the classical treatment, we provide a quantum mechanics explanation for that. We have performed the calculations considering first the action of the magnetic field as well as the nonlinearity. The results indicate that for low values of the nonlinear parameter U the vortices remain stationary while preserving the form. For greater values of the parameter the picture gets distorted, the more so, the greater the nonlinearity. As for the inclusion of the electric field, we note that for small U, the wave packet propagates perpendicular to the applied field, until for greater values of U the wave gets partially localized in a definite region of the lattice. That is, for strong nonlinearity the wave packet gets partially trapped, while the tail of it can propagate through the lattice. Note that this tail propagation is responsible for the over-diffusion for long times of the wave packet under the action of an electric field. We have produced short films that show clearly the time evolution of the wave packet, which can add to the understanding of the dynamics.

REVIEWS OF TOPICAL PROBLEMS: Acceleration of cosmic rays by shock waves

NASA Astrophysics Data System (ADS)

Berezhko, E. G.; Krymskiĭ, G. F.

1988-01-01

Theoretical work on various processes by which shock waves accelerate cosmic rays is reviewed. The most efficient of these processes, Fermi acceleration, is singled out for special attention. A linear theory for this process is presented. The results found on the basis of nonlinear models of Fermi acceleration, which incorporate the modification of the structure caused by the accelerated particles, are reported. There is a discussion of various possibilities for explaining the generation of high-energy particles observed in interplanetary and interstellar space on the basis of a Fermi acceleration mechanism. The acceleration by shock waves from supernova explosions is discussed as a possible source of galactic cosmic rays. The most important unresolved questions in the theory of acceleration of charged particles by shock waves are pointed out.

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.

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.

Travelling-wave resonant four-wave mixing breaks the limits of cavity-enhanced all-optical wavelength conversion.

PubMed

Morichetti, Francesco; Canciamilla, Antonio; Ferrari, Carlo; Samarelli, Antonio; Sorel, Marc; Melloni, Andrea

2011-01-01

Wave mixing inside optical resonators, while experiencing a large enhancement of the nonlinear interaction efficiency, suffers from strong bandwidth constraints, preventing its practical exploitation for processing broad-band signals. Here we show that such limits are overcome by the new concept of travelling-wave resonant four-wave mixing (FWM). This approach combines the efficiency enhancement provided by resonant propagation with a wide-band conversion process. Compared with conventional FWM in bare waveguides, it exhibits higher robustness against chromatic dispersion and propagation loss, while preserving transparency to modulation formats. Travelling-wave resonant FWM has been demonstrated in silicon-coupled ring resonators and was exploited to realize a 630-μm-long wavelength converter operating over a wavelength range wider than 60 nm and with 28-dB gain with respect to a bare waveguide of the same physical length. Full compatibility of the travelling-wave resonant FWM with optical signal processing applications has been demonstrated through signal retiming and reshaping at 10 Gb s(-1).

Travelling-wave resonant four-wave mixing breaks the limits of cavity-enhanced all-optical wavelength conversion

PubMed Central

Morichetti, Francesco; Canciamilla, Antonio; Ferrari, Carlo; Samarelli, Antonio; Sorel, Marc; Melloni, Andrea

2011-01-01

Wave mixing inside optical resonators, while experiencing a large enhancement of the nonlinear interaction efficiency, suffers from strong bandwidth constraints, preventing its practical exploitation for processing broad-band signals. Here we show that such limits are overcome by the new concept of travelling-wave resonant four-wave mixing (FWM). This approach combines the efficiency enhancement provided by resonant propagation with a wide-band conversion process. Compared with conventional FWM in bare waveguides, it exhibits higher robustness against chromatic dispersion and propagation loss, while preserving transparency to modulation formats. Travelling-wave resonant FWM has been demonstrated in silicon-coupled ring resonators and was exploited to realize a 630-μm-long wavelength converter operating over a wavelength range wider than 60 nm and with 28-dB gain with respect to a bare waveguide of the same physical length. Full compatibility of the travelling-wave resonant FWM with optical signal processing applications has been demonstrated through signal retiming and reshaping at 10 Gb s−1 PMID:21540838

Rossby and drift wave turbulence and zonal flows: The Charney-Hasegawa-Mima model and its extensions

NASA Astrophysics Data System (ADS)

Connaughton, Colm; Nazarenko, Sergey; Quinn, Brenda

2015-12-01

A detailed study of the Charney-Hasegawa-Mima model and its extensions is presented. These simple nonlinear partial differential equations suggested for both Rossby waves in the atmosphere and drift waves in a magnetically-confined plasma, exhibit some remarkable and nontrivial properties, which in their qualitative form, survive in more realistic and complicated models. As such, they form a conceptual basis for understanding the turbulence and zonal flow dynamics in real plasma and geophysical systems. Two idealised scenarios of generation of zonal flows by small-scale turbulence are explored: a modulational instability and turbulent cascades. A detailed study of the generation of zonal flows by the modulational instability reveals that the dynamics of this zonal flow generation mechanism differ widely depending on the initial degree of nonlinearity. The jets in the strongly nonlinear case further roll up into vortex streets and saturate, while for the weaker nonlinearities, the growth of the unstable mode reverses and the system oscillates between a dominant jet, which is slightly inclined to the zonal direction, and a dominant primary wave. A numerical proof is provided for the extra invariant in Rossby and drift wave turbulence-zonostrophy. While the theoretical derivations of this invariant stem from the wave kinetic equation which assumes weak wave amplitudes, it is shown to be relatively well-conserved for higher nonlinearities also. Together with the energy and enstrophy, these three invariants cascade into anisotropic sectors in the k-space as predicted by the Fjørtoft argument. The cascades are characterised by the zonostrophy pushing the energy to the zonal scales. A small scale instability forcing applied to the model has demonstrated the well-known drift wave-zonal flow feedback loop. The drift wave turbulence is generated from this primary instability. The zonal flows are then excited by either one of the generation mechanisms, extracting energy from the drift waves as they grow. Eventually the turbulence is completely suppressed and the zonal flows saturate. The turbulence spectrum is shown to diffuse in a manner which has been mathematically predicted. The insights gained from this simple model could provide a basis for equivalent studies in more sophisticated plasma and geophysical fluid dynamics models in an effort to fully understand the zonal flow generation, the turbulent transport suppression and the zonal flow saturation processes in both the plasma and geophysical contexts as well as other wave and turbulence systems where order evolves from chaos.

Flow Around Steep Topography

DTIC Science & Technology

2015-09-30

interest in these activities. These tours are being coordinated with the Coral Reef Research Foundation (CRRF), a research organization in Palau...form drag, lee waves , eddy generation) over small-scale topographic features and (ii) fundamentally nonlinear processes (turbulent island wakes...detail in another annual report. From 9 October to 12 November 2015, another SeaSoar cruise on Revelle will focus on wakes and arrested lee waves near

Studies of nonlinear interactions between counter-propagating Alfv'en waves in the LAPD

NASA Astrophysics Data System (ADS)

Auerbach, D. W.; Perez, J. C.; Carter, T. A.; Boldyrev, S.

2007-11-01

From a weak turbulence point of view, nonlinear interactions between shear Alfv'en waves are fundamental to the energy cascade in low-frequency magnetic turbulence. We report here on an experimental study of counter-propagating Alfv'en wave interactions in the Large Plasma Device (LAPD) at UCLA. Colliding, orthogonally polarized kinetic Alfv'en waves are generated by two antennae, separated by 5m along the guide magnetic field. Magnetic field and langmuir probes record plasma behavior between the antennae. When each antenna is operated separately, linearly polarized Alfv'en waves propagate in opposite directions along the guide field. When two antennae simultaneously excite counter propagating waves, we observe multiple side bands in the frequency domain, whose amplitude scales quadratically with wave amplitude. In the spatial domain we observe non-linear superposition in the 2D structure of the waves and spectral broadening in the perpendicular wave-number spectrum. This indicates the presence of nonlinear interaction of the counter propagating Alfv'en waves, and opens the possiblity to investigate Alfv'enic plasma turbulence in controlled and reproducible laboratory experiments.

Amplification of nonlinear surface waves by wind

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

Leblanc, Stephane

2007-10-15

A weakly nonlinear analysis is conducted to study the evolution of slowly varying wavepackets with small but finite amplitudes, that evolve at the interface between air and water under the effect of wind. In the inviscid assumption, wave envelopes are governed by cubic nonlinear Schroedinger or Davey-Stewartson equations forced by a linear term corresponding to Miles' mechanism of wave generation. Under fair wind, it is shown that Stokes waves grow exponentially and that Benjamin-Feir instability becomes explosive.

A coherent nonlinear theory of auroral Langmuir-Alfven-whistler (LAW) events in the planetary magnetosphere.

NASA Astrophysics Data System (ADS)

Lopes, S. R.; Chian, A. C.-L.

1996-01-01

A coherent nonlinear theory of three-wave coupling involving Langmuir, Alfven and whistler waves is formulated and applied to the observation of auroral LAW events in the planetary magnetosphere. The effects of pump depletion, dissipation and frequency mismatch in the nonlinear wave dynamics are analyzed. The relevance of this theory for understanding the fine structures of auroral whistler-mode emissions and amplitude modulations of auroral Langmuir waves is discussed.

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.

Nonlinear dispersion effects in elastic plates: numerical modelling and validation

NASA Astrophysics Data System (ADS)

Kijanka, Piotr; Radecki, Rafal; Packo, Pawel; Staszewski, Wieslaw J.; Uhl, Tadeusz; Leamy, Michael J.

2017-04-01

Nonlinear features of elastic wave propagation have attracted significant attention recently. The particular interest herein relates to complex wave-structure interactions, which provide potential new opportunities for feature discovery and identification in a variety of applications. Due to significant complexity associated with wave propagation in nonlinear media, numerical modeling and simulations are employed to facilitate design and development of new measurement, monitoring and characterization systems. However, since very high spatio- temporal accuracy of numerical models is required, it is critical to evaluate their spectral properties and tune discretization parameters for compromise between accuracy and calculation time. Moreover, nonlinearities in structures give rise to various effects that are not present in linear systems, e.g. wave-wave interactions, higher harmonics generation, synchronism and | recently reported | shifts to dispersion characteristics. This paper discusses local computational model based on a new HYBRID approach for wave propagation in nonlinear media. The proposed approach combines advantages of the Local Interaction Simulation Approach (LISA) and Cellular Automata for Elastodynamics (CAFE). The methods are investigated in the context of their accuracy for predicting nonlinear wavefields, in particular shifts to dispersion characteristics for finite amplitude waves and secondary wavefields. The results are validated against Finite Element (FE) calculations for guided waves in copper plate. Critical modes i.e., modes determining accuracy of a model at given excitation frequency - are identified and guidelines for numerical model parameters are proposed.

Composite nonlinear structure within the magnetosonic soliton interactions in a spin-1/2 degenerate quantum plasma

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

Han, Jiu-Ning, E-mail: hanjiuning@126.com; Luo, Jun-Hua; Li, Jun-Xiu

2015-06-15

We study the basic physical properties of composite nonlinear structure induced by the head-on collision of magnetosonic solitons. Solitary waves are assumed to propagate in a quantum electron-ion magnetoplasma with spin-1/2 degenerate electrons. The main interest of the present work is to investigate the time evolution of the merged composite structure during a specific time interval of the wave interaction process. We consider three cases of colliding-situation, namely, compressive-rarefactive solitons interaction, compressive-compressive solitons interaction, and rarefactive-rarefactive solitons interaction, respectively. Compared with the last two colliding cases, the changing process of the composite structure is more complex for the first situation.more » Moreover, it is found that they are obviously different for the last two colliding cases.« less

Longitudinal nonlinear wave propagation through soft tissue.

PubMed

Valdez, M; Balachandran, B

2013-04-01

In this paper, wave propagation through soft tissue is investigated. A primary aim of this investigation is to gain a fundamental understanding of the influence of soft tissue nonlinear material properties on the propagation characteristics of stress waves generated by transient loadings. Here, for computational modeling purposes, the soft tissue is modeled as a nonlinear visco-hyperelastic material, the geometry is assumed to be one-dimensional rod geometry, and uniaxial propagation of longitudinal waves is considered. By using the linearized model, a basic understanding of the characteristics of wave propagation is developed through the dispersion relation and in terms of the propagation speed and attenuation. In addition, it is illustrated as to how the linear system can be used to predict brain tissue material parameters through the use of available experimental ultrasonic attenuation curves. Furthermore, frequency thresholds for wave propagation along internal structures, such as axons in the white matter of the brain, are obtained through the linear analysis. With the nonlinear material model, the authors analyze cases in which one of the ends of the rods is fixed and the other end is subjected to a loading. Two variants of the nonlinear model are analyzed and the associated predictions are compared with the predictions of the corresponding linear model. The numerical results illustrate that one of the imprints of the nonlinearity on the wave propagation phenomenon is the steepening of the wave front, leading to jump-like variations in the stress wave profiles. This phenomenon is a consequence of the dependence of the local wave speed on the local deformation of the material. As per the predictions of the nonlinear material model, compressive waves in the structure travel faster than tensile waves. Furthermore, it is found that wave pulses with large amplitudes and small elapsed times are attenuated over shorter spans. This feature is due to the elevated strain-rates introduced at the end of the structure where the load is applied. In addition, it is shown that when steep wave fronts are generated in the nonlinear viscoelastic material, energy dissipation is focused in those wave fronts implying deposition of energy in a highly localized region of the material. Novel mechanisms for brain tissue damage are proposed based on the results obtained. The first mechanism is related to the dissipation of energy at steep wave fronts, while the second one is related to the interaction of steep wave fronts with axons encountered on its way through the structure. Copyright © 2013 Elsevier Ltd. All rights reserved.

Bright, dark and W-shaped solitons with extended nonlinear Schrödinger's equation for odd and even higher-order terms

NASA Astrophysics Data System (ADS)

Bendahmane, Issam; Triki, Houria; Biswas, Anjan; Saleh Alshomrani, Ali; Zhou, Qin; Moshokoa, Seithuti P.; Belic, Milivoj

2018-02-01

We present solitary wave solutions of an extended nonlinear Schrödinger equation with higher-order odd (third-order) and even (fourth-order) terms by using an ansatz method. The including high-order dispersion terms have significant physical applications in fiber optics, the Heisenberg spin chain, and ocean waves. Exact envelope solutions comprise bright, dark and W-shaped solitary waves, illustrating the potentially rich set of solitary wave solutions of the extended model. Furthermore, we investigate the properties of these solitary waves in nonlinear and dispersive media. Moreover, specific constraints on the system parameters for the existence of these structures are discussed exactly. The results show that the higher-order dispersion and nonlinear effects play a crucial role for the formation and properties of propagating waves.

Nonlinear Electromagnetic Waves and Spherical Arc-Polarized Waves in Space Plasmas

NASA Technical Reports Server (NTRS)

Tsurutani, B.; Ho, Christian M.; Arballo, John K.; Lakhina, Gurbax S.; Glassmeier, Karl-Heinz; Neubauer, Fritz M.

1997-01-01

We review observations of nonlinear plasma waves detected by interplanetary spacecraft. For this paper we will focus primarily on the phase-steepened properties of such waves. Plasma waves at comet Giacobini-Zinner measured by the International Cometary Explorer (ICE), at comets Halley and Grigg-Skjellerup measured by Giotto, and interplanetary Alfven waves measured by Ulysses, will be discussed and intercompared.

Focusing of Shear Shock Waves

NASA Astrophysics Data System (ADS)

Giammarinaro, Bruno; Espíndola, David; Coulouvrat, François; Pinton, Gianmarco

2018-01-01

Focusing is a ubiquitous way to transform waves. Recently, a new type of shock wave has been observed experimentally with high-frame-rate ultrasound: shear shock waves in soft solids. These strongly nonlinear waves are characterized by a high Mach number, because the shear wave velocity is much slower, by 3 orders of magnitude, than the longitudinal wave velocity. Furthermore, these waves have a unique cubic nonlinearity which generates only odd harmonics. Unlike longitudinal waves for which only compressional shocks are possible, shear waves exhibit cubic nonlinearities which can generate positive and negative shocks. Here we present the experimental observation of shear shock wave focusing, generated by the vertical motion of a solid cylinder section embedded in a soft gelatin-graphite phantom to induce linearly vertically polarized motion. Raw ultrasound data from high-frame-rate (7692 images per second) acquisitions in combination with algorithms that are tuned to detect small displacements (approximately 1 μ m ) are used to generate quantitative movies of gel motion. The features of shear shock wave focusing are analyzed by comparing experimental observations with numerical simulations of a retarded-time elastodynamic equation with cubic nonlinearities and empirical attenuation laws for soft solids.

Nonlinear tunneling of bright and dark rogue waves in combined nonlinear Schrödinger and Maxwell-Bloch systems

NASA Astrophysics Data System (ADS)

Raju, Thokala Soloman; Pal, Ritu

2018-05-01

We derive the analytical rogue wave solutions for the generalized inhomogeneous nonlinear Schrödinger-Maxwell-Bloch (GINLS-MB) equation describing the pulse propagation in erbium-doped fibre system. Then by suitably choosing the inhomogeneous parameters, we delineate the tunneling properties of rogue waves through dispersion and nonlinearity barriers or wells. Finally, we demonstrate the propagating characteristics of optical solitons by considering their tunneling through periodic barriers by the proper choice of external potential.

Nonlinear propagation of electromagnetic waves in negative-refraction-index composite materials.

PubMed

Kourakis, I; Shukla, P K

2005-07-01

We investigate the nonlinear propagation of electromagnetic waves in left-handed materials. For this purpose, we consider a set of coupled nonlinear Schrödinger (CNLS) equations, which govern the dynamics of coupled electric and magnetic field envelopes. The CNLS equations are used to obtain a nonlinear dispersion, which depicts the modulational stability profile of the coupled plane-wave solutions in left-handed materials. An exact (in)stability criterion for modulational interactions is derived, and analytical expressions for the instability growth rate are obtained.

Planning for coordinated space and ground-based ionospheric modification experiments

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

Lee, M.C.

1990-10-01

The planning and conducting of coordinated space and ground-based ionospheric modification experiments are discussed. The purpose of these experiments is to investigate (1) the nonlinear VLF wave interaction with the ionospheric plasmas, and (2) the nonlinear propagation of VLF waves in the HF-modified ionosphere. It is expected that the HY-induced ionospheric density striations can render the nonlinear mode conversion of VLF waves into lower hybrid waves. Lower hybrid waves can also be excited parametrically by the VLF waves in the absence of the density striations if the VLF waves are intense enough. Laboratory experiments are planned for crosschecking the resultsmore » obtained from the field experiments.« less

Orbital stability of solitary waves for generalized Boussinesq equation with two nonlinear terms

NASA Astrophysics Data System (ADS)

Zhang, Weiguo; Li, Xiang; Li, Shaowei; Chen, Xu

2018-06-01

This paper investigates the orbital stability and instability of solitary waves for the generalized Boussinesq equation with two nonlinear terms. Firstly, according to the theory of Grillakis-Shatah-Strauss orbital stability, we present the general results to judge orbital stability of the solitary waves. Further, we deduce the explicit expression of discrimination d‧‧(c) to judge the stability of the two solitary waves, and give the stable wave speed interval. Moreover, we analyze the influence of the interaction between two nonlinear terms on the stable wave speed interval, and give the maximal stable range for the wave speed. Finally, some conclusions are given in this paper.

Nonlinear Decay of Alfvén Waves Driven by Interplaying Two- and Three-dimensional Nonlinear Interactions

NASA Astrophysics Data System (ADS)

Zhao, J. S.; Voitenko, Y.; De Keyser, J.; Wu, D. J.

2018-04-01

We study the decay of Alfvén waves in the solar wind, accounting for the joint operation of two-dimensional (2D) scalar and three-dimensional (3D) vector nonlinear interactions between Alfvén and slow waves. These interactions have previously been studied separately in long- and short-wavelength limits where they lead to 2D scalar and 3D vector decays, correspondingly. The joined action of the scalar and vector interactions shifts the transition between 2D and 3D decays to significantly smaller wavenumbers than was predicted by Zhao et al. who compared separate scalar and vector decays. In application to the broadband Alfvén waves in the solar wind, this means that the vector nonlinear coupling dominates in the extended wavenumber range 5 × 10‑4 ≲ ρ i k 0⊥ ≲ 1, where the decay is essentially 3D and nonlocal, generating product Alfvén and slow waves around the ion gyroscale. Here ρ i is the ion gyroradius, and k 0⊥ is the pump Alfvén wavenumber. It appears that, except for the smallest wavenumbers at and below {ρ }i{k}0\\perp ∼ {10}-4 in Channel I, the nonlinear decay of magnetohydrodynamic Alfvén waves propagating from the Sun is nonlocal and cannot generate counter-propagating Alfvén waves with similar scales needed for the turbulent cascade. Evaluation of the nonlinear frequency shift shows that product Alfvén waves can still be approximately described as normal Alfvénic eigenmodes. On the contrary, nonlinearly driven slow waves deviate considerably from normal modes and are therefore difficult to identify on the basis of their phase velocities and/or polarization.

Parametric traveling wave amplifier with a low pump frequency

NASA Astrophysics Data System (ADS)

Marchenko, V. F.; Streltsov, A. M.; Zhmurov, S. E.

1983-01-01

Consideration is given to the model of a parametric traveling wave amplifier with a cubic nonlinearity in the form of an LF filter with MOS varactors. The operation of the amplifier is analyzed with allowance for wave damping and nonlinearity saturation, and the nonlinear mode of operation is examined. Experimental results are discussed, with emphasis on the amplitude-frequency response characteristics.

Anderson localisation and optical-event horizons in rogue-soliton generation.

PubMed

Saleh, Mohammed F; Conti, Claudio; Biancalana, Fabio

2017-03-06

We unveil the relation between the linear Anderson localisation process and nonlinear modulation instability. Anderson localised modes are formed in certain temporal intervals due to the random background noise. Such localised modes seed the formation of solitary waves that will appear during the modulation instability process at those preferred intervals. Afterwards, optical-event horizon effects between dispersive waves and solitons produce an artificial collective acceleration that favours the collision of solitons, which could eventually lead to a rogue-soliton generation.

Integrated optical circuit engineering IV; Proceedings of the Meeting, Cambridge, MA, Sept. 16, 17, 1986

NASA Astrophysics Data System (ADS)

Mentzer, Mark A.; Sriram, S.

The design and implementation of integrated optical circuits are discussed in reviews and reports. Topics addressed include lithium niobate devices, silicon integrated optics, waveguide phenomena, coupling considerations, processing technology, nonlinear guided-wave optics, integrated optics for fiber systems, and systems considerations and applications. Also included are eight papers and a panel discussion from an SPIE conference on the processing of guided-wave optoelectronic materials (held in Los Angeles, CA, on January 21-22, 1986).

Numerical Simulation of Focused Shock Shear Waves in Soft Solids and a Two-Dimensional Nonlinear Homogeneous Model of the Brain

PubMed Central

Giammarinaro, B.; Coulouvrat, F.; Pinton, G.

2016-01-01

Shear waves that propagate in soft solids, such as the brain, are strongly nonlinear and can develop into shock waves in less than one wavelength. We hypothesize that these shear shock waves could be responsible for certain types of traumatic brain injuries (TBI) and that the spherical geometry of the skull bone could focus shear waves deep in the brain, generating diffuse axonal injuries. Theoretical models and numerical methods that describe nonlinear polarized shear waves in soft solids such as the brain are presented. They include the cubic nonlinearities that are characteristic of soft solids and the specific types of nonclassical attenuation and dispersion observed in soft tissues and the brain. The numerical methods are validated with analytical solutions, where possible, and with self-similar scaling laws where no known solutions exist. Initial conditions based on a human head X-ray microtomography (CT) were used to simulate focused shear shock waves in the brain. Three regimes are investigated with shock wave formation distances of 2.54 m, 0.018 m, and 0.0064 m. We demonstrate that under realistic loading scenarios, with nonlinear properties consistent with measurements in the brain, and when the shock wave propagation distance and focal distance coincide, nonlinear propagation can easily overcome attenuation to generate shear shocks deep inside the brain. Due to these effects, the accelerations in the focal are larger by a factor of 15 compared to acceleration at the skull surface. These results suggest that shock wave focusing could be responsible for diffuse axonal injuries. PMID:26833489

Nonlinear viscous higher harmonics generation due to incident and reflecting internal wave beam collision

NASA Astrophysics Data System (ADS)

Aksu, Anil A.

2017-09-01

In this paper, we have considered the non-linear effects arising due to the collision of incident and reflected internal wave beams. It has already been shown analytically [Tabaei et al., "Nonlinear effects in reflecting and colliding internal wave beams," J. Fluid Mech. 526, 217-243 (2005)] and numerically [Rodenborn et al., "Harmonic generation by reflecting internal waves," Phys. Fluids 23, 026601 (2011)] that the internal wave beam collision generates the higher harmonics and mean flow in a linear stratification. In this paper, similar to previous analytical work, small amplitude wave theory is employed; however, it is formulated from energetics perspective which allows considering internal wave beams as the product of slowly varying amplitude and fast complex exponential. As a result, the mean energy propagation equation for the second harmonic wave is obtained. Finally, a similar dependence on the angle of incidence is obtained for the non-linear energy transfer to the second harmonic with previous analyses. A possible physical mechanism for this angle dependence on the second harmonic generation is also discussed here. In addition to previous studies, the viscous effects are also included in the mean energy propagation equation for the incident, the reflecting, and the second harmonic waves. Moreover, even though the mean flow obtained here is only confined to the interaction region, it is also affected by viscosity via the decay in the incident and the reflecting internal wave beams. Furthermore, a framework for the non-linear harmonic generation in non-linear stratification is also proposed here.

A numerical investigation on the influence of engine shape and mixing processes on wave engine performance

NASA Astrophysics Data System (ADS)

Erickson, Robert R.

Wave engines are a class of unsteady, air-breathing propulsion devices that use an intermittent combustion process to generate thrust. The inherently simple mechanical design of the wave engine allows for a relatively low cost per unit propulsion system, yet unsatisfactory overall performance has severely limited the development of commercially successful wave engines. The primary objective of this investigation was to develop a more detailed physical understanding of the influence of gas dynamic nonlinearities, unsteady combustion processes, and engine shape on overall wave engine performance. Within this study, several numerical models were developed and applied to wave engines and related applications. The first portion of this investigation examined the influence of duct shape on driven oscillations in acoustic compression devices, which represent a simplified physical system closely related in several ways to the wave engine. A numerical model based on an application of the Galerkin method was developed to simulate large amplitude, one-dimensional acoustic waves driven in closed ducts. Results from this portion of the investigation showed that gas-dynamic nonlinearities significantly influence the properties of driven oscillations by transferring acoustic energy from the fundamental driven mode into higher harmonic modes. The second portion of this investigation presented and analyzed results from a numerical model of wave engine dynamics based on the quasi one-dimensional conservation equations in addition to separate sub-models for mixing and heat release. This model was then used to perform parametric studies of the characteristics of mixing and engine shape. The objectives of these studies were to determine the influence of mixing characteristics and engine shape on overall wave engine performance and to develop insight into the physical processes controlling overall performance trends. Results from this model showed that wave engine performance was strongly dependent on the coupling between the unsteady heat release that drives oscillations in the engine and the characteristics that determine the acoustic properties of the engine such as engine shape and mean property gradients. Simulation results showed that average thrust generation decreased dramatically when the natural acoustic mode frequencies of the engine and the frequency content of the unsteady heat release were not aligned.

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.

Self-action of propagating and standing Lamb waves in the plates exhibiting hysteretic nonlinearity: Nonlinear zero-group velocity modes.

PubMed

Gusev, Vitalyi E; Lomonosov, Alexey M; Ni, Chenyin; Shen, Zhonghua

2017-09-01

An analytical theory accounting for the influence of hysteretic nonlinearity of micro-inhomogeneous plate material on the Lamb waves near the S 1 zero group velocity point is developed. The theory predicts that the main effect of the hysteretic quadratic nonlinearity consists in the modification of the frequency and the induced absorption of the Lamb modes. The effects of the nonlinear self-action in the propagating and standing Lamb waves are expected to be, respectively, nearly twice and three times stronger than those in the plane propagating acoustic waves. The theory is restricted to the simplest hysteretic nonlinearity, which is influencing only one of the Lamé moduli of the materials. However, possible extensions of the theory to the cases of more general hysteretic nonlinearities are discussed as well as the perspectives of its experimental testing. Applications include nondestructive evaluation of micro-inhomogeneous and cracked plates. Copyright © 2017 Elsevier B.V. All rights reserved.

Nonlinear Hysteretic Torsional Waves

NASA Astrophysics Data System (ADS)

Cabaret, J.; Béquin, P.; Theocharis, G.; Andreev, V.; Gusev, V. E.; Tournat, V.

2015-07-01

We theoretically study and experimentally report the propagation of nonlinear hysteretic torsional pulses in a vertical granular chain made of cm-scale, self-hanged magnetic beads. As predicted by contact mechanics, the torsional coupling between two beads is found to be nonlinear hysteretic. This results in a nonlinear pulse distortion essentially different from the distortion predicted by classical nonlinearities and in a complex dynamic response depending on the history of the wave particle angular velocity. Both are consistent with the predictions of purely hysteretic nonlinear elasticity and the Preisach-Mayergoyz hysteresis model, providing the opportunity to study the phenomenon of nonlinear dynamic hysteresis in the absence of other types of material nonlinearities. The proposed configuration reveals a plethora of interesting phenomena including giant amplitude-dependent attenuation, short-term memory, as well as dispersive properties. Thus, it could find interesting applications in nonlinear wave control devices such as strong amplitude-dependent filters.

Constraints on Nonlinear and Stochastic Growth Theories for Type 3 Solar Radio Bursts from the Corona to 1 AU

NASA Technical Reports Server (NTRS)

Cairns, Iver H.; Robinson, P. A.

1998-01-01

Existing, competing theories for coronal and interplanetary type III solar radio bursts appeal to one or more of modulational instability, electrostatic (ES) decay processes, or stochastic growth physics to preserve the electron beam, limit the levels of Langmuir-like waves driven by the beam, and produce wave spectra capable of coupling nonlinearly to generate the observed radio emission. Theoretical constraints exist on the wavenumbers and relative sizes of the wave bandwidth and nonlinear growth rate for which Langmuir waves are subject to modulational instability and the parametric and random phase versions of ES decay. A constraint also exists on whether stochastic growth theory (SGT) is appropriate. These constraints are evaluated here using the beam, plasma, and wave properties (1) observed in specific interplanetary type III sources, (2) predicted nominally for the corona, and (3) predicted at heliocentric distances greater than a few solar radii by power-law models based on interplanetary observations. It is found that the Langmuir waves driven directly by the beam have wavenumbers that are almost always too large for modulational instability but are appropriate to ES decay. Even for waves scattered to lower wavenumbers (by ES decay, for instance), the wave bandwidths are predicted to be too large and the nonlinear growth rates too small for modulational instability to occur for the specific interplanetary events studied or the great majority of Langmuir wave packets in type III sources at arbitrary heliocentric distances. Possible exceptions are for very rare, unusually intense, narrowband wave packets, predominantly close to the Sun, and for the front portion of very fast beams traveling through unusually dilute, cold solar wind plasmas. Similar arguments demonstrate that the ES decay should proceed almost always as a random phase process rather than a parametric process, with similar exceptions. These results imply that it is extremely rare for modulational instability or parametric decay to proceed in type III sources at any heliocentric distance: theories for type III bursts based on modulational instability or parametric decay are therefore not viable in general. In contrast, the constraint on SGT can be satisfied and random phase ES decay can proceed at all heliocentric distances under almost all circumstances. (The contrary circumstances involve unusually slow, broad beams moving through unusually hot regions of the Corona.) The analyses presented here strongly justify extending the existing SGT-based model for interplanetary type III bursts (which includes SGT physics, random phase ES decay, and specific electromagnetic emission mechanisms) into a general theory for type III bursts from the corona to beyond 1 AU. This extended theory enjoys strong theoretical support, explains the characteristics of specific interplanetary type III bursts very well, and can account for the detailed dynamic spectra of type III bursts from the lower corona and solar wind.

Stress evaluation of metallic material under steady state based on nonlinear critically refracted longitudinal wave

NASA Astrophysics Data System (ADS)

Mao, Hanling; Zhang, Yuhua; Mao, Hanying; Li, Xinxin; Huang, Zhenfeng

2018-06-01

This paper presents the study of applying the nonlinear ultrasonic wave to evaluate the stress state of metallic materials under steady state. The pre-stress loading method is applied to guarantee components with steady stress. Three kinds of nonlinear ultrasonic experiments based on critically refracted longitudinal wave are conducted on components which the critically refracted longitudinal wave propagates along x, x1 and x2 direction. Experimental results indicate the second and third order relative nonlinear coefficients monotonically increase with stress, and the normalized relationship is consistent with simplified dislocation models, which indicates the experimental result is logical. The combined ultrasonic nonlinear parameter is proposed, and three stress evaluation models at x direction are established based on three ultrasonic nonlinear parameters, which the estimation error is below 5%. Then two stress detection models at x1 and x2 direction are built based on combined ultrasonic nonlinear parameter, the stress synthesis method is applied to calculate the magnitude and direction of principal stress. The results show the prediction error is within 5% and the angle deviation is within 1.5°. Therefore the nonlinear ultrasonic technique based on LCR wave could be applied to nondestructively evaluate the stress of metallic materials under steady state which the magnitude and direction are included.

Extensions of the Ferry shear wave model for active linear and nonlinear microrheology

PubMed Central

Mitran, Sorin M.; Forest, M. Gregory; Yao, Lingxing; Lindley, Brandon; Hill, David B.

2009-01-01

The classical oscillatory shear wave model of Ferry et al. [J. Polym. Sci. 2:593-611, (1947)] is extended for active linear and nonlinear microrheology. In the Ferry protocol, oscillation and attenuation lengths of the shear wave measured from strobe photographs determine storage and loss moduli at each frequency of plate oscillation. The microliter volumes typical in biology require modifications of experimental method and theory. Microbead tracking replaces strobe photographs. Reflection from the top boundary yields counterpropagating modes which are modeled here for linear and nonlinear viscoelastic constitutive laws. Furthermore, bulk imposed strain is easily controlled, and we explore the onset of normal stress generation and shear thinning using nonlinear viscoelastic models. For this paper, we present the theory, exact linear and nonlinear solutions where possible, and simulation tools more generally. We then illustrate errors in inverse characterization by application of the Ferry formulas, due to both suppression of wave reflection and nonlinearity, even if there were no experimental error. This shear wave method presents an active and nonlinear analog of the two-point microrheology of Crocker et al. [Phys. Rev. Lett. 85: 888 - 891 (2000)]. Nonlocal (spatially extended) deformations and stresses are propagated through a small volume sample, on wavelengths long relative to bead size. The setup is ideal for exploration of nonlinear threshold behavior. PMID:20011614

Shallow near-fault material self organizes so it is just nonlinear in typical strong shaking

NASA Astrophysics Data System (ADS)

Sleep, N. H.

2011-12-01

Cracking within shallow compliant fault zones self-organizes so that strong dynamic stresses marginally exceed the elastic limit. To the first order, the compliant material experiences strain boundary conditions imposed by underlying stiffer rock. A major strike-slip fault yields simple dimensional relations. The near-field velocity pulse is essentially a Love wave. The dynamic strain is the ratio of the measured particle velocity over the deep S-wave velocity. The shallow dynamic stress is this quantity times the local shear modulus. I obtain the equilibrium shear modulus by starting a sequence of earthquakes with intact stiff rock surrounding the shallow fault zone. The imposed dynamic strain in stiff rock causes Coulomb failure and leaves cracks in it wake. Cracked rock is more compliant than the original intact rock. Each subsequent event causes more cracking until the rock becomes compliant enough that it just reaches its elastic limit. Further events maintain the material at the shear modulus where it just fails. Analogously, shallow damaged regolith forms with its shear modulus and S-wave velocity increasing with depth so it just reaches failure during typical strong shaking. The general conclusion is that shallow rocks in seismically active areas just become nonlinear during typical shaking. This process causes transient changes in S-wave velocity, but not strong nonlinear attenuation of seismic waves. Wave amplitudes significantly larger than typical ones would strongly attenuate and strongly damage the rock. The equilibrium shear modulus and S-wave velocity depend only modestly on the effective coefficient of internal friction.

Improving demodulation accuracy of low-coherence interferometer against spatial-frequency nonlinearity

NASA Astrophysics Data System (ADS)

Wang, Shuang; Liu, Tiegen; Jiang, Junfeng; Liu, Kun; Yin, Jinde; Wu, Fan; Zhao, Bofu; Xue, Lei; Mei, Yunqiao; Wu, Zhenhai

2013-12-01

We present an effective method to compensate the spatial-frequency nonlinearity for polarized low-coherence interferometer with location-dependent dispersion element. Through the use of location-dependent dispersive characteristics, the method establishes the exact relationship between wave number and discrete Fourier transform (DFT) serial number. The jump errors in traditional absolute phase algorithm are also avoided with nonlinearity compensation. We carried out experiments with an optical fiber Fabry-Perot (F-P) pressure sensing system to verify the effectiveness. The demodulated error is less than 0.139kPa in the range of 170kPa when using our nonlinearity compensation process in the demodulation.

Localized spatially nonlinear matter waves in atomic-molecular Bose-Einstein condensates with space-modulated nonlinearity

PubMed Central

Yao, Yu-Qin; Li, Ji; Han, Wei; Wang, Deng-Shan; Liu, Wu-Ming

2016-01-01

The intrinsic nonlinearity is the most remarkable characteristic of the Bose-Einstein condensates (BECs) systems. Many studies have been done on atomic BECs with time- and space- modulated nonlinearities, while there is few work considering the atomic-molecular BECs with space-modulated nonlinearities. Here, we obtain two kinds of Jacobi elliptic solutions and a family of rational solutions of the atomic-molecular BECs with trapping potential and space-modulated nonlinearity and consider the effect of three-body interaction on the localized matter wave solutions. The topological properties of the localized nonlinear matter wave for no coupling are analysed: the parity of nonlinear matter wave functions depends only on the principal quantum number n, and the numbers of the density packets for each quantum state depend on both the principal quantum number n and the secondary quantum number l. When the coupling is not zero, the localized nonlinear matter waves given by the rational function, their topological properties are independent of the principal quantum number n, only depend on the secondary quantum number l. The Raman detuning and the chemical potential can change the number and the shape of the density packets. The stability of the Jacobi elliptic solutions depends on the principal quantum number n, while the stability of the rational solutions depends on the chemical potential and Raman detuning. PMID:27403634

Plasma Waves Associated with Mass-Loaded Comets

NASA Technical Reports Server (NTRS)

Tsurutani, Bruce; Glassmeier, Karl-Heinz

2015-01-01

Plasma waves and instabilities are integrally involved with the plasma "pickup" process and the mass loading of the solar wind (thus the formation of ion tails and the magnetic tails). Anisotropic plasmas generated by solar wind-comet interactions (the bow shock, magnetic field pileup) cause the generation of plasma waves which in turn "smooth out" these discontinuities. The plasma waves evolve and form plasma turbulence. Comets are perhaps the best "laboratories" to study waves and turbulence because over time (and distance) one can identify the waves and their evolution. We will argue that comets in some ways are better laboratories than magnetospheres, interplanetary space and fusion devices to study nonlinear waves and their evolution.

Effects of obliquely opposing and following currents on wave propagation in a new 3D wave-current basin

NASA Astrophysics Data System (ADS)

Lieske, Mike; Schlurmann, Torsten

2016-04-01

INTRODUCTION & MOTIVATION The design of structures in coastal and offshore areas and their maintenance are key components of coastal protection. Usually, assessments of processes and loads on coastal structures are derived from experiments with flow and wave parameters in separate physical models. However, Peregrin (1976) already points out that processes in natural shallow coastal waters flow and sea state processes do not occur separately, but influence each other nonlinearly. Kemp & Simons (1982) perform 2D laboratory tests and study the interactions between a turbulent flow and following waves. They highlight the significance of wave-induced changes in the current properties, especially in the mean flow profiles, and draw attention to turbulent fluctuations and bottom shear stresses. Kemp & Simons (1983) also study these processes and features with opposing waves. Studies on the wave-current interaction in three-dimensional space for a certain wave height, wave period and water depth were conducted by MacIver et al. (2006). The research focus is set on the investigation of long-crested waves on obliquely opposing and following currents in the new 3D wave-current basin. METHODOLOGY In a first step the flow analysis without waves is carried out and includes measurements of flow profiles in the sweet spot of the basin at predefined measurement positions. Five measuring points in the water column have been delineated in different water depths in order to obtain vertical flow profiles. For the characterization of the undisturbed flow properties in the basin, an uniformly distributed flow was generated in the wave basin. In the second step wave analysis without current, the unidirectional wave propagation and wave height were investigated for long-crested waves in intermediate wave conditions. In the sweet spot of the wave basin waves with three different wave directions, three wave periods and uniform wave steepness were examined. For evaluation, we applied a common 3D wave analysis method, the Bayesian Directional Spectrum method (BDM). BDM was presented by Hashimoto et al. (1988). Lastly, identification of the wave-current interaction, the results from experiment with simultaneous waves and currents are compared with results for only-currents and only-waves in order to identify and exemplify the significance of nonlinear interaction processes. RESULTS The first results of the wave-current interaction show, as expected, a reduction in the wave height in the direction of flow and an increase in wave heights against the flow with unidirectional monochromatic waves. The superposition of current and orbital velocities cannot be conducted linearly. Furthermore, the results show a current domination for low wave periods and wave domination for larger wave periods. The criterion of a current or wave domination will be presented in the presentation. ACKNOWLEDGEMENT The support of the KFKI research project "Seegangsbelastungen (Seele)" (Contract No. 03KIS107) by the German "Federal Ministry of Education and Research (BMBF)" is gratefully acknowledged.

Topological approximation of the nonlinear Anderson model

NASA Astrophysics Data System (ADS)

Milovanov, Alexander V.; Iomin, Alexander

2014-06-01

We study the phenomena of Anderson localization in the presence of nonlinear interaction on a lattice. A class of nonlinear Schrödinger models with arbitrary power nonlinearity is analyzed. We conceive the various regimes of behavior, depending on the topology of resonance overlap in phase space, ranging from a fully developed chaos involving Lévy flights to pseudochaotic dynamics at the onset of delocalization. It is demonstrated that the quadratic nonlinearity plays a dynamically very distinguished role in that it is the only type of power nonlinearity permitting an abrupt localization-delocalization transition with unlimited spreading already at the delocalization border. We describe this localization-delocalization transition as a percolation transition on the infinite Cayley tree (Bethe lattice). It is found in the vicinity of the criticality that the spreading of the wave field is subdiffusive in the limit t →+∞. The second moment of the associated probability distribution grows with time as a power law ∝ tα, with the exponent α =1/3 exactly. Also we find for superquadratic nonlinearity that the analog pseudochaotic regime at the edge of chaos is self-controlling in that it has feedback on the topology of the structure on which the transport processes concentrate. Then the system automatically (without tuning of parameters) develops its percolation point. We classify this type of behavior in terms of self-organized criticality dynamics in Hilbert space. For subquadratic nonlinearities, the behavior is shown to be sensitive to the details of definition of the nonlinear term. A transport model is proposed based on modified nonlinearity, using the idea of "stripes" propagating the wave process to large distances. Theoretical investigations, presented here, are the basis for consistency analysis of the different localization-delocalization patterns in systems with many coupled degrees of freedom in association with the asymptotic properties of the transport.

Nonlinear wave interaction in a plasma column

NASA Technical Reports Server (NTRS)

Larsen, J.

1972-01-01

Two particular cases of nonlinear wave interaction in a plasma column were investigated. The frequencies of the waves were on the order of magnitude of the electron plasma frequency, and ion motion was neglected. The nonlinear coupling of slow waves on a plasma column was studied by means of cold plasma theory, and the case of a plasma column surrounded by an infinite dielectric in the absence of a magnetic field was also examined. Nonlinear scattering from a plasma column in an electromagnetic field having it's magnetic field parallel to the axis of the column was investigated. Some experimental results on mode conversion in the presence of loss are presented along with some observations of nonlinear scattering, The effect of the earth's magnetic field and of discharge symmetry on the radiation pattern are discussed.

Evidence for self-refraction in a convergence zone: NPE (Nonlinear progressive wave equation) model results

NASA Technical Reports Server (NTRS)

Mcdonald, B. Edward; Plante, Daniel R.

1989-01-01

The nonlinear progressive wave equation (NPE) model was developed by the Naval Ocean Research and Development Activity during 1982 to 1987 to study nonlinear effects in long range oceanic propagation of finite amplitude acoustic waves, including weak shocks. The NPE model was applied to propagation of a generic shock wave (initial condition provided by Sandia Division 1533) in a few illustrative environments. The following consequences of nonlinearity are seen by comparing linear and nonlinear NPE results: (1) a decrease in shock strength versus range (a well-known result of entropy increases at the shock front); (2) an increase in the convergence zone range; and (3) a vertical meandering of the energy path about the corresponding linear ray path. Items (2) and (3) are manifestations of self-refraction.

Nonlinear Waves in the Terrestrial Quasiparallel Foreshock.

PubMed

Hnat, B; Kolotkov, D Y; O'Connell, D; Nakariakov, V M; Rowlands, G

2016-12-02

We provide strongly conclusive evidence that the cubic nonlinearity plays an important part in the evolution of the large amplitude magnetic structures in the terrestrial foreshock. Large amplitude nonlinear wave trains at frequencies above the proton cyclotron frequency are identified after nonharmonic slow variations are filtered out by applying the empirical mode decomposition. Numerical solutions of the derivative nonlinear Schrödinger equation, predicted analytically by the use of a pseudopotential approach, are found to be consistent with the observed wave forms. The approximate phase speed of these nonlinear waves, indicated by the parameters of numerical solutions, is of the order of the local Alfvén speed. We suggest that the feedback of the large amplitude fluctuations on background plasma is reflected in the evolution of the pseudopotential.

Modelization of highly nonlinear waves in coastal regions

NASA Astrophysics Data System (ADS)

Gouin, Maïté; Ducrozet, Guillaume; Ferrant, Pierre

2015-04-01

The proposed work deals with the development of a highly non-linear model for water wave propagation in coastal regions. The accurate modelization of surface gravity waves is of major interest in ocean engineering, especially in the field of marine renewable energy. These marine structures are intended to be settled in coastal regions where the effect of variable bathymetry may be significant on local wave conditions. This study presents a numerical model for the wave propagation with complex bathymetry. It is based on High-Order Spectral (HOS) method, initially limited to the propagation of non-linear wave fields over flat bottom. Such a model has been developed and validated at the LHEEA Lab. (Ecole Centrale Nantes) over the past few years and the current developments will enlarge its application range. This new numerical model will keep the interesting numerical properties of the original pseudo-spectral approach (convergence, efficiency with the use of FFTs, …) and enable the possibility to propagate highly non-linear wave fields over long time and large distance. Different validations will be provided in addition to the presentation of the method. At first, Bragg reflection will be studied with the proposed approach. If the Bragg condition is satisfied, the reflected wave generated by a sinusoidal bottom patch should be amplified as a result of resonant quadratic interactions between incident wave and bottom. Comparisons will be provided with experiments and reference solutions. Then, the method will be used to consider the transformation of a non-linear monochromatic wave as it propagates up and over a submerged bar. As the waves travel up the front slope of the bar, it steepens and high harmonics are generated due to non-linear interactions. Comparisons with experimental data will be provided. The different test cases will assess the accuracy and efficiency of the method proposed.

Nonlinear wave-wave interactions in the subauroral ionosphere on the basis of ISIS-2 satellite observations of Siple station VLF signals

NASA Technical Reports Server (NTRS)

Ohnami, S.; Hayakawa, M.; Bell, T. F.; Ondoh, T.

1993-01-01

Nonlinear wave-wave interaction between signals from a ground-based VLF transmitter and narrow-band ELF emissions in the subauroral ionosphere is studied by means of the bispectrum and bicoherence analysis. A bicoherence analysis has indicated that the sideband structures around the Siple transmitter signal received onboard the ISIS satellite are due to the nonlinear interaction between the Siple VLF signal and the pre-existing ELF emission.

Initial-value problem for the Gardner equation applied to nonlinear internal waves

NASA Astrophysics Data System (ADS)

Rouvinskaya, Ekaterina; Kurkina, Oxana; Kurkin, Andrey; Talipova, Tatiana; Pelinovsky, Efim

2017-04-01

The Gardner equation is a fundamental mathematical model for the description of weakly nonlinear weakly dispersive internal waves, when cubic nonlinearity cannot be neglected. Within this model coefficients of quadratic and cubic nonlinearity can both be positive as well as negative, depending on background conditions of the medium, where waves propagate (sea water density stratification, shear flow profile) [Rouvinskaya et al., 2014, Kurkina et al., 2011, 2015]. For the investigation of weakly dispersive behavior in the framework of nondimensional Gardner equation with fixed (positive) sign of quadratic nonlinearity and positive or negative cubic nonlinearity {eq1} partial η/partial t+6η( {1± η} )partial η/partial x+partial ^3η/partial x^3=0, } the series of numerical experiments of initial-value problem was carried out for evolution of a bell-shaped impulse of negative polarity (opposite to the sign of quadratic nonlinear coefficient): {eq2} η(x,t=0)=-asech2 ( {x/x0 } ), for which amplitude a and width x0 was varied. Similar initial-value problem was considered in the paper [Trillo et al., 2016] for the Korteweg - de Vries equation. For the Gardner equation with different signs of cubic nonlinearity the initial-value problem for piece-wise constant initial condition was considered in detail in [Grimshaw et al., 2002, 2010]. It is widely known, for example, [Pelinovsky et al., 2007], that the Gardner equation (1) with negative cubic nonlinearity has a family of classic solitary wave solutions with only positive polarity,and with limiting amplitude equal to 1. Therefore evolution of impulses (2) of negative polarity (whose amplitudes a were varied from 0.1 to 3, and widths at the level of a/2 were equal to triple width of solitons with the same amplitude for a 1) was going on a universal scenario with the generation of nonlinear Airy wave. For the Gardner equation (1) with the positive cubic nonlinearity coefficient there exist two one-parametric families of solitons (family with positive polarity, and family with negative polarity bounded below by the amplitude of 2) and two-parametric family of breathers (oscillatory wave packets). In this case varying amplitude and width of bell-shaped initial impulse leads to plenty of different evolutionary scenarios with the generation of solitary waves, breathers, solibores and nonlinear Airy wave in their various combinations. Statistical analysis of the wave field in time shows almost permanent substantial exceedance of the level of the significant wave height in some position in spatial coordinate. Evolution of Fourier spectrum of the wave field is also analyzed, and its behavior after a long time of initial wave evolution demonstrates the power asymptotic for small wave numbers and exponential asymptotic for large wave numbers. The presented results of research are obtained with the support of the grant of the President of the Russian Federation for state support of the young Russian scientists - Candidates of Sciences (MK-5208.2016.5) and Russian Foundation for Basic Research grant 16-05-00049. References: Grimshaw R., Pelinovsky D., Pelinovsky E and Slunyaev A. Generation of large-amplitude solitons in the extended Korteweg-de Vries equation // Chaos, 2002. - V.12. - No 4. - 1070-1076. Grimshaw, R., Slunyaev, A., and Pelinovsky, E. Generation of solitons and breathers in the extended Korteweg-de Vries equation with positive cubic nonlinearity //Chaos, 2010. - vol. 20.-013102. Kurkina O.E., Kurkin A.A., Soomere T., Pelinovsky E.N., Rouvinskaya E.A. Higher-order (2+4) Korteweg-de Vries - like equation for interfacial waves in a symmetric three-layer fluid // Physics of Fluids, 2011. - Volume 23. - Issue 11. - p.116602--1--13. Kurkina O., Rouvinskaya E., Talipova T., Kurkin A., Pelinovsky E. Nonlinear disintegration of sine wave in the framework of the Gardner equation // Physica D: Nonlinear Phenomena, 2015. - doi:10.1016/j.physd.2015.12.007. Pelinovsky E., Polukhina O., Slunyaev A., Talipova T. Internal solitary waves // Chapter 4 in the book ``Solitary Waves in Fluids''. WIT Press. Southampton, Boston. 2007. P. 85 - 110. Rouvinskaya E., Kurkina O., Kurkin A. Dynamics of nonlinear internal gravity waves in layered fluids // NNSTU n.a. R.E. Alekseev Press - Nizhny Novgorod, 2014 - 160 p. [In Russian] Trillo S., Klein M., Clauss G., Onorato M. Observation of dispersive shock waves developing from initial depressions in shallow water // Physica D, 2016. - http://dx.doi.org/10.1016/j.physd.2016.01.007.

Mode Identification of High-Amplitude Pressure Waves in Liquid Rocket Engines

NASA Astrophysics Data System (ADS)

EBRAHIMI, R.; MAZAHERI, K.; GHAFOURIAN, A.

2000-01-01

Identification of existing instability modes from experimental pressure measurements of rocket engines is difficult, specially when steep waves are present. Actual pressure waves are often non-linear and include steep shocks followed by gradual expansions. It is generally believed that interaction of these non-linear waves is difficult to analyze. A method of mode identification is introduced. After presumption of constituent modes, they are superposed by using a standard finite difference scheme for solution of the classical wave equation. Waves are numerically produced at each end of the combustion tube with different wavelengths, amplitudes, and phases with respect to each other. Pressure amplitude histories and phase diagrams along the tube are computed. To determine the validity of the presented method for steep non-linear waves, the Euler equations are numerically solved for non-linear waves, and negligible interactions between these waves are observed. To show the applicability of this method, other's experimental results in which modes were identified are used. Results indicate that this simple method can be used in analyzing complicated pressure signal measurements.

Multiscale Approach For Simulating Nonlinear Wave Propagation In Materials with Localized Microdamage

NASA Astrophysics Data System (ADS)

Vanaverbeke, Sigfried; Van Den Abeele, Koen

2006-05-01

A multiscale model for the simulation of two-dimensional nonlinear wave propagation in microcracked materials exhibiting hysteretic nonlinearity is presented. We use trigger-like elements with a two state nonlinear stress-strain relation to simulate microcracks at the microlevel. A generalized Preisach space approach, based on the eigenstress-eigenstrain formulation, upscales the microscopic state relation to the mesoscopic level. The macroscopic response of the sample to an arbitrary excitation signal is then predicted using a staggered grid Elastodynamic Finite Integration Technique (EFIT) formalism. We apply the model to investigate spectral changes of a pulsed signal traversing a localized microdamaged region with hysteretic nonlinearity in a plate, and to study the influence of a superficial region with hysteretic nonlinearity on the nonlinear Rayleigh wave propagation.

Two Step Acceleration Process of Electrons in the Outer Van Allen Radiation Belt by Time Domain Electric Field Bursts and Large Amplitude Chorus Waves

NASA Astrophysics Data System (ADS)

Agapitov, O. V.; Mozer, F.; Artemyev, A.; Krasnoselskikh, V.; Lejosne, S.

2014-12-01

A huge number of different non-linear structures (double layers, electron holes, non-linear whistlers, etc) have been observed by the electric field experiment on the Van Allen Probes in conjunction with relativistic electron acceleration in the Earth's outer radiation belt. These structures, found as short duration (~0.1 msec) quasi-periodic bursts of electric field in the high time resolution electric field waveform, have been called Time Domain Structures (TDS). They can quite effectively interact with radiation belt electrons. Due to the trapping of electrons into these non-linear structures, they are accelerated up to ~10 keV and their pitch angles are changed, especially for low energies (˜1 keV). Large amplitude electric field perturbations cause non-linear resonant trapping of electrons into the effective potential of the TDS and these electrons are then accelerated in the non-homogeneous magnetic field. These locally accelerated electrons create the "seed population" of several keV electrons that can be accelerated by coherent, large amplitude, upper band whistler waves to MeV energies in this two step acceleration process. All the elements of this chain acceleration mechanism have been observed by the Van Allen Probes.

New method to determine the refractive index and the absorption coefficient of organic nonlinear crystals in the ultra-wideband THz region.

PubMed

Ohno, Seigo; Miyamoto, Katsuhiko; Minamide, Hiroaki; Ito, Hiromasa

2010-08-02

A method for simultaneously measuring the refractive index and absorption coefficient of nonlinear optical crystals in the ultra-wideband terahertz (THz) region is described. This method is based on the analysis of a collinear difference frequency generation (DFG) process using a tunable, dual-wavelength, optical parametric oscillator. The refractive index and the absorption coefficient in the organic nonlinear crystal DAST were experimentally determined in the frequency range 2.5-26.2 THz by measuring the THz-wave output using DFG. The resultant refractive index in the x-direction was approximately 2.3, while the absorption spectrum was in good agreement with FT-IR measurements. The output of the DAST-DFG THz-wave source was optimized to the phase-matching condition using the measured refractive index spectrum in THz region, which resulted in an improvement in the output power of up to a factor of nine.

Semiempirical Dissipation Source Functions for Ocean Waves. Part 1: Definition, Calibration, and Validation

DTIC Science & Technology

2010-09-01

REPORT DATE (DD-MM- YYYY) 02-03-2011 2. REPORT TYPE Journal Article 3 . DATES COVERED (From - To) 4. TITLE AND SUBTITLE Semiempirical Dissipation...Spectral wave modeling has been performed for the "£_ <• , r. , r , r M> l . en • .u u i .• rll ;imi nl .K. •ihr (l’ last...wind output). The nonlinear scattering term Sn\\ repre- sents all processes that lead to an exchange of wave en - ergy between the different spectral

Nonlinear waves in reaction-diffusion systems: The effect of transport memory

NASA Astrophysics Data System (ADS)

Manne, K. K.; Hurd, A. J.; Kenkre, V. M.

2000-04-01

Motivated by the problem of determining stress distributions in granular materials, we study the effect of finite transport correlation times on the propagation of nonlinear wave fronts in reaction-diffusion systems. We obtain results such as the possibility of spatial oscillations in the wave-front shape for certain values of the system parameters and high enough wave-front speeds. We also generalize earlier known results concerning the minimum wave-front speed and shape-speed relationships stemming from the finiteness of the correlation times. Analytic investigations are made possible by a piecewise linear representation of the nonlinearity.

High-order rogue waves in vector nonlinear Schrödinger equations.

PubMed

Ling, Liming; Guo, Boling; Zhao, Li-Chen

2014-04-01

We study the dynamics of high-order rogue waves (RWs) in two-component coupled nonlinear Schrödinger equations. We find that four fundamental rogue waves can emerge from second-order vector RWs in the coupled system, in contrast to the high-order ones in single-component systems. The distribution shape can be quadrilateral, triangle, and line structures by varying the proper initial excitations given by the exact analytical solutions. The distribution pattern for vector RWs is more abundant than that for scalar rogue waves. Possibilities to observe these new patterns for rogue waves are discussed for a nonlinear fiber.

Excitation of plasma waves by nonlinear currents induced by a high-frequency electromagnetic pulse

NASA Astrophysics Data System (ADS)

Grishkov, V. E.; Uryupin, S. A.

2017-03-01

Excitation of plasma waves by nonlinear currents induced by a high-frequency electromagnetic pulse is analyzed within the kinetic approach. It is shown that the most efficient source of plasma waves is the nonlinear current arising due to the gradient of the energy density of the high-frequency field. Generation of plasma waves by the drag current is usually less efficient but not negligibly small at relatively high frequencies of electron-ion collisions. The influence of electron collisions on the excitation of plasma waves by pulses of different duration is described quantitatively.

Excitation of plasma waves by nonlinear currents induced by a high-frequency electromagnetic pulse

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

Grishkov, V. E.; Uryupin, S. A., E-mail: uryupin@sci.lebedev.ru

Excitation of plasma waves by nonlinear currents induced by a high-frequency electromagnetic pulse is analyzed within the kinetic approach. It is shown that the most efficient source of plasma waves is the nonlinear current arising due to the gradient of the energy density of the high-frequency field. Generation of plasma waves by the drag current is usually less efficient but not negligibly small at relatively high frequencies of electron–ion collisions. The influence of electron collisions on the excitation of plasma waves by pulses of different duration is described quantitatively.

Four wave mixing as a probe of the vacuum

NASA Astrophysics Data System (ADS)

Tennant, Daniel M.

2016-06-01

Much attention has been paid to the quantum structure of the vacuum. Higher order processes in quantum electrodynamics are strongly believed to cause polarization and even breakdown of the vacuum in the presence of strong fields soon to be accessible in high intensity laser experiments. Less explored consequences of strong field electrodynamics include effects from Born-Infeld type of electromagnetic theories, a nonlinear electrodynamics that follows from classical considerations as opposed to coupling to virtual fluctuations. In this article, I will demonstrate how vacuum four wave mixing has the possibility to differentiate between these two types of vacuum responses: quantum effects on one hand and nonlinear classical extensions on the other.

Observation of Dispersive Shock Waves, Solitons, and Their Interactions in Viscous Fluid Conduits.

PubMed

Maiden, Michelle D; Lowman, Nicholas K; Anderson, Dalton V; Schubert, Marika E; Hoefer, Mark A

2016-04-29

Dispersive shock waves and solitons are fundamental nonlinear excitations in dispersive media, but dispersive shock wave studies to date have been severely constrained. Here, we report on a novel dispersive hydrodynamic test bed: the effectively frictionless dynamics of interfacial waves between two high viscosity contrast, miscible, low Reynolds number Stokes fluids. This scenario is realized by injecting from below a lighter, viscous fluid into a column filled with high viscosity fluid. The injected fluid forms a deformable pipe whose diameter is proportional to the injection rate, enabling precise control over the generation of symmetric interfacial waves. Buoyancy drives nonlinear interfacial self-steepening, while normal stresses give rise to the dispersion of interfacial waves. Extremely slow mass diffusion and mass conservation imply that the interfacial waves are effectively dissipationless. This enables high fidelity observations of large amplitude dispersive shock waves in this spatially extended system, found to agree quantitatively with a nonlinear wave averaging theory. Furthermore, several highly coherent phenomena are investigated including dispersive shock wave backflow, the refraction or absorption of solitons by dispersive shock waves, and the multiphase merging of two dispersive shock waves. The complex, coherent, nonlinear mixing of dispersive shock waves and solitons observed here are universal features of dissipationless, dispersive hydrodynamic flows.

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

Quantum X waves with orbital angular momentum in nonlinear dispersive media

NASA Astrophysics Data System (ADS)

Ornigotti, Marco; Conti, Claudio; Szameit, Alexander

2018-06-01

We present a complete and consistent quantum theory of generalised X waves with orbital angular momentum in dispersive media. We show that the resulting quantised light pulses are affected by neither dispersion nor diffraction and are therefore resilient against external perturbations. The nonlinear interaction of quantised X waves in quadratic and Kerr nonlinear media is also presented and studied in detail.

Device and method for generating a beam of acoustic energy from a borehole, and applications thereof

DOEpatents

Vu, Cung Khac; Sinha, Dipen N.; Pantea, Cristian; Nihei, Kurt T.; Schmitt, Denis P.; Skelt, Chirstopher

2013-10-15

In some aspects of the invention, a method of generating a beam of acoustic energy in a borehole is disclosed. The method includes generating a first acoustic wave at a first frequency; generating a second acoustic wave at a second frequency different than the first frequency, wherein the first acoustic wave and second acoustic wave are generated by at least one transducer carried by a tool located within the borehole; transmitting the first and the second acoustic waves into an acoustically non-linear medium, wherein the composition of the non-linear medium produces a collimated beam by a non-linear mixing of the first and second acoustic waves, wherein the collimated beam has a frequency based upon a difference between the first frequency range and the second frequency, and wherein the non-linear medium has a velocity of sound between 100 m/s and 800 m/s.

Towards improved NDE and SHM methodologies incorporating nonlinear structural features

NASA Astrophysics Data System (ADS)

Chillara, Vamshi Krishna

Ultrasound is widely employed in Nondestructive Evaluation (NDE) and Structural Health Monitoring (SHM) applications to detect and characterize damage/defects in materials. In particular, ultrasonic guided waves are considered a foremost candidate for in-situ monitoring applications. Conventional ultrasonic techniques rely on changes/discontinuities in linear elastic material properties, namely the Young's modulus and shear modulus to detect damage. On the other hand, nonlinear ultrasonic techniques that rely on micro-scale nonlinear material/structural behavior are proven to be sensitive to damage induced microstructural changes that precede macro-scale damage and are hence capable of early damage detection. The goal of this thesis is to investigate the capabilities of nonlinear guided waves --- a fusion of nonlinear ultrasonic techniques with the guided wave methodologies for early damage detection. To that end, the thesis focuses on two important aspects of the problem: 1. Wavemechanics - deals with ultrasonic guided wave propagation in nonlinear waveguides; 2. Micromechanics - deals with correlating ultrasonic response with micro-scale nonlinear material behavior. For the development of efficient NDE and SHM methodologies that incorporate nonlinear structural features, a detailed understanding of the above aspects is indispensable. In this thesis, the wavemechanics aspect of the problem is dealt with from both theoretical and numerical standpoints. A generalized theoretical framework is developed to study higher harmonic guided waves in plates. This was employed to study second harmonic guided waves in pipes using a large-radius asymptotic approximation. Second harmonic guided waves in plates are studied from a numerical standpoint. Theoretical predictions are validated and some key aspects of higher harmonic generation in waveguides are outlined. Finally, second harmonic guided waves in plates with inhomogeneous and localized nonlinearities are studied and some important aspects of guided wave mode selection are addressed. The other part of the work focused on developing a micromechanics based understanding of ultrasonic higher harmonic generation. Three important aspects of micro-scale material behavior, namely tension-compression asymmetry, shearnormal coupling and deformation induced asymmetry are identified and their role in ultrasonic higher harmonic generation is discussed. Tension-compression asymmetry is identified to cause second (even) harmonic generation in materials. Then, shearnormal coupling is identified to cause generation of secondary waves of different polarity than the primary waves. In addition, deformation induced anisotropy due to the presence of residual stress/strain and its contribution to ultrasonic higher harmonic generation is qualitatively discussed. Also, the tension-compression asymmetry in the material is quantified using an energy based measure. The above measure is employed to develop a homogenization based approach amenable to multi-scale analysis to correlate microstructure with ultrasonic higher harmonic generation. Finally, experimental investigations concerning third harmonic SH wave generation in plates are carried out and the effect of load and temperature changes on nonlinear ultrasonic measurements are discussed in the context of SHM. It was found that while nonlinear ultrasound is sensitive to micro-scale damage, the relative nonlinearity parameter may not always be the best measure to quantify the nonlinearity as it is subject to spurious effects from changes in environmental factors such as loads and temperature.

Correcting wave predictions with artificial neural networks

NASA Astrophysics Data System (ADS)

Makarynskyy, O.; Makarynska, D.

2003-04-01

The predictions of wind waves with different lead times are necessary in a large scope of coastal and open ocean activities. Numerical wave models, which usually provide this information, are based on deterministic equations that do not entirely account for the complexity and uncertainty of the wave generation and dissipation processes. An attempt to improve wave parameters short-term forecasts based on artificial neural networks is reported. In recent years, artificial neural networks have been used in a number of coastal engineering applications due to their ability to approximate the nonlinear mathematical behavior without a priori knowledge of interrelations among the elements within a system. The common multilayer feed-forward networks, with a nonlinear transfer functions in the hidden layers, were developed and employed to forecast the wave characteristics over one hour intervals starting from one up to 24 hours, and to correct these predictions. Three non-overlapping data sets of wave characteristics, both from a buoy, moored roughly 60 miles west of the Aran Islands, west coast of Ireland, were used to train and validate the neural nets involved. The networks were trained with error back propagation algorithm. Time series plots and scatterplots of the wave characteristics as well as tables with statistics show an improvement of the results achieved due to the correction procedure employed.

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.

The existence of electron-acoustic shock waves and their interactions in a non-Maxwellian plasma with q-nonextensive distributed electrons

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

Han, Jiu-Ning; He, Yong-Lin; Han, Zhen-Hai

2013-07-15

We present a theoretical investigation for the nonlinear interaction between electron-acoustic shock waves in a nonextensive two-electron plasma. The interaction is governed by a pair of Korteweg-de Vries-Burgers equations. We focus on studying the colliding effects on the propagation of shock waves, more specifically, we have studied the effects of plasma parameters, i.e., the nonextensive parameter q, the “hot” to “cold” electron number density ratio α, and the normalized electron kinematic viscosity η{sub 0} on the trajectory changes (phase shifts) of shock waves. It is found that there are trajectory changes (phase shifts) for both colliding shock waves in themore » present plasma system. We also noted that the nonlinearity has no decisive effect on the trajectory changes, the occurrence of trajectory changes may be due to the combined role played by the dispersion and dissipation of the nonlinear structure. Our theoretical study may be beneficial to understand the propagation and interaction of nonlinear electrostatic waves and may brings a possibility to develop the nonlinear theory of electron-acoustic waves in astrophysical plasma systems.« less

Light Diffraction by Large Amplitude Ultrasonic Waves in Liquids

NASA Technical Reports Server (NTRS)

Adler, Laszlo; Cantrell, John H.; Yost, William T.

2016-01-01

Light diffraction from ultrasound, which can be used to investigate nonlinear acoustic phenomena in liquids, is reported for wave amplitudes larger than that typically reported in the literature. Large amplitude waves result in waveform distortion due to the nonlinearity of the medium that generates harmonics and produces asymmetries in the light diffraction pattern. For standing waves with amplitudes above a threshold value, subharmonics are generated in addition to the harmonics and produce additional diffraction orders of the incident light. With increasing drive amplitude above the threshold a cascade of period-doubling subharmonics are generated, terminating in a region characterized by a random, incoherent (chaotic) diffraction pattern. To explain the experimental results a toy model is introduced, which is derived from traveling wave solutions of the nonlinear wave equation corresponding to the fundamental and second harmonic standing waves. The toy model reduces the nonlinear partial differential equation to a mathematically more tractable nonlinear ordinary differential equation. The model predicts the experimentally observed cascade of period-doubling subharmonics terminating in chaos that occurs with increasing drive amplitudes above the threshold value. The calculated threshold amplitude is consistent with the value estimated from the experimental data.

The effects of five-order nonlinear on the dynamics of dark solitons in optical fiber.

PubMed

He, Feng-Tao; Wang, Xiao-Lin; Duan, Zuo-Liang

2013-01-01

We study the influence of five-order nonlinear on the dynamic of dark soliton. Starting from the cubic-quintic nonlinear Schrodinger equation with the quadratic phase chirp term, by using a similarity transformation technique, we give the exact solution of dark soliton and calculate the precise expressions of dark soliton's width, amplitude, wave central position, and wave velocity which can describe the dynamic behavior of soliton's evolution. From two different kinds of quadratic phase chirps, we mainly analyze the effect on dark soliton's dynamics which different fiver-order nonlinear term generates. The results show the following two points with quintic nonlinearities coefficient increasing: (1) if the coefficients of the quadratic phase chirp term relate to the propagation distance, the solitary wave displays a periodic change and the soliton's width increases, while its amplitude and wave velocity reduce. (2) If the coefficients of the quadratic phase chirp term do not depend on propagation distance, the wave function only emerges in a fixed area. The soliton's width increases, while its amplitude and the wave velocity reduce.

The Effects of Five-Order Nonlinear on the Dynamics of Dark Solitons in Optical Fiber

PubMed Central

Wang, Xiao-Lin; Duan, Zuo-Liang

2013-01-01

We study the influence of five-order nonlinear on the dynamic of dark soliton. Starting from the cubic-quintic nonlinear Schrodinger equation with the quadratic phase chirp term, by using a similarity transformation technique, we give the exact solution of dark soliton and calculate the precise expressions of dark soliton's width, amplitude, wave central position, and wave velocity which can describe the dynamic behavior of soliton's evolution. From two different kinds of quadratic phase chirps, we mainly analyze the effect on dark soliton's dynamics which different fiver-order nonlinear term generates. The results show the following two points with quintic nonlinearities coefficient increasing: (1) if the coefficients of the quadratic phase chirp term relate to the propagation distance, the solitary wave displays a periodic change and the soliton's width increases, while its amplitude and wave velocity reduce. (2) If the coefficients of the quadratic phase chirp term do not depend on propagation distance, the wave function only emerges in a fixed area. The soliton's width increases, while its amplitude and the wave velocity reduce. PMID:23818814

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.

Ion acoustic wave assisted laser beat wave terahertz generation in a plasma channel

NASA Astrophysics Data System (ADS)

Tyagi, Yachna; Tripathi, Deepak; Walia, Keshav; Garg, Deepak

2018-04-01

Resonant excitation of terahertz (THz) radiation by non-linear mixing of two lasers in the presence of an electrostatic wave is investigated. The electrostatic wave assists in k matching and contributes to non-linear coupling. In this plasma channel, the electron plasma frequency becomes minimum on the axis. The beat frequency ponderomotive force imparts an oscillating velocity to the electrons. In the presence of an ion-acoustic wave, density perturbation due to the ion-acoustic wave couples with the oscillating velocity of the electrons and give rise to non-linear current that gives rise to an ion-acoustic wave frequency assisted THz radiation field. The normalized field amplitude of ion acoustic wave assisted THz varies inversely for ω/ωp . The field amplitude of ion acoustic wave assisted THz decreases as ω/ωp increases.

Generation mechanism of nonlinear ultrasonic Lamb waves in thin plates with randomly distributed micro-cracks.

PubMed

Zhao, Youxuan; Li, Feilong; Cao, Peng; Liu, Yaolu; Zhang, Jianyu; Fu, Shaoyun; Zhang, Jun; Hu, Ning

2017-08-01

Since the identification of micro-cracks in engineering materials is very valuable in understanding the initial and slight changes in mechanical properties of materials under complex working environments, numerical simulations on the propagation of the low frequency S 0 Lamb wave in thin plates with randomly distributed micro-cracks were performed to study the behavior of nonlinear Lamb waves. The results showed that while the influence of the randomly distributed micro-cracks on the phase velocity of the low frequency S 0 fundamental waves could be neglected, significant ultrasonic nonlinear effects caused by the randomly distributed micro-cracks was discovered, which mainly presented as a second harmonic generation. By using a Monte Carlo simulation method, we found that the acoustic nonlinear parameter increased linearly with the micro-crack density and the size of micro-crack zone, and it was also related to the excitation frequency and friction coefficient of the micro-crack surfaces. In addition, it was found that the nonlinear effect of waves reflected by the micro-cracks was more noticeable than that of the transmitted waves. This study theoretically reveals that the low frequency S 0 mode of Lamb waves can be used as the fundamental waves to quantitatively identify micro-cracks in thin plates. Copyright © 2017 Elsevier B.V. All rights reserved.

Stabilization of domain walls between traveling waves by nonlinear mode coupling in Taylor-Couette flow.

PubMed

Heise, M; Hoffmann, Ch; Abshagen, J; Pinter, A; Pfister, G; Lücke, M

2008-02-15

We present a new mechanism that allows the stable existence of domain walls between oppositely traveling waves in pattern-forming systems far from onset. It involves a nonlinear mode coupling that results directly from the nonlinearities in the underlying momentum balance. Our work provides the first observation and explanation of such strongly nonlinearly driven domain walls that separate structured states by a phase generating or annihilating defect. Furthermore, the influence of a symmetry breaking externally imposed flow on the wave domains and the domain walls is studied. The results are obtained for vortex waves in the Taylor-Couette system by combining numerical simulations of the full Navier-Stokes equations and experimental measurements.

Nonlinear runup resonance in a finite bay of variable parabolic cross-section

NASA Astrophysics Data System (ADS)

Postacioglu, Nazmi; Sinan Özeren, M.

2017-04-01

During the recent years, several interesting studies published on the non-linear runup of Tsunamis and other incident waves in channels and bays. Most of these studies use Riemann invariants to tackle the nonlinearities associate with both the incident and reflected phases. However, all of these studies assume that the waves get generated within the bay (essentially assuming bays extending into infinity), rather than conisdering a wave that has been generated in the open sea. Such waves would be reflected not just by the shoreline but also by the bay mouth. This is a setting where a resonance can be induced within the bay. We investigate this problem nonlinearly with a modal approach.

Nonlinear aspects of acoustic radiation force in biomedical applications

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

Ostrovsky, Lev, E-mail: Lev.A.Ostrovsky@noaa.gov; Tsyuryupa, Sergey; Sarvazyan, Armen, E-mail: armen@artannlabs.com

In the past decade acoustic radiation force (ARF) became a powerful tool in numerous biomedical applications. ARF from a focused ultrasound beam acts as a virtual “finger” for remote probing of internal anatomical structures and obtaining diagnostic information. This presentation deals with generation of shear waves by nonlinear focused beams. Albeit the ARF has intrinsically nonlinear origin, in most cases the primary ultrasonic wave was considered in the linear approximation. In this presentation, we consider the effects of nonlinearly distorted beams on generation of shear waves by such beams.

Nonlinear aspects of acoustic radiation force in biomedical applications

NASA Astrophysics Data System (ADS)

Ostrovsky, Lev; Tsyuryupa, Sergey; Sarvazyan, Armen

2015-10-01

In the past decade acoustic radiation force (ARF) became a powerful tool in numerous biomedical applications. ARF from a focused ultrasound beam acts as a virtual "finger" for remote probing of internal anatomical structures and obtaining diagnostic information. This presentation deals with generation of shear waves by nonlinear focused beams. Albeit the ARF has intrinsically nonlinear origin, in most cases the primary ultrasonic wave was considered in the linear approximation. In this presentation, we consider the effects of nonlinearly distorted beams on generation of shear waves by such beams.

AKNS eigenvalue spectrum for densely spaced envelope solitary waves

NASA Astrophysics Data System (ADS)

Slunyaev, Alexey; Starobor, Alexey

2010-05-01

The problem of the influence of one envelope soliton to the discrete eigenvalues of the associated scattering problem for the other envelope soliton, which is situated close to the first one, is discussed. Envelope solitons are exact solutions of the integrable nonlinear Schrödinger equation (NLS). Their generalizations (taking into account the background nonlinear waves [1-4] or strongly nonlinear effects [5, 6]) are possible candidates to rogue waves in the ocean. The envelope solitary waves could be in principle detected in the stochastic wave field by approaches based on the Inverse Scattering Technique in terms of ‘unstable modes' (see [1-3]), or envelope solitons [7-8]. However, densely spaced intense groups influence the spectrum of the associated scattering problem, so that the solitary trains cannot be considered alone. Here we solve the initial-value problem exactly for some simplified configurations of the wave field, representing two closely placed intense wave groups, within the frameworks of the NLS equation by virtue of the solution of the AKNS system [9]. We show that the analogues of the level splitting and the tunneling effects, known in quantum physics, exist in the context of the NLS equation, and thus may be observed in application to sea waves [10]. These effects make the detecting of single solitary wave groups surrounded by other nonlinear wave groups difficult. [1]. A.L. Islas, C.M. Schober (2005) Predicting rogue waves in random oceanic sea states. Phys. Fluids 17, 031701-1-4. [2]. A.R. Osborne, M. Onorato, M. Serio (2005) Nonlinear Fourier analysis of deep-water random surface waves: Theoretical formulation and and experimental observations of rogue waves. 14th Aha Huliko's Winter Workshop, Honolulu, Hawaii. [3]. C.M. Schober, A. Calini (2008) Rogue waves in higher order nonlinear Schrödinger models. In: Extreme Waves (Eds.: E. Pelinovsky & C. Kharif), Springer. [4]. N. Akhmediev, A. Ankiewicz, M. Taki (2009) Waves that appear from nowhere and disappear without a trace. Phys. Lett. A 373, 675-678. [5]. A.I. Dyachenko, V.E. Zakharov (2008) On the formation of freak waves on the surface of deep water. JETP Lett. 88 (5), 307-311. [6]. A.V. Slunyaev (2009) Numerical simulation of "limiting" envelope solitons of gravity waves on deep water. JETP 109, 676-686. [7]. A. Slunyaev, E. Pelinovsky, and C. Guedes Soares (2005) Modeling freak waves from the North Sea. Appl. Ocean Res. 27, 12-22. [8]. A. Slunyaev (2006) Nonlinear analysis and simulations of measured freak wave time series. Eur. J. Mech. B / Fluids 25, 621-635. [9]. M.J. Ablowitz, D.J. Kaup, A.C. Newell, H. Segur (1974) The inverse scattering transform - Fourier analysis for nonlinear problems. Stud. Appl. Math. 53, 249-315. [10]. A.V. Starobor (2009) Interpretation of the inverse scattering data for the analysis of wave groups on water surface. Bachelor degree thesis. N. Novgorod State University, in Russian.

Statistical properties of nonlinear one-dimensional wave fields

NASA Astrophysics Data System (ADS)

Chalikov, D.

2005-06-01

A numerical model for long-term simulation of gravity surface waves is described. The model is designed as a component of a coupled Wave Boundary Layer/Sea Waves model, for investigation of small-scale dynamic and thermodynamic interactions between the ocean and atmosphere. Statistical properties of nonlinear wave fields are investigated on a basis of direct hydrodynamical modeling of 1-D potential periodic surface waves. The method is based on a nonstationary conformal surface-following coordinate transformation; this approach reduces the principal equations of potential waves to two simple evolutionary equations for the elevation and the velocity potential on the surface. The numerical scheme is based on a Fourier transform method. High accuracy was confirmed by validation of the nonstationary model against known solutions, and by comparison between the results obtained with different resolutions in the horizontal. The scheme allows reproduction of the propagation of steep Stokes waves for thousands of periods with very high accuracy. The method here developed is applied to simulation of the evolution of wave fields with large number of modes for many periods of dominant waves. The statistical characteristics of nonlinear wave fields for waves of different steepness were investigated: spectra, curtosis and skewness, dispersion relation, life time. The prime result is that wave field may be presented as a superposition of linear waves is valid only for small amplitudes. It is shown as well, that nonlinear wave fields are rather a superposition of Stokes waves not linear waves. Potential flow, free surface, conformal mapping, numerical modeling of waves, gravity waves, Stokes waves, breaking waves, freak waves, wind-wave interaction.

Test particle simulation study of whistler wave packets observed near Comet Giacobini-Zinner

NASA Astrophysics Data System (ADS)

Kaya, N.; Matsumoto, H.; Tsurutani, B. T.

1989-01-01

Nonlinear interactions of water group ions with large-amplitude whistler wave packets detected at the leading edge of steepened magnetosonic waves observed near Comet Giacobini-Zinner (GZ) are studied using test particle simulations of water-ion interactions with a model wave based on GZ data. Some of the water ions are found to be decelerated in the steepened portion of the magnetosonic wave to the resonance velocity with the whistler wave packets. Through resonance and related nonlinear interaction with the large-amplitude whistler waves, the water ions become trapped by the packet. An energy balance calculation demonstrates that the trapped ions lose their kinetic energy during the trapped motion in the packet. Thus, the nonlinear trapping motion in the wave structure leads to effective energy transfer from the water group ions to the whistler wave packets in the leading edge of the steepened MHD waves.

Internal transport barrier triggered by non-linear lower hybrid wave deposition under condition of beam-driven toroidal rotation

NASA Astrophysics Data System (ADS)

Gao, Q. D.; Budny, R. V.

2015-03-01

By using gyro-Landau fluid transport model (GLF23), time-dependent integrated modeling is carried out using TRANSP to explore the dynamic process of internal transport barrier (ITB) formation in the neutral beam heating discharges. When the current profile is controlled by LHCD (lower hybrid current drive), with appropriate neutral beam injection, the nonlinear interplay between the transport determined gradients in the plasma temperature (Ti,e) and toroidal velocity (Vϕ) and the E×B flow shear (including q-profile) produces transport bifurcations, generating spontaneously a stepwise growing ITB. In the discharge, the constraints imposed by the wave propagation condition causes interplay of the LH driven current distribution with the plasma configuration modification, which constitutes non-linearity in the LH wave deposition. The non-linear effects cause bifurcation in LHCD, generating two distinct quasi-stationary reversed magnetic shear configurations. The change of current profile during the transition period between the two quasi-stationary states results in increase of the E×B shearing flow arising from toroidal rotation. The turbulence transport suppression by sheared E×B flow during the ITB development is analysed, and the temporal evolution of some parameters characterized the plasma confinement is examined. Ample evidence shows that onset of the ITB development is correlated with the enhancement of E×B shearing rate caused by the bifurcation in LHCD. It is suggested that the ITB triggering is associated with the non-linear effects of the LH power deposition.

Location identification of closed crack based on Duffing oscillator transient transition

NASA Astrophysics Data System (ADS)

Liu, Xiaofeng; Bo, Lin; Liu, Yaolu; Zhao, Youxuan; Zhang, Jun; Deng, Mingxi; Hu, Ning

2018-02-01

The existence of a closed micro-crack in plates can be detected by using the nonlinear harmonic characteristics of the Lamb wave. However, its location identification is difficult. By considering the transient nonlinear Lamb under the noise interference, we proposed a location identification method for the closed crack based on the quantitative measurement of Duffing oscillator transient transfer in the phase space. The sliding short-time window was used to create a window truncation of to-be-detected signal. And then, the periodic extension processing for transient nonlinear Lamb wave was performed to ensure that the Duffing oscillator has adequate response time to reach a steady state. The transient autocorrelation method was used to reduce the occurrence of missed harmonic detection due to the random variable phase of nonlinear Lamb wave. Moreover, to overcome the deficiency in the quantitative analysis of Duffing system state by phase trajectory diagram and eliminate the misjudgment caused by harmonic frequency component contained in broadband noise, logic operation method of oscillator state transition function based on circular zone partition was adopted to establish the mapping relation between the oscillator transition state and the nonlinear harmonic time domain information. Final state transition discriminant function of Duffing oscillator was used as basis for identifying the reflected and transmitted harmonics from the crack. Chirplet time-frequency analysis was conducted to identify the mode of generated harmonics and determine the propagation speed. Through these steps, accurate position identification of the closed crack was achieved.

Mechano-optic logic gate controlled by third-order nonlinear optical properties in a rotating ZnO:Au thin film

NASA Astrophysics Data System (ADS)

Carrillo-Delgado, C.; García-Gil, C. I.; Trejo-Valdez, M.; Torres-Torres, C.; García-Merino, J. A.; Martínez-Gutiérrez, H.; Khomenko, A. V.; Torres-Martínez, R.

2016-01-01

Measurements of the third-order nonlinear optical properties exhibited by a ZnO thin solid film deposited on a SnO2 substrate are presented. The samples were prepared by a spray pyrolysis processing route. Scanning electron microscopy analysis and UV-Vis spectroscopy studies were carried out. The picosecond response at 1064 nm was explored by the z-scan technique. A large optical Kerr effect with two-photon absorption was obtained. The inhibition of the nonlinear optical absorption together with a noticeable enhancement in the optical Kerr effect in the sample was achieved by the incorporation of Au nanoparticles into the ZnO film. Additionally, a two-wave mixing configuration at 532 nm was performed and an optical Kerr effect was identified as the main cause of the nanosecond third-order optical nonlinearity. The relaxation time of the photothermal response of the sample was estimated to be about 1 s when the sample was excited by nanosecond single-shots. The rotation of the sample during the nanosecond two-wave mixing experiments was analyzed. It was stated that a non-monotonic relation between rotating frequency and pulse repetition rate governs the thermal contribution to the nonlinear refractive index exhibited by a rotating film. Potential applications for switching photothermal interactions in rotating samples can be contemplated. A rotary logic system dependent on Kerr transmittance in a two-wave mixing experiment was proposed.

Nonlinear Brillouin amplification of finite-duration seeds in the strong coupling regime

NASA Astrophysics Data System (ADS)

Lehmann, G.; Spatschek, K. H.

2013-07-01

Parametric plasma processes received renewed interest in the context of generating ultra-intense and ultra-short laser pulses up to the exawatt-zetawatt regime. Both Raman as well as Brillouin amplifications of seed pulses were proposed. Here, we investigate Brillouin processes in the one-dimensional (1D) backscattering geometry with the help of numerical simulations. For optimal seed amplification, Brillouin scattering is considered in the so called strong coupling (sc) regime. Special emphasis lies on the dependence of the amplification process on the finite duration of the initial seed pulses. First, the standard plane-wave instability predictions are generalized to pulse models, and the changes of initial seed pulse forms due to parametric instabilities are investigated. Three-wave-interaction results are compared to predictions by a new (kinetic) Vlasov code. The calculations are then extended to the nonlinear region with pump depletion. Generation of different seed layers is interpreted by self-similar solutions of the three-wave interaction model. Similar to Raman amplification, shadowing of the rear layers by the leading layers of the seed occurs. The shadowing is more pronounced for initially broad seed pulses. The effect is quantified for Brillouin amplification. Kinetic Vlasov simulations agree with the three-wave interaction predictions and thereby affirm the universal validity of self-similar layer formation during Brillouin seed amplification in the strong coupling regime.

Rogue waves: from nonlinear Schrödinger breather solutions to sea-keeping test.

PubMed

Onorato, Miguel; Proment, Davide; Clauss, Günther; Klein, Marco

2013-01-01

Under suitable assumptions, the nonlinear dynamics of surface gravity waves can be modeled by the one-dimensional nonlinear Schrödinger equation. Besides traveling wave solutions like solitons, this model admits also breather solutions that are now considered as prototypes of rogue waves in ocean. We propose a novel technique to study the interaction between waves and ships/structures during extreme ocean conditions using such breather solutions. In particular, we discuss a state of the art sea-keeping test in a 90-meter long wave tank by creating a Peregrine breather solution hitting a scaled chemical tanker and we discuss its potential devastating effects on the ship.

Rogue Waves: From Nonlinear Schrödinger Breather Solutions to Sea-Keeping Test

PubMed Central

Onorato, Miguel; Proment, Davide; Clauss, Günther; Klein, Marco

2013-01-01

Under suitable assumptions, the nonlinear dynamics of surface gravity waves can be modeled by the one-dimensional nonlinear Schrödinger equation. Besides traveling wave solutions like solitons, this model admits also breather solutions that are now considered as prototypes of rogue waves in ocean. We propose a novel technique to study the interaction between waves and ships/structures during extreme ocean conditions using such breather solutions. In particular, we discuss a state of the art sea-keeping test in a 90-meter long wave tank by creating a Peregrine breather solution hitting a scaled chemical tanker and we discuss its potential devastating effects on the ship. PMID:23405086

Stability of Nonlinear Wave Patterns to the Bipolar Vlasov-Poisson-Boltzmann System

NASA Astrophysics Data System (ADS)

Li, Hailiang; Wang, Yi; Yang, Tong; Zhong, Mingying

2018-04-01

The main purpose of the present paper is to investigate the nonlinear stability of viscous shock waves and rarefaction waves for the bipolar Vlasov-Poisson-Boltzmann (VPB) system. To this end, motivated by the micro-macro decomposition to the Boltzmann equation in Liu and Yu (Commun Math Phys 246:133-179, 2004) and Liu et al. (Physica D 188:178-192, 2004), we first set up a new micro-macro decomposition around the local Maxwellian related to the bipolar VPB system and give a unified framework to study the nonlinear stability of the basic wave patterns to the system. Then, as applications of this new decomposition, the time-asymptotic stability of the two typical nonlinear wave patterns, viscous shock waves and rarefaction waves are proved for the 1D bipolar VPB system. More precisely, it is first proved that the linear superposition of two Boltzmann shock profiles in the first and third characteristic fields is nonlinearly stable to the 1D bipolar VPB system up to some suitable shifts without the zero macroscopic mass conditions on the initial perturbations. Then the time-asymptotic stability of the rarefaction wave fan to compressible Euler equations is proved for the 1D bipolar VPB system. These two results are concerned with the nonlinear stability of wave patterns for Boltzmann equation coupled with additional (electric) forces, which together with spectral analysis made in Li et al. (Indiana Univ Math J 65(2):665-725, 2016) sheds light on understanding the complicated dynamic behaviors around the wave patterns in the transportation of charged particles under the binary collisions, mutual interactions, and the effect of the electrostatic potential forces.

General analytic results for nonlinear waves and solitons in molecular clouds

NASA Technical Reports Server (NTRS)

Adams, Fred C.; Fatuzzo, Marco; Watkins, Richard

1994-01-01

We study nonlinear wave phenomena in self-gravitating fluid systems, with a particular emphasis on applications to molecular clouds. This paper presents analytical results for one spatial dimension. We show that a large class of physical systems can be described by theories with a 'charge density' q(rho); this quantity replaces the density on the right-hand side of the Poisson equation for the gravitational potential. We use this formulation to prove general results about nonlinear wave motions in self-gravitating systems. We show that in order for stationary waves to exist, the total charge (the integral of the charge density over the wave profile) must vanish. This 'no-charge' property for solitary waves is related to the capability of a system to be stable to gravitational perturbations for arbitrarily long wavelengths. We find necessary and sufficient conditions on the charge density for the existence of solitary waves and stationary waves. We study nonlinear wave motions for Jeans-type theories (where q(rho) = rho-rho(sub 0)) and find that nonlinear waves of large amplitude are confined to a rather narrow range of wavelengths. We also study wave motions for molecular clouds threaded by magnetic fields and show how the allowed range of wavelengths is affected by the field strength. Since the gravitational force in one spatial dimension does not fall off with distance, we consider two classes of models with more realistic gravity: Yukawa potentials and a pseudo two-dimensional treatment. We study the allowed types of wave behavior for these models. Finally, we discuss the implications of this work for molecular cloud structure. We argue that molecular clouds can support a wide variety of wave motions and suggest that stationary waves (such as those considered in this paper) may have already been observed.

Fluid nonlinear frequency shift of nonlinear ion acoustic waves in multi-ion species plasmas in the small wave number region

NASA Astrophysics Data System (ADS)

Feng, Q. S.; Xiao, C. Z.; Wang, Q.; Zheng, C. Y.; Liu, Z. J.; Cao, L. H.; He, X. T.

2016-08-01

The properties of the nonlinear frequency shift (NFS), especially the fluid NFS from the harmonic generation of the ion-acoustic wave (IAW) in multi-ion species plasmas, have been researched by Vlasov simulation. Pictures of the nonlinear frequency shift from harmonic generation and particle trapping are shown to explain the mechanism of NFS qualitatively. The theoretical model of the fluid NFS from harmonic generation in multi-ion species plasmas is given, and the results of Vlasov simulation are consistent with the theoretical result of multi-ion species plasmas. When the wave number k λD e is small, such as k λD e=0.1 , the fluid NFS dominates in the total NFS and will reach as large as nearly 15 % when the wave amplitude |e ϕ / Te|˜0.1 , which indicates that in the condition of small k λD e , the fluid NFS dominates in the saturation of stimulated Brillouin scattering, especially when the nonlinear IAW amplitude is large.

Fluid nonlinear frequency shift of nonlinear ion acoustic waves in multi-ion species plasmas in the small wave number region.

PubMed

Feng, Q S; Xiao, C Z; Wang, Q; Zheng, C Y; Liu, Z J; Cao, L H; He, X T

2016-08-01

The properties of the nonlinear frequency shift (NFS), especially the fluid NFS from the harmonic generation of the ion-acoustic wave (IAW) in multi-ion species plasmas, have been researched by Vlasov simulation. Pictures of the nonlinear frequency shift from harmonic generation and particle trapping are shown to explain the mechanism of NFS qualitatively. The theoretical model of the fluid NFS from harmonic generation in multi-ion species plasmas is given, and the results of Vlasov simulation are consistent with the theoretical result of multi-ion species plasmas. When the wave number kλ_{De} is small, such as kλ_{De}=0.1, the fluid NFS dominates in the total NFS and will reach as large as nearly 15% when the wave amplitude |eϕ/T_{e}|∼0.1, which indicates that in the condition of small kλ_{De}, the fluid NFS dominates in the saturation of stimulated Brillouin scattering, especially when the nonlinear IAW amplitude is large.

Interharmonic modulation products as a means to quantify nonlinear D-region interactions

NASA Astrophysics Data System (ADS)

Moore, Robert

Experimental observations performed during dual beam ionospheric HF heating experiments at the High frequency Active Auroral Research Program (HAARP) HF transmitter in Gakona, Alaska are used to quantify the relative importance of specific nonlinear interactions that occur within the D region ionosphere. During these experiments, HAARP broadcast two amplitude modulated HF beams whose center frequencies were separated by less than 20 kHz. One beam was sinusoidally modulated at 500 Hz while the second beam was sinusoidally modulated using a 1-7 kHz linear frequency-time chirp. ELF/VLF observations performed at two different locations (3 and 98 km from HAARP) provide clear evidence of strong interactions between all field components of the two HF beams in the form of low and high order interharmonic modulation products. From a theoretical standpoint, the observed interharmonic modulation products could be produced by several different nonlinearities. The two primary nonlinearities take the form of wave-medium interactions (i.e., cross modulation), wherein the ionospheric conductivity modulation produced by one signal crosses onto the other signal via collision frequency modification, and wave-wave interactions, wherein the conduction current associated with one wave mixes with the electric field of the other wave to produce electron temperature oscillations. We are able to separate and quantify these two different nonlinearities, and we conclude that the wave-wave interactions dominate the wave-medium interactions by a factor of two. These results are of great importance for the modeling of transioinospheric radio wave propagation, in that both the wave-wave and the wave-medium interactions could be responsible for a significant amount of anomalous absorption.

Head-on collision of the second mode internal solitary waves

NASA Astrophysics Data System (ADS)

Terletska, Kateryna; Maderich, Vladimir; Jung, Kyung Tae

2017-04-01

Second mode internal waves are widespread in offshore areas, and they frequently follow the first mode internal waves on the oceanic shelf. Large amplitude internal solitary waves (ISW) of second mode containing trapped cores associated with closed streamlines can also transport plankton and nutrients. An interaction of ISWs with trapped cores takes place in a specific manner. It motivated us to carry out a computational study of head-on collision of ISWs of second mode propagating in a laboratory-scale numerical tank using the nonhydrostatic 3D numerical model based on the Navier-Stokes equations for a continuously stratified fluid. Three main classes of ISW of second mode propagating in the pycnocline layer of thickness h between homogeneous deep layers can be identified: (i) the weakly nonlinear waves; (ii) the stable strongly nonlinear waves with trapped cores; and (iii) the shear unstable strongly nonlinear waves (Maderich et al., 2015). Four interaction regimes for symmetric collision were separated from simulation results using this classification: (A) an almost elastic interaction of the weakly nonlinear waves; (B) a non-elastic interaction of waves with trapped cores when ISW amplitudes were close to critical non-dimensional amplitude a/h; (C) an almost elastic interaction of stable strongly nonlinear waves with trapped cores; (D) non-elastic interaction of the unstable strongly nonlinear waves. The unexpected result of simulation was that relative loss of energy due to the collision was maximal for regime B. New regime appeared when ISW of different amplitudes belonged to class (ii) collide. In result of interaction the exchange of mass between ISW occurred: the trapped core of smaller wave was entrained by core of larger ISW without mixing forming a new ISW of larger amplitude whereas in smaller ISW core of smaller wave totally substituted by fluid from larger wave. Overall, the wave characteristics induced by head-on collision agree well with the results of several available laboratory experiments. References [1] V. Maderich, K. T. Jung, K. Terletska, I. Brovchenko, T. Talipova, "Incomplete similarity of internal solitary waves with trapped core," Fluid Dynamics Research 47, 035511 (2015).

Some problems of nonlinear waves in solid propellant rocket motors

NASA Technical Reports Server (NTRS)

Culick, F. E. C.

1979-01-01

An approximate technique for analyzing nonlinear waves in solid propellant rocket motors is presented which inexpensively provides accurate results up to amplitudes of ten percent. The connection with linear stability analysis is shown. The method is extended to third order in the amplitude of wave motion in order to study nonlinear stability, or triggering. Application of the approximate method to the behavior of pulses is described.

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

Nonlinear coupling of left and right handed circularly polarized dispersive Alfvén wave

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

Sharma, R. P., E-mail: rpsharma@ces.iitd.ac.in; Sharma, Swati, E-mail: swati.sharma704@gmail.com; Gaur, Nidhi, E-mail: nidhiphysics@gmail.com

2014-07-15

The nonlinear phenomena are of prominent interests in understanding the particle acceleration and transportation in the interplanetary space. The ponderomotive nonlinearity causing the filamentation of the parallel propagating circularly polarized dispersive Alfvén wave having a finite frequency may be one of the mechanisms that contribute to the heating of the plasmas. The contribution will be different of the left (L) handed mode, the right (R) handed mode, and the mix mode. The contribution also depends upon the finite frequency of the circularly polarized waves. In the present paper, we have investigated the effect of the nonlinear coupling of the Lmore » and R circularly polarized dispersive Alfvén wave on the localized structures formation and the respective power spectra. The dynamical equations are derived in the presence of the ponderomotive nonlinearity of the L and R pumps and then studied semi-analytically as well as numerically. The ponderomotive nonlinearity accounts for the nonlinear coupling between both the modes. In the presence of the adiabatic response of the density fluctuations, the nonlinear dynamical equations satisfy the modified nonlinear Schrödinger equation. The equations thus obtained are solved in solar wind regime to study the coupling effect on localization and the power spectra. The effect of coupling is also studied on Faraday rotation and ellipticity of the wave caused due to the difference in the localization of the left and the right modes with the distance of propagation.« less

Numerical assessment of factors affecting nonlinear internal waves in the South China Sea

NASA Astrophysics Data System (ADS)

Li, Qiang

2014-02-01

Nonlinear internal waves in the South China Sea exhibit diverse characteristics, which are associated with the complex conditions in Luzon Strait, such as the double ridge topography, the Earth’s rotation, variations in stratification and the background current induced by the Kuroshio. These effects are individually assessed using the MITgcm. The performance of the model is first validated through comparison with field observations. Because of in-phased ray interaction, the western ridge in Luzon Strait intensifies the semidiurnal internal tides generated from the eastern ridge, thus reinforcing the formation of nonlinear internal waves. However, the ray interaction for K1 forcing becomes anti-phased so that the K1 internal tide generation is reduced by the western ridge. Not only does the rotational dispersion suppress internal tide generation, it also inhibits nonlinear steepening and consequent internal solitary wave formation. As a joint effect, the double ridges and the rotational dispersion result in a paradoxical phenomenon: diurnal barotropic tidal forcing is dominant in Luzon Strait, but semidiurnal internal tides prevail in the deep basin of the South China Sea. The seasonal variation of the Kuroshio is consistent with the seasonal appearance of nonlinear internal waves in the South China Sea. The model results show that the westward inflow due to the Kuroshio intrusion reduces the amplitude of internal tides in the South China Sea, causing the weakening or absence of internal solitary waves. Winter stratification cannot account for the significant reduction of nonlinear internal waves, because the amplitude growth of internal tides due to increased thermocline tilting counteracts the reduced nonlinearity caused by thermocline deepening.

Early time evolution of a localized nonlinear excitation in the β-FPUT chain

NASA Astrophysics Data System (ADS)

Kashyap, Rahul; Westley, Alexandra; Datta, Amitava; Sen, Surajit

2017-04-01

We present the detailed dynamics of the particles in the β-Fermi-Pasta-Ulam-Tsingou (FPUT) chain after the initiation of a localized nonlinear excitation (LNE) by squeezing a central bond in the monodispersed chain at time t = 0 while all other particles remain in their original relaxed positions. In the absence of phonons in the system, the LNE appears to initiate its relaxation process by symmetrically emitting two very weak solitary waves. The next stage involves the spreading of the LNE and the formation of nonsolitary wave-like objects to broaden the excitation region until a stage is reached when many weak solitary wave-like objects can be emitted as the system begins its journey to quasi-equilibrium and then to equilibrium. In addition to being of fundamental interest, these systems may be realized using cantilever systems and could well hold the key to constructing the next generation of broadband energy harvesting systems.

Introduction to nonlinear acoustics

NASA Astrophysics Data System (ADS)

Bjørnø, Leif

2010-01-01

A brief review of the basic principles of fluid mechanics needed for development of linear and nonlinear ultrasonic concepts will be given. The fundamental equations of nonlinear ultrasonics will be derived and their physical properties explained. It will be shown how an originally monochromatic finite-amplitude ultrasonic wave, due to nonlinear effects, will distort during its propagation in time and space to form higher harmonics to its fundamental frequency. The concepts of shock formation will be presented. The material nonlinearity, described by the nonlinearity parameter B/A of the material, and the convective nonlinearity, described by the ultrasonic Mach Number, will be explained. Two procedures for determination of B/A will briefly be described and some B/A-values characterizing biological materials will be presented. Shock formation, described by use of the Goldberg Number,and Ultrasonic Saturation will be discussed.. An introduction to focused ultrasonic fields will be given and it will be shown how the ultrasonic intensity will vary axially and laterally in and near the focal region and how the field parameters of interest to biomedical applications may be described by use of the KZK-Model. Finally, an introduction will be given to the parametric acoustic array formed by mixing and interaction of two monochromatic, finite-amplitude ultrasonic waves in a liquid and the potentials of this mixing process in biomedical ultrasound will briefly be mentioned.

Mathematical Methods in Wave Propagation: Part 2--Non-Linear Wave Front Analysis

ERIC Educational Resources Information Center

Jeffrey, Alan

1971-01-01

The paper presents applications and methods of analysis for non-linear hyperbolic partial differential equations. The paper is concluded by an account of wave front analysis as applied to the piston problem of gas dynamics. (JG)

Generation of whistler waves by continuous HF heating of the upper ionosphere

NASA Astrophysics Data System (ADS)

Vartanyan, A.; Milikh, G. M.; Eliasson, B. E.; Sharma, A.; Chang, C.; Parrot, M.; Papadopoulos, K.

2013-12-01

We report observations of VLF waves by the DEMETER satellite overflying the HAARP facility during ionospheric heating experiments. The detected VLF waves were in the range 8-17 kHz and coincided with times of continuous heating. The experiments indicate whistler generation due to conversion of artificial lower hybrid waves to whistlers on small scale field-aligned plasma density striations. The observations are compared with theoretical models, taking into account both linear and nonlinear processes. Implications of the mode conversion technique on VLF generation with subsequent injection into the radiation belts to trigger particle precipitation are discussed.

Langmuir wave phase-mixing in warm electron-positron-dusty plasmas

NASA Astrophysics Data System (ADS)

Pramanik, Sourav; Maity, Chandan

2018-04-01

An analytical study on nonlinear evolution of Langmuir waves in warm electron-positron-dusty plasmas is presented. The massive dust grains of either positively or negatively charged are assumed to form a fixed charge neutralizing background. A perturbative analysis of the fluid-Maxwell's equations confirms that the excited Langmuir waves phase-mix and eventually break, even at arbitrarily low amplitudes. It is shown that the nature of the dust-charge as well as the amount of dust grains can significantly influence the Langmuir wave phase-mixing process. The phase-mixing time is also found to increase with the temperature.

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.

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

El-Labany, S. K., E-mail: skellabany@hotmail.com; Zedan, N. A., E-mail: nesreenplasma@yahoo.com; El-Taibany, W. F., E-mail: eltaibany@hotmail.com, E-mail: eltaibany@du.edu.eg

The nonplanar amplitude modulation of dust acoustic (DA) envelope solitary waves in a strongly coupled dusty plasma (SCDP) has been investigated. By using a reductive perturbation technique, a modified nonlinear Schrödinger equation (NLSE) including the effects of geometry, polarization, and ion superthermality is derived. The modulational instability (MI) of the nonlinear DA wave envelopes is investigated in both planar and nonplanar geometries. There are two stable regions for the DA wave propagation strongly affected by polarization and ion superthermality. Moreover, it is found that the nonlinear DA waves in spherical geometry are the more structurally stable. The larger growth ratemore » of the nonlinear DA MI is observed in the cylindrical geometry. The salient characteristics of the MI in the nonplanar geometries cannot be found in the planar one. The DA wave propagation and the NLSE solutions are investigated both analytically and numerically.« less

Multi-photon absorption limits to heralded single photon sources

PubMed Central

Husko, Chad A.; Clark, Alex S.; Collins, Matthew J.; De Rossi, Alfredo; Combrié, Sylvain; Lehoucq, Gaëlle; Rey, Isabella H.; Krauss, Thomas F.; Xiong, Chunle; Eggleton, Benjamin J.

2013-01-01

Single photons are of paramount importance to future quantum technologies, including quantum communication and computation. Nonlinear photonic devices using parametric processes offer a straightforward route to generating photons, however additional nonlinear processes may come into play and interfere with these sources. Here we analyse spontaneous four-wave mixing (SFWM) sources in the presence of multi-photon processes. We conduct experiments in silicon and gallium indium phosphide photonic crystal waveguides which display inherently different nonlinear absorption processes, namely two-photon (TPA) and three-photon absorption (ThPA), respectively. We develop a novel model capturing these diverse effects which is in excellent quantitative agreement with measurements of brightness, coincidence-to-accidental ratio (CAR) and second-order correlation function g(2)(0), showing that TPA imposes an intrinsic limit on heralded single photon sources. We build on these observations to devise a new metric, the quantum utility (QMU), enabling further optimisation of single photon sources. PMID:24186400

Low-Dispersion Scheme for Nonlinear Acoustic Waves in Nonuniform Flow

NASA Technical Reports Server (NTRS)

Baysal, Oktay; Kaushik, Dinesh K.; Idres, Moumen

1997-01-01

The linear dispersion-relation-preserving scheme and its boundary conditions have been extended to the nonlinear Euler equations. This allowed computing, a nonuniform flowfield and a nonlinear acoustic wave propagation in such a medium, by the same scheme. By casting all the equations, boundary conditions, and the solution scheme in generalized curvilinear coordinates, the solutions were made possible for non-Cartesian domains and, for the better deployment of the grid points, nonuniform grid step sizes could be used. It has been tested for a number of simple initial-value and periodic-source problems. A simple demonstration of the difference between a linear and nonlinear propagation was conducted. The wall boundary condition, derived from the momentum equations and implemented through a pressure at a ghost point, and the radiation boundary condition, derived from the asymptotic solution to the Euler equations, have proven to be effective for the nonlinear equations and nonuniform flows. The nonreflective characteristic boundary conditions also have shown success but limited to the nonlinear waves in no mean flow, and failed for nonlinear waves in nonuniform flow.

Nonlinear instabilities of multi-site breathers in Klein-Gordon lattices

DOE PAGES

Cuevas-Maraver, Jesus; Kevrekidis, Panayotis G.; Pelinovsky, Dmitry E.

2016-08-01

Here, we explore the possibility of multi-site breather states in a nonlinear Klein–Gordon lattice to become nonlinearly unstable, even if they are found to be spectrally stable. The mechanism for this nonlinear instability is through the resonance with the wave continuum of a multiple of an internal mode eigenfrequency in the linearization of excited breather states. For the nonlinear instability, the internal mode must have its Krein signature opposite to that of the wave continuum. This mechanism is not only theoretically proposed, but also numerically corroborated through two concrete examples of the Klein–Gordon lattice with a soft (Morse) and amore » hard (Φ 4) potential. Compared to the case of the nonlinear Schrödinger lattice, the Krein signature of the internal mode relative to that of the wave continuum may change depending on the period of the multi-site breather state. For the periods for which the Krein signatures of the internal mode and the wave continuum coincide, multi-site breather states are observed to be nonlinearly stable.« less

Experimental investigation of the effect of pump incoherence on nonlinear pump spectral broadening and continuous-wave supercontinuum generation

NASA Astrophysics Data System (ADS)

Martin-Lopez, S.; Carrasco-Sanz, A.; Corredera, P.; Abrardi, L.; Hernanz, M. L.; Gonzalez-Herraez, M.

2006-12-01

The development of high-power cw fiber lasers has triggered a great interest in the phenomena of nonlinear pump spectral broadening and cw supercontinuum generation. These effects have very convenient applications in Raman amplification, optical fiber metrology, and fiber sensing. In particular, it was recently shown that pump incoherence has a strong impact in these processes. We study experimentally the effect of pump incoherence in nonlinear pump spectral broadening and cw supercontinuum generation in optical fibers. We show that under certain experimental conditions an optimum degree of pump incoherence yields the best performance in the broadening process. We qualitatively explain these results, and we point out that these results may have important implications in cw supercontinuum optimization.

Near-planar TS waves and longitudinal vortices in channel flow: Nonlinear interaction and focusing

NASA Technical Reports Server (NTRS)

Hall, P.; Smith, F. T.

1989-01-01

The nonlinear interaction between planar or near-planar Tollmien-Schlichting waves and longitudinal vortices, induced or input, is considered theoretically for channel flows at high Reynolds numbers. Several kinds of nonlinear interaction, dependent on the input amplitudes and wavenumbers or on previously occurring interactions, are found and inter-related. The first, Type 1, is studied the most here and it usually produces spanwise focusing of both the wave and the vortex motion, within a finite scaled time, along with enhancement of both their amplitudes. This then points to the nonlinear interaction Type 2 where new interactive effects come into force to drive the wave and the vortex nonlinearly. Types 3, 4 correspond to still higher amplitudes, with 3 being related to 2, while 4 is connected with a larger-scale interaction 5 studied in an allied paper. Both 3, 4 are subsets of the full three-dimensional triple-deck-lie interaction, 6. The strongest nonlinear interactions are those of 4, 5, 6 since they alter the mean-flow profile substantially, i.e., by an 0(1) relative amount. All the types of nonlinear interaction however can result in the formation of focussed responses in the sense of spanwise concentrations and/or amplifications of vorticity and wave amplitude.

A Locally Generated High-Mode Nonlinear Internal Wave Detected on the Shelf of the Northern South China Sea From Marine Seismic Observations

NASA Astrophysics Data System (ADS)

Tang, Qunshu; Xu, Min; Zheng, Chan; Xu, Xing; Xu, Jiang

2018-02-01

In this work, a secondary nonlinear internal wave (NIW) on the continental shelf of the northern South China Sea is investigated using high-resolution seismic imaging and joint inversion of water structure properties combined with in situ hydrographic observations. It is an extraordinary wave combination with two mode-2 NIWs and one elevated NIW occurring within a short distance of 2 km. The most energetic part of the NIW could be regarded as a mode-2 NIW in the upper layer between 40 and 120 m depth. The vertical particle velocity of ˜41 cm/s may exceed the critical value of wave breaking and thus collapse the strong stratification followed by a series of processes including internal wave breaking, overturning, Kelvin-Helmholtz instability, stratification splitting, and eventual restratification. Among these processes, the shear-induced Kelvin-Helmholtz instability is directly imaged using the seismic method for the first time. The stratification splitting and restratification show that the unstable stage lasts only for a few hours and spans several kilometers. It is a new observation that the elevated NIW could be generated in a deepwater region (as deep as ˜370 m). Different from the periodical NIWs originating from the Luzon Strait, this secondary NIW is most likely generated locally, at the continental shelf break during ebb tide.

Asymmetric Rogue Waves, Breather-to-Soliton Conversion, and Nonlinear Wave Interactions in the Hirota-Maxwell-Bloch System

NASA Astrophysics Data System (ADS)

Wang, Lei; Zhu, Yu-Jie; Wang, Zi-Qi; Xu, Tao; Qi, Feng-Hua; Xue, Yu-Shan

2016-02-01

We study the nonlinear localized waves on constant backgrounds of the Hirota-Maxwell-Bloch (HMB) system arising from the erbium doped fibers. We derive the asymmetric breather, rogue wave (RW) and semirational solutions of the HMB system. We show that the breather and RW solutions can be converted into various soliton solutions. Under different conditions of parameters, we calculate the locus of the eigenvalues on the complex plane which converts the breathers or RWs into solitons. Based on the second-order solutions, we investigate the interactions among different types of nonlinear waves including the breathers, RWs and solitons.

Excitation and propagation of nonlinear waves in a rotating fluid

NASA Astrophysics Data System (ADS)

Hanazaki, Hideshi

1993-09-01

A numerical study of the nonlinear waves excited in an axisymmetric rotating flow through a circular tube is described. The waves are excited by either an undulation of the tube wall or an obstacle on the axis of the tube. The results are compared with the weakly nonlinear theory (forced KdV equation). The computations are done when the upstream swirling velocity is that of Burgers' vortex type. The flow behaves like the solution of the forced KdV equation, and the upstream advancing of the waves appear even when the flow is critical or slightly supercritical to the fastest inertial wave mode.

Nonlinear to Linear Elastic Code Coupling in 2-D Axisymmetric Media.

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

Preston, Leiph

Explosions within the earth nonlinearly deform the local media, but at typical seismological observation distances, the seismic waves can be considered linear. Although nonlinear algorithms can simulate explosions in the very near field well, these codes are computationally expensive and inaccurate at propagating these signals to great distances. A linearized wave propagation code, coupled to a nonlinear code, provides an efficient mechanism to both accurately simulate the explosion itself and to propagate these signals to distant receivers. To this end we have coupled Sandia's nonlinear simulation algorithm CTH to a linearized elastic wave propagation code for 2-D axisymmetric media (axiElasti)more » by passing information from the nonlinear to the linear code via time-varying boundary conditions. In this report, we first develop the 2-D axisymmetric elastic wave equations in cylindrical coordinates. Next we show how we design the time-varying boundary conditions passing information from CTH to axiElasti, and finally we demonstrate the coupling code via a simple study of the elastic radius.« less

Localized nonlinear waves and dynamical stability in spinor Bose–Einstein condensates with time–space modulation

NASA Astrophysics Data System (ADS)

Yao, Yu-Qin; Han, Wei; Li, Ji; Liu, Wu-Ming

2018-05-01

Nonlinearity is one of the most remarkable characteristics of Bose–Einstein condensates (BECs). Much work has been done on one- and two-component BECs with time- or space-modulated nonlinearities, while there is little work on spinor BECs with space–time-modulated nonlinearities. In the present paper we investigate localized nonlinear waves and dynamical stability in spinor Bose–Einstein condensates with nonlinearities dependent on time and space. We solve the three coupled Gross–Pitaevskii equations by similarity transformation and obtain two families of exact matter wave solutions in terms of Jacobi elliptic functions and the Mathieu equation. The localized states of the spinor matter wave describe the dynamics of vector breathing solitons, moving breathing solitons, quasi-breathing solitons and resonant solitons. The results show that one-order vector breathing solitons, quasi-breathing solitons, resonant solitons and the moving breathing solitons ψ ±1 are all stable, but the moving breathing soliton ψ 0 is unstable. We also present the experimental parameters to realize these phenomena in future experiments.

Existence regimes for the formation of nonlinear dissipative structures in inhomogeneous magnetoplasmas with non-Maxwellian electrons

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

Masood, W.; National Centre for Physics, Shahdara Valley Road, Islamabad; Zahoor, Sara

2016-09-15

Nonlinear dissipative structures are studied in one and two dimensions in nonuniform magnetized plasmas with non-Maxwellian electrons. The dissipation is incorporated in the system through ion-neutral collisions. Employing the drift approximation, nonlinear drift waves are derived in 1D, whereas coupled drift-ion acoustic waves are derived in 2D in the weak nonlinearity limit. It is found that the ratio of the diamagnetic drift velocity to the velocity of nonlinear structure determines the nature (compressive or rarefactive) of the shock structure. The upper and lower bounds for velocity of the nonlinear shock structures are also found. It is noticed that the existencemore » regimes for the drift shock waves in one and two dimensions for Cairns distributed electrons are very distinct from those with kappa distributed electrons. Interestingly, it is found that both compressive and rarefactive shock structures could be obtained for the one dimensional drift waves with kappa distributed electrons.« less

Existence regimes for the formation of nonlinear dissipative structures in inhomogeneous magnetoplasmas with non-Maxwellian electrons

NASA Astrophysics Data System (ADS)

Masood, W.; Zahoor, Sara; Gul-e-Ali, Ahmad, Ali

2016-09-01

Nonlinear dissipative structures are studied in one and two dimensions in nonuniform magnetized plasmas with non-Maxwellian electrons. The dissipation is incorporated in the system through ion-neutral collisions. Employing the drift approximation, nonlinear drift waves are derived in 1D, whereas coupled drift-ion acoustic waves are derived in 2D in the weak nonlinearity limit. It is found that the ratio of the diamagnetic drift velocity to the velocity of nonlinear structure determines the nature (compressive or rarefactive) of the shock structure. The upper and lower bounds for velocity of the nonlinear shock structures are also found. It is noticed that the existence regimes for the drift shock waves in one and two dimensions for Cairns distributed electrons are very distinct from those with kappa distributed electrons. Interestingly, it is found that both compressive and rarefactive shock structures could be obtained for the one dimensional drift waves with kappa distributed electrons.

Simulation of Vortex Structure in Supersonic Free Shear Layer Using Pse Method

NASA Astrophysics Data System (ADS)

Guo, Xin; Wang, Qiang

The method of parabolized stability equations (PSE) are applied in the analysis of nonlinear stability and the simulation of flow structure in supersonic free shear layer. High accuracy numerical techniques including self-similar basic flow, high order differential method, appropriate transformation and decomposition of nonlinear terms are adopted and developed to solve the PSE effectively for free shear layer. The spatial evolving unstable waves which dominate the flow structure are investigated through nonlinear coupling spatial marching methods. The nonlinear interactions between harmonic waves are further analyzed and instantaneous flow field are obtained by adding the harmonic waves into basic flow. Relevant data agree well with that of DNS. The results demonstrate that T-S wave does not keeping growing exponential as the linear evolution, the energy transfer to high order harmonic modes and finally all harmonic modes get saturation due to the nonlinear interaction; Mean flow distortion is produced by the nonlinear interaction between the harmonic and its conjugate harmonic, makes great change to the average flow and increases the thickness of shear layer; PSE methods can well capture the large scale nonlinear flow structure in the supersonic free shear layer such as vortex roll-up, vortex pairing and nonlinear saturation.

Stability of nonlinear waves and patterns and related topics

NASA Astrophysics Data System (ADS)

Ghazaryan, Anna; Lafortune, Stephane; Manukian, Vahagn

2018-04-01

Periodic and localized travelling waves such as wave trains, pulses, fronts and patterns of more complex structure often occur in natural and experimentally built systems. In mathematics, these objects are realized as solutions of nonlinear partial differential equations. The existence, dynamic properties and bifurcations of those solutions are of interest. In particular, their stability is important for applications, as the waves that are observable are usually stable. When the waves are unstable, further investigation is warranted of the way the instability is exhibited, i.e. the nature of the instability, and also coherent structures that appear as a result of an instability of travelling waves. A variety of analytical, numerical and hybrid techniques are used to study travelling waves and their properties. This article is part of the theme issue `Stability of nonlinear waves and patterns and related topics'.

Nonlinear excitation of fast magnetosonic waves via quasi-electrostatic whistler wave mixing

NASA Astrophysics Data System (ADS)

Zechar, Nathan; Sotnikov, Vladimir; Caplinger, James; Chu, Arthur

2017-10-01

We report on experiments of nonlinear simultaneous generation of low frequency fast magnetosonic waves and electromagnetic whistler waves using two loop antennas in the afterglow of a cold magnetized helium plasma. The exciting antennas each have a frequency that is below half the electron cyclotron frequency, and the difference between the two is just below the lower hybrid frequency. They both directly excite whistler waves, however their nonlinear interaction excite the low frequency fast magnetosonic waves at the frequency given by their difference. Plasma is generated using a helicon plasma source in a one meter length cylindrical chamber. The spatial and temporal data of the electromagnetic and electrostatic components of the plasma waves are then captured with developed diagnostic techniques. Wave spectra, general structure and time domain frequencies observed will be reported.

Single-wave-number representation of nonlinear energy spectrum in elastic-wave turbulence of the Föppl-von Kármán equation: energy decomposition analysis and energy budget.

PubMed

Yokoyama, Naoto; Takaoka, Masanori

2014-12-01

A single-wave-number representation of a nonlinear energy spectrum, i.e., a stretching-energy spectrum, is found in elastic-wave turbulence governed by the Föppl-von Kármán (FvK) equation. The representation enables energy decomposition analysis in the wave-number space and analytical expressions of detailed energy budgets in the nonlinear interactions. We numerically solved the FvK equation and observed the following facts. Kinetic energy and bending energy are comparable with each other at large wave numbers as the weak turbulence theory suggests. On the other hand, stretching energy is larger than the bending energy at small wave numbers, i.e., the nonlinearity is relatively strong. The strong correlation between a mode a(k) and its companion mode a(-k) is observed at the small wave numbers. The energy is input into the wave field through stretching-energy transfer at the small wave numbers, and dissipated through the quartic part of kinetic-energy transfer at the large wave numbers. Total-energy flux consistent with energy conservation is calculated directly by using the analytical expression of the total-energy transfer, and the forward energy cascade is observed clearly.

Nonlinear Internal Wave Interaction in the China Seas

NASA Technical Reports Server (NTRS)

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

1998-01-01

This project researched the nonlinear wave interactions in the East China Sea, and the South China Sea, using Synthetic Aperture Radar (SAR) images. The complicated nature of the internal wave field, including the generation mechanisms, was studied, and is discussed. Discussion of wave-wave interactions in the East China Sea, the area of the China Sea northeast of Taiwan, and the Yellow Sea is included.

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.

Linear and nonlinear propagation of water wave groups

NASA Technical Reports Server (NTRS)

Pierson, W. J., Jr.; Donelan, M. A.; Hui, W. H.

1992-01-01

Results are presented from a study of the evolution of waveforms with known analytical group shapes, in the form of both transient wave groups and the cloidal (cn) and dnoidal (dn) wave trains as derived from the nonlinear Schroedinger equation. The waveforms were generated in a long wind-wave tank of the Canada Centre for Inland Waters. It was found that the low-amplitude transients behaved as predicted by the linear theory and that the cn and dn wave trains of moderate steepness behaved almost as predicted by the nonlinear Schroedinger equation. Some of the results did not fit into any of the available theories for waves on water, but they provide important insight on how actual groups of waves propagate and on higher-order effects for a transient waveform.

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.

Probing the interior of a solid volume with time reversal and nonlinear elastic wave spectroscopy.

PubMed

Le Bas, P Y; Ulrich, T J; Anderson, B E; Guyer, R A; Johnson, P A

2011-10-01

A nonlinear scatterer is simulated in the body of a sample and demonstrates a technique to locate and define the elastic nature of the scatterer. Using the principle of time reversal, elastic wave energy is focused at the interface between blocks of optical grade glass and aluminum. Focusing of energy at the interface creates nonlinear wave scattering that can be detected on the sample perimeter with time-reversal mirror elements. The nonlinearly generated scattered signal is bandpass filtered about the nonlinearly generated components, time reversed and broadcast from the same mirror elements, and the signal is focused at the scattering location on the interface. © 2011 Acoustical Society of America

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.

Towards high fidelity numerical wave tanks for modelling coastal and ocean engineering processes

NASA Astrophysics Data System (ADS)

Cozzuto, G.; Dimakopoulos, A.; de Lataillade, T.; Kees, C. E.

2017-12-01

With the increasing availability of computational resources, the engineering and research community is gradually moving towards using high fidelity Comutational Fluid Mechanics (CFD) models to perform numerical tests for improving the understanding of physical processes pertaining to wave propapagation and interaction with the coastal environment and morphology, either physical or man-made. It is therefore important to be able to reproduce in these models the conditions that drive these processes. So far, in CFD models the norm is to use regular (linear or nonlinear) waves for performing numerical tests, however, only random waves exist in nature. In this work, we will initially present the verification and validation of numerical wave tanks based on Proteus, an open-soruce computational toolkit based on finite element analysis, with respect to the generation, propagation and absorption of random sea states comprising of long non-repeating wave sequences. Statistical and spectral processing of results demonstrate that the methodologies employed (including relaxation zone methods and moving wave paddles) are capable of producing results of similar quality to the wave tanks used in laboratories (Figure 1). Subsequently cases studies of modelling complex process relevant to coastal defences and floating structures such as sliding and overturning of composite breakwaters, heave and roll response of floating caissons are presented. Figure 1: Wave spectra in the numerical wave tank (coloured symbols), compared against the JONSWAP distribution

Nonlinear Excitation of Acoustic Modes by Large Amplitude Alfvén waves in the Large Plasma Device (LAPD)

NASA Astrophysics Data System (ADS)

Dorfman, S. E.; Carter, T. A.; Pribyl, P.; Tripathi, S.; Van Compernolle, B.; Vincena, S. T.; Sydora, R. D.

2013-12-01

Alfvén waves, a fundamental mode of magnetized plasmas, are ubiquitous in space plasmas. While the linear behavior of these waves has been extensively studied [1], non-linear effects are important in many real systems, including the solar corona and solar wind. In particular, a parametric decay process in which a large amplitude Alfvén wave decays into an ion acoustic wave and backward propagating Alfvén wave may play an important role in the coronal heating problem. Specifically, the decay of large-amplitude Alfvén waves propagating outward from the photosphere could lead to heating of the corona by the daughter ion acoustic modes [2]. As direct observational evidence of parametric decay is limited [3], laboratory experiments may play an important role in validating simple theoretical predictions and aiding in the interpretation of space measurements. Recent counter-propagating Alfvén wave experiments in the Large Plasma Device (LAPD) have recorded the first laboratory observation of the Alfvén-acoustic mode coupling at the heart of this parametric decay instability [4]. A resonance in the beat wave response produced by the two launched Alfvén waves is observed and is identified as a damped ion acoustic mode based on the measured dispersion relation. Other properties of the interaction including the spatial profile of the beat mode and response amplitude are also consistent with theoretical predictions for a three-wave interaction driven by a nonlinear ponderomotive force. Strong damping observed after the pump Alfvén waves are turned off is under investigation; a novel ion acoustic wave launcher is under development to launch the mode directly for damping studies. New experiments also aim to identify decay instabilities from a single large-amplitude Alfvén wave. In conjunction with these experiments, gyrokinetic simulation efforts are underway to scope out the relevant parameter space. [1] W. Gekelman, et. al., Phys. Plasmas 18, 055501 (2011). [2] F. Pruneti, F and M. Velli, ESA Spec. Pub. 404, 623 (1997). [3] S. R. Spangler, et. al., Phys. Plasmas 4, 846 (1997). [4] S. Dorfman and T. Carter, Phys. Rev. Lett. 110, 195001 (2013).

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.

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.

Self-action of Bessel wave packets in a system of coupled light guides and formation of light bullets

NASA Astrophysics Data System (ADS)

Balakin, A. A.; Mironov, V. A.; Skobelev, S. A.

2017-01-01

The self-action of two-dimensional and three-dimensional Bessel wave packets in a system of coupled light guides is considered using the discrete nonlinear Schrödinger equation. The features of the self-action of such wave fields are related to their initial strong spatial inhomogeneity. The numerical simulation shows that for the field amplitude exceeding a critical value, the development of an instability typical of a medium with the cubic nonlinearity is observed. Various regimes are studied: the self-channeling of a wave beam in one light guide at powers not strongly exceeding a critical value, the formation of the "kaleidoscopic" picture of a wave packet during the propagation of higher-power radiation along a stratified medium, the formation of light bullets during competition between self-focusing and modulation instabilities in the case of three-dimensional wave packets, etc. In the problem of laser pulse shortening, the situation is considered when the wave-field stratification in the transverse direction dominates. This process is accompanied by the self-compression of laser pulses in well enough separated light guides. The efficiency of conversion of the initial Bessel field distribution to two flying parallel light bullets is about 50%.

A Study of Electron and Phonon Dynamics by Broadband Two-Dimensional THz Time-Domain Spectroscopy

NASA Astrophysics Data System (ADS)

Fu, Zhengping

Terahertz (THz) wave interacts with semiconductors in many ways, such as resonant excitation of lattice vibration, intraband transition and polaron formation. Different from the optical waves, THz wave has lower photon energy (1 THz = 4.14 meV) and is suitable for studying dynamics of low-energy excitations. Recently the studies of the interaction of THz wave and semiconductors have been extending from the linear regime to the nonlinear regime, owing to the advance of the high-intensity THz generation and detection methods. Two-dimensional (2D) spectroscopy, as a useful tool to unravel the nonlinearity of materials, has been well developed in nuclear magnetic resonance and infrared region. However, the counterpart in THz region has not been well developed and was only demonstrated at frequency around 20 THz due to the lack of intense broadband THz sources. Using laser-induced plasma as the THz source, we developed collinear broadband 2D THz time-domain spectroscopy covering from 0.5 THz to 20 THz. Broadband intense THz pulses emitted from laser-induced plasma provide access to a variety of nonlinear properties of materials. Ultrafast optical and THz pulses make it possible to resolve the transient change of the material properties with temporal resolution of tens of femtoseconds. This thesis focuses on the linear and nonlinear interaction of the THz wave with semiconductors. Since a great many physical processes, including vibrational motion of lattice and plasma oscillation, has resonant frequency in the THz range, rich physics can be studies in our experiment. The thesis starts from the linear interaction of the THz wave with semiconductors. In the narrow band gap semiconductor InSb, the plasma absorption edge, Restrahlen band and dispersion of polaritons are observed. The nonlinear response of InSb in high THz field is verified in the frequency-resolved THz Z-scan experiment. The third harmonic generations due to the anharmonicity of plasma oscillation and the second order signal due to the plasma-phonon interaction are observed in 2D THz transmission spectra. In this thesis, the coherent phonons excited by THz pulses are experimentally demonstrated for the first time in both GaAs and InSb. The resonant excitation using THz pulses enables the coherent control of the lattice motion via direct interaction of atoms and electromagnetic wave, without inducing electronic transition as reported in the optical excitation of coherent phonons. The classic model is used to explain both excitation and detection mechanisms. An increase of the damping rate of the coherent lattice motion due to higher carrier density is observed in our experiment. Transient reflectivity change of GaAs induced by THz pulses is studied in 2D THz-pump/optical-probe configuration. Using the perturbative analysis of nonlinear electrooptic effect, we conclude that the nonlinear response of GaAs to two phase-locked THz pulses is mainly caused by the nonlinearity of the electronic response.

Nonlinear Interaction of Detuned Instability Waves in Boundary-Layer Transition: Resonant-Triad Interaction

NASA Technical Reports Server (NTRS)

Lee, Sang Soo

1998-01-01

The non-equilibrium critical-layer analysis of a system of frequency-detuned resonant-triads is presented using the generalized scaling of Lee. It is shown that resonant-triads can interact nonlinearly within the common critical layer when their (fundamental) Strouhal numbers are different by a factor whose magnitude is of the order of the growth rate multiplied by the wavenumber of the instability wave. Since the growth rates of the instability modes become larger and the critical layers become thicker as the instability waves propagate downstream, the frequency-detuned resonant-triads that grow independently of each other in the upstream region can interact nonlinearly in the later downstream stage. In the final stage of the non-equilibrium critical-layer evolution, a wide range of instability waves with the scaled frequencies differing by almost an Order of (l) can nonlinearly interact. Low-frequency modes are also generated by the nonlinear interaction between oblique waves in the critical layer. The system of partial differential critical-layer equations along with the jump equations are presented here. The amplitude equations with their numerical solutions are given in Part 2. The nonlinearly generated low-frequency components are also investigated in Part 2.

Methods for discrete solitons in nonlinear lattices.

PubMed

Ablowitz, Mark J; Musslimani, Ziad H; Biondini, Gino

2002-02-01

A method to find discrete solitons in nonlinear lattices is introduced. Using nonlinear optical waveguide arrays as a prototype application, both stationary and traveling-wave solitons are investigated. In the limit of small wave velocity, a fully discrete perturbative analysis yields formulas for the mode shapes and velocity.

Ultrasound wave propagation in tissue and scattering from microbubbles for echo particle image velocimetry technique.

PubMed

Mukdadi, Osama; Shandas, Robin

2004-01-01

Nonlinear wave propagation in tissue can be employed for tissue harmonic imaging, ultrasound surgery, and more effective tissue ablation for high intensity focused ultrasound (HIFU). Wave propagation in soft tissue and scattering from microbubbles (ultrasound contrast agents) are modeled to improve detectability, signal-to-noise ratio, and contrast harmonic imaging used for echo particle image velocimetry (Echo-PIV) technique. The wave motion in nonlinear material (tissue) is studied using KZK-type parabolic evolution equation. This model considers ultrasound beam diffraction, attenuation, and tissue nonlinearity. Time-domain numerical model is based on that originally developed by Lee and Hamilton [J. Acoust. Soc. Am 97:906-917 (1995)] for axi-symmetric acoustic field. The initial acoustic waveform emitted from the transducer is assumed to be a broadband wave modulated by Gaussian envelope. Scattering from microbubbles seeded in the blood stream is characterized. Hence, we compute the pressure field impinges the wall of a coated microbubble; the dynamics of oscillating microbubble can be modeled using Rayleigh-Plesset-type equation. Here, the continuity and the radial-momentum equation of encapsulated microbubbles are used to account for the lipid layer surrounding the microbubble. Numerical results show the effects of tissue and microbubble nonlinearities on the propagating pressure wave field. These nonlinearities have a strong influence on the waveform distortion and harmonic generation of the propagating and scattering waves. Results also show that microbubbles have stronger nonlinearity than tissue, and thus improves S/N ratio. These theoretical predictions of wave phenomena provide further understanding of biomedical imaging technique and provide better system design.

Nonlinear helicons bearing multi-scale structures

NASA Astrophysics Data System (ADS)

Abdelhamid, Hamdi M.; Yoshida, Zensho

2017-02-01

The helicon waves exhibit varying characters depending on plasma parameters, geometry, and wave numbers. Here, we elucidate an intrinsic multi-scale property embodied by the combination of the dispersive effect and nonlinearity. The extended magnetohydrodynamics model (exMHD) is capable of describing a wide range of parameter space. By using the underlying Hamiltonian structure of exMHD, we construct an exact nonlinear solution, which turns out to be a combination of two distinct modes, the helicon and Trivelpiece-Gould (TG) waves. In the regime of relatively low frequency or high density, however, the combination is made of the TG mode and an ion cyclotron wave (slow wave). The energy partition between these modes is determined by the helicities carried by the wave fields.

Evans functions and bifurcations of nonlinear waves of some nonlinear reaction diffusion equations

NASA Astrophysics Data System (ADS)

Zhang, Linghai

2017-10-01

The main purposes of this paper are to accomplish the existence, stability, instability and bifurcation of the nonlinear waves of the nonlinear system of reaction diffusion equations ut =uxx + α [ βH (u - θ) - u ] - w, wt = ε (u - γw) and to establish the existence, stability, instability and bifurcation of the nonlinear waves of the nonlinear scalar reaction diffusion equation ut =uxx + α [ βH (u - θ) - u ], under different conditions on the model constants. To establish the bifurcation for the system, we will study the existence and instability of a standing pulse solution if 0 < 2 (1 + αγ) θ < αβγ; the existence and stability of two standing wave fronts if 2 (1 + αγ) θ = αβγ and γ2 ε > 1; the existence and instability of two standing wave fronts if 2 (1 + αγ) θ = αβγ and 0 <γ2 ε < 1; the existence and instability of an upside down standing pulse solution if 0 < (1 + αγ) θ < αβγ < 2 (1 + αγ) θ. To establish the bifurcation for the scalar equation, we will study the existence and stability of a traveling wave front as well as the existence and instability of a standing pulse solution if 0 < 2 θ < β; the existence and stability of two standing wave fronts if 2 θ = β; the existence and stability of a traveling wave front as well as the existence and instability of an upside down standing pulse solution if 0 < θ < β < 2 θ. By the way, we will also study the existence and stability of a traveling wave back of the nonlinear scalar reaction diffusion equation ut =uxx + α [ βH (u - θ) - u ] -w0, where w0 = α (β - 2 θ) > 0 is a positive constant, if 0 < 2 θ < β. To achieve the main goals, we will make complete use of the special structures of the model equations and we will construct Evans functions and apply them to study the eigenvalues and eigenfunctions of several eigenvalue problems associated with several linear differential operators. It turns out that a complex number λ0 is an eigenvalue of the linear differential operator, if and only if λ0 is a zero of the Evans function. The stability, instability and bifurcations of the nonlinear waves follow from the zeros of the Evans functions. A very important motivation to study the existence, stability, instability and bifurcations of the nonlinear waves is to study the existence and stability/instability of infinitely many fast/slow multiple traveling pulse solutions of the nonlinear system of reaction diffusion equations. The existence and stability of infinitely many fast multiple traveling pulse solutions are of great interests in mathematical neuroscience.

Application of nonlinear deterministic decomposition to the prediction and energy dissipation of long-crested irregular ocean surface waves

NASA Astrophysics Data System (ADS)

Meza Conde, Eustorgio

The Hybrid Wave Model (HWM) is a deterministic nonlinear wave model developed for the computation of wave properties in the vicinity of ocean wave measurements. The HWM employs both Mode-Coupling and Phase Modulation Methods to model the wave-wave interactions in an ocean wave field. Different from other nonlinear wave models, the HWM decouples the nonlinear wave interactions from ocean wave field measurements and decomposes the wave field into a set of free-wave components. In this dissertation the HWM is applied to the prediction of wave elevation from pressure measurements and to the quantification of energy during breaking of long-crested irregular surface waves. 1.A transient wave train was formed in a two-dimensional wave flume by sequentially generating a series of waves from high to low frequencies that superposed at a downstream location. The predicted wave elevation using the HWM based on the pressure measurement of a very steep transient wave train is in excellent agreement with the corresponding elevation measurement, while that using Linear Wave Theory (LWT) has relatively large discrepancies. Furthermore, the predicted elevation using the HWM is not sensitive to the choice of the cutoff frequency, while that using LWT is very sensitive. 2.Several transient wave trains containing an isolated plunging or spilling breaker at a prescribed location were generated in a two-dimensional wave flume using the same superposition technique. Surface elevation measurements of each transient wave train were made at locations before and after breaking. Applying the HWM nonlinear deterministic decomposition to the measured elevation, the free-wave components comprising the transient wave train were derived. By comparing the free-wave spectra before and after breaking it is found that energy loss was almost exclusively from wave components at frequencies higher than the spectral peak frequency. Even though the wave components near the peak frequency are the largest, they do not significantly gain or lose energy after breaking. It was also observed that wave components of frequencies significantly below or near the peak frequency gain a small portion of energy lost by the high-frequency waves. These findings may have important implications to the ocean wave energy budget.

The soliton transform and a possible application to nonlinear Alfven waves in space

NASA Technical Reports Server (NTRS)

Hada, T.; Hamilton, R. L.; Kennel, C. F.

1993-01-01

The inverse scattering transform (IST) based on the derivative nonlinear Schroedinger (DNLS) equation is applied to a complex time series of nonlinear Alfven wave data generated by numerical simulation. The IST describes the long-time evolution of quasi-parallel Alfven waves more efficiently than the Fourier transform, which is adapted to linear rather than nonlinear problems. When dissipation is added, so the conditions for the validity of the DNLS are not strictly satisfied, the IST continues to provide a compact description of the wavefield in terms of a small number of decaying envelope solitons.

Parametric Excitation of Electrostatic Dust-Modes by Ion-Cyclotron Waves in a Dusty Plasma

NASA Astrophysics Data System (ADS)

Islam, M. K.; Salahuddin, M.; Ferdous, T.; Salimullah, M.

A large amplitude electrostatic ion-cyclotron wave propagating through a magnetized and collisional dusty plasma undergoes strong parametric instability off the low-frequency dust-modes. The presence of the dust-component has effect on the nonlinear coupling via the dust-modes. The ion-neutral collisions are seen to have significant effect on the damping and consequent overall growth of the parametric excitation process.

Shuttle wave experiments. [space plasma investigations: design and instrumentation

NASA Technical Reports Server (NTRS)

Calvert, W.

1976-01-01

Wave experiments on shuttle are needed to verify dispersion relations, to study nonlinear and exotic phenomena, to support other plasma experiments, and to test engineering designs. Techniques based on coherent detection and bistatic geometry are described. New instrumentation required to provide modules for a variety of missions and to incorporate advanced signal processing and control techniques is discussed. An experiment for Z to 0 coupling is included.

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.

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.

Toward a System-Based Approach to Electromagnetic Ion Cyclotron Waves in Earth's Magnetosphere

NASA Astrophysics Data System (ADS)

Gamayunov, K. V.; Engebretson, M. J.; Rassoul, H.

2015-12-01

We consider a nonlinear wave energy cascade from the low frequency range into the higher frequency domain of electromagnetic ion cyclotron (EMIC) wave generation as a possible source of seed fluctuations for EMIC wave growth due to the ion cyclotron instability in Earth's magnetosphere. The theoretical analysis shows that energy cascade from the Pc 4-5 frequency range (2-22 mHz) into the range of Pc 1-2 pulsations (0.1-5 Hz) is able to supply the level of seed fluctuations that guarantees growth of EMIC waves up to an observable level during one pass through the near equatorial region where the ion cyclotron instability takes place. We also analyze magnetic field data from the Polar and Van Allen Probes spacecraft to test this nonlinear mechanism. We restrict our analysis to magnetic spectra only. We do not analyze the third-order moment for total energy of the magnetic and velocity fluctuations, but judge whether a nonlinear energy cascade is present or whether it is not by only analyzing the appearance of power-law distributions in the low frequency part of the magnetic field spectra. While the power-law spectrum alone does not guarantee that a nonlinear cascade is present, the power-law distribution is a strong indication of the possible development of a nonlinear cascade. Our data analysis shows that a nonlinear energy cascade is indeed observed in both the outer and inner magnetosphere, and EMIC waves are growing from this nonthermal background. All the analyzed data are in good agreement with the theoretical model presented in this study. Overall, the results of this study support a nonlinear energy cascade in Earth's magnetosphere as a mechanism which is responsible for supplying seed fluctuating energy in the higher frequency domain where EMIC waves grow due to the ion cyclotron instability. Keywords: nonlinear energy cascade, ultra low frequency waves, electromagnetic ion cyclotron waves, seed fluctuationsAcknowledgments: This paper is based upon work supported by the National Science Foundation under Grant Number AGS-1203516.

Measurement and fitting techniques for the assessment of material nonlinearity using nonlinear Rayleigh waves

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

Torello, David; Kim, Jin-Yeon; Qu, Jianmin

2015-03-31

This research considers the effects of diffraction, attenuation, and the nonlinearity of generating sources on measurements of nonlinear ultrasonic Rayleigh wave propagation. A new theoretical framework for correcting measurements made with air-coupled and contact piezoelectric receivers for the aforementioned effects is provided based on analytical models and experimental considerations. A method for extracting the nonlinearity parameter β{sub 11} is proposed based on a nonlinear least squares curve-fitting algorithm that is tailored for Rayleigh wave measurements. Quantitative experiments are conducted to confirm the predictions for the nonlinearity of the piezoelectric source and to demonstrate the effectiveness of the curve-fitting procedure. Thesemore » experiments are conducted on aluminum 2024 and 7075 specimens and a β{sub 11}{sup 7075}/β{sub 11}{sup 2024} measure of 1.363 agrees well with previous literature and earlier work.« less

Numerical investigation of nonlinear interactions between multimodal guided waves and delamination in composite structures

NASA Astrophysics Data System (ADS)

Shen, Yanfeng

2017-04-01

This paper presents a numerical investigation of the nonlinear interactions between multimodal guided waves and delamination in composite structures. The elastodynamic wave equations for anisotropic composite laminate were formulated using an explicit Local Interaction Simulation Approach (LISA). The contact dynamics was modeled using the penalty method. In order to capture the stick-slip contact motion, a Coulomb friction law was integrated into the computation procedure. A random gap function was defined for the contact pairs to model distributed initial closures or openings to approximate the nature of rough delamination interfaces. The LISA procedure was coded using the Compute Unified Device Architecture (CUDA), which enables the highly parallelized computation on powerful graphic cards. Several guided wave modes centered at various frequencies were investigated as the incident wave. Numerical case studies of different delamination locations across the thickness were carried out. The capability of different wave modes at various frequencies to trigger the Contact Acoustic Nonlinearity (CAN) was studied. The correlation between the delamination size and the signal nonlinearity was also investigated. Furthermore, the influence from the roughness of the delamination interfaces was discussed as well. The numerical investigation shows that the nonlinear features of wave delamination interactions can enhance the evaluation capability of guided wave Structural Health Monitoring (SHM) system. This paper finishes with discussion, concluding remarks, and suggestions for future work.

Tailorable stimulated Brillouin scattering in nanoscale silicon waveguides

PubMed Central

Shin, Heedeuk; Qiu, Wenjun; Jarecki, Robert; Cox, Jonathan A.; Olsson, Roy H.; Starbuck, Andrew; Wang, Zheng; Rakich, Peter T.

2013-01-01

Nanoscale modal confinement is known to radically enhance the effect of intrinsic Kerr and Raman nonlinearities within nanophotonic silicon waveguides. By contrast, stimulated Brillouin-scattering nonlinearities, which involve coherent coupling between guided photon and phonon modes, are stifled in conventional nanophotonics, preventing the realization of a host of Brillouin-based signal-processing technologies in silicon. Here we demonstrate stimulated Brillouin scattering in silicon waveguides, for the first time, through a new class of hybrid photonic–phononic waveguides. Tailorable travelling-wave forward-stimulated Brillouin scattering is realized—with over 1,000 times larger nonlinearity than reported in previous systems—yielding strong Brillouin coupling to phonons from 1 to 18 GHz. Experiments show that radiation pressures, produced by subwavelength modal confinement, yield enhancement of Brillouin nonlinearity beyond those of material nonlinearity alone. In addition, such enhanced and wideband coherent phonon emission paves the way towards the hybridization of silicon photonics, microelectromechanical systems and CMOS signal-processing technologies on chip. PMID:23739586

Particle simulations of mode conversion between slow mode and fast mode in lower hybrid range of frequencies

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

Jia, Guozhang; Xiang, Nong; Huang, Yueheng

2016-01-15

The propagation and mode conversion of lower hybrid waves in an inhomogeneous plasma are investigated by using the nonlinear δf algorithm in a two-dimensional particle-in-cell simulation code based on the gyrokinetic electron and fully kinetic ion (GeFi) scheme [Lin et al., Plasma Phys. Controlled Fusion 47, 657 (2005)]. The characteristics of the simulated waves, such as wavelength, frequency, phase, and group velocities, agree well with the linear theoretical analysis. It is shown that a significant reflection component emerges in the conversion process between the slow mode and the fast mode when the scale length of the density variation is comparablemore » to the local wavelength. The dependences of the reflection coefficient on the scale length of the density variation are compared with the results based on the linear full wave model for cold plasmas. It is indicated that the mode conversion for the waves with a frequency of 2.45 GHz (ω ∼ 3ω{sub LH}, where ω{sub LH} represents the lower hybrid resonance) and within Tokamak relevant amplitudes can be well described in the linear scheme. As the frequency decreases, the modification due to the nonlinear term becomes important. For the low-frequency waves (ω ∼ 1.3ω{sub LH}), the generations of the high harmonic modes and sidebands through nonlinear mode-mode coupling provide new power channels and thus could reduce the reflection significantly.« less

Solutions of the cylindrical nonlinear Maxwell equations.

PubMed

Xiong, Hao; Si, Liu-Gang; Ding, Chunling; Lü, Xin-You; Yang, Xiaoxue; Wu, Ying

2012-01-01

Cylindrical nonlinear optics is a burgeoning research area which describes cylindrical electromagnetic wave propagation in nonlinear media. Finding new exact solutions for different types of nonlinearity and inhomogeneity to describe cylindrical electromagnetic wave propagation is of great interest and meaningful for theory and application. This paper gives exact solutions for the cylindrical nonlinear Maxwell equations and presents an interesting connection between the exact solutions for different cylindrical nonlinear Maxwell equations. We also provide some examples and discussion to show the application of the results we obtained. Our results provide the basis for solving complex systems of nonlinearity and inhomogeneity with simple systems.

Optical frequency comb generation based on the dual-mode square microlaser and a nonlinear fiber loop

NASA Astrophysics Data System (ADS)

Weng, Hai-Zhong; Han, Jun-Yuan; Li, Qing; Yang, Yue-De; Xiao, Jin-Long; Qin, Guan-Shi; Huang, Yong-Zhen

2018-05-01

A novel approach using a dual-mode square microlaser as the pump source is demonstrated to produce wideband optical frequency comb (OFC). The enhanced nonlinear frequency conversion processes are accomplished in a nonlinear fiber loop, which can reduce the stimulated Brillouin scattering threshold and then generate a dual-mode Brillouin laser with improved optical signal-to-noise ratio. An OFC with 130 nm bandwidth and 76 GHz repetition rate is successfully generated under the four-wave mixing, and the number of the comb lines is enhanced by 26 times compared with the system without fiber loop. In addition, the repetition rate of the comb can be adjusted by changing the injection current of the microlaser. The pulse width of the comb spectrum is also compressed from 3 to 1 ps with an extra amplification-nonlinear process.

Nonlinear reflection of shock shear waves in soft elastic media.

PubMed

Pinton, Gianmarco; Coulouvrat, François; Gennisson, Jean-Luc; Tanter, Mickaël

2010-02-01

For fluids, the theoretical investigation of shock wave reflection has a good agreement with experiments when the incident shock Mach number is large. But when it is small, theory predicts that Mach reflections are physically unrealistic, which contradicts experimental evidence. This von Neumann paradox is investigated for shear shock waves in soft elastic solids with theory and simulations. The nonlinear elastic wave equation is approximated by a paraxial wave equation with a cubic nonlinear term. This equation is solved numerically with finite differences and the Godunov scheme. Three reflection regimes are observed. Theory is developed for shock propagation by applying the Rankine-Hugoniot relations and entropic constraints. A characteristic parameter relating diffraction and non-linearity is introduced and its theoretical values are shown to match numerical observations. The numerical solution is then applied to von Neumann reflection, where curved reflected and Mach shocks are observed. Finally, the case of weak von Neumann reflection, where there is no reflected shock, is examined. The smooth but non-monotonic transition between these three reflection regimes, from linear Snell-Descartes to perfect grazing case, provides a solution to the acoustical von Neumann paradox for the shear wave equation. This transition is similar to the quadratic non-linearity in fluids.

Salient features of solitary waves in dusty plasma under the influence of Coriolis force

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

Das, G. C.; Nag, Apratim; Department of Physics, G. C. College, Silchar-788004

The main interest is to study the nonlinear acoustic wave in rotating dusty plasma augmented through the derivation of a modified Sagdeev potential equation. Small rotation causes the interaction of Coriolis force in the dynamical system, and leads to the complexity in the derivation of the nonlinear wave equation. As a result, the finding of solitary wave propagation in dusty plasma ought to be of merit. However, the nonlinear wave equation has been successfully solved by the use of the hyperbolic method. Main emphasis has been given to the changes on the evolution and propagation of soliton, and the variationmore » caused by the dusty plasma constituents as well as by the Coriolis force have been highlighted. Some interesting nonlinear wave behavior has been found which can be elaborately studied for the interest of laboratory and space plasmas. Further, to support the theoretical investigations, numeric plasma parameters have been taken for finding the inherent features of solitons.« less

Modulational instability, beak-shaped rogue waves, multi-dark-dark solitons and dynamics in pair-transition-coupled nonlinear Schrödinger equations.

PubMed

Zhang, Guoqiang; Yan, Zhenya; Wen, Xiao-Yong

2017-07-01

The integrable coupled nonlinear Schrödinger equations with four-wave mixing are investigated. We first explore the conditions for modulational instability of continuous waves of this system. Secondly, based on the generalized N -fold Darboux transformation (DT), beak-shaped higher-order rogue waves (RWs) and beak-shaped higher-order rogue wave pairs are derived for the coupled model with attractive interaction in terms of simple determinants. Moreover, we derive the simple multi-dark-dark and kink-shaped multi-dark-dark solitons for the coupled model with repulsive interaction through the generalizing DT. We explore their dynamics and classifications by different kinds of spatial-temporal distribution structures including triangular, pentagonal, 'claw-like' and heptagonal patterns. Finally, we perform the numerical simulations to predict that some dark solitons and RWs are stable enough to develop within a short time. The results would enrich our understanding on nonlinear excitations in many coupled nonlinear wave systems with transition coupling effects.

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.).

Compressive Spectral Method for the Simulation of the Nonlinear Gravity Waves

PubMed Central

Bayındır, Cihan

2016-01-01

In this paper an approach for decreasing the computational effort required for the spectral simulations of the fully nonlinear ocean waves is introduced. The proposed approach utilizes the compressive sampling algorithm and depends on the idea of using a smaller number of spectral components compared to the classical spectral method. After performing the time integration with a smaller number of spectral components and using the compressive sampling technique, it is shown that the ocean wave field can be reconstructed with a significantly better efficiency compared to the classical spectral method. For the sparse ocean wave model in the frequency domain the fully nonlinear ocean waves with Jonswap spectrum is considered. By implementation of a high-order spectral method it is shown that the proposed methodology can simulate the linear and the fully nonlinear ocean waves with negligible difference in the accuracy and with a great efficiency by reducing the computation time significantly especially for large time evolutions. PMID:26911357

Nonlinear electric field structures in the inner magnetosphere

DOE PAGES

Malaspina, D. M.; Andersson, L.; Ergun, R. E.; ...

2014-08-28

Recent observations by the Van Allen Probes spacecraft have demonstrated that a variety of electric field structures and nonlinear waves frequently occur in the inner terrestrial magnetosphere, including phase space holes, kinetic field-line resonances, nonlinear whistler-mode waves, and several types of double layer. However, it is nuclear whether such structures and waves have a significant impact on the dynamics of the inner magnetosphere, including the radiation belts and ring current. To make progress toward quantifying their importance, this study statistically evaluates the correlation of such structures and waves with plasma boundaries. A strong correlation is found. These statistical results, combinedmore » with observations of electric field activity at propagating plasma boundaries, are consistent with the identification of these boundaries as the source of free energy responsible for generating the electric field structures and nonlinear waves of interest. Therefore, the ability of these structures and waves to influence plasma in the inner magnetosphere is governed by the spatial extent and dynamics of macroscopic plasma boundaries in that region.« less

Verification of nonlinear particle simulation of radio frequency waves in fusion plasmas

NASA Astrophysics Data System (ADS)

Kuley, Animesh; Bao, Jian; Lin, Zhihong

2015-11-01

Nonlinear global particle simulation model has been developed in GTC to study the nonlinear interactions of radio frequency (RF) waves with plasmas in tokamak. In this model, ions are considered as fully kinetic particles using the Vlasov equation and electrons are treated as guiding centers using the drift kinetic. Boris push scheme for the ion motion has been implemented in the toroidal geometry using magnetic coordinates and successfully verified for the ion cyclotron, ion Bernstein and lower hybrid waves. The nonlinear GTC simulation of the lower hybrid wave shows that the amplitude of the electrostatic potential is oscillatory due to the trapping of resonant electrons by the electric field of the lower hybrid wave. The nonresonant parametric decay is observed an IBW sideband and an ion cyclotron quasimode (ICQM). The ICQM induces an ion perpendicular heating with a heating rate proportional to the pump wave intensity. This work is supported by PPPL subcontract number S013849-F and US Department of Energy (DOE) SciDAC GSEP Program.

Nonlinear Problems in Fluid Dynamics and Inverse Scattering

DTIC Science & Technology

1993-05-31

nonlinear Kadomtsev - Petviashvili (KP) equations , have solutions which will become infinite in finite time. This phenomenon is sometimes referred to as...40 (November 1992). 4 7. Wave Collapse and Instability of Solitary Waves of a Generalized Nonlinear Kaoiomtsev- Petviashvili Equation , X.P. Wang, M.J...words) The inverse scattering of a class of differential-difference equations and multidimensional operators has been constructed. Solutions of nonlinear

On Wave Processes in the Solar Atmosphere

NASA Technical Reports Server (NTRS)

Musielak, Z. E.

1998-01-01

This grant was awarded by NASA/MSFC to The University of Alabama in Huntsville (UAH) to investigate the physical processes responsible for heating and wind acceleration in the solar atmosphere, and to construct theoretical, self-consistent and time-dependent solar wind models based on the momentum deposition by finite amplitude and nonlinear Alfven waves. In summary, there are three main goals of the proposed research: (1) Calculate the wave energy spectra and wave energy fluxes carried by magnetic non- magnetic waves. (2) Find out which mechanism dominates in supplying the wave energy to different parts of the solar atmosphere. (3) Use the results obtained in (1) and (2) to construct theoretical, self-consistent and time- dependent models of the solar wind. We have completed the first goal by calculating the amount of non-radiative energy generated in the solar convection zone as acoustic waves and as magnetic tube waves. To calculate the amount of wave energy carried by acoustic waves, we have used the Lighthill-Stein theory for sound generation modified by Musielak, Rosner, Stein & Ulmschneider (1994). The acoustic wave energy fluxes for stars located in different regions of the Hertzsprung-Russell (H-R) diagram have also been computed. The wave energy fluxes carried by longitudinal and transverse waves along magnetic flux tubes have been calculated by using both analytical and numerical methods. Our analytical approach is based a theory developed by Musielak, Rosner & Ulmschnelder and Musielak, Rosner, Gall & Ulmschneider, which allows computing the wave energy fluxes for linear tube waves. A numerical approach has been developed by Huang, Musielak & Ulmschneider and Ulmschneider & Musielak to compute the energy fluxes for nonlinear tube waves. Both methods have been used to calculate the wave energy fluxes for stars located in different regions of the HR diagram (Musielak, Rosner & Ulmschneider 1998; Ulmschneider, Musielak & Fawzy 1998). Having obtained the wave energy fluxes for acoustic and magnetic tube waves, we have investigated the behavior of these waves in the solar and stellar atmospheres. The results of our extensive studies have been published in many papers and presented at numerous scientific meetings. In these studies we have investigated different aspects of propagation of acoustic and magnetic waves, the efficiency of energy transfer along magnetic structures in the solar atmosphere, and behavior of Alfven waves in stgeady and expanding solar and stellar atmospheres. Recently, we have used some of these results to construct first purely theoretical, two component and time-dependent models of solar and stellar chromospheres. Finally, to address the third goal, we have constructed first fully theoretical, self-consistent and time dependent wind models based on the momentum deposition by non-linear Alfven waves. The full set of single-fluid MHD equations with the background flow has been solved by using a modified version of the ZEUS MHD code. The constructed wind models are radially symmetric with the magnetic field decreasing radially and the initial outflow is described by the standard Parker wind solution. In contrast to previous studies, no assumptions regarding wave linearity, wave damping, and wave-flow interaction are made; the models thus naturally account for the backreaction of the wind on the waves as well as for the nonlinear interaction between different types of MHD waves. The models have been used to explain the origin of fast speed streams in solar coronal holes. The obtained results clearly demonstrate that the momentum deposition by Alfven waves in the solar wind can be sufficient to explain the origin of fast stream components of the solar wind. The range of wave amplitudes required to obtain the desired results seems to be in good agreement with recent observations.

Nonlinear density waves in planetary rings

NASA Technical Reports Server (NTRS)

Borderies, Nicole; Goldreich, Peter; Tremaine, Scott

1986-01-01

The steady-state structure of planetary rings in the presence of density waves at the Lindblad resonances of a satellite is indicated. The study is based on the dispersion relation and damping rate for nonlinear density waves, derived by Shu et al. (1985) and by Borderies, Goldreich, and Tremaine (1985). It is shown that strong density waves lead to an enhancement of the background surface density in the wave zone.

Thermal responses in a coronal loop maintained by wave heating mechanisms

NASA Astrophysics Data System (ADS)

Matsumoto, Takuma

2018-05-01

A full 3-dimensional compressible magnetohydrodynamic (MHD) simulation is conducted to investigate the thermal responses of a coronal loop to the dynamic dissipation processes of MHD waves. When the foot points of the loop are randomly and continuously forced, the MHD waves become excited and propagate upward. Then, 1-MK temperature corona is produced naturally as the wave energy dissipates. The excited wave packets become non-linear just above the magnetic canopy, and the wave energy cascades into smaller spatial scales. Moreover, collisions between counter-propagating Alfvén wave packets increase the heating rate, resulting in impulsive temperature increases. Our model demonstrates that the heating events in the wave-heated loops can be nanoflare-like in the sense that they are spatially localized and temporally intermittent.

Numerical modeling of the atmosphere with an isentropic vertical coordinate

NASA Technical Reports Server (NTRS)

Hsu, Yueh-Jiuan G.; Arakawa, Akio

1990-01-01

A theta-coordinate model simulating the nonlinear evolution of a baroclinic wave is presented. In the model, vertical discretization maintains important integral constraints such as conservation of the angular momentum and total energy. A massless-layer approach is used in the treatment of the intersections of coordinate surfaces with the lower boundary. This formally eliminates the intersection problem, but raises other computational problems. Horizontal discretization of the continuity and momentum equations in the model are designed to overcome these problems. Selected results from a 10-day integration with the 25-layer, beta-plane version of the model are presented. It is concluded that the model can simulate the nonlinear evolution of a baroclinic wave and associated dynamical processes without major computational difficulties.

Capillary waves in the subcritical nonlinear Schroedinger equation

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

Kozyreff, G.

2010-01-15

We expand recent results on the nonlinear Schroedinger equation with cubic-quintic nonlinearity to show that some solutions are described by the Bernoulli equation in the presence of surface tension. As a consequence, capillary waves are predicted and found numerically at the interface between regions of large and low amplitude.

Physics, Nonlinear Time Series Analysis, Data Assimilation and Hyperfast Modeling of Nonlinear Ocean Waves

DTIC Science & Technology

2010-09-30

Hyperfast Modeling of Nonlinear Ocean Waves A. R. Osborne Dipartimento di Fisica Generale, Università di Torino Via Pietro Giuria 1, 10125...PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) Universit?i Torino,Dipartimento di Fisica Generale,Via Pietro Giuria 1,10125 Torino, Italy, 8. PERFORMING

Studies of nonlinear femtosecond pulse propagation in bulk materials

NASA Astrophysics Data System (ADS)

Eaton, Hilary Kaye

2000-10-01

Femtosecond pulse lasers are finding widespread application in a variety of fields including medical research, optical switching and communications, plasma formation, high harmonic generation, and wavepacket formation and control. As the number of applications for femtosecond pulses increases, so does the need to fully understand the linear and nonlinear processes involved in propagating these pulses through materials under various conditions. Recent advances in pulse measurement techniques, such as frequency-resolved optical gating (FROG), allow measurement of the full electric field of the pulse and have made detailed investigations of short- pulse propagation effects feasible. In this thesis, I present detailed experimental studies of my work involving nonlinear propagation of femtosecond pulses in bulk media. Studies of plane-wave propagation in fused silica extend the SHG form of FROG from a simple pulse diagnostic to a useful method of interrogating the nonlinear response of a material. Studies of nonlinear propagation are also performed in a regime where temporal pulse splitting occurs. Experimental results are compared with a three- dimensional nonlinear Schrödinger equation. This comparison fuels the development of a more complete model for pulse splitting. Experiments are also performed at peak input powers above those at which pulse splitting is observed. At these higher intensities, a broadband continuum is generated. This work presents a detailed study of continuum behavior and power loss as well as the first near-field spatial- spectral measurements of the generated continuum light. Nonlinear plane-wave propagation of short pulses in liquids is also investigated, and a non-instantaneous nonlinearity with a surprisingly short response time of 10 fs is observed in methanol. Experiments in water confirm that this effect in methanol is indeed real. Possible explanations for the observed effect are discussed and several are experimentally rejected. This thesis applies FROG as a powerful tool for science and not just a useful pulse diagnostic technique. Studies of three-dimensional propagation provide an in-depth understanding of the processes involved in femtosecond pulse splitting. In addition, the experimental investigations of continuum generation and pulse propagation in liquids provide new insights into the possible processes involved and should provide a useful comparison for developing theories.

Dynamics of periodic mechanical structures containing bistable elastic elements: From elastic to solitary wave propagation

NASA Astrophysics Data System (ADS)

Nadkarni, Neel; Daraio, Chiara; Kochmann, Dennis M.

2014-08-01

We investigate the nonlinear dynamics of a periodic chain of bistable elements consisting of masses connected by elastic springs whose constraint arrangement gives rise to a large-deformation snap-through instability. We show that the resulting negative-stiffness effect produces three different regimes of (linear and nonlinear) wave propagation in the periodic medium, depending on the wave amplitude. At small amplitudes, linear elastic waves experience dispersion that is controllable by the geometry and by the level of precompression. At moderate to large amplitudes, solitary waves arise in the weakly and strongly nonlinear regime. For each case, we present closed-form analytical solutions and we confirm our theoretical findings by specific numerical examples. The precompression reveals a class of wave propagation for a partially positive and negative potential. The presented results highlight opportunities in the design of mechanical metamaterials based on negative-stiffness elements, which go beyond current concepts primarily based on linear elastic wave propagation. Our findings shed light on the rich effective dynamics achievable by nonlinear small-scale instabilities in solids and structures.

Nonlinear Lamb waves for fatigue damage identification in FRP-reinforced steel plates.

PubMed

Wang, Yikuan; Guan, Ruiqi; Lu, Ye

2017-09-01

A nonlinear Lamb-wave-based method for fatigue crack detection in steel plates with and without carbon fibre reinforcement polymer (CFRP) reinforcement is presented in this study. Both numerical simulation and experimental evaluation were performed for Lamb wave propagation and its interaction with a fatigue crack on these two steel plate types. With the generation of the second harmonic, the damage-induced wave nonlinearities were identified by surface-bonded piezoelectric sensors. Numerical simulation revealed that the damage-induced wave component at the second harmonic was slightly affected by the existence of CFRP laminate, although the total wave energy was decreased because of wave leakage into the CFRP laminate. Due to unavoidable nonlinearity from the experimental environments, it was impractical to directly extract the time-of-flight of the second harmonic for locating the crack. To this end, the correlation coefficient of benchmark and signal with damage at double frequency in the time domain was calculated, based on which an imaging method was introduced to locate the fatigue crack in steel plates with and without CFRP laminates. Copyright © 2017 Elsevier B.V. All rights reserved.

Nonlinear modeling of wave-topography interactions, shear instabilities and shear induced wave breaking using vortex method

NASA Astrophysics Data System (ADS)

Guha, Anirban

2017-11-01

Theoretical studies on linear shear instabilities as well as different kinds of wave interactions often use simple velocity and/or density profiles (e.g. constant, piecewise) for obtaining good qualitative and quantitative predictions of the initial disturbances. Moreover, such simple profiles provide a minimal model to obtain a mechanistic understanding of shear instabilities. Here we have extended this minimal paradigm into nonlinear domain using vortex method. Making use of unsteady Bernoulli's equation in presence of linear shear, and extending Birkhoff-Rott equation to multiple interfaces, we have numerically simulated the interaction between multiple fully nonlinear waves. This methodology is quite general, and has allowed us to simulate diverse problems that can be essentially reduced to the minimal system with interacting waves, e.g. spilling and plunging breakers, stratified shear instabilities (Holmboe, Taylor-Caulfield, stratified Rayleigh), jet flows, and even wave-topography interaction problem like Bragg resonance. We found that the minimal models capture key nonlinear features (e.g. wave breaking features like cusp formation and roll-ups) which are observed in experiments and/or extensive simulations with smooth, realistic profiles.