On nonlinear evolution of low-frequency Alfvén waves in weakly-expanding solar wind plasmas

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

Nariyuki, Y.

A multi-dimensional nonlinear evolution equation for Alfvén waves in weakly-expanding solar wind plasmas is derived by using the reductive perturbation method. The expansion of solar wind plasma parcels is modeled by an expanding box model, which includes the accelerating expansion. It is shown that the resultant equation agrees with the Wentzel-Kramers-Brillouin prediction of the low-frequency Alfvén waves in the linear limit. In the cold and one-dimensional limit, a modified derivative nonlinear Schrodinger equation is obtained. Direct numerical simulations are carried out to discuss the effect of the expansion on the modulational instability of monochromatic Alfvén waves and the propagation ofmore » Alfvén solitons. By using the instantaneous frequency, it is quantitatively shown that as far as the expansion rate is much smaller than wave frequencies, effects of the expansion are almost adiabatic. It is also confirmed that while shapes of Alfvén solitons temporally change due to the expansion, some of them can stably propagate after their collision in weakly-expanding plasmas.« less

The modulational instability for the TDNLS equations for weakly nonlinear dispersive MHD waves

NASA Technical Reports Server (NTRS)

Webb, G. M.; Brio, M.; Zank, G. P.

1995-01-01

In this paper we study the modulational instability for the TDNLS equations derived by Hada (1993) and Brio, Hunter, and Johnson to describe the propagation of weakly nonlinear dispersive MHD waves in beta approximately 1 plasmas. We employ Whitham's averaged Lagrangian method to study the modulational instability. This complements studies of the modulational instability by Hada (1993) and Hollweg (1994), who did not use the averaged Lagrangian approach.

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.

Magnetosonic shock wave in collisional pair-ion plasma

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

Adak, Ashish, E-mail: ashish-adak@yahoo.com; Khan, Manoranjan, E-mail: mkhan.ju@gmail.com; Sikdar, Arnab, E-mail: arnabs.ju@gmail.com

2016-06-15

Nonlinear propagation of magnetosonic shock wave has been studied in collisional magnetized pair-ion plasma. The masses of both ions are same but the temperatures are slightly different. Two fluid model has been taken to describe the model. Two different modes of the magnetosonic wave have been obtained. The dynamics of the nonlinear magnetosonic wave is governed by the Korteweg-de Vries Burgers' equation. It has been shown that the ion-ion collision is the source of dissipation that causes the Burgers' term which is responsible for the shock structures in equal mass pair-ion plasma. The numerical investigations reveal that the magnetosonic wavemore » exhibits both oscillatory and monotonic shock structures depending on the strength of the dissipation. The nonlinear wave exhibited the oscillatory shock wave for strong magnetic field (weak dissipation) and monotonic shock wave for weak magnetic field (strong dissipation). The results have been discussed in the context of the fullerene pair-ion plasma experiments.« less

Kelvin-wave cascade in the vortex filament model

NASA Astrophysics Data System (ADS)

Baggaley, Andrew W.; Laurie, Jason

2014-01-01

The small-scale energy-transfer mechanism in zero-temperature superfluid turbulence of helium-4 is still a widely debated topic. Currently, the main hypothesis is that weakly nonlinear interacting Kelvin waves (KWs) transfer energy to sufficiently small scales such that energy is dissipated as heat via phonon excitations. Theoretically, there are at least two proposed theories for Kelvin-wave interactions. We perform the most comprehensive numerical simulation of weakly nonlinear interacting KWs to date and show, using a specially designed numerical algorithm incorporating the full Biot-Savart equation, that our results are consistent with the nonlocal six-wave KW interactions as proposed by L'vov and Nazarenko.

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.

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

A Weakly Nonlinear Model for the Damping of Resonantly Forced Density Waves in Dense Planetary Rings

NASA Astrophysics Data System (ADS)

Lehmann, Marius; Schmidt, Jürgen; Salo, Heikki

2016-10-01

In this paper, we address the stability of resonantly forced density waves in dense planetary rings. Goldreich & Tremaine have already argued that density waves might be unstable, depending on the relationship between the ring’s viscosity and the surface mass density. In the recent paper Schmidt et al., we have pointed out that when—within a fluid description of the ring dynamics—the criterion for viscous overstability is satisfied, forced spiral density waves become unstable as well. In this case, linear theory fails to describe the damping, but nonlinearity of the underlying equations guarantees a finite amplitude and eventually a damping of the wave. We apply the multiple scale formalism to derive a weakly nonlinear damping relation from a hydrodynamical model. This relation describes the resonant excitation and nonlinear viscous damping of spiral density waves in a vertically integrated fluid disk with density dependent transport coefficients. The model consistently predicts density waves to be (linearly) unstable in a ring region where the conditions for viscous overstability are met. Sufficiently far away from the Lindblad resonance, the surface mass density perturbation is predicted to saturate to a constant value due to nonlinear viscous damping. The wave’s damping lengths of the model depend on certain input parameters, such as the distance to the threshold for viscous overstability in parameter space and the ground state surface mass density.

Rotation-induced nonlinear wavepackets in internal waves

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

Whitfield, A. J., E-mail: ashley.whitfield.12@ucl.ac.uk; Johnson, E. R., E-mail: e.johnson@ucl.ac.uk

2014-05-15

The long time effect of weak rotation on an internal solitary wave is the decay into inertia-gravity waves and the eventual formation of a localised wavepacket. Here this initial value problem is considered within the context of the Ostrovsky, or the rotation-modified Korteweg-de Vries (KdV), equation and a numerical method for obtaining accurate wavepacket solutions is presented. The flow evolutions are described in the regimes of relatively-strong and relatively-weak rotational effects. When rotational effects are relatively strong a second-order soliton solution of the nonlinear Schrödinger equation accurately predicts the shape, and phase and group velocities of the numerically determined wavepackets.more » It is suggested that these solitons may form from a local Benjamin-Feir instability in the inertia-gravity wave-train radiated when a KdV solitary wave rapidly adjusts to the presence of strong rotation. When rotational effects are relatively weak the initial KdV solitary wave remains coherent longer, decaying only slowly due to weak radiation and modulational instability is no longer relevant. Wavepacket solutions in this regime appear to consist of a modulated KdV soliton wavetrain propagating on a slowly varying background of finite extent.« less

Shock waves in weakly compressed granular media.

PubMed

van den Wildenberg, Siet; van Loo, Rogier; van Hecke, Martin

2013-11-22

We experimentally probe nonlinear wave propagation in weakly compressed granular media and observe a crossover from quasilinear sound waves at low impact to shock waves at high impact. We show that this crossover impact grows with the confining pressure P0, whereas the shock wave speed is independent of P0-two hallmarks of granular shocks predicted recently. The shocks exhibit surprising power law attenuation, which we model with a logarithmic law implying that shock dissipation is weak and qualitatively different from other granular dissipation mechanisms. We show that elastic and potential energy balance in the leading part of the shocks.

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

NASA Astrophysics Data System (ADS)

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

2018-03-01

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

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.

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.

Dark solitons, modulation instability and breathers in a chain of weakly nonlinear oscillators with cyclic symmetry

NASA Astrophysics Data System (ADS)

Fontanela, F.; Grolet, A.; Salles, L.; Chabchoub, A.; Hoffmann, N.

2018-01-01

In the aerospace industry the trend for light-weight structures and the resulting complex dynamic behaviours currently challenge vibration engineers. In many cases, these light-weight structures deviate from linear behaviour, and complex nonlinear phenomena can be expected. We consider a cyclically symmetric system of coupled weakly nonlinear undamped oscillators that could be considered a minimal model for different cyclic and symmetric aerospace structures experiencing large deformations. The focus is on localised vibrations that arise from wave envelope modulation of travelling waves. For the defocussing parameter range of the approximative nonlinear evolution equation, we show the possible existence of dark solitons and discuss their characteristics. For the focussing parameter range, we characterise modulation instability and illustrate corresponding nonlinear breather dynamics. Furthermore, we show that for stronger nonlinearity or randomness in initial conditions, transient breather-type dynamics and decay into bright solitons appear. The findings suggest that significant vibration localisation may arise due to mechanisms of nonlinear modulation dynamics.

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.

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

Quon, Eliot; Platt, Andrew; Yu, Yi-Hsiang

Extreme loads are often a key cost driver for wave energy converters (WECs). As an alternative to exhaustive Monte Carlo or long-term simulations, the most likely extreme response (MLER) method allows mid- and high-fidelity simulations to be used more efficiently in evaluating WEC response to events at the edges of the design envelope, and is therefore applicable to system design analysis. The study discussed in this paper applies the MLER method to investigate the maximum heave, pitch, and surge force of a point absorber WEC. Most likely extreme waves were obtained from a set of wave statistics data based onmore » spectral analysis and the response amplitude operators (RAOs) of the floating body; the RAOs were computed from a simple radiation-and-diffraction-theory-based numerical model. A weakly nonlinear numerical method and a computational fluid dynamics (CFD) method were then applied to compute the short-term response to the MLER wave. Effects of nonlinear wave and floating body interaction on the WEC under the anticipated 100-year waves were examined by comparing the results from the linearly superimposed RAOs, the weakly nonlinear model, and CFD simulations. Overall, the MLER method was successfully applied. In particular, when coupled to a high-fidelity CFD analysis, the nonlinear fluid dynamics can be readily captured.« less

Undular bore theory for the Gardner equation

NASA Astrophysics Data System (ADS)

Kamchatnov, A. M.; Kuo, Y.-H.; Lin, T.-C.; Horng, T.-L.; Gou, S.-C.; Clift, R.; El, G. A.; Grimshaw, R. H. J.

2012-09-01

We develop modulation theory for undular bores (dispersive shock waves) in the framework of the Gardner, or extended Korteweg-de Vries (KdV), equation, which is a generic mathematical model for weakly nonlinear and weakly dispersive wave propagation, when effects of higher order nonlinearity become important. Using a reduced version of the finite-gap integration method we derive the Gardner-Whitham modulation system in a Riemann invariant form and show that it can be mapped onto the well-known modulation system for the Korteweg-de Vries equation. The transformation between the two counterpart modulation systems is, however, not invertible. As a result, the study of the resolution of an initial discontinuity for the Gardner equation reveals a rich phenomenology of solutions which, along with the KdV-type simple undular bores, include nonlinear trigonometric bores, solibores, rarefaction waves, and composite solutions representing various combinations of the above structures. We construct full parametric maps of such solutions for both signs of the cubic nonlinear term in the Gardner equation. Our classification is supported by numerical simulations.

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.

Weakly nonlinear dynamics of near-CJ detonation waves

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

Bdzil, J.B.; Klein, R.

1993-01-01

The renewed interest in safety issues for large scale industrial devices and in high speed combustion has driven recent intense efforts to gain a deeper theoretical understanding of detonation wave dynamics. Linear stability analyses, weakly nonlinear bifurcation calculations as well as full scale multi-dimensional direct numerical simulations have been pursued for a standard model problem based on the reactive Euler equations for an ideal gas with constant specific heat capacities and simplified chemical reaction models. Most of these studies are concerned with overdriven detonations. This is true despite the fact that the majority of all detonations observed in nature aremore » running at speeds close to the Chapman-Jouguet (CJ) limit value. By focusing on overdriven waves one removes an array of difficulties from the analysis that is associated with the sonic flow conditions in the wake of a CJ-detonation. In particular, the proper formulation of downstream boundary conditions in the CJ-case is a yet unsolved analytical problem. A proper treatment of perturbations in the back of a Chapman-Jouguet detonation has to account for two distinct weakly nonlinear effects in the forward acoustic wave component. The first is a nonlinear interactionof highly temperature sensitive chemistry with the forward acoustic wave component in a transonic boundary layer near the end of the reaction zone. The second is a cumulative three-wave-resonance in the sense of Majda et al. which is active in the near-sonic burnt gas flow and which is essentially independent of the details of the chemical model. In this work, we consider detonations in mixtures with moderate state sensitivity of the chemical reactions. Then, the acoustic perturbations do not influence the chemistry at the order considered and we may concentrate on the second effect; the three-wave resonance.« less

Weakly nonlinear dynamics of near-CJ detonation waves

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

Bdzil, J.B.; Klein, R.

1993-02-01

The renewed interest in safety issues for large scale industrial devices and in high speed combustion has driven recent intense efforts to gain a deeper theoretical understanding of detonation wave dynamics. Linear stability analyses, weakly nonlinear bifurcation calculations as well as full scale multi-dimensional direct numerical simulations have been pursued for a standard model problem based on the reactive Euler equations for an ideal gas with constant specific heat capacities and simplified chemical reaction models. Most of these studies are concerned with overdriven detonations. This is true despite the fact that the majority of all detonations observed in nature aremore » running at speeds close to the Chapman-Jouguet (CJ) limit value. By focusing on overdriven waves one removes an array of difficulties from the analysis that is associated with the sonic flow conditions in the wake of a CJ-detonation. In particular, the proper formulation of downstream boundary conditions in the CJ-case is a yet unsolved analytical problem. A proper treatment of perturbations in the back of a Chapman-Jouguet detonation has to account for two distinct weakly nonlinear effects in the forward acoustic wave component. The first is a nonlinear interactionof highly temperature sensitive chemistry with the forward acoustic wave component in a transonic boundary layer near the end of the reaction zone. The second is a cumulative three-wave-resonance in the sense of Majda et al. which is active in the near-sonic burnt gas flow and which is essentially independent of the details of the chemical model. In this work, we consider detonations in mixtures with moderate state sensitivity of the chemical reactions. Then, the acoustic perturbations do not influence the chemistry at the order considered and we may concentrate on the second effect; the three-wave resonance.« less

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.

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

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

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

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

Simulation of linear and nonlinear Landau damping of lower hybrid waves

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

Qi, Lei; Wang, X. Y.; Lin, Y.

2013-06-15

The linear physics of lower hybrid waves (LHWs) and their nonlinear interaction with particles through Landau damping are studied with the gyrokinetic electron and fully kinetic ion (GeFi) particle simulation model in the electrostatic limit. Unlike most other wave modes, the LHWs can resonantly interact with both electrons and ions, with the former being highly magnetized and latter nearly unmagnetized around the lower hybrid frequency. Direct interactions of LHWs with electrons and/or ions are investigated for cases with various k{sub ∥}/k,T{sub i}/T{sub e}, and wave amplitudes. In the linear electron Landau damping (ELD), the dispersion relation and the linear dampingmore » rate obtained from our simulation agree well with the analytical linear theory. As the wave amplitude increases, the nonlinear Landau effects are present, and a transition from strong decay at smaller amplitudes to weak decay at larger amplitudes is observed. In the nonlinear stage, the LHWs in the long time evolution finally exhibit a steady Bernstein-Greene-Kruskal mode, in which the wave amplitude is saturated above the noise level. While the resonant electrons are trapped in the wave field in the nonlinear ELD, the resonant ions are untrapped in the LHW time scales. The ion Landau damping is thus predominantly in a linear fashion, leading to a wave saturation level significantly lower than that in the ELD. On the long time scales, however, the ions are still weakly trapped. The results show a coupling between the LHW frequency and the ion cyclotron frequency during the long-time LHW evolution.« less

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

Symmetries of the TDNLS equations for weakly nonlinear dispersive MHD waves

NASA Technical Reports Server (NTRS)

Webb, G. M.; Brio, M.; Zank, G. P.

1995-01-01

In this paper we consider the symmetries and conservation laws for the TDNLS equations derived by Hada (1993) and Brio, Hunter and Johnson, to describe the propagation of weakly nonlinear dispersive MHD waves in beta approximately 1 plasmas. The equations describe the interaction of the Alfven and magnetoacoustic modes near the triple umbilic, where the fast magnetosonic, slow magnetosonic and Alfven speeds coincide and a(g)(exp 2) = V(A)(exp 2) where a(g) is the gas sound speed and V(A) is the Alfven speed. We discuss Lagrangian and Hamiltonian formulations, and similarity solutions for the equations.

Guided solitary waves.

PubMed

Miles, J

1980-04-01

Transversely periodic solitary-wave solutions of the Boussinesq equations (which govern wave propagation in a weakly dispersive, weakly nonlinear physical system) are determined. The solutions for negative dispersion (e.g., gravity waves) are singular and therefore physically unacceptable. The solutions for positive dispersion (e.g., capillary waves or magnetosonic waves in a plasma) are physically acceptable except in a limited parametric interval, in which they are complex. The two end points of this interval are associated with (two different) resonant interactions among three basic solitary waves, two of which are two-dimensional complex conjugates and the third of which is one-dimensional and real.

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).

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.

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.

A maximally informative version of inelastic scattering of electromagnetic waves by Langmuir waves

NASA Astrophysics Data System (ADS)

Erofeev, V. I.

2015-09-01

The concept of informativeness of nonlinear plasma physics scenarios is explained. Natural ideas of developing highly informative models of plasma kinetics are spelled out. A maximally informative version of inelastic scattering of electromagnetic waves by Langmuir waves in a weakly turbulent inhomogeneous plasma is developed with consideration of possible changes in wave polarization. In addition, a new formula for wave drift in spatial positions and wave vectors is derived. New scenarios of the respective wave drift and inelastic scattering are compared with the previous visions. The results indicate the need for further revision of the traditional understanding of nonlinear plasma phenomena.

O Wave Interactions: Explosive Resonant Triads and Critical Layers.

NASA Astrophysics Data System (ADS)

Mahoney, Daniel J.

This thesis considers the phenomenon of explosive resonant triads in weakly nonlinear, dispersive wave systems. These are nearly linear waves with slowly varying amplitudes which become unbounded in finite time. It is shown that such interactions are much stronger than previously thought. These waves can be thought of as a nonlinear instability, in the sense that a weakly nonlinear perturbation to some system grows to such magnitudes that the behavior of the system is governed by strongly nonlinear effects. This may occur for systems which are linearly or neutrally stable. This is contrasted with previous resolutions of this problem, which treated such perturbations as being large amplitude, nearly linear waves. Analytical and numerical evidence is presented to support these claims. These waves represent a potentially important effect in a variety of physical systems, most notably plasma physics. Attention here is turned to their occurrence in fluid mechanics. Here previous work is extended to include flow systems with continuously varying basic velocities and densities. Many of the problems encountered here will be found to be of a singular nature themselves, and the techniques for analyzing these difficulties will be developed. This will involve the concept of a critical layer in a fluid, a level at which a wave phase speed equals the unperturbed fluid velocity in the direction of propagation. Examples of such waves in this context will be presented. (Copies available exclusively from MIT Libraries, Rm. 14-0551, Cambridge, MA 02139-4307. Ph. 617-253-5668; Fax 617-253 -1690.).

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.

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.

Nonlinear low-frequency electrostatic wave dynamics in a two-dimensional quantum plasma

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

Ghosh, Samiran, E-mail: sran_g@yahoo.com; Chakrabarti, Nikhil, E-mail: nikhil.chakrabarti@saha.ac.in

2016-08-15

The problem of two-dimensional arbitrary amplitude low-frequency electrostatic oscillation in a quasi-neutral quantum plasma is solved exactly by elementary means. In such quantum plasmas we have treated electrons quantum mechanically and ions classically. The exact analytical solution of the nonlinear system exhibits the formation of dark and black solitons. Numerical simulation also predicts the possible periodic solution of the nonlinear system. Nonlinear analysis reveals that the system does have a bifurcation at a critical Mach number that depends on the angle of propagation of the wave. The small-amplitude limit leads to the formation of weakly nonlinear Kadomstev–Petviashvili solitons.

Finite-amplitude strain waves in laser-excited plates.

PubMed

Mirzade, F Kh

2008-07-09

The governing equations for two-dimensional finite-amplitude longitudinal strain waves in isotropic laser-excited solid plates are derived. Geometric and weak material nonlinearities are included, and the interaction of longitudinal displacements with the field of concentration of non-equilibrium laser-generated atomic defects is taken into account. An asymptotic approach is used to show that the equations are reducible to the Kadomtsev-Petviashvili-Burgers nonlinear evolution equation for a longitudinal self-consistent strain field. It is shown that two-dimensional shock waves can propagate in plates.

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.

A Simple Theory of Capillary-Gravity Wave Turbulence

NASA Technical Reports Server (NTRS)

Glazman, Roman E.

1995-01-01

Employing a recently proposed 'multi-wave interaction' theory, inertial spectra of capillary gravity waves are derived. This case is characterized by a rather high degree of nonlinearity and a complicated dispersion law. The absence of scale invariance makes this and some other problems of wave turbulence (e.g., nonlinear inertia gravity waves) intractable by small-perturbation techniques, even in the weak-turbulence limit. The analytical solution obtained in the present work for an arbitrary degree of nonlinearity is shown to be in reasonable agreement with experimental data. The theory explains the dependence of the wave spectrum on wind input and describes the accelerated roll-off of the spectral density function in the narrow sub-range separating scale-invariant regimes of purely gravity and capillary waves, while the appropriate (long- and short-wave) limits yield power laws corresponding to the Zakharov-Filonenko and Phillips spectra.

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.

Models for short-wave instability in inviscid shear flows

NASA Astrophysics Data System (ADS)

Grimshaw, Roger

1999-11-01

The generation of instability in an invsicid fluid occurs by a resonance between two wave modes, where here the resonance occurs by a coincidence of phase speeds for a finite, non-zero wavenumber. We show that in the weakly nonlinear limit, the appropriate model consists of two coupled equations for the envelopes of the wave modes, in which the nonlinear terms are balanced with low-order cross-coupling linear dispersive terms rather than the more familiar high-order terms which arise in the nonlinear Schrodinger equation, for instance. We will show that this system may either contain gap solitons as solutions in the linearly stable case, or wave breakdown in the linearly unstable case. In this latter circumstance, the system either exhibits wave collapse in finite time, or disintegration into fine-scale structures.

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.

Nonlinear interaction of kinetic Alfven wave and whistler: Turbulent spectra and anisotropic scaling

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

Kumar Dwivedi, Navin; Sharma, R. P.

2013-04-15

In this work, we are presenting the excitation of oblique propagating whistler wave as a consequence of nonlinear interaction between whistler wave and kinetic Alfven wave (KAW) in intermediate beta plasmas. Numerical simulation has been done to study the transient evolution of magnetic field structures of KAW when the nonlinearity arises due to ponderomotive effects by taking the adiabatic response of the background density. Weak oblique propagating whistler signals in these nonlinear plasma density filaments (produced by KAW localization) get amplified. The spectral indices of the power spectrum at different times are calculated with given initial conditions of the simulations.more » Anisotropic scaling laws for KAW and whistlers are presented. The relevance of the present investigation to solar wind turbulence and its acceleration is also pointed out.« less

Experimental investigation of three-wave interactions of capillary surface-waves

NASA Astrophysics Data System (ADS)

Berhanu, Michael; Cazaubiel, Annette; Deike, Luc; Jamin, Timothee; Falcon, Eric

2014-11-01

We report experiments studying the non-linear interaction between two crossing wave-trains of gravity-capillary surface waves generated in a closed laboratory tank. Using a capacitive wave gauge and Diffusive Light Photography method, we detect a third wave of smaller amplitude whose frequency and wavenumber are in agreement with the weakly non-linear triadic resonance interaction mechanism. By performing experiments in stationary and transient regimes and taking into account the viscous dissipation, we estimate directly the growth rate of the resonant mode in comparison with theory. These results confirm at least qualitatively and extend earlier experimental results obtained only for unidirectional wave train. Finally we discuss relevance of three-wave interaction mechanisms in recent experiment studying capillary wave turbulence.

Propagation regimes and populations of internal waves in the Mediterranean Sea basin

NASA Astrophysics Data System (ADS)

Kurkina, Oxana; Rouvinskaya, Ekaterina; Talipova, Tatiana; Soomere, Tarmo

2017-02-01

The geographical and seasonal distributions of kinematic and nonlinear parameters of long internal waves are derived from the Generalized Digital Environmental Model (GDEM) climatology for the Mediterranean Sea region, including the Black Sea. The considered parameters are phase speed of long internal waves and the coefficients at the dispersion, quadratic and cubic terms of the weakly-nonlinear Korteweg-de Vries-type models (in particular, the Gardner model). These parameters govern the possible polarities and shapes of solitary internal waves, their limiting amplitudes and propagation speeds. The key outcome is an express estimate of the expected parameters of internal waves for different regions of the Mediterranean basin.

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.

On the integrable elliptic cylindrical Kadomtsev-Petviashvili equation.

PubMed

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

2013-03-01

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

Optical proposals for controlled delayed-choice experiment based on weak cross-Kerr nonlinearities

NASA Astrophysics Data System (ADS)

Dong, Li; Lin, Yan-Fang; Li, Qing-Yang; Xiu, Xiao-Ming; Dong, Hai-Kuan; Gao, Ya-Jun

2017-05-01

Employing polarization modes of a photon, we propose two theoretical proposals to exhibit the wave-particle duality of the photon with the assistance of weak cross-Kerr nonlinearities. The first proposal is a classical controlled delayed-choice experiment (that is, Wheeler's delayed-choice experiment), where we can observe selectively wave property or particle property of the photon relying on the experimenter's selection, whereas the second proposal is a quantum controlled delayed-choice experiment, by which the mixture phenomenon of a wave and a particle will be exhibited. Both of them can be realized with near-unity probability and embody the charming characteristics of quantum mechanics. The employment of the mature techniques and simple operations (e.g., Homodyne measurement, classical feed forward, and single-photon transformations) provides the feasibility of the delayed-choice experiment proposals presented here.

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

PubMed

Whitfield, A J; Johnson, E R

2015-05-01

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

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

PubMed

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

2014-01-01

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

Wave kinetics of random fibre lasers

PubMed Central

Churkin, D V.; Kolokolov, I V.; Podivilov, E V.; Vatnik, I D.; Nikulin, M A.; Vergeles, S S.; Terekhov, I S.; Lebedev, V V.; Falkovich, G.; Babin, S A.; Turitsyn, S K.

2015-01-01

Traditional wave kinetics describes the slow evolution of systems with many degrees of freedom to equilibrium via numerous weak non-linear interactions and fails for very important class of dissipative (active) optical systems with cyclic gain and losses, such as lasers with non-linear intracavity dynamics. Here we introduce a conceptually new class of cyclic wave systems, characterized by non-uniform double-scale dynamics with strong periodic changes of the energy spectrum and slow evolution from cycle to cycle to a statistically steady state. Taking a practically important example—random fibre laser—we show that a model describing such a system is close to integrable non-linear Schrödinger equation and needs a new formalism of wave kinetics, developed here. We derive a non-linear kinetic theory of the laser spectrum, generalizing the seminal linear model of Schawlow and Townes. Experimental results agree with our theory. The work has implications for describing kinetics of cyclical systems beyond photonics. PMID:25645177

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.

Traveling wave solution of driven nonlinear Schrödinger equation

NASA Astrophysics Data System (ADS)

Akbari-Moghanjoughi, M.

2017-09-01

The traveling solitary and cnoidal wave solutions of the one dimensional driven nonlinear Schrödinger equation with a generalized form of nonlinearity are presented in this paper. We examine the modulation of nonlinear solitary excitations in two known weakly nonlinear models of classic oscillators, namely, the Helmholtz and Duffing oscillators and envelope structure formations for different oscillator and driver parameters. It is shown that two distinct regimes of subcritical and supercritical modulations may occur for nonlinear excitations with propagation speeds v <√{4 F0 } and v >√{4 F0 } , respectively, in which F0 is the driver force strength. The envelope soliton and cnoidal waves in these regimes are observed to be fundamentally different. The effect of pseudoenergy on the structure of the modulated envelope excitations is studied in detail for both sub- and supercritical modulation types. The current model for traveling envelope excitations may be easily extended to pseudopotentials with full nonlinearity relevant to more realistic gases, fluids, and plasmas.

Wave turbulence in shallow water models.

PubMed

Clark di Leoni, P; Cobelli, P J; Mininni, P D

2014-06-01

We study wave turbulence in shallow water flows in numerical simulations using two different approximations: the shallow water model and the Boussinesq model with weak dispersion. The equations for both models were solved using periodic grids with up to 2048{2} points. In all simulations, the Froude number varies between 0.015 and 0.05, while the Reynolds number and level of dispersion are varied in a broader range to span different regimes. In all cases, most of the energy in the system remains in the waves, even after integrating the system for very long times. For shallow flows, nonlinear waves are nondispersive and the spectrum of potential energy is compatible with ∼k{-2} scaling. For deeper (Boussinesq) flows, the nonlinear dispersion relation as directly measured from the wave and frequency spectrum (calculated independently) shows signatures of dispersion, and the spectrum of potential energy is compatible with predictions of weak turbulence theory, ∼k{-4/3}. In this latter case, the nonlinear dispersion relation differs from the linear one and has two branches, which we explain with a simple qualitative argument. Finally, we study probability density functions of the surface height and find that in all cases the distributions are asymmetric. The probability density function can be approximated by a skewed normal distribution as well as by a Tayfun distribution.

Envelope of coda waves for a double couple source due to non-linear elasticity

NASA Astrophysics Data System (ADS)

Calisto, Ignacia; Bataille, Klaus

2014-10-01

Non-linear elasticity has recently been considered as a source of scattering, therefore contributing to the coda of seismic waves, in particular for the case of explosive sources. This idea is analysed further here, theoretically solving the expression for the envelope of coda waves generated by a point moment tensor in order to compare with earthquake data. For weak non-linearities, one can consider each point of the non-linear medium as a source of scattering within a homogeneous and linear medium, for which Green's functions can be used to compute the total displacement of scattered waves. These sources of scattering have specific radiation patterns depending on the incident and scattered P or S waves, respectively. In this approach, the coda envelope depends on three scalar parameters related to the specific non-linearity of the medium; however these parameters only change the scale of the coda envelope. The shape of the coda envelope is sensitive to both the source time function and the intrinsic attenuation. We compare simulations using this model with data from earthquakes in Taiwan, with a good fit.

Harmonic Phase Response of Nonlinear Radar Targets

DTIC Science & Technology

2015-10-01

while allowing its harmonics to pass through. The weak harmonic responses are then amplified to allow for easier detection and measurement . 4...where the phase of the 2nd and 3rd harmonic of the received electromagnetic wave from nonlinear targets was measured and plotted against the frequency

Dispersive optical soliton solutions for higher order nonlinear Sasa-Satsuma equation in mono mode fibers via new auxiliary equation method

NASA Astrophysics Data System (ADS)

Khater, Mostafa M. A.; Seadawy, Aly R.; Lu, Dianchen

2018-01-01

In this research, we apply new technique for higher order nonlinear Schrödinger equation which is representing the propagation of short light pulses in the monomode optical fibers and the evolution of slowly varying packets of quasi-monochromatic waves in weakly nonlinear media that have dispersion. Nonlinear Schrödinger equation is one of the basic model in fiber optics. We apply new auxiliary equation method for nonlinear Sasa-Satsuma equation to obtain a new optical forms of solitary traveling wave solutions. Exact and solitary traveling wave solutions are obtained in different kinds like trigonometric, hyperbolic, exponential, rational functions, …, etc. These forms of solutions that we represent in this research prove the superiority of our new technique on almost thirteen powerful methods. The main merits of this method over the other methods are that it gives more general solutions with some free parameters.

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.

Shock-induced heating and millisecond boiling in gels and tissue due to high intensity focused ultrasound

PubMed Central

Canney, Michael S.; Khokhlova, Vera A.; Bessonova, Olga V.; Bailey, Michael R.; Crum, Lawrence A.

2009-01-01

Nonlinear propagation causes high intensity ultrasound waves to distort and generate higher harmonics, which are more readily absorbed and converted to heat than the fundamental frequency. Although such nonlinear effects have previously been investigated and found not to significantly alter high intensity focused ultrasound (HIFU) treatments, two results reported here change this paradigm. One is that at clinically relevant intensity levels, HIFU waves not only become distorted but form shock waves in tissue. The other is that the generated shock waves heat the tissue to boiling in much less time than predicted for undistorted or weakly distorted waves. In this study, a 2-MHz HIFU source operating at peak intensities up to 25,000 W/cm2 was used to heat transparent tissue-mimicking phantoms and ex vivo bovine liver samples. Initiation of boiling was detected using high-speed photography, a 20-MHz passive cavitation detector, and fluctuation of the drive voltage at the HIFU source. The time to boil obtained experimentally was used to quantify heating rates and was compared to calculations using weak shock theory and the shock amplitudes obtained from nonlinear modeling and from measurements with a fiber optic hydrophone. As observed experimentally and predicted by calculations, shocked focal waveforms produced boiling in as little as 3 ms and the time to initiate boiling was sensitive to small changes in HIFU output. Nonlinear heating due to shock waves is therefore important to HIFU and clinicians should be aware of the potential for very rapid boiling since it alters treatments. PMID:20018433

Integrated analysis of energy transfers in elastic-wave turbulence.

PubMed

Yokoyama, Naoto; Takaoka, Masanori

2017-08-01

In elastic-wave turbulence, strong turbulence appears in small wave numbers while weak turbulence does in large wave numbers. Energy transfers in the coexistence of these turbulent states are numerically investigated in both the Fourier space and the real space. An analytical expression of a detailed energy balance reveals from which mode to which mode energy is transferred in the triad interaction. Stretching energy excited by external force is transferred nonlocally and intermittently to large wave numbers as the kinetic energy in the strong turbulence. In the weak turbulence, the resonant interactions according to the weak turbulence theory produce cascading net energy transfer to large wave numbers. Because the system's nonlinearity shows strong temporal intermittency, the energy transfers are investigated at active and moderate phases separately. The nonlocal interactions in the Fourier space are characterized by the intermittent bundles of fibrous structures in the real space.

An Experimental Concept for Probing Nonlinear Physics in Radiation Belts

NASA Astrophysics Data System (ADS)

Crabtree, C. E.; Ganguli, G.; Tejero, E. M.; Amatucci, B.; Siefring, C. L.

2017-12-01

A sounding rocket experiment, Space Measurement of Rocket-Released Turbulence (SMART), can be used to probe the nonlinear response to a known stimulus injected into the radiation belt. Release of high-speed neutral barium atoms (8- 10 km/s) generated by a shaped charge explosion in the ionosphere can be used as the source of free energy to seed weak turbulence in the ionosphere. The Ba atoms are photo-ionized forming a ring velocity distribution of heavy Ba+ that is known to generate lower hybrid waves. Induced nonlinear scattering will convert the lower hybrid waves into EM whistler/magnetosonic waves. The escape of the whistlers from the ionospheric region into the radiation belts has been studied and their observable signatures quantified. The novelty of the SMART experiment is to make coordinated measurement of the cause and effect of the turbulence in space plasmas and from that to deduce the role of nonlinear scattering in the radiation belts. Sounding rocket will carry a Ba release module and an instrumented daughter section that includes vector wave magnetic and electric field sensors, Langmuir probes and energetic particle detectors. The goal of these measurements is to determine the whistler and lower hybrid wave amplitudes and spectrum in the ionospheric source region and look for precipitated particles. The Ba release may occur at 600-700 km near apogee. Ground based cameras and radio diagnostics can be used to characterize the Ba and Ba+ release. The Van Allen Probes can be used to detect the propagation of the scattering-generated whistler waves and their effects in the radiation belts. By detecting whistlers and measuring their energy density in the radiation belts the SMART mission will confirm the nonlinear generation of whistlers through scattering of lower hybrid along with other nonlinear responses of the radiation belts and their connection to weak turbulence.

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.

Nonlinear and Dissipation Characteristics of Ocean Surface Waves in Estuarine Environments

DTIC Science & Technology

2010-01-01

determines the time scale over which the interactions occur, in the manner of Hill and Foda (1998) and Jamali et al. (2003). RESULTS Contrary to...the intermediate-depth work of Hill and Foda (1998) and Jamali et al. (2003), the interactions in this wealky-dispersive, weakly-nonlinear model...occur very quickly. Figure 1 shows the amplitude of one surface wave mode and two interface mode as a function of time resulting from the analysis . We

Vertical structure of internal wave induced velocity for mode I and II solitary waves in two- and three-layer fluid

NASA Astrophysics Data System (ADS)

Gigiyatullin, Ayrat; Kurkin, Andrey; Kurkina, Oxana; Rouvinskaya, Ekaterina; Rybin, Artem

2017-04-01

With the use of the Gardner equation, or its variable-coefficient forms, the velocity components of fluid particles in the vertical section induced by a passage of internal waves can be estimated in weakly nonlinear limit. The horizontal velocity gives the greatest contribution into the local current speed. This is a typical property of long waves. This feature of an internal wave field may greatly contribute to the local sediment transport and/or resuspension. The velocity field induced by mode I and II internal solitary waves are studied. The contribution from second-order terms in asymptotic expansion into the horizontal velocity is estimated for the models of two- and three-layer fluid density stratification for solitons of positive and negative polarity, as well as for breathers of different shapes and amplitudes. The influence of the nonlinear correction manifests itself firstly in the shape of the lines of zero horizontal velocity: they are curved and the shape depends on the soliton amplitude and polarity while for the leading-order wave field they are horizontal. Also the wavefield accounting for the nonlinear correction for mode I waves has smaller maximal absolute values of negative velocities (near-surface for the soliton of elevation, and near-bottom for the soliton of depression) and larger maximums of positive velocities. Thus for the solitary internal waves of positive polarity weakly nonlinear theory overestimates the near-bottom velocities and underestimates the near-surface current. For solitary waves of negative polarity, which are the most typical for hydrological conditions of low and middle latitudes, the situation is the opposite. Similar estimations are produced for mode II waves, which possess more complex structure. The presented results of research are obtained with the support of the Russian Foundation for Basic Research grant 16-35-00413.

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.

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.

Recurrence in truncated Boussinesq models for nonlinear waves in shallow water

NASA Technical Reports Server (NTRS)

Elgar, Steve; Freilich, M. H.; Guza, R. T.

1990-01-01

The rapid spatial recurrence of weakly nonlinear and weakly dispersive progressive shallow-water waves is examined using a numerical integration technique on the discretized and truncated form of the Boussinesq equations. This study primarily examines recurrence in wave fields with Ursell number O(1) and characterizes the sensitivity of recurrence to initial spectral shape and number of allowed frequency modes. It is shown that the rapid spatial recurrence is not an inherent property of the considered Boussinesq systems for evolution distances of 10-50 wavelengths. The main result of the study is that highly truncated Boussinesq models of resonant shallow-water ocean surface gravity waves predict rapid multiple recurrence cycles, but that this is an artifact dependent on the number of allowed modes. For initial conditions consisting of essentially all energy concentrated in a single mode, damping of the recurrence cycles increases as the number of low-power background modes increases. When more than 32 modes are allowed, the recurrence behavior is relatively insensitive to the number of allowed modes.

Effects of Density Fluctuations on Weakly Nonlinear Alfven Waves: An IST Perspective

NASA Astrophysics Data System (ADS)

Hamilton, R.; Hadley, N.

2012-12-01

The effects of random density fluctuations on oblique, 1D, weakly nonlinear Alfven waves is examined through a numerical study of an analytical model developed by Ruderman [M.S. Ruderman, Phys. Plasmas, 9 (7), pp. 2940-2945, (2002).]. Consistent with Ruderman's application to the one-parameter dark soliton, the effects on both one-parameter bright and dark solitons, the two-parameter soliton as well as pairs of one-parameter solitons were similar to that of Ohmic dissipation found by Hamilton et al. [R. Hamilton, D. Peterson, and S. Libby, J. Geophys. Res 114, A03104,doi:10.1029/2008JA013582 (2009).] It was found in all cases where bright or two-parameter solitons are present initially, that the effects of density fluctuations results in the eventual damping of such compressive wave forms and the formation of a train of dark solitons, or magnetic depressions.

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.

Nonlinear internal waves in the Gulf of Guinea: observations and modeling

NASA Astrophysics Data System (ADS)

Baquet, Emeric; Pichon, Annick; Raynaud, Stephane; Carton, Xavier

2017-04-01

Nonlinear internal waves are known hazards to offshore operations. They have been observed at different locations around the world and have been studied for a long time in Southeast Asia. However in West Africa, they are less documented. This research presents original data of currentmeters in northeastern part of the Gulf of Guinea, in the vicinity of offshore oil platforms. Nonlinear internal waves were observed. Their characteristics were determined under the assumptions of the weakly nonlinear and non-hydrostatic Korteweg-de Vries equation. Their directions of propagation were studied to determine generation zones. The monthly distribution was shown to assess seasonal variability. Their main generation mechanism was the barotropic tides over the shelf break, but other processes were at work too. The seasonal variability due to the monsoon, river discharges also played a part in the nonlinear internal wave dynamics. Since several processes, of different time and space scales, are at work, interactions between them must be investigated. Thus, a two-layered numerical model was used to reproduce nonlinear internal waves. Sensitivity experiments were made, in order to investigate the balance between nonlinearities, Coriolis and non-hydrostatic dispersions. The impact of non-uniform bathymetry and the presence of another flow in addition to the tides were also tested.

On nonlinear Tollmien-Schlichting/vortex interaction in three-dimensional boundary layers

NASA Technical Reports Server (NTRS)

Davis, Dominic A. R.; Smith, Frank T.

1993-01-01

The instability of an incompressible three-dimensional boundary layer (that is, one with cross-flow) is considered theoretically and computationally in the context of vortex/wave interactions. Specifically the work centers on two low amplitude, lower-branch Tollmien-Schlichting waves which mutually interact to induce a weak longitudinal vortex flow; the vortex motion, in turn, gives rise to significant wave-modulation via wall-shear forcing. The characteristic Reynolds number is taken as a large parameter and, as a consequence, the waves' and the vortex motion are governed primarily by triple-deck theory. The nonlinear interaction is captured by a viscous partial-differential system for the vortex coupled with a pair of amplitude equations for each wave pressure. Three distinct possibilities were found to emerge for the nonlinear behavior of the flow solution downstream - an algebraic finite-distance singularity, far downstream saturation or far-downstream wave-decay (leaving pure vortex flow) - depending on the input conditions, the wave angles, and the size of the cross-flow.

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.

Propagation of electromagnetic soliton in a spin polarized current driven weak ferromagnetic nanowire

NASA Astrophysics Data System (ADS)

Senthil Kumar, V.; Kavitha, L.; Gopi, D.

2017-11-01

We investigate the nonlinear spin dynamics of a spin polarized current driven anisotropic ferromagnetic nanowire with Dzyaloshinskii-Moriya interaction (DMI) under the influence of electromagnetic wave (EMW) propagating along the axis of the nanowire. The magnetization dynamics and electromagnetic wave propagation in the ferromagnetic nanowire with weak anti-symmetric interaction is governed by a coupled vector Landau-Lifshitz-Gilbert and Maxwell's equations. These coupled nonlinear vector equations are recasted into the extended derivative nonlinear Schrödinger (EDNLS) equation in the framework of reductive perturbation method. As it is well known, the modulational instability is a precursor for the emergence of localized envelope structures of various kinds, we compute the instability criteria for the weak ferromagnetic nanowire through linear stability analysis. Further, we invoke the homogeneous balance method to construct kink and anti-solitonic like electromagnetic (EM) soliton profiles for the EDNLS equation. We also explore the appreciable effect of the anti-symmetric weak interaction on the magnetization components of the propagating EM soliton. We find that the combination of spin-polarized current and the anti-symmetric DMI have a profound effect on the propagating EMW in a weak ferromagnetic nanowire. Thus, the anti-symmetric DMI in a spin polarized current driven ferromagnetic nanowire supports the lossless propagation of EM solitons, which may have potential applications in magnetic data storage devices.

Moderately nonlinear ultrasound propagation in blood-mimicking fluid.

PubMed

Kharin, Nikolay A; Vince, D Geoffrey

2004-04-01

In medical diagnostic ultrasound (US), higher than-in-water nonlinearity of body fluids and tissue usually does not produce strong nonlinearly distorted waves because of the high absorption. The relative influence of absorption and nonlinearity can be characterized by the Gol'dberg number Gamma. There are two limiting cases in nonlinear acoustics: weak waves (Gamma < 1) or strong waves (Gamma > 1). However, at diagnostic frequencies in tissue and body fluids, the nonlinear effects and effects of absorption more likely are comparable (Gol'dberg number Gamma approximately 1). The aim of this work was to study the nonlinear propagation of a moderately nonlinear US second harmonic signal in a blood-mimicking fluid. Quasilinear solutions to the KZK equation are presented, assuming radiation from a flat and geometrically focused circular Gaussian source. The solutions are expressed in a new simplified closed form and are in very good agreement with those of previous studies measuring and modeling Gaussian beams. The solutions also show good agreement with the measurements of the beams produced by commercially available transducers, even without special Gaussian shading.

Nonlinear Instability of Hypersonic Flow past a Wedge

NASA Technical Reports Server (NTRS)

Seddougui, Sharon O.; Bassom, Andrew P.

1991-01-01

The nonlinear stability of a compressible flow past a wedge is investigated in the hypersonic limit. The analysis follows the ideas of a weakly nonlinear approach. Interest is focussed on Tollmien-Schlichting waves governed by a triple deck structure and it is found that the attached shock can profoundly affect the stability characteristics of the flow. In particular, it is shown that nonlinearity tends to have a stabilizing influence. The nonlinear evolution of the Tollmien-Schlichting mode is described in a number of asymptotic limits.

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.

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.

A numerical study on weak-dissipative two-mode perturbed Burgers' and Ostrovsky models: right-left moving waves

NASA Astrophysics Data System (ADS)

Jaradat, Imad; Alquran, Marwan; Ali, Mohammed

2018-04-01

The purpose of this study is threefold. First, it derives newly developed two-mode nonlinear equations, two-mode perturbed Burgers' and two-mode Ostrovsky models. Second, it investigates the values of the nonlinearity and dispersion parameters that support the existence of two right-left (R-L) moving wave solutions to these models. Finally, it provides a graphical analysis of the "two-mode" concept and the impact of its phase velocity on the field function.

Detuned resonances of Tollmien-Schlichting waves in an airfoil boundary layer: Experiment, theory, and direct numerical simulation

NASA Astrophysics Data System (ADS)

Würz, W.; Sartorius, D.; Kloker, M.; Borodulin, V. I.; Kachanov, Y. S.; Smorodsky, B. V.

2012-09-01

Transition prediction in two-dimensional laminar boundary layers developing on airfoil sections at subsonic speeds and very low turbulence levels is still a challenge. The commonly used semi-empirical prediction tools are mainly based on linear stability theory and do not account for nonlinear effects present unavoidably starting with certain stages of transition. One reason is the lack of systematic investigations of the weakly nonlinear stages of transition, especially of the strongest interactions of the instability modes predominant in non-self-similar boundary layers. The present paper is devoted to the detailed experimental, numerical, and theoretical study of weakly nonlinear subharmonic resonances of Tollmien-Schlichting waves in an airfoil boundary layer, representing main candidates for the strongest mechanism of these initial nonlinear stages. The experimental approach is based on phase-locked hot-wire measurements under controlled disturbance conditions using a new disturbance source being capable to produce well-defined, complex wave compositions in a wide range of streamwise and spanwise wave numbers. The tests were performed in a low-turbulence wind tunnel at a chord Reynolds number of Re = 0.7 × 106. Direct numerical simulations (DNS) were utilized to provide a detailed comparison for the test cases. The results of weakly nonlinear theory (WNT) enabled a profound understanding of the underlying physical mechanisms observed in the experiments and DNS. The data obtained in experiment, DNS and WNT agree basically and provide a high degree of reliability of the results. Interactions occurring between components of various initial frequency-wavenumber spectra of instability waves are investigated by systematic variation of parameters. It is shown that frequency-detuned and spanwise-wavenumber-detuned subharmonic-type resonant interactions have an extremely large spectral width. Similar to results obtained for self-similar base flows it is found that the amplification factors in the frequency-detuned resonances can be even higher than in tuned cases, in spite of the strong base-flow non-self-similarity. An explanation of this unusual phenomenon is found based on the theoretical analysis and comparison of experimental, theoretical, and DNS data.

Two types of nonlinear wave equations for diffractive beams in bubbly liquids with nonuniform bubble number density.

PubMed

Kanagawa, Tetsuya

2015-05-01

This paper theoretically treats the weakly nonlinear propagation of diffracted sound beams in nonuniform bubbly liquids. The spatial distribution of the number density of the bubbles, initially in a quiescent state, is assumed to be a slowly varying function of the spatial coordinates; the amplitude of variation is assumed to be small compared to the mean number density. A previous derivation method of nonlinear wave equations for plane progressive waves in uniform bubbly liquids [Kanagawa, Yano, Watanabe, and Fujikawa (2010). J. Fluid Sci. Technol. 5(3), 351-369] is extended to handle quasi-plane beams in weakly nonuniform bubbly liquids. The diffraction effect is incorporated by adding a relation that scales the circular sound source diameter to the wavelength into the original set of scaling relations composed of nondimensional physical parameters. A set of basic equations for bubbly flows is composed of the averaged equations of mass and momentum, the Keller equation for bubble wall, and supplementary equations. As a result, two types of evolution equations, a nonlinear Schrödinger equation including dissipation, diffraction, and nonuniform effects for high-frequency short-wavelength case, and a Khokhlov-Zabolotskaya-Kuznetsov equation including dispersion and nonuniform effects for low-frequency long-wavelength case, are derived from the basic set.

Falling films on flexible inclines

NASA Astrophysics Data System (ADS)

Matar, O. K.; Craster, R. V.; Kumar, S.

2007-11-01

The nonlinear stability and dynamic behavior of falling fluid films is studied for flow over a flexible substrate. We use asymptotic methods to deduce governing equations valid in various limits. Long-wave theory is used to derive Benney-like coupled equations for the film thickness and substrate deflection. Weakly nonlinear equations are then derived from these equations that, in the limit of large wall damping and/or large wall tension, reduce to the Kuramoto-Sivashinsky equation. These models break down when inertia becomes more significant, so we also use a long-wave approximation in conjunction with integral theory to derive three strongly coupled nonlinear evolution equations for the film thickness, substrate deflection, and film volumetric flow rate valid at higher Reynolds numbers. These equations, accounting for inertia, capillary, viscous, wall tension, and damping effects, are solved over a wide range of parameters. Our results suggest that decreasing wall damping and/or wall tension can promote the development of chaos in the weakly nonlinear regime and lead to severe substrate deformations in the strongly nonlinear regime; these can give rise to situations in which the free surface and underlying substrate come into contact in finite time.

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.

Nonlinear periodic wavetrains in thin liquid films falling on a uniformly heated horizontal plate

NASA Astrophysics Data System (ADS)

Issokolo, Remi J. Noumana; Dikandé, Alain M.

2018-05-01

A thin liquid film falling on a uniformly heated horizontal plate spreads into fingering ripples that can display a complex dynamics ranging from continuous waves, nonlinear spatially localized periodic wave patterns (i.e., rivulet structures) to modulated nonlinear wavetrain structures. Some of these structures have been observed experimentally; however, conditions under which they form are still not well understood. In this work, we examine profiles of nonlinear wave patterns formed by a thin liquid film falling on a uniformly heated horizontal plate. For this purpose, the Benney model is considered assuming a uniform temperature distribution along the film propagation on the horizontal surface. It is shown that for strong surface tension but a relatively small Biot number, spatially localized periodic-wave structures can be analytically obtained by solving the governing equation under appropriate conditions. In the regime of weak nonlinearity, a multiple-scale expansion combined with the reductive perturbation method leads to a complex Ginzburg-Landau equation: the solutions of which are modulated periodic pulse trains which amplitude and width and period are expressed in terms of characteristic parameters of the model.

Nonlinear interactions in mixing layers and compressible heated round jets. Ph.D. Thesis Final Report

NASA Technical Reports Server (NTRS)

Jarrah, Yousef Mohd

1989-01-01

The nonlinear interactions between a fundamental instability mode and both its harmonics and the changing mean flow are studied using the weakly nonlinear stability theory of Stuart and Watson, and numerical solutions of coupled nonlinear partial differential equations. The first part focuses on incompressible cold (or isothermal; constant temperature throughout) mixing layers, and for these, the first and second Landau constants are calculated as functions of wavenumber and Reynolds number. It is found that the dominant contribution to the Landau constants arises from the mean flow changes and not from the higher harmonics. In order to establish the range of validity of the weakly nonlinear theory, the weakly nonlinear and numerical solutions are compared and the limitation of each is discussed. At small amplitudes and at low-to-moderate Reynolds numbers, the two results compare well in describing the saturation of the fundamental, the distortion of the mean flow, and the initial stages of vorticity roll-up. At larger amplitudes, the interaction between the fundamental, second harmonic, and the mean flow is strongly nonlinear and the numerical solution predicts flow oscillations, whereas the weakly nonlinear theory yields saturation. In the second part, the weakly nonlinear theory is extended to heated (or nonisothermal; mean temperature distribution) subsonic round jets where quadratic and cubic nonlinear interactions are present, and the Landau constants also depend on jet temperature ratio, Mach number and azimuthal mode number. Under exponential growth and nonlinear saturation, it is found that heating and compressibility suppress the growth of instability waves, that the first azimuthal mode is the dominant instability mode, and that the weakly nonlinear solution describes the early stages of the roll-up of an axisymmetric shear layer. The receptivity of a typical jet flow to pulse type input disturbance is also studied by solving the initial value problem and then examining the behavior of the long-time solution.

Ion acoustic solitary wave with weakly transverse perturbations in quantum electron-positron-ion plasma

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

Mushtaq, A.; Khan, S. A.; Department of Physics, COMSATS Institute of Information Technology, Islamabad

2007-05-15

The characteristics and stability of ion acoustic solitary wave with transverse perturbations are examined in ultracold quantum magnetospheric plasma consisting of electrons, positrons, and ions. Using the quantum hydrodynamic model, a dispersion relation in the linear regime, and the Kadomtsev-Petviashvili equation in the nonlinear regime are derived. The quantum corrections are studied through quantum statistics and diffraction effects. It is found that compressive solitary wave can propagate in this system. The quantum effects are also studied graphically for both linear and nonlinear profiles of ion acoustic wave. Using energy consideration method, conditions for existence of stable solitary waves are obtained.more » It is found that stable solitary waves depend on quantum corrections, positron concentration, and direction cosine of the wave vector k along the x axis.« less

Large-Amplitude Long-Wave Instability of a Supersonic Shear Layer

NASA Technical Reports Server (NTRS)

Messiter, A. F.

1995-01-01

For sufficiently high Mach numbers, small disturbances on a supersonic vortex sheet are known to grow in amplitude because of slow nonlinear wave steepening. Under the same external conditions, linear theory predicts slow growth of long-wave disturbances to a thin supersonic shear layer. An asymptotic formulation is given here which adds nonzero shear-layer thickness to the weakly nonlinear formulation for a vortex sheet. Spatial evolution is considered, for a spatially periodic disturbance having amplitude of the same order, in Reynolds number, as the shear-layer thickness. A quasi-equilibrium inviscid nonlinear critical layer is found, with effects of diffusion and slow growth appearing through nonsecularity condition. Other limiting cases are also considered, in an attempt to determine a relationship between the vortex-sheet limit and the long-wave limit for a thin shear layer; there appear to be three special limits, corresponding to disturbances of different amplitudes at different locations along the shear layer.

Dissipative nonlinear waves in a gravitating quantum fluid

NASA Astrophysics Data System (ADS)

Sahu, Biswajit; Sinha, Anjana; Roychoudhury, Rajkumar

2018-02-01

Nonlinear wave propagation is studied in a dissipative, self-gravitating Bose-Einstein condensate, starting from the Gross-Pitaevskii equation. In the absence of an exact analytical result, approximate methods like the linear analysis and perturbative approach are applied. The linear dispersion relation puts a restriction on the permissible range of the dissipation parameter. The waves get damped due to dissipation. The small amplitude analysis using reductive perturbation technique is found to yield a modified form of KdV equation, which is solved both analytically as well as numerically. Interestingly, the analytical and numerical plots match excellently with each other, in the realm of weak dissipation.

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.

Two dimensional kinetic analysis of electrostatic harmonic plasma waves

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

Fonseca-Pongutá, E. C.; Ziebell, L. F.; Gaelzer, R.

2016-06-15

Electrostatic harmonic Langmuir waves are virtual modes excited in weakly turbulent plasmas, first observed in early laboratory beam-plasma experiments as well as in rocket-borne active experiments in space. However, their unequivocal presence was confirmed through computer simulated experiments and subsequently theoretically explained. The peculiarity of harmonic Langmuir waves is that while their existence requires nonlinear response, their excitation mechanism and subsequent early time evolution are governed by essentially linear process. One of the unresolved theoretical issues regards the role of nonlinear wave-particle interaction process over longer evolution time period. Another outstanding issue is that existing theories for these modes aremore » limited to one-dimensional space. The present paper carries out two dimensional theoretical analysis of fundamental and (first) harmonic Langmuir waves for the first time. The result shows that harmonic Langmuir wave is essentially governed by (quasi)linear process and that nonlinear wave-particle interaction plays no significant role in the time evolution of the wave spectrum. The numerical solutions of the two-dimensional wave spectra for fundamental and harmonic Langmuir waves are also found to be consistent with those obtained by direct particle-in-cell simulation method reported in the literature.« less

Weakly Nonlinear Description of Parametric Instabilities in Vibrating Flows

NASA Technical Reports Server (NTRS)

Knobloch, E.; Vega, J. M.

1999-01-01

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

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.

Real world ocean rogue waves explained without the modulational instability.

PubMed

Fedele, Francesco; Brennan, Joseph; Ponce de León, Sonia; Dudley, John; Dias, Frédéric

2016-06-21

Since the 1990s, the modulational instability has commonly been used to explain the occurrence of rogue waves that appear from nowhere in the open ocean. However, the importance of this instability in the context of ocean waves is not well established. This mechanism has been successfully studied in laboratory experiments and in mathematical studies, but there is no consensus on what actually takes place in the ocean. In this work, we question the oceanic relevance of this paradigm. In particular, we analyze several sets of field data in various European locations with various tools, and find that the main generation mechanism for rogue waves is the constructive interference of elementary waves enhanced by second-order bound nonlinearities and not the modulational instability. This implies that rogue waves are likely to be rare occurrences of weakly nonlinear random seas.

Real world ocean rogue waves explained without the modulational instability

PubMed Central

Fedele, Francesco; Brennan, Joseph; Ponce de León, Sonia; Dudley, John; Dias, Frédéric

2016-01-01

Since the 1990s, the modulational instability has commonly been used to explain the occurrence of rogue waves that appear from nowhere in the open ocean. However, the importance of this instability in the context of ocean waves is not well established. This mechanism has been successfully studied in laboratory experiments and in mathematical studies, but there is no consensus on what actually takes place in the ocean. In this work, we question the oceanic relevance of this paradigm. In particular, we analyze several sets of field data in various European locations with various tools, and find that the main generation mechanism for rogue waves is the constructive interference of elementary waves enhanced by second-order bound nonlinearities and not the modulational instability. This implies that rogue waves are likely to be rare occurrences of weakly nonlinear random seas. PMID:27323897

Experimental study of three-wave interactions among capillary-gravity surface waves

NASA Astrophysics Data System (ADS)

Haudin, Florence; Cazaubiel, Annette; Deike, Luc; Jamin, Timothée; Falcon, Eric; Berhanu, Michael

2016-04-01

In propagating wave systems, three- or four-wave resonant interactions constitute a classical nonlinear mechanism exchanging energy between the different scales. Here we investigate three-wave interactions for gravity-capillary surface waves in a closed laboratory tank. We generate two crossing wave trains and we study their interaction. Using two optical methods, a local one (laser doppler vibrometry) and a spatiotemporal one (diffusive light photography), a third wave of smaller amplitude is detected, verifying the three-wave resonance conditions in frequency and in wave number. Furthermore, by focusing on the stationary regime and by taking into account viscous dissipation, we directly estimate the growth rate of the resonant mode. The latter is then compared to the predictions of the weakly nonlinear triadic resonance interaction theory. The obtained results confirm qualitatively and extend previous experimental results obtained only for collinear wave trains. Finally, we discuss the relevance of three-wave interaction mechanisms in recent experiments studying gravity-capillary turbulence.

Experimental study of three-wave interactions among capillary-gravity surface waves.

PubMed

Haudin, Florence; Cazaubiel, Annette; Deike, Luc; Jamin, Timothée; Falcon, Eric; Berhanu, Michael

2016-04-01

In propagating wave systems, three- or four-wave resonant interactions constitute a classical nonlinear mechanism exchanging energy between the different scales. Here we investigate three-wave interactions for gravity-capillary surface waves in a closed laboratory tank. We generate two crossing wave trains and we study their interaction. Using two optical methods, a local one (laser doppler vibrometry) and a spatiotemporal one (diffusive light photography), a third wave of smaller amplitude is detected, verifying the three-wave resonance conditions in frequency and in wave number. Furthermore, by focusing on the stationary regime and by taking into account viscous dissipation, we directly estimate the growth rate of the resonant mode. The latter is then compared to the predictions of the weakly nonlinear triadic resonance interaction theory. The obtained results confirm qualitatively and extend previous experimental results obtained only for collinear wave trains. Finally, we discuss the relevance of three-wave interaction mechanisms in recent experiments studying gravity-capillary turbulence.

Theoretical and experimental evidence of non-symmetric doubly localized rogue waves.

PubMed

He, Jingsong; Guo, Lijuan; Zhang, Yongshuai; Chabchoub, Amin

2014-11-08

We present determinant expressions for vector rogue wave (RW) solutions of the Manakov system, a two-component coupled nonlinear Schrödinger (NLS) equation. As a special case, we generate a family of exact and non-symmetric RW solutions of the NLS equation up to third order, localized in both space and time. The derived non-symmetric doubly localized second-order solution is generated experimentally in a water wave flume for deep-water conditions. Experimental results, confirming the characteristic non-symmetric pattern of the solution, are in very good agreement with theory as well as with numerical simulations, based on the modified NLS equation, known to model accurately the dynamics of weakly nonlinear wave packets in deep water.

Theoretical and experimental evidence of non-symmetric doubly localized rogue waves

PubMed Central

He, Jingsong; Guo, Lijuan; Zhang, Yongshuai; Chabchoub, Amin

2014-01-01

We present determinant expressions for vector rogue wave (RW) solutions of the Manakov system, a two-component coupled nonlinear Schrödinger (NLS) equation. As a special case, we generate a family of exact and non-symmetric RW solutions of the NLS equation up to third order, localized in both space and time. The derived non-symmetric doubly localized second-order solution is generated experimentally in a water wave flume for deep-water conditions. Experimental results, confirming the characteristic non-symmetric pattern of the solution, are in very good agreement with theory as well as with numerical simulations, based on the modified NLS equation, known to model accurately the dynamics of weakly nonlinear wave packets in deep water. PMID:25383023

Nonlinear pulse propagation and phase velocity of laser-driven plasma waves

NASA Astrophysics Data System (ADS)

Benedetti, Carlo; Rossi, Francesco; Schroeder, Carl; Esarey, Eric; Leemans, Wim

2014-10-01

We investigate and characterize the laser evolution and plasma wave excitation by a relativistically intense, short-pulse laser propagating in a preformed parabolic plasma channel, including the effects of pulse steepening, frequency redshifting, and energy depletion. We derived in 3D, and in the weakly relativistic intensity regime, analytical expressions for the laser energy depletion, the pulse self-steepening rate, the laser intensity centroid velocity, and the phase velocity of the plasma wave. Analytical results have been validated numerically using the 2D-cylindrical, ponderomotive code INF&RNO. We also discuss the extension of these results to the nonlinear regime, where an analytical theory of the nonlinear wake phase velocity is lacking. Work supported by the Office of Science, Office of High Energy Physics, of the U.S. Department of Energy under Contract No. DE-AC02-05CH11231.

Energy transport in weakly nonlinear wave systems with narrow frequency band excitation.

PubMed

Kartashova, Elena

2012-10-01

A novel discrete model (D model) is presented describing nonlinear wave interactions in systems with small and moderate nonlinearity under narrow frequency band excitation. It integrates in a single theoretical frame two mechanisms of energy transport between modes, namely, intermittency and energy cascade, and gives the conditions under which each regime will take place. Conditions for the formation of a cascade, cascade direction, conditions for cascade termination, etc., are given and depend strongly on the choice of excitation parameters. The energy spectra of a cascade may be computed, yielding discrete and continuous energy spectra. The model does not require statistical assumptions, as all effects are derived from the interaction of distinct modes. In the example given-surface water waves with dispersion function ω(2)=gk and small nonlinearity-the D model predicts asymmetrical growth of side-bands for Benjamin-Feir instability, while the transition from discrete to continuous energy spectrum, excitation parameters properly chosen, yields the saturated Phillips' power spectrum ~g(2)ω(-5). The D model can be applied to the experimental and theoretical study of numerous wave systems appearing in hydrodynamics, nonlinear optics, electrodynamics, plasma, convection theory, etc.

Intermittency and emergence of coherent structures in wave turbulence of a vibrating plate.

PubMed

Mordant, Nicolas; Miquel, Benjamin

2017-10-01

We report numerical investigations of wave turbulence in a vibrating plate. The possibility to implement advanced measurement techniques and long-time numerical simulations makes this system extremely valuable for wave turbulence studies. The purely 2D character of dynamics of the elastic plate makes it much simpler to handle compared to much more complex 3D physical systems that are typical of geo- and astrophysical issues (ocean surface or internal waves, magnetized plasmas or strongly rotating and/or stratified flows). When the forcing is small the observed wave turbulence is consistent with the predictions of the weak turbulent theory. Here we focus on the case of stronger forcing for which coherent structures can be observed. These structures look similar to the folds and D-cones that are commonly observed for strongly deformed static thin elastic sheets (crumpled paper) except that they evolve dynamically in our forced system. We describe their evolution and show that their emergence is associated with statistical intermittency (lack of self similarity) of strongly nonlinear wave turbulence. This behavior is reminiscent of intermittency in Navier-Stokes turbulence. Experimental data show hints of the weak to strong turbulence transition. However, due to technical limitations and dissipation, the strong nonlinear regime remains out of reach of experiments and therefore has been explored numerically.

Intermittency and emergence of coherent structures in wave turbulence of a vibrating plate

NASA Astrophysics Data System (ADS)

Mordant, Nicolas; Miquel, Benjamin

2017-10-01

We report numerical investigations of wave turbulence in a vibrating plate. The possibility to implement advanced measurement techniques and long-time numerical simulations makes this system extremely valuable for wave turbulence studies. The purely 2D character of dynamics of the elastic plate makes it much simpler to handle compared to much more complex 3D physical systems that are typical of geo- and astrophysical issues (ocean surface or internal waves, magnetized plasmas or strongly rotating and/or stratified flows). When the forcing is small the observed wave turbulence is consistent with the predictions of the weak turbulent theory. Here we focus on the case of stronger forcing for which coherent structures can be observed. These structures look similar to the folds and D-cones that are commonly observed for strongly deformed static thin elastic sheets (crumpled paper) except that they evolve dynamically in our forced system. We describe their evolution and show that their emergence is associated with statistical intermittency (lack of self similarity) of strongly nonlinear wave turbulence. This behavior is reminiscent of intermittency in Navier-Stokes turbulence. Experimental data show hints of the weak to strong turbulence transition. However, due to technical limitations and dissipation, the strong nonlinear regime remains out of reach of experiments and therefore has been explored numerically.

Schlieren imaging of loud sounds and weak shock waves in air near the limit of visibility

NASA Astrophysics Data System (ADS)

Hargather, Michael John; Settles, Gary S.; Madalis, Matthew J.

2010-02-01

A large schlieren system with exceptional sensitivity and a high-speed digital camera are used to visualize loud sounds and a variety of common phenomena that produce weak shock waves in the atmosphere. Frame rates varied from 10,000 to 30,000 frames/s with microsecond frame exposures. Sound waves become visible to this instrumentation at frequencies above 10 kHz and sound pressure levels in the 110 dB (6.3 Pa) range and above. The density gradient produced by a weak shock wave is examined and found to depend upon the profile and thickness of the shock as well as the density difference across it. Schlieren visualizations of weak shock waves from common phenomena include loud trumpet notes, various impact phenomena that compress a bubble of air, bursting a toy balloon, popping a champagne cork, snapping a wooden stick, and snapping a wet towel. The balloon burst, snapping a ruler on a table, and snapping the towel and a leather belt all produced readily visible shock-wave phenomena. In contrast, clapping the hands, snapping the stick, and the champagne cork all produced wave trains that were near the weak limit of visibility. Overall, with sensitive optics and a modern high-speed camera, many nonlinear acoustic phenomena in the air can be observed and studied.

A contrast source method for nonlinear acoustic wave fields in media with spatially inhomogeneous attenuation.

PubMed

Demi, L; van Dongen, K W A; Verweij, M D

2011-03-01

Experimental data reveals that attenuation is an important phenomenon in medical ultrasound. Attenuation is particularly important for medical applications based on nonlinear acoustics, since higher harmonics experience higher attenuation than the fundamental. Here, a method is presented to accurately solve the wave equation for nonlinear acoustic media with spatially inhomogeneous attenuation. Losses are modeled by a spatially dependent compliance relaxation function, which is included in the Westervelt equation. Introduction of absorption in the form of a causal relaxation function automatically results in the appearance of dispersion. The appearance of inhomogeneities implies the presence of a spatially inhomogeneous contrast source in the presented full-wave method leading to inclusion of forward and backward scattering. The contrast source problem is solved iteratively using a Neumann scheme, similar to the iterative nonlinear contrast source (INCS) method. The presented method is directionally independent and capable of dealing with weakly to moderately nonlinear, large scale, three-dimensional wave fields occurring in diagnostic ultrasound. Convergence of the method has been investigated and results for homogeneous, lossy, linear media show full agreement with the exact results. Moreover, the performance of the method is demonstrated through simulations involving steered and unsteered beams in nonlinear media with spatially homogeneous and inhomogeneous attenuation. © 2011 Acoustical Society of America

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

Benisti, Didier; Morice, Olivier; Gremillet, Laurent

The propagation of an electrostatic wave packet inside a collisionless and initially Maxwellian plasma is always dissipative because of the irreversible acceleration of the electrons by the wave. Then, in the linear regime, the wave packet is Landau damped, so that in the reference frame moving at the group velocity, the wave amplitude decays exponentially with time. In the nonlinear regime, once phase mixing has occurred and when the electron motion is nearly adiabatic, the damping rate is strongly reduced compared to the Landau one, so that the wave amplitude remains nearly constant along the characteristics. Yet, we show heremore » that the electrons are still globally accelerated by the wave packet, and in one dimension, this leads to a non local amplitude dependence of the group velocity. As a result, a freely propagating wave packet would shrink, and therefore, so would its total energy. In more than one dimension, not only does the magnitude of the group velocity nonlinearly vary, but also its direction. In the weakly nonlinear regime, when the collisionless damping rate is still significant compared to its linear value, the group velocity is directed towards the outside of the wave packet and tends to increase its transverse extent, while the opposite is true once the wave is essentially undamped. The impact of the nonlinear variation of the group velocity on the transverse size of the wave packet is quantified, and compared to that induced by the self-focussing due to wave front bowing.« less

On the dispersionless Kadomtsev-Petviashvili equation with arbitrary nonlinearity and dimensionality: exact solutions, longtime asymptotics of the Cauchy problem, wave breaking and shocks

NASA Astrophysics Data System (ADS)

Santucci, F.; Santini, P. M.

2016-10-01

We study the generalization of the dispersionless Kadomtsev-Petviashvili (dKP) equation in n+1 dimensions and with nonlinearity of degree m+1, a model equation describing the propagation of weakly nonlinear, quasi one-dimensional waves in the absence of dispersion and dissipation, and arising in several physical contexts, like acoustics, plasma physics, hydrodynamics and nonlinear optics. In 2 + 1 dimensions and with quadratic nonlinearity, this equation is integrable through a novel inverse scattering transform, and it has been recently shown to be a prototype model equation in the description of the two-dimensional wave breaking of localized initial data. In higher dimensions and with higher nonlinearity, the generalized dKP equations are not integrable, but their invariance under motions on the paraboloid allows one to construct in this paper a family of exact solutions describing waves constant on their paraboloidal wave front and breaking simultaneously in all points of it, developing after breaking either multivaluedness or single-valued discontinuous profiles (shocks). Then such exact solutions are used to build the longtime behavior of the solutions of the Cauchy problem, for small and localized initial data, showing that wave breaking of small initial data takes place in the longtime regime if and only if m(n-1)≤slant 2. Lastly, the analytic aspects of such wave breaking are investigated in detail in terms of the small initial data, in both cases in which the solution becomes multivalued after breaking or it develops a shock. These results, contained in the 2012 master’s thesis of one of the authors (FS) [1], generalize those obtained in [2] for the dKP equation in n+1 dimensions with quadratic nonlinearity, and are obtained following the same strategy.

Marginal Matter

NASA Astrophysics Data System (ADS)

van Hecke, Martin

2013-03-01

All around us, things are falling apart. The foam on our cappuccinos appears solid, but gentle stirring irreversibly changes its shape. Skin, a biological fiber network, is firm when you pinch it, but soft under light touch. Sand mimics a solid when we walk on the beach but a liquid when we pour it out of our shoes. Crucially, a marginal point separates the rigid or jammed state from the mechanical vacuum (freely flowing) state - at their marginal points, soft materials are neither solid nor liquid. Here I will show how the marginal point gives birth to a third sector of soft matter physics: intrinsically nonlinear mechanics. I will illustrate this with shock waves in weakly compressed granular media, the nonlinear rheology of foams, and the nonlinear mechanics of weakly connected elastic networks.

Wave-vortex interactions in the nonlinear Schrödinger equation

NASA Astrophysics Data System (ADS)

Guo, Yuan; Bühler, Oliver

2014-02-01

This is a theoretical study of wave-vortex interaction effects in the two-dimensional nonlinear Schrödinger equation, which is a useful conceptual model for the limiting dynamics of superfluid quantum condensates at zero temperature. The particular wave-vortex interaction effects are associated with the scattering and refraction of small-scale linear waves by the straining flows induced by quantized point vortices and, crucially, with the concomitant nonlinear back-reaction, the remote recoil, that these scattered waves exert on the vortices. Our detailed model is a narrow, slowly varying wavetrain of small-amplitude waves refracted by one or two vortices. Weak interactions are studied using a suitable perturbation method in which the nonlinear recoil force on the vortex then arises at second order in wave amplitude, and is computed in terms of a Magnus-type force expression for both finite and infinite wavetrains. In the case of an infinite wavetrain, an explicit asymptotic formula for the scattering angle is also derived and cross-checked against numerical ray tracing. Finally, under suitable conditions a wavetrain can be so strongly refracted that it collapses all the way onto a zero-size point vortex. This is a strong wave-vortex interaction by definition. The conditions for such a collapse are derived and the validity of ray tracing theory during the singular collapse is investigated.

Finite-amplitude, pulsed, ultrasonic beams

NASA Astrophysics Data System (ADS)

Coulouvrat, François; Frøysa, Kjell-Eivind

An analytical, approximate solution of the inviscid KZK equation for a nonlinear pulsed sound beam radiated by an acoustic source with a Gaussian velocity distribution, is obtained by means of the renormalization method. This method involves two steps. First, the transient, weakly nonlinear field is computed. However, because of cumulative nonlinear effects, that expansion is non-uniform and breaks down at some distance away from the source. So, in order to extend its validity, it is re-written in a new frame of co-ordinates, better suited to following the nonlinear distorsion of the wave profile. Basically, the nonlinear coordinate transform introduces additional terms in the expansion, which are chosen so as to counterbalance the non-uniform ones. Special care is devoted to the treatment of shock waves. Finally, comparisons with the results of a finite-difference scheme turn out favorable, and show the efficiency of the method for a rather large range of parameters.

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).

A new mathematical approach for shock-wave solution in a dusty plasma

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

Das, G.C.; Dwivedi, C.B.; Talukdar, M.

1997-12-01

The problem of nonlinear Burger equation in a plasma contaminated with heavy dust grains has been revisited. As discussed earlier [C. B. Dwivedi and B. P. Pandey, Phys. Plasmas {bold 2}, 9 (1995)], the Burger equation originates due to dust charge fluctuation dynamics. A new alternate mathematical approach based on a simple traveling wave formalism has been applied to find out the solution of the derived Burger equation, and the method recovers the known shock-wave solution. This technique, although having its own limitation, predicts successfully the salient features of the weak shock-wave structure in a dusty plasma with dust chargemore » fluctuation dynamics. It is emphasized that this approach of the traveling wave formalism is being applied for the first time to solve the nonlinear wave equation in plasmas. {copyright} {ital 1997 American Institute of Physics.}« less

High-informative version of nonlinear transformation of Langmuir waves to electromagnetic waves

NASA Astrophysics Data System (ADS)

Erofeev, Vasily I.; Erofeev

2014-04-01

The concept of informativeness of nonlinear plasma physical scenario is discussed. Basic principles for heightening the informativeness of plasma kinetic models are explained. Former high-informative correlation analysis of plasma kinetics (Erofeev, V. 2011 High-Informative Plasma Theory, Saarbrücken: LAP) is generalized for studies of weakly turbulent plasmas that contain fields of solenoidal plasma waves apart from former potential ones. Respective machinery of plasma kinetic modeling is applied to an analysis of fusion of Langmuir waves with transformation to electromagnetic waves. It is shown that the customary version of this phenomenon (Terashima, Y. and Yajima, N. 1963 Prog. Theor. Phys. 30, 443; Akhiezer, I. A., Danelia, I. A. and Tsintsadze, N. L. 1964 Sov. Phys. JETP 19, 208; Al'tshul', L. M. and Karpman, V. I. 1965 Sov. Phys. JETP 20, 1043) substantially distorts the picture of merging of Langmuir waves with long wavelengths (λ >~ c/ωpe ).

Study of Linear and Nonlinear Wave Excitation

NASA Astrophysics Data System (ADS)

Chu, Feng; Berumen, Jorge; Hood, Ryan; Mattingly, Sean; Skiff, Frederick

2013-10-01

We report an experimental study of externally excited low-frequency waves in a cylindrical, magnetized, singly-ionized Argon inductively-coupled gas discharge plasma that is weakly collisional. Wave excitation in the drift wave frequency range is accomplished by low-percentage amplitude modulation of the RF plasma source. Laser-induced fluorescence is adopted to study ion-density fluctuations in phase space. The laser is chopped to separate LIF from collisional fluorescence. A single negatively-biased Langmuir probe is used to detect ion-density fluctuations in the plasma. A ring array of Langmuir probes is also used to analyze the spatial and spectral structure of the excited waves. We apply coherent detection with respect to the wave frequency to obtain the ion distribution function associated with externally generated waves. Higher-order spectra are computed to evaluate the nonlinear coupling between fluctuations at various frequencies produced by the externally generated waves. Parametric decay of the waves is observed. This work is supported by U.S. DOE Grant No. DE-FG02-99ER54543.

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.

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.

Nonlinear and Dissipation Characteristics of Ocean Surface Waves in Estuarine Environments

DTIC Science & Technology

2013-09-30

developed models while using the general framework of operational wave models. We will conduct robustness tests of the system to determine the...and Guza (1984) model is weakly dispersive, in line with the assumptions behind the Boussinesq equations from which it was derived. The Kaihatu and...interactions across both frequency and directions. This system of equations is solved over a 2D frequency (f) and shore parallel wave number (κ) space. The

Double-Diffusive Convection at Low Prandtl Number

NASA Astrophysics Data System (ADS)

Garaud, Pascale

2018-01-01

This work reviews present knowledge of double-diffusive convection at low Prandtl number obtained using direct numerical simulations, in both the fingering regime and the oscillatory regime. Particular emphasis is given to modeling the induced turbulent mixing and its impact in various astrophysical applications. The nonlinear saturation of fingering convection at low Prandtl number usually drives small-scale turbulent motions whose transport properties can be predicted reasonably accurately using a simple semi-analytical model. In some instances, large-scale internal gravity waves can be excited by a collective instability and eventually cause layering. The nonlinear saturation of oscillatory double-diffusive convection exhibits much more complex behavior. Weakly stratified systems always spontaneously transition into layered convection associated with very efficient mixing. More strongly stratified systems remain dominated by weak wave turbulence unless they are initialized into a layered state. The effects of rotation, shear, lateral gradients, and magnetic fields are briefly discussed.

A new energy transfer model for turbulent free shear flow

NASA Technical Reports Server (NTRS)

Liou, William W.-W.

1992-01-01

A new model for the energy transfer mechanism in the large-scale turbulent kinetic energy equation is proposed. An estimate of the characteristic length scale of the energy containing large structures is obtained from the wavelength associated with the structures predicted by a weakly nonlinear analysis for turbulent free shear flows. With the inclusion of the proposed energy transfer model, the weakly nonlinear wave models for the turbulent large-scale structures are self-contained and are likely to be independent flow geometries. The model is tested against a plane mixing layer. Reasonably good agreement is achieved. Finally, it is shown by using the Liapunov function method, the balance between the production and the drainage of the kinetic energy of the turbulent large-scale structures is asymptotically stable as their amplitude saturates. The saturation of the wave amplitude provides an alternative indicator for flow self-similarity.

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

Raman parametric excitation effect upon the third harmonic generation by a metallic nanoparticle lattice

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

Sepehri Javan, N., E-mail: sepehri-javan@uma.ac.ir

2015-08-21

This work is a theoretical study on third harmonic generation in the nonlinear propagation of an intense laser pulse through a periodic three-dimensional lattice of nanoparticles. Using a perturbative method, the nonlinear equations that describe the laser–nanoparticle interaction in the weakly relativistic regime are derived. Additionally, the nonlinear dispersion relation and the amplitude of the third harmonic are obtained. Finally, the effects of the nanoparticle radius and separation length, the distribution of the nanoparticle electron density, and the laser frequency upon the third harmonic efficiency are investigated. In addition to the expected resonance that occurs when the third harmonic resonatesmore » with the plasmon wave, another resonance appears when the nonlinear interaction of the fundamental mode with the third harmonic excites a longitudinal collective plasmon wave via the parametric Raman mechanism.« less

A Locally Modal B-Spline Based Full-Vector Finite-Element Method with PML for Nonlinear and Lossy Plasmonic Waveguide

NASA Astrophysics Data System (ADS)

Karimi, Hossein; Nikmehr, Saeid; Khodapanah, Ehsan

2016-09-01

In this paper, we develop a B-spline finite-element method (FEM) based on a locally modal wave propagation with anisotropic perfectly matched layers (PMLs), for the first time, to simulate nonlinear and lossy plasmonic waveguides. Conventional approaches like beam propagation method, inherently omit the wave spectrum and do not provide physical insight into nonlinear modes especially in the plasmonic applications, where nonlinear modes are constructed by linear modes with very close propagation constant quantities. Our locally modal B-spline finite element method (LMBS-FEM) does not suffer from the weakness of the conventional approaches. To validate our method, first, propagation of wave for various kinds of linear, nonlinear, lossless and lossy materials of metal-insulator plasmonic structures are simulated using LMBS-FEM in MATLAB and the comparisons are made with FEM-BPM module of COMSOL Multiphysics simulator and B-spline finite-element finite-difference wide angle beam propagation method (BSFEFD-WABPM). The comparisons show that not only our developed numerical approach is computationally more accurate and efficient than conventional approaches but also it provides physical insight into the nonlinear nature of the propagation modes.

Two different kinds of rogue waves in weakly crossing sea states

NASA Astrophysics Data System (ADS)

Ruban, V. P.

2009-06-01

Formation of giant waves in sea states with two spectral maxima centered at close wave vectors k0±Δk/2 in the Fourier plane is numerically simulated using the fully nonlinear model for long-crested water waves [V. P. Ruban, Phys. Rev. E 71, 055303(R) (2005)]. Depending on an angle θ between the vectors k0 and Δk , which determines a typical orientation of interference stripes in the physical plane, rogue waves arise having different spatial structure. If θ≲arctan(1/2) , then typical giant waves are relatively long fragments of essentially two-dimensional (2D) ridges, separated by wide valleys and consisting of alternating oblique crests and troughs. At nearly perpendicular k0 and Δk , the interference minima develop to coherent structures similar to the dark solitons of the nonlinear Schrodinger equation, and a 2D freak wave looks much as a piece of a one-dimensional freak wave bounded in the transversal direction by two such dark solitons.

Solitary waves with weak transverse perturbations in quantum dusty plasmas

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

Ur-Rehman, H.; Masood, W.; Siddiq, M.

2008-12-15

Using the quantum hydrodynamic model, quantum dust ion-acoustic solitary waves are investigated in the presence of weak transverse perturbations. The linear dispersion relation is obtained using the Fourier analysis. The two-dimensional (2D) propagation of small amplitude nonlinear waves is studied by deriving the Kadomtsev-Petviashvili (KP) equation. The traveling wave solution of the KP equation is obtained by employing the tanh method. By dint of this solution, the effects of quantum Bohm pressure and the dust concentration on the 2D solitary structure are studied. The effect of quantum Bohm potential on the stability of the KP soliton is also investigated. Themore » results are supported by the numerical analysis and the relevance of the present investigation in dense astrophysical environments is also pointed out.« less

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.

Nonlinear Korteweg-de Vries-Burger equation for ion acoustic shock waves in a weakly relativistic electron-positron-ion plasma with thermal ions

NASA Astrophysics Data System (ADS)

Saeed, R.; Shah, Asif

2010-03-01

The nonlinear propagation of ion acoustic waves in electron-positron-ion plasma comprising of Boltzmannian electrons, positrons, and relativistic thermal ions has been examined. The Korteweg-de Vries-Burger equation has been derived by reductive perturbation technique, and its shock like solution is determined analytically through tangent hyperbolic method. The effect of various plasma parameters on strength and structure of shock wave is investigated. The pert graphical view of the results has been presented for illustration. It is observed that strength and steepness of the shock wave enervate with an increase in the ion temperature, relativistic streaming factor, positron concentrations, electron temperature and they accrue with an increase in coefficient of kinematic viscosity. The convective, dispersive, and dissipative properties of the plasma are also discussed. It is determined that the electron temperature has remarkable influence on the propagation and structure of nonlinear wave in such relativistic plasmas. The numerical analysis has been done based on the typical numerical data from a pulsar magnetosphere.

Conical wave propagation and diffraction in two-dimensional hexagonally packed granular lattices

DOE PAGES

Chong, C.; Kevrekidis, P. G.; Ablowitz, M. J.; ...

2016-01-25

We explore linear and nonlinear mechanisms for conical wave propagation in two-dimensional lattices in the realm of phononic crystals. As a prototypical example, a statically compressed granular lattice of spherical particles arranged in a hexagonal packing configuration is analyzed. Upon identifying the dispersion relation of the underlying linear problem, the resulting diffraction properties are considered. Analysis both via a heuristic argument for the linear propagation of a wave packet and via asymptotic analysis leading to the derivation of a Dirac system suggests the occurrence of conical diffraction. This analysis is valid for strong precompression, i.e., near the linear regime. Formore » weak precompression, conical wave propagation is still possible, but the resulting expanding circular wave front is of a nonoscillatory nature, resulting from the complex interplay among the discreteness, nonlinearity, and geometry of the packing. Lastly, the transition between these two types of propagation is explored.« less

Study of solar wind spectra by nonlinear waves interaction

NASA Astrophysics Data System (ADS)

Dwivedi, Navin; Sharma, Rampal; Narita, Yasuhito

2014-05-01

The nature of small-scale turbulent fluctuations in the solar wind (SW) turbulence is a topic that is being investigated extensively nowadays, both theoretically and observationally. Although recent observations predict the evidence of the dominance of kinetic Alfvén waves (KAW) at sub-ion scales with frequency below than ion cyclotron frequency, while other studies suggest that the KAW mode cannot carry the turbulence cascade down to electron scales and that the whistler mode is more relevant. In the present work, nonlinear interaction of kinetic Alfvén wave with whistler wave is considered as one of the possible cause responsible for the solar wind turbulence. A set of coupled dimensionless equations are derived for the intermediate beta plasmas and the nonlinear interaction between these two wave modes has been studied. As a consequence of ponderomotive nonlinearity, the pump KAW becomes filamented when its power exceeds the threshold for the filamentation instability. Whistler is considered to be weak and thus doesn't have enough intensity to initiate its own localization. It gets localized while propagating through the density channel created by KAW localization. In addition, spectral scales of power spectra of KAW and whistler are also calculated. The steeper spectra are found with scaling greater than -5/3. This type of nonlinear interaction between different wave modes and steeper spectra is one of the reasons for the solar wind turbulence and particles acceleration. This work is partially supported by DST (India) and FP7/STORM (313038)

Traveling wave solutions of the nonlinear Schrödinger equation

NASA Astrophysics Data System (ADS)

Akbari-Moghanjoughi, M.

2017-10-01

In this paper, we investigate the traveling soliton and the periodic wave solutions of the nonlinear Schrödinger equation (NLSE) with generalized nonlinear functionality. We also explore the underlying close connection between the well-known KdV equation and the NLSE. It is remarked that both one-dimensional KdV and NLSE models share the same pseudoenergy spectrum. We also derive the traveling wave solutions for two cases of weakly nonlinear mathematical models, namely, the Helmholtz and the Duffing oscillators' potentials. It is found that these models only allow gray-type NLSE solitary propagations. It is also found that the pseudofrequency ratio for the Helmholtz potential between the nonlinear periodic carrier and the modulated sinusoidal waves is always in the range 0.5 ≤ Ω/ω ≤ 0.537285 regardless of the potential parameter values. The values of Ω/ω = {0.5, 0.537285} correspond to the cnoidal waves modulus of m = {0, 1} for soliton and sinusoidal limits and m = 0.5, respectively. Moreover, the current NLSE model is extended to fully NLSE (FNLSE) situation for Sagdeev oscillator pseudopotential which can be derived using a closed set of hydrodynamic fluid equations with a fully integrable Hamiltonian system. The generalized quasi-three-dimensional traveling wave solution is also derived. The current simple hydrodynamic plasma model may also be generalized to two dimensions and other complex situations including different charged species and cases with magnetic or gravitational field effects.

Special discontinuities in nonlinearly elastic media

NASA Astrophysics Data System (ADS)

Chugainova, A. P.

2017-06-01

Solutions of a nonlinear hyperbolic system of equations describing weakly nonlinear quasitransverse waves in a weakly anisotropic elastic medium are studied. The influence of small-scale processes of dissipation and dispersion is investigated. The small-scale processes determine the structure of discontinuities (shocks) and a set of discontinuities with a stationary structure. Among the discontinuities with a stationary structure, there are special ones that, in addition to relations following from conservation laws, satisfy additional relations required for the existence of their structure. In the phase plane, the structure of such discontinuities is represented by an integral curve joining two saddles. Special discontinuities lead to nonunique self-similar solutions of the Riemann problem. Asymptotics of non-self-similar problems for equations with dissipation and dispersion are found numerically. These asymptotics correspond to self-similar solutions of the problems.

Mach stem formation in reflection and focusing of weak shock acoustic pulses.

PubMed

Karzova, Maria M; Khokhlova, Vera A; Salze, Edouard; Ollivier, Sébastien; Blanc-Benon, Philippe

2015-06-01

The aim of this study is to show the evidence of Mach stem formation for very weak shock waves with acoustic Mach numbers on the order of 10(-3) to 10(-2). Two representative cases are considered: reflection of shock pulses from a rigid surface and focusing of nonlinear acoustic beams. Reflection experiments are performed in air using spark-generated shock pulses. Shock fronts are visualized using a schlieren system. Both regular and irregular types of reflection are observed. Numerical simulations are performed to demonstrate the Mach stem formation in the focal region of periodic and pulsed nonlinear beams in water.

Experimental investigation of gravity wave turbulence and of non-linear four wave interactions..

NASA Astrophysics Data System (ADS)

Berhanu, Michael

2017-04-01

Using the large basins of the Ecole Centrale de Nantes (France), non-linear interactions of gravity surface waves are experimentally investigated. In a first part we study statistical properties of a random wave field regarding the insights from the Wave Turbulence Theory. In particular freely decaying gravity wave turbulence is generated in a closed basin. No self-similar decay of the spectrum is observed, whereas its Fourier modes decay first as a time power law due to nonl-inear mechanisms, and then exponentially due to linear viscous damping. We estimate the linear, non-linear and dissipative time scales to test the time scale separation. By estimation of the mean energy flux from the initial decay of wave energy, the Kolmogorov-Zakharov constant of the weak turbulence theory is evaluated. In a second part, resonant interactions of oblique surface gravity waves in a large basin are studied. We generate two oblique waves crossing at an acute angle. These mother waves mutually interact and give birth to a resonant wave whose properties (growth rate, resonant response curve and phase locking) are fully characterized. All our experimental results are found in good quantitative agreement with four-wave interaction theory. L. Deike, B. Miquel, P. Gutiérrez, T. Jamin, B. Semin, M. Berhanu, E. Falcon and F. Bonnefoy, Role of the basin boundary conditions in gravity wave turbulence, Journal of Fluid Mechanics 781, 196 (2015) F. Bonnefoy, F. Haudin, G. Michel, B. Semin, T. Humbert, S. Aumaître, M. Berhanu and E. Falcon, Observation of resonant interactions among surface gravity waves, Journal of Fluid Mechanics (Rapids) 805, R3 (2016)

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

Non-Destructive Evaluation of Material System Using Highly Nonlinear Acoustic Waves

NASA Astrophysics Data System (ADS)

Khatri, Devvrath

A chain of granular particles is one of the most studied examples of highly nonlinear systems deriving its response from the nonlinear Hertzian contact interaction between particles. Interest in these systems derives from their tunable dynamic response, encompassing linear, weakly nonlinear, and strongly nonlinear regimes, controlled by varying the static and dynamic load applied. In chains with a very weak (or zero) static precompression, the system supports the formation and propagation of highly nonlinear solitary waves (HNSWs). The dual-nonlinear interaction between particles (i.e., a power-law type contact potential in compression, and zero strength in tension) combined with discreteness of the system, makes the granular system highly tunable. The propagation properties of these waves, such as traveling pulse width, wave speed, number of separated pulses (single or train of pulses), etc., can be controlled by modifying one or many of the parameters, like the particle's dimension, material properties, static and dynamic force amplitude, the type and duration of the initial excitation applied to the system, and/or the periodicity of the chain. The ability to control the wave properties in such chains has been proposed for several different practical engineering applications. The dynamic properties of these granular chains have been conventionally studied using discrete particle models (DPMs) which consider the particles in the chains as point masses connected by nonlinear Hertzian springs with the neighboring particles. Although, this is a good approximation under proper circumstances, it does not capture many features of the three dimensional elastic particles such as the elastic wave propagation within the particles, the local deformation of the particles in the vicinity of the contact point, the corresponding changes in the contact area, and the collective vibrations of the particles among others. This thesis focuses on the development of a finite element model (FEM) using the commercially available software Abaqus, which takes into account many of these characteristic features. The finite element model discretizes particles by considering them as three-dimensional deformable bodies of revolution and describes the nonlinear dynamic response of one-dimensional granular chains composed of particles with various geometries and orientations. We showed that particles' geometries and orientations provide additional design parameters for controlling the dynamic response of the system, compared to chains composed of spherical particles. We also showed that the tunable and compact nature of these waves can be used to tailor the properties of HNSWs for specific application, such as information carriers for actuation and sensing of mechanical properties and boundary effects of adjoining media in Non-Destructive Evaluation (NDE) and Structural Health Monitoring (SHM). Using experiments and numerics, we characterized interface dynamics between granular media and adjoining linear elastic media, and found that the coupling produced temporary localization of the incident waves at the boundaries between the two media and their decomposition into reflected waves. We monitored the formation of reflected solitary waves propagating back from the interface and found that their properties are sensitive to the geometric and material properties of the adjoining media. The work done in this research enhances our understanding of the basic physics and tunability of nonlinear granular media, and further establishes a theoretical and numerical foundation in the applications of HNSWs as information carriers.

Nonlinear self-reflection of intense ultra-wideband femtosecond pulses in optical fiber

NASA Astrophysics Data System (ADS)

Konev, Leonid S.; Shpolyanskiy, Yuri A.

2013-05-01

We simulated propagation of few-cycle femtosecond pulses in fused silica fiber based on the set of first-order equations for forward and backward waves that generalizes widely used equation of unidirectional approximation. Appearance of a weak reflected field in conditions default to the unidirectional approach is observed numerically. It arises from nonmatched initial field distribution with the nonlinear medium response. Besides additional field propagating forward along with the input pulse is revealed. The analytical solution of a simplified set of equations valid over distances of a few wavelengths confirms generation of reflected and forward-propagating parts of the backward wave. It allowed us to find matched conditions when the reflected field is eliminated and estimate the amplitude of backward wave via medium properties. The amplitude has the order of the nonlinear contribution to the refractive index divided by the linear refractive index. It is small for the fused silica so the conclusions obtained in the unidirectional approach are valid. The backward wave should be proportionally higher in media with stronger nonlinear response. We did not observe in simulations additional self-reflection not related to non-matched boundary conditions.

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.

Damping of Resonantly Forced Density Waves in Dense Planetary Rings

NASA Astrophysics Data System (ADS)

Lehmann, Marius; Schmidt, Jürgen; Salo, Heikki

2016-10-01

We address the stability of resonantly forced density waves in dense planetary rings.Already by Goldreich and Tremaine (1978) it has been argued that density waves might be unstable, depending on the relationship between the ring's viscosity and the surface mass density. In the recent paper (Schmidt et al. 2016) we have pointed out that when - within a fluid description of the ring dynamics - the criterion for viscous overstability is satisfied, forced spiral density waves become unstable as well. In this case, linear theory fails to describe the damping.We apply the multiple scale formalism to derive a weakly nonlinear damping relation from a hydrodynamical model.This relation describes the resonant excitation and nonlinear viscous damping of spiral density waves in a vertically integrated fluid disk with density dependent transport coefficients. The model consistently predicts linear instability of density waves in a ring region where the conditions for viscous overstability are met. In this case, sufficiently far away from the Lindblad resonance, the surface mass density perturbation is predicted to saturate to a constant value due to nonlinear viscous damping. In general the model wave damping lengths depend on a set of input parameters, such as the distance to the threshold for viscous overstability and the ground state surface mass density.Our new model compares reasonably well with the streamline model for nonlinear density waves of Borderies et al. 1986.Deviations become substantial in the highly nonlinear regime, corresponding to strong satellite forcing.Nevertheless, we generally observe good or at least qualitative agreement between the wave amplitude profiles of both models. The streamline approach is superior at matching the total wave profile of waves observed in Saturn's rings, while our new damping relation is a comparably handy tool to gain insight in the evolution of the wave amplitude with distance from resonance, and the different regimes of wave formation and the dependence on the parameters of the model.

Collision of Identical Solitary Waves in Hertzian Chains

NASA Astrophysics Data System (ADS)

Sen, Surajit; Manciu, Marian; Hurd, Alan J.

2000-03-01

We consider a chain of elastic beads, which repel upon contact according to the non-linear Hertz potential. We further assume that the chain is under zero loading, i.e., the grains have zero initial overlap. We show via careful numerical solution of the equations of motion that an impulse propagates as a solitary wave and that the collision of identical solitary waves propagating in opposite directions along the chain spawns a hierarchy of multiple weak solitary waves [1]. [1] M. Manciu, S. Sen and A.J. Hurd, Phys Lett A (submitted).

Complete energy conversion by autoresonant three-wave mixing in nonuniform media.

PubMed

Yaakobi, O; Caspani, L; Clerici, M; Vidal, F; Morandotti, R

2013-01-28

Resonant three-wave interactions appear in many fields of physics e.g. nonlinear optics, plasma physics, acoustics and hydrodynamics. A general theory of autoresonant three-wave mixing in a nonuniform media is derived analytically and demonstrated numerically. It is shown that due to the medium nonuniformity, a stable phase-locked evolution is automatically established. For a weak nonuniformity, the efficiency of the energy conversion between the interacting waves can reach almost 100%. One of the potential applications of our theory is the design of highly-efficient optical parametric amplifiers.

Nonlinear stability of Halley comethosheath with transverse plasma motion

NASA Technical Reports Server (NTRS)

Srivastava, Krishna M.; Tsurutani, Bruce T.

1994-01-01

Weakly nonlinear Magneto Hydrodynamic (MHD) stability of the Halley cometosheath determined by the balance between the outward ion-neutral drag force and the inward Lorentz force is investigated including the transverse plasma motion as observed in the flanks with the help of the method of multiple scales. The eigenvalues and the eigenfunctions are obtained for the linear problem and the time evolution of the amplitude is obtained using the solvability condition for the solution of the second order problem. The diamagnetic cavity boundary and the adjacent layer of about 100 km thickness is found unstable for the travelling waves of certain wave numbers. Halley ionopause has been observed to have strong ripples with a wavelength of several hundred kilometers. It is found that nonlinear effects have stabilizing effect.

The polarized Debye sheath effect on Kadomtsev-Petviashvili electrostatic structures in strongly coupled dusty plasma

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

Shahmansouri, M.; Alinejad, H.

2015-04-15

We give a theoretical investigation on the dynamics of nonlinear electrostatic waves in a strongly coupled dusty plasma with strong electrostatic interaction between dust grains in the presence of the polarization force (i.e., the force due to the polarized Debye sheath). Adopting a reductive perturbation method, we derived a three-dimensional Kadomtsev-Petviashvili equation that describes the evolution of weakly nonlinear electrostatic localized waves. The energy integral equation is used to study the existence domains of the localized structures. The analysis provides the localized structure existence region, in terms of the effects of strong interaction between the dust particles and polarization force.

Weakly decaying solutions of nonlinear Schrödinger equation in the plane

NASA Astrophysics Data System (ADS)

Villarroel, Javier; Prada, Julia; Estévez, Pilar G.

2017-12-01

We show that the nonlinear Schrödinger equation in 2  +  1 dimensions possesses a class of regular and rationally decaying solutions associated to interacting solitons. The interesting dynamics of the associated pulses is studied in detail and related to homothetic Lagrange configurations of certain N- body problems. These solutions correspond to the discrete spectrum of the Lax pair associated operator. A natural characterization of this spectrum is given. We show that a certain subset of solutions correspond to rogue waves, localized along curves in the plane. Other configurations like grey solitons, cnoidal waves and general N- lumps solutions are also described.

Millimeter-wave interconnects for microwave-frequency quantum machines

NASA Astrophysics Data System (ADS)

Pechal, Marek; Safavi-Naeini, Amir H.

2017-10-01

Superconducting microwave circuits form a versatile platform for storing and manipulating quantum information. A major challenge to further scalability is to find approaches for connecting these systems over long distances and at high rates. One approach is to convert the quantum state of a microwave circuit to optical photons that can be transmitted over kilometers at room temperature with little loss. Many proposals for electro-optic conversion between microwave and optics use optical driving of a weak three-wave mixing nonlinearity to convert the frequency of an excitation. Residual absorption of this optical pump leads to heating, which is problematic at cryogenic temperatures. Here we propose an alternative approach where a nonlinear superconducting circuit is driven to interconvert between microwave-frequency (7 ×109 Hz) and millimeter-wave-frequency photons (3 ×1011 Hz). To understand the potential for quantum state conversion between microwave and millimeter-wave photons, we consider the driven four-wave mixing quantum dynamics of nonlinear circuits. In contrast to the linear dynamics of the driven three-wave mixing converters, the proposed four-wave mixing converter has nonlinear decoherence channels that lead to a more complex parameter space of couplings and pump powers that we map out. We consider physical realizations of such converter circuits by deriving theoretically the upper bound on the maximum obtainable nonlinear coupling between any two modes in a lossless circuit, and synthesizing an optimal circuit based on realistic materials that saturates this bound. Our proposed circuit dissipates less than 10-9 times the energy of current electro-optic converters per qubit. Finally, we outline the quantum link budget for optical, microwave, and millimeter-wave connections, showing that our approach is viable for realizing interconnected quantum processors for intracity or quantum data center environments.

The exact rogue wave recurrence in the NLS periodic setting via matched asymptotic expansions, for 1 and 2 unstable modes

NASA Astrophysics Data System (ADS)

Grinevich, P. G.; Santini, P. M.

2018-04-01

The focusing Nonlinear Schrödinger (NLS) equation is the simplest universal model describing the modulation instability (MI) of quasi monochromatic waves in weakly nonlinear media, the main physical mechanism for the generation of rogue (anomalous) waves (RWs) in Nature. In this paper we investigate the x-periodic Cauchy problem for NLS for a generic periodic initial perturbation of the unstable constant background solution, in the case of N = 1 , 2 unstable modes. We use matched asymptotic expansion techniques to show that the solution of this problem describes an exact deterministic alternate recurrence of linear and nonlinear stages of MI, and that the nonlinear RW stages are described by the N-breather solution of Akhmediev type, whose parameters, different at each RW appearance, are always given in terms of the initial data through elementary functions. This paper is motivated by a preceding work of the authors in which a different approach, the finite gap method, was used to investigate periodic Cauchy problems giving rise to RW recurrence.

Azimuthal Seismic Amplitude Variation with Offset and Azimuth Inversion in Weakly Anisotropic Media with Orthorhombic Symmetry

NASA Astrophysics Data System (ADS)

Pan, Xinpeng; Zhang, Guangzhi; Yin, Xingyao

2018-01-01

Seismic amplitude variation with offset and azimuth (AVOaz) inversion is well known as a popular and pragmatic tool utilized to estimate fracture parameters. A single set of vertical fractures aligned along a preferred horizontal direction embedded in a horizontally layered medium can be considered as an effective long-wavelength orthorhombic medium. Estimation of Thomsen's weak-anisotropy (WA) parameters and fracture weaknesses plays an important role in characterizing the orthorhombic anisotropy in a weakly anisotropic medium. Our goal is to demonstrate an orthorhombic anisotropic AVOaz inversion approach to describe the orthorhombic anisotropy utilizing the observable wide-azimuth seismic reflection data in a fractured reservoir with the assumption of orthorhombic symmetry. Combining Thomsen's WA theory and linear-slip model, we first derive a perturbation in stiffness matrix of a weakly anisotropic medium with orthorhombic symmetry under the assumption of small WA parameters and fracture weaknesses. Using the perturbation matrix and scattering function, we then derive an expression for linearized PP-wave reflection coefficient in terms of P- and S-wave moduli, density, Thomsen's WA parameters, and fracture weaknesses in such an orthorhombic medium, which avoids the complicated nonlinear relationship between the orthorhombic anisotropy and azimuthal seismic reflection data. Incorporating azimuthal seismic data and Bayesian inversion theory, the maximum a posteriori solutions of Thomsen's WA parameters and fracture weaknesses in a weakly anisotropic medium with orthorhombic symmetry are reasonably estimated with the constraints of Cauchy a priori probability distribution and smooth initial models of model parameters to enhance the inversion resolution and the nonlinear iteratively reweighted least squares strategy. The synthetic examples containing a moderate noise demonstrate the feasibility of the derived orthorhombic anisotropic AVOaz inversion method, and the real data illustrate the inversion stabilities of orthorhombic anisotropy in a fractured reservoir.

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.

Route to thermalization in the α-Fermi–Pasta–Ulam system

PubMed Central

Onorato, Miguel; Vozella, Lara; Lvov, Yuri V.

2015-01-01

We study the original α-Fermi–Pasta–Ulam (FPU) system with N = 16, 32, and 64 masses connected by a nonlinear quadratic spring. Our approach is based on resonant wave–wave interaction theory; i.e., we assume that, in the weakly nonlinear regime (the one in which Fermi was originally interested), the large time dynamics is ruled by exact resonances. After a detailed analysis of the α-FPU equation of motion, we find that the first nontrivial resonances correspond to six-wave interactions. Those are precisely the interactions responsible for the thermalization of the energy in the spectrum. We predict that, for small-amplitude random waves, the timescale of such interactions is extremely large and it is of the order of 1/ϵ8, where ϵ is the small parameter in the system. The wave–wave interaction theory is not based on any threshold: Equipartition is predicted for arbitrary small nonlinearity. Our results are supported by extensive numerical simulations. A key role in our finding is played by the Umklapp (flip-over) resonant interactions, typical of discrete systems. The thermodynamic limit is also briefly discussed. PMID:25805822

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.

A dynamical model of plasma turbulence in the solar wind

PubMed Central

Howes, G. G.

2015-01-01

A dynamical approach, rather than the usual statistical approach, is taken to explore the physical mechanisms underlying the nonlinear transfer of energy, the damping of the turbulent fluctuations, and the development of coherent structures in kinetic plasma turbulence. It is argued that the linear and nonlinear dynamics of Alfvén waves are responsible, at a very fundamental level, for some of the key qualitative features of plasma turbulence that distinguish it from hydrodynamic turbulence, including the anisotropic cascade of energy and the development of current sheets at small scales. The first dynamical model of kinetic turbulence in the weakly collisional solar wind plasma that combines self-consistently the physics of Alfvén waves with the development of small-scale current sheets is presented and its physical implications are discussed. This model leads to a simplified perspective on the nature of turbulence in a weakly collisional plasma: the nonlinear interactions responsible for the turbulent cascade of energy and the formation of current sheets are essentially fluid in nature, while the collisionless damping of the turbulent fluctuations and the energy injection by kinetic instabilities are essentially kinetic in nature. PMID:25848075

Second sound shock waves and critical velocities in liquid helium 2. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Turner, T. N.

1979-01-01

Large amplitude second-sound shock waves were generated and the experimental results compared to the theory of nonlinear second-sound. The structure and thickness of second-sound shock fronts are calculated and compared to experimental data. Theoretically it is shown that at T = 1.88 K, where the nonlinear wave steepening vanishes, the thickness of a very weak shock must diverge. In a region near this temperature, a finite-amplitude shock pulse evolves into an unusual double-shock configuration consisting of a front steepened, temperature raising shock followed by a temperature lowering shock. Double-shocks are experimentally verified. It is experimentally shown that very large second-sound shock waves initiate a breakdown in the superfluidity of helium 2, which is dramatically displayed as a limit to the maximum attainable shock strength. The value of the maximum shock-induced relative velocity represents a significant lower bound to the intrinsic critical velocity of helium 2.

Hurricane genesis: on the breaking African easterly waves and critical layers

NASA Astrophysics Data System (ADS)

Asaadi, Ali; Brunet, Gilbert; Yau, Peter

2015-04-01

This study bring new understanding on the decades-old hurricane genesis problem that starts with westward travelling African easterly waves that can evolve into coherent cyclonic vortices depending on their strength and other nonlinear wave breaking processes. In general, observations indicate that only a small fraction of the African easterly waves that occur in a single hurricane season contribute to tropical cyclogenesis. However, this small fraction includes a large portion of named storms. In addition, a recent study by Dunkerton et al. (2009) has shown that named storms in the Atlantic and eastern Pacific basins are almost all associated with a cyclonic Kelvin "cat's eye" of a tropical easterly wave typical of critical layers, located equatorward of the easterly jet axis. To better understand the dynamics involved in hurricane genesis, the flow characteristics and the physical and dynamical mechanisms by which easterly waves form cat's eyes are investigated with the help of atmospheric reanalyzes and numerical simulations. We perform a climatological study of developing easterly waves covering the 1998-2001 hurricane seasons using ERA-Interim 6-hourly reanalysis data. Composite analyses for all named storms show a monotonic potential vorticity (PV) profile with weak meridional PV gradient and a cyclonic (i.e., south of the easterly jet axis) critical line for time periods of several days preceding the cat's eye formation. In addition, the developing PV anomaly composite shows a statistically significant companion wave-packet of non-developing easterly waves. A barotropic shallow water model is used to study the initial value and forced problems of disturbances on a parabolic jet and realistic profiles associated with weak basic state meridional PV gradients, leading to Kelvin cat's eye formation around the jet axis. The results highlight the synergy of the dynamical mechanisms, including wave breaking and PV redistribution within the nonlinear critical layer characterized by weak PV gradients, and the thermodynamical mechanisms such as convectively generated PV anomalies in the cat's eye formation in tropical cyclogenesis. These findings are consistent with the analytical theory of free and forced disturbances to an easterly parabolic jet (Brunet and Warn, 1990; Brunet and Haynes, 1995; Choboter et al., 2000). 1) Dunkerton, T. J., M. T. Montgomery, and Z. Wang, 2009: Tropical cyclogenesis in a tropical wave critical layer: Easterly waves. Atmos. Chem. Phys., 9, 5587-5646. 2) Brunet, G., and T. Warn, 1990: Rossby Wave Critical Layers on a Jet. J. Atmos. Sci., 47, 1173-1178. 3) Brunet, and P. H. Haynes, 1995: The Nonlinear Evolution of Disturbances to a Parabolic Jet. J. Atmos. Sci., 52, 464-477. 4) Choboter, P. F., G. Brunet, and S. A. Maslowe, 2000: Forced Disturbances in a Zero Absolute Vorticity Gradient Environment. J. Atmos. Sci., 57, 1406-1419.

Estimation of Dry Fracture Weakness, Porosity, and Fluid Modulus Using Observable Seismic Reflection Data in a Gas-Bearing Reservoir

NASA Astrophysics Data System (ADS)

Chen, Huaizhen; Zhang, Guangzhi

2017-05-01

Fracture detection and fluid identification are important tasks for a fractured reservoir characterization. Our goal is to demonstrate a direct approach to utilize azimuthal seismic data to estimate fluid bulk modulus, porosity, and dry fracture weaknesses, which decreases the uncertainty of fluid identification. Combining Gassmann's (Vier. der Natur. Gesellschaft Zürich 96:1-23, 1951) equations and linear-slip model, we first establish new simplified expressions of stiffness parameters for a gas-bearing saturated fractured rock with low porosity and small fracture density, and then we derive a novel PP-wave reflection coefficient in terms of dry background rock properties (P-wave and S-wave moduli, and density), fracture (dry fracture weaknesses), porosity, and fluid (fluid bulk modulus). A Bayesian Markov chain Monte Carlo nonlinear inversion method is proposed to estimate fluid bulk modulus, porosity, and fracture weaknesses directly from azimuthal seismic data. The inversion method yields reasonable estimates in the case of synthetic data containing a moderate noise and stable results on real data.

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.

Simulation of Nonlinear Instabilities in an Attachment-Line Boundary Layer

NASA Technical Reports Server (NTRS)

Joslin, Ronald D.

1996-01-01

The linear and the nonlinear stability of disturbances that propagate along the attachment line of a three-dimensional boundary layer is considered. The spatially evolving disturbances in the boundary layer are computed by direct numerical simulation (DNS) of the unsteady, incompressible Navier-Stokes equations. Disturbances are introduced either by forcing at the in ow or by applying suction and blowing at the wall. Quasi-parallel linear stability theory and a nonparallel theory yield notably different stability characteristics for disturbances near the critical Reynolds number; the DNS results con rm the latter theory. Previously, a weakly nonlinear theory and computations revealed a high wave-number region of subcritical disturbance growth. More recent computations have failed to achieve this subcritical growth. The present computational results indicate the presence of subcritically growing disturbances; the results support the weakly nonlinear theory. Furthermore, an explanation is provided for the previous theoretical and computational discrepancy. In addition, the present results demonstrate that steady suction can be used to stabilize disturbances that otherwise grow subcritically along the attachment line.

Superdiffusive transport and energy localization in disordered granular crystals

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

Martinez, Alejandro J.; Kevrekidis, Panagiotis G.; Porter, Mason A.

We study the spreading of initially localized excitations in one-dimensional disordered granular crystals. We thereby investigate localization phenomena in strongly nonlinear systems, which we demonstrate to be fundamentally different from localization in linear and weakly nonlinear systems. We conduct a thorough comparison of wave dynamics in chains with three different types of disorder: an uncorrelated (Anderson-like) disorder and two types of correlated disorders (which are produced by random dimer arrangements), and for two families of initial conditions: displacement perturbations and velocity perturbations. We find for strongly precompressed (i.e., weakly nonlinear) chains that the dynamics strongly depends on the initial condition.more » Furthermore, for displacement perturbations, the long-time asymptotic behavior of the second moment m ~2 has oscillations that depend on the type of disorder, with a complex trend that is markedly different from a power law and which is particularly evident for an Anderson-like disorder.« less

Superdiffusive transport and energy localization in disordered granular crystals

DOE PAGES

Martinez, Alejandro J.; Kevrekidis, Panagiotis G.; Porter, Mason A.

2016-02-12

We study the spreading of initially localized excitations in one-dimensional disordered granular crystals. We thereby investigate localization phenomena in strongly nonlinear systems, which we demonstrate to be fundamentally different from localization in linear and weakly nonlinear systems. We conduct a thorough comparison of wave dynamics in chains with three different types of disorder: an uncorrelated (Anderson-like) disorder and two types of correlated disorders (which are produced by random dimer arrangements), and for two families of initial conditions: displacement perturbations and velocity perturbations. We find for strongly precompressed (i.e., weakly nonlinear) chains that the dynamics strongly depends on the initial condition.more » Furthermore, for displacement perturbations, the long-time asymptotic behavior of the second moment m ~2 has oscillations that depend on the type of disorder, with a complex trend that is markedly different from a power law and which is particularly evident for an Anderson-like disorder.« less

Relativistic cosmic-ray spectra in the fully nonlinear theory of shock acceleration

NASA Technical Reports Server (NTRS)

Ellison, D. C.; Eichler, D.

1985-01-01

The non-linear theory of shock acceleration was generalized to include wave dynamics. In the limit of rapid wave damping, it is found that a finite wave velocity tempers the acceleration of high Mach number shocks and limits the maximum compression ratio even when energy loss is important. For a given spectrum, the efficiency of relativistic particle production is essentially independent of v sub Ph. For the three families shown, the percentage of kinetic energy flux going into relativistic particles is (1) 72 percent, (2) 44 percent, and (3) 26 percent (this includes the energy loss at the upper energy cutoff). Even small v sub ph, typical of the HISM, produce quasi-universal spectra that depend only weakly on the acoustic Mach number. These spectra should be close enough to e(-2) to satisfy cosmic ray source requirements.

On the interaction of Tollmien-Schlichting waves in axisymmetric supersonic flows

NASA Technical Reports Server (NTRS)

Duck, P. W.; Hall, P.

1988-01-01

Two-dimensional lower branch Tollmien-Schlichting waves described by triple-deck theory are always stable for planar supersonic flows. The possible occurrence of axisymmetric unstable modes in the supersonic flow around an axisymmetric body is investigated. In particular flows around bodies with typical radii comparable with the thickness of the upper deck are considered. It is shown that such unstable modes exist below a critical nondimensional radius of the body a sub 0. At values of the radius above a sub 0 all the modes are stable while if unstable modes exist they are found to occur in pairs. The interaction of these modes in the nonlinear regime is investigated using a weakly nonlinear approach and it is found that, dependent on the frequencies of the imposed Tollmien-Schlichting waves, either of the modes can be set up.

On the interaction of Tollmien-Schlichting waves in axisymmetric supersonic flows

NASA Technical Reports Server (NTRS)

Duck, P. W.; Hall, P.

1989-01-01

Two-dimensional lower branch Tollmien-Schlichting waves described by triple-deck theory are always stable for planar supersonic flows. The possible occurrence of axisymmetric unstable modes in the supersonic flow around an axisymmetric body is investigated. In particular flows around bodies with typical radii comparable with the thickness of the upper deck are considered. It is shown that such unstable modes exist below a critical nondimensional radius of the body a sub O. At values of the radius above a sub O all the modes are stable while if unstable modes exist they are found to occur in pairs. The interaction of these modes in the nonlinear regime is investigated using a weakly nonlinear approach and it is found that, dependent on the frequencies of the imposed Tollmien-Schlichting waves, either of the modes can be set up.

Nonlinear water waves: introduction and overview

NASA Astrophysics Data System (ADS)

Constantin, A.

2017-12-01

For more than two centuries progress in the study of water waves proved to be interdependent with innovative and deep developments in theoretical and experimental directions of investigation. In recent years, considerable progress has been achieved towards the understanding of waves of large amplitude. Within this setting one cannot rely on linear theory as nonlinearity becomes an essential feature. Various analytic methods have been developed and adapted to come to terms with the challenges encountered in settings where approximations (such as those provided by linear or weakly nonlinear theory) are ineffective. Without relying on simpler models, progress becomes contingent upon the discovery of structural properties, the exploitation of which requires a combination of creative ideas and state-of-the-art technical tools. The successful quest for structure often reveals unexpected patterns and confers aesthetic value on some of these studies. The topics covered in this issue are both multi-disciplinary and interdisciplinary: there is a strong interplay between mathematical analysis, numerical computation and experimental/field data, interacting with each other via mutual stimulation and feedback. This theme issue reflects some of the new important developments that were discussed during the programme `Nonlinear water waves' that took place at the Isaac Newton Institute for Mathematical Sciences (Cambridge, UK) from 31st July to 25th August 2017. A cross-section of the experts in the study of water waves who participated in the programme authored the collected papers. These papers illustrate the diversity, intensity and interconnectivity of the current research activity in this area. They offer new insight, present emerging theoretical methodologies and computational approaches, and describe sophisticated experimental results. This article is part of the theme issue 'Nonlinear water waves'.

Nonlinear water waves: introduction and overview.

PubMed

Constantin, A

2018-01-28

For more than two centuries progress in the study of water waves proved to be interdependent with innovative and deep developments in theoretical and experimental directions of investigation. In recent years, considerable progress has been achieved towards the understanding of waves of large amplitude. Within this setting one cannot rely on linear theory as nonlinearity becomes an essential feature. Various analytic methods have been developed and adapted to come to terms with the challenges encountered in settings where approximations (such as those provided by linear or weakly nonlinear theory) are ineffective. Without relying on simpler models, progress becomes contingent upon the discovery of structural properties, the exploitation of which requires a combination of creative ideas and state-of-the-art technical tools. The successful quest for structure often reveals unexpected patterns and confers aesthetic value on some of these studies. The topics covered in this issue are both multi-disciplinary and interdisciplinary: there is a strong interplay between mathematical analysis, numerical computation and experimental/field data, interacting with each other via mutual stimulation and feedback. This theme issue reflects some of the new important developments that were discussed during the programme 'Nonlinear water waves' that took place at the Isaac Newton Institute for Mathematical Sciences (Cambridge, UK) from 31st July to 25th August 2017. A cross-section of the experts in the study of water waves who participated in the programme authored the collected papers. These papers illustrate the diversity, intensity and interconnectivity of the current research activity in this area. They offer new insight, present emerging theoretical methodologies and computational approaches, and describe sophisticated experimental results.This article is part of the theme issue 'Nonlinear water waves'. © 2017 The Author(s).

An algorithm for continuum modeling of rocks with multiple embedded nonlinearly-compliant joints [Continuum modeling of elasto-plastic media with multiple embedded nonlinearly-compliant joints

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

Hurley, R. C.; Vorobiev, O. Y.; Ezzedine, S. M.

Here, we present a numerical method for modeling the mechanical effects of nonlinearly-compliant joints in elasto-plastic media. The method uses a series of strain-rate and stress update algorithms to determine joint closure, slip, and solid stress within computational cells containing multiple “embedded” joints. This work facilitates efficient modeling of nonlinear wave propagation in large spatial domains containing a large number of joints that affect bulk mechanical properties. We implement the method within the massively parallel Lagrangian code GEODYN-L and provide verification and examples. We highlight the ability of our algorithms to capture joint interactions and multiple weakness planes within individualmore » computational cells, as well as its computational efficiency. We also discuss the motivation for developing the proposed technique: to simulate large-scale wave propagation during the Source Physics Experiments (SPE), a series of underground explosions conducted at the Nevada National Security Site (NNSS).« less

An algorithm for continuum modeling of rocks with multiple embedded nonlinearly-compliant joints [Continuum modeling of elasto-plastic media with multiple embedded nonlinearly-compliant joints

DOE PAGES

Hurley, R. C.; Vorobiev, O. Y.; Ezzedine, S. M.

2017-04-06

Here, we present a numerical method for modeling the mechanical effects of nonlinearly-compliant joints in elasto-plastic media. The method uses a series of strain-rate and stress update algorithms to determine joint closure, slip, and solid stress within computational cells containing multiple “embedded” joints. This work facilitates efficient modeling of nonlinear wave propagation in large spatial domains containing a large number of joints that affect bulk mechanical properties. We implement the method within the massively parallel Lagrangian code GEODYN-L and provide verification and examples. We highlight the ability of our algorithms to capture joint interactions and multiple weakness planes within individualmore » computational cells, as well as its computational efficiency. We also discuss the motivation for developing the proposed technique: to simulate large-scale wave propagation during the Source Physics Experiments (SPE), a series of underground explosions conducted at the Nevada National Security Site (NNSS).« less

Properties of internal solitary waves in a symmetric three-layer fluid

NASA Astrophysics Data System (ADS)

Vladykina, E. A.; Polukhina, O. E.; Kurkin, A. A.

2009-04-01

Though all the natural media have smooth density stratifications (with the exception of special cases such as sea surface, inversion layer in the atmosphere), the scales of density variations can be different, and some of them can be considered as very sharp. Therefore for the description of internal wave propagation and interaction in the ocean and atmosphere the n-layer models are often used. In these models density profile is usually approximated by a piecewise-constant function. The advantage of the layered models is the finite number of parameters and relatively simple solutions of linear and weakly nonlinear problems. Layered models are also very popular in the laboratory experiments with stratified fluid. In this study we consider symmetric, continuously stratified, smoothed three-layer fluid bounded by rigid horizontal surface and bottom. Three-layer stratification is proved to be a proper approximation of sea water density profile in some basins in the World Ocean with specific hydrological conditions. Such a medium is interesting from the point of view of internal gravity wave dynamics, because in the symmetric case it leads to disappearing of quadratic nonlinearity when described in the framework of weakly nonlinear evolutionary models, that are derived through the asymptotic expansion in small parameters of nonlinearity and dispersion. The goal of our study is to determine the properties of localized stationary internal gravity waveforms (solitary waves) in this symmetric three-layer fluid. The investigation is carried out in the framework of improved mathematical model describing the transformation of internal wave fields generated by an initial disturbance. The model is based on the program complex for the numerical simulation of the two-dimensional (vertical plane) fully nonlinear Euler equations for incompressible stratified fluid under the Boussinesq approximation. Initial disturbances of both polarities evolve into stationary, solitary-like waves of corresponding polarity, for which we found the amplitude-width, amplitude-velocity, mass-amplitude, and energy-amplitude relations. Small-amplitude impulses to a good approximation can be described by the modified Korteweg-de Vries equation, but larger waves tend to become wide, and absolute value of their amplitude is bounded by the upper limit. Authors thank prof. K.G. Lamb for the opportunity to use the program code for numerical simulations of Euler equations. The research was supported by RFBR (09-05-00447, 09-05-00204) and by President of RF (MD-3024.2008.5 for young doctors of science).

Modulational instability in a PT-symmetric vector nonlinear Schrödinger system

NASA Astrophysics Data System (ADS)

Cole, J. T.; Makris, K. G.; Musslimani, Z. H.; Christodoulides, D. N.; Rotter, S.

2016-12-01

A class of exact multi-component constant intensity solutions to a vector nonlinear Schrödinger (NLS) system in the presence of an external PT-symmetric complex potential is constructed. This type of uniform wave pattern displays a non-trivial phase whose spatial dependence is induced by the lattice structure. In this regard, light can propagate without scattering while retaining its original form despite the presence of inhomogeneous gain and loss. These constant-intensity continuous waves are then used to perform a modulational instability analysis in the presence of both non-hermitian media and cubic nonlinearity. A linear stability eigenvalue problem is formulated that governs the dynamical evolution of the periodic perturbation and its spectrum is numerically determined using Fourier-Floquet-Bloch theory. In the self-focusing case, we identify an intensity threshold above which the constant-intensity modes are modulationally unstable for any Floquet-Bloch momentum belonging to the first Brillouin zone. The picture in the self-defocusing case is different. Contrary to the bulk vector case, where instability develops only when the waves are strongly coupled, here an instability occurs in the strong and weak coupling regimes. The linear stability results are supplemented with direct (nonlinear) numerical simulations.

3D numerical simulation of the long range propagation of acoustical shock waves through a heterogeneous and moving medium

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

Luquet, David; Marchiano, Régis; Coulouvrat, François, E-mail: francois.coulouvrat@upmc.fr

2015-10-28

Many situations involve the propagation of acoustical shock waves through flows. Natural sources such as lightning, volcano explosions, or meteoroid atmospheric entries, emit loud, low frequency, and impulsive sound that is influenced by atmospheric wind and turbulence. The sonic boom produced by a supersonic aircraft and explosion noises are examples of intense anthropogenic sources in the atmosphere. The Buzz-Saw-Noise produced by turbo-engine fan blades rotating at supersonic speed also propagates in a fast flow within the engine nacelle. Simulating these situations is challenging, given the 3D nature of the problem, the long range propagation distances relative to the central wavelength,more » the strongly nonlinear behavior of shocks associated to a wide-band spectrum, and finally the key role of the flow motion. With this in view, the so-called FLHOWARD (acronym for FLow and Heterogeneous One-Way Approximation for Resolution of Diffraction) method is presented with three-dimensional applications. A scalar nonlinear wave equation is established in the framework of atmospheric applications, assuming weak heterogeneities and a slow wind. It takes into account diffraction, absorption and relaxation properties of the atmosphere, quadratic nonlinearities including weak shock waves, heterogeneities of the medium in sound speed and density, and presence of a flow (assuming a mean stratified wind and 3D turbulent ? flow fluctuations of smaller amplitude). This equation is solved in the framework of the one-way method. A split-step technique allows the splitting of the non-linear wave equation into simpler equations, each corresponding to a physical effect. Each sub-equation is solved using an analytical method if possible, and finite-differences otherwise. Nonlinear effects are solved in the time domain, and others in the frequency domain. Homogeneous diffraction is handled by means of the angular spectrum method. Ground is assumed perfectly flat and rigid. Due to the 3D aspect, the code was massively parallelized using the single program, multiple data paradigm with the Message Passing Interfaces (MPI) for distributed memory architectures. This allows us to handle problems in the order of a thousand billion mesh points in the four dimensions (3 dimensions of space plus time). The validity of the method has been thoroughly evaluated on many cases with known solutions: linear piston, scattering of plane wave by a heterogeneous sphere, propagation in a waveguide with a shear flow, scattering by a finite amplitude vortex and nonlinear propagation in a thermoviscous medium. This validation process allows for a detailed assessment of the advantages and limitations of the method. Finally, applications to atmospheric propagation of shock waves will be presented.« less

3D numerical simulation of the long range propagation of acoustical shock waves through a heterogeneous and moving medium

NASA Astrophysics Data System (ADS)

Luquet, David; Marchiano, Régis; Coulouvrat, François

2015-10-01

Many situations involve the propagation of acoustical shock waves through flows. Natural sources such as lightning, volcano explosions, or meteoroid atmospheric entries, emit loud, low frequency, and impulsive sound that is influenced by atmospheric wind and turbulence. The sonic boom produced by a supersonic aircraft and explosion noises are examples of intense anthropogenic sources in the atmosphere. The Buzz-Saw-Noise produced by turbo-engine fan blades rotating at supersonic speed also propagates in a fast flow within the engine nacelle. Simulating these situations is challenging, given the 3D nature of the problem, the long range propagation distances relative to the central wavelength, the strongly nonlinear behavior of shocks associated to a wide-band spectrum, and finally the key role of the flow motion. With this in view, the so-called FLHOWARD (acronym for FLow and Heterogeneous One-Way Approximation for Resolution of Diffraction) method is presented with three-dimensional applications. A scalar nonlinear wave equation is established in the framework of atmospheric applications, assuming weak heterogeneities and a slow wind. It takes into account diffraction, absorption and relaxation properties of the atmosphere, quadratic nonlinearities including weak shock waves, heterogeneities of the medium in sound speed and density, and presence of a flow (assuming a mean stratified wind and 3D turbulent ? flow fluctuations of smaller amplitude). This equation is solved in the framework of the one-way method. A split-step technique allows the splitting of the non-linear wave equation into simpler equations, each corresponding to a physical effect. Each sub-equation is solved using an analytical method if possible, and finite-differences otherwise. Nonlinear effects are solved in the time domain, and others in the frequency domain. Homogeneous diffraction is handled by means of the angular spectrum method. Ground is assumed perfectly flat and rigid. Due to the 3D aspect, the code was massively parallelized using the single program, multiple data paradigm with the Message Passing Interfaces (MPI) for distributed memory architectures. This allows us to handle problems in the order of a thousand billion mesh points in the four dimensions (3 dimensions of space plus time). The validity of the method has been thoroughly evaluated on many cases with known solutions: linear piston, scattering of plane wave by a heterogeneous sphere, propagation in a waveguide with a shear flow, scattering by a finite amplitude vortex and nonlinear propagation in a thermoviscous medium. This validation process allows for a detailed assessment of the advantages and limitations of the method. Finally, applications to atmospheric propagation of shock waves will be presented.

Computation of Large-Scale Structure Jet Noise Sources With Weak Nonlinear Effects Using Linear Euler

NASA Technical Reports Server (NTRS)

Dahl, Milo D.; Hixon, Ray; Mankbadi, Reda R.

2003-01-01

An approximate technique is presented for the prediction of the large-scale turbulent structure sound source in a supersonic jet. A linearized Euler equations code is used to solve for the flow disturbances within and near a jet with a given mean flow. Assuming a normal mode composition for the wave-like disturbances, the linear radial profiles are used in an integration of the Navier-Stokes equations. This results in a set of ordinary differential equations representing the weakly nonlinear self-interactions of the modes along with their interaction with the mean flow. Solutions are then used to correct the amplitude of the disturbances that represent the source of large-scale turbulent structure sound in the jet.

Analysis and gyrokinetic simulation of MHD Alfven wave interactions

NASA Astrophysics Data System (ADS)

Nielson, Kevin Derek

The study of low-frequency turbulence in magnetized plasmas is a difficult problem due to both the enormous range of scales involved and the variety of physics encompassed over this range. Much of the progress that has been made in turbulence theory is based upon a result from incompressible magnetohydrodynamics (MHD), in which energy is only transferred from large scales to small via the collision of Alfven waves propagating oppositely along the mean magnetic field. Improvements in laboratory devices and satellite measurements have demonstrated that, while theories based on this premise are useful over inertial ranges, describing turbulence at scales that approach particle gyroscales requires new theory. In this thesis, we examine the limits of incompressible MHD theory in describing collisions between pairs of Alfven waves. This interaction represents the fundamental unit of plasma turbulence. To study this interaction, we develop an analytic theory describing the nonlinear evolution of interacting Alfven waves and compare this theory to simulations performed using the gyrokinetic code AstroGK. Gyrokinetics captures a much richer set of physics than that described by incompressible MHD, and is well-suited to describing Alfvenic turbulence around the ion gyroscale. We demonstrate that AstroGK is well suited to the study of physical Alfven waves by reproducing laboratory Alfven dispersion data collected using the LAPD. Additionally, we have developed an initialization alogrithm for use with AstroGK that allows exact Alfven eigenmodes to be initialized with user specified amplitudes and phases. We demonstrate that our analytic theory based upon incompressible MHD gives excellent agreement with gyrokinetic simulations for weakly turbulent collisions in the limit that k⊥rho i << 1. In this limit, agreement is observed in the time evolution of nonlinear products, and in the strength of nonlinear interaction with respect to polarization and scale. We also examine the effect of wave amplitude upon the validity of our analytic solution, exploring the nature of strong turbulence. In the kinetic limit where k⊥ rhoi ≳ 1 where incompressible MHD is no longer a valid description, we illustrate how the nonlinear evolution departs from our analytic expression. The analytic theory we develop provides a framework from which more sophisticated of weak and strong inertial-range turbulence theories may be developed. Characterization of the limits of this theory may provide guidance in the development of kinetic Alfven wave turbulence.

Bandwidth Limitations in Characterization of High Intensity Focused Ultrasound Fields in the Presence of Shocks

NASA Astrophysics Data System (ADS)

Khokhlova, V. A.; Bessonova, O. V.; Soneson, J. E.; Canney, M. S.; Bailey, M. R.; Crum, L. A.

2010-03-01

Nonlinear propagation effects result in the formation of weak shocks in high intensity focused ultrasound (HIFU) fields. When shocks are present, the wave spectrum consists of hundreds of harmonics. In practice, shock waves are modeled using a finite number of harmonics and measured with hydrophones that have limited bandwidths. The goal of this work was to determine how many harmonics are necessary to model or measure peak pressures, intensity, and heat deposition rates of the HIFU fields. Numerical solutions of the Khokhlov-Zabolotskaya-Kuznetzov-type (KZK) nonlinear parabolic equation were obtained using two independent algorithms, compared, and analyzed for nonlinear propagation in water, in gel phantom, and in tissue. Measurements were performed in the focus of the HIFU field in the same media using fiber optic probe hydrophones of various bandwidths. Experimental data were compared to the simulation results.

Shock wave structure in a strongly nonlinear lattice with viscous dissipation.

PubMed

Herbold, E B; Nesterenko, V F

2007-02-01

The shock wave structure in a one-dimensional lattice (e.g., granular chain of elastic particles) with a power law dependence of force on displacement between particles (F proportional to delta(n)) with viscous dissipation is considered and compared to the corresponding long wave approximation. A dissipative term depending on the relative velocity between neighboring particles is included to investigate its influence on the shape of a steady shock. The critical viscosity coefficient p(c), defining the transition from an oscillatory to a monotonic shock profile in strongly nonlinear systems, is obtained from the long-wave approximation for arbitrary values of the exponent n. The expression for the critical viscosity is comparable to the value obtained in the numerical analysis of a discrete system with a Hertzian contact interaction (n=3/2) . The expression for p(c) in the weakly nonlinear case converges to the known equation for the critical viscosity. An initial disturbance in a discrete system approaches a stationary shock profile after traveling a short distance that is comparable to the width of the leading pulse of a stationary shock front. The shock front width is minimized when the viscosity is equal to its critical value.

Experimental Observation of Dark Solitons on Water Surface

DTIC Science & Technology

2016-06-13

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

Avalanches, breathers, and flow reversal in a continuous Lorenz-96 model

NASA Astrophysics Data System (ADS)

Blender, R.; Wouters, J.; Lucarini, V.

2013-07-01

For the discrete model suggested by Lorenz in 1996, a one-dimensional long-wave approximation with nonlinear excitation and diffusion is derived. The model is energy conserving but non-Hamiltonian. In a low-order truncation, weak external forcing of the zonal mean flow induces avalanchelike breather solutions which cause reversal of the mean flow by a wave-mean flow interaction. The mechanism is an outburst-recharge process similar to avalanches in a sandpile model.

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

The laboratory investigation of surface envelope solitons: reflection from a vertical wall and collisions of solitons

NASA Astrophysics Data System (ADS)

Slunyaev, Alexey; Klein, Marco; Clauss, Günther F.

2016-04-01

Envelope soliton solutions are key elements governing the nonlinear wave dynamics within a simplified theory for unidirectional weakly modulated weakly nonlinear wave groups on the water surface. Within integrable models the solitons preserve their structure in collisions with other waves; they do not disperse and can carry energy infinitively long. Steep and short soliton-like wave groups have been shown to exist in laboratory tests [1] and, even earlier, in numerical simulations [2, 3]. Thus, long-living wave groups may play important role in the dynamics of intense sea waves and wave-structure interactions. The solitary wave groups may change the wave statistics and can be taken into account when developing approaches for the deterministic forecasting of dangerous waves, including so-called rogue waves. An experimental campaign has been conducted in the wave basin of the Technical University of Berlin on simulations of intense solitary wave groups. The first successful experimental observation of intense envelope solitons took place in this facility [1]. The new experiments aimed at following main goals: 1) to reproduce intense envelope solitons with different carrier wave lengths; 2) to estimate the rate of envelope soliton dissipation; 3) to consider the reflection of envelope solitons on a vertical wall; 4) to consider head-on collisions of envelope solitons, and 5) to consider overtaking interactions of envelope solitons. Up to 9 wave gauges were used in each experimental run, which enabled registration of the surface movement at different distances from the wavemaker, at different locations across the wave flume and near the wall. Besides surface displacements, the group envelope shapes were directly recorded, with use of phase shifts applied to the modulated waves generated by the wavemaker. [1] A. Slunyaev, G.F. Clauss, M. Klein, M. Onorato, Simulations and experiments of short intense envelope solitons of surface water waves. Phys. Fluids 25, 067105 (2013). [2] A.I. Dyachenko, V.E. Zakharov, On the formation of freak waves on the surface of deep water. JETP Lett. 88, 307 (2008). [3] A.V. Slunyaev, Numerical simulation of "limiting" envelope solitons of gravity waves on deep water. JETP 109, 676 (2009).

Wave propagation in a strongly nonlinear locally resonant granular crystal

NASA Astrophysics Data System (ADS)

Vorotnikov, K.; Starosvetsky, Y.; Theocharis, G.; Kevrekidis, P. G.

2018-02-01

In this work, we study the wave propagation in a recently proposed acoustic structure, the locally resonant granular crystal. This structure is composed of a one-dimensional granular crystal of hollow spherical particles in contact, containing linear resonators. The relevant model is presented and examined through a combination of analytical approximations (based on ODE and nonlinear map analysis) and of numerical results. The generic dynamics of the system involves a degradation of the well-known traveling pulse of the standard Hertzian chain of elastic beads. Nevertheless, the present system is richer, in that as the primary pulse decays, secondary ones emerge and eventually interfere with it creating modulated wavetrains. Remarkably, upon suitable choices of parameters, this interference "distills" a weakly nonlocal solitary wave (a "nanopteron"). This motivates the consideration of such nonlinear structures through a separate Fourier space technique, whose results suggest the existence of such entities not only with a single-side tail, but also with periodic tails on both ends. These tails are found to oscillate with the intrinsic oscillation frequency of the out-of-phase motion between the outer hollow bead and its internal linear attachment.

Linear and nonlinear ion-acoustic waves in nonrelativistic quantum plasmas with arbitrary degeneracy.

PubMed

Haas, Fernando; Mahmood, Shahzad

2015-11-01

Linear and nonlinear ion-acoustic waves are studied in a fluid model for nonrelativistic, unmagnetized quantum plasma with electrons with an arbitrary degeneracy degree. The equation of state for electrons follows from a local Fermi-Dirac distribution function and applies equally well both to fully degenerate and classical, nondegenerate limits. Ions are assumed to be cold. Quantum diffraction effects through the Bohm potential are also taken into account. A general coupling parameter valid for dilute and dense plasmas is proposed. The linear dispersion relation of the ion-acoustic waves is obtained and the ion-acoustic speed is discussed for the limiting cases of extremely dense or dilute systems. In the long-wavelength limit, the results agree with quantum kinetic theory. Using the reductive perturbation method, the appropriate Korteweg-de Vries equation for weakly nonlinear solutions is obtained and the corresponding soliton propagation is analyzed. It is found that soliton hump and dip structures are formed depending on the value of the quantum parameter for the degenerate electrons, which affect the phase velocities in the dispersive medium.

Linear and nonlinear ion-acoustic waves in nonrelativistic quantum plasmas with arbitrary degeneracy

NASA Astrophysics Data System (ADS)

Haas, Fernando; Mahmood, Shahzad

2015-11-01

Linear and nonlinear ion-acoustic waves are studied in a fluid model for nonrelativistic, unmagnetized quantum plasma with electrons with an arbitrary degeneracy degree. The equation of state for electrons follows from a local Fermi-Dirac distribution function and applies equally well both to fully degenerate and classical, nondegenerate limits. Ions are assumed to be cold. Quantum diffraction effects through the Bohm potential are also taken into account. A general coupling parameter valid for dilute and dense plasmas is proposed. The linear dispersion relation of the ion-acoustic waves is obtained and the ion-acoustic speed is discussed for the limiting cases of extremely dense or dilute systems. In the long-wavelength limit, the results agree with quantum kinetic theory. Using the reductive perturbation method, the appropriate Korteweg-de Vries equation for weakly nonlinear solutions is obtained and the corresponding soliton propagation is analyzed. It is found that soliton hump and dip structures are formed depending on the value of the quantum parameter for the degenerate electrons, which affect the phase velocities in the dispersive medium.

Dispersive shock waves in systems with nonlocal dispersion of Benjamin-Ono type

NASA Astrophysics Data System (ADS)

El, G. A.; Nguyen, L. T. K.; Smyth, N. F.

2018-04-01

We develop a general approach to the description of dispersive shock waves (DSWs) for a class of nonlinear wave equations with a nonlocal Benjamin-Ono type dispersion term involving the Hilbert transform. Integrability of the governing equation is not a pre-requisite for the application of this method which represents a modification of the DSW fitting method previously developed for dispersive-hydrodynamic systems of Korteweg-de Vries (KdV) type (i.e. reducible to the KdV equation in the weakly nonlinear, long wave, unidirectional approximation). The developed method is applied to the Calogero-Sutherland dispersive hydrodynamics for which the classification of all solution types arising from the Riemann step problem is constructed and the key physical parameters (DSW edge speeds, lead soliton amplitude, intermediate shelf level) of all but one solution type are obtained in terms of the initial step data. The analytical results are shown to be in excellent agreement with results of direct numerical simulations.

Modulational instability and higher-order rogue waves with parameters modulation in a coupled integrable AB system via the generalized Darboux transformation.

PubMed

Wen, Xiao-Yong; Yan, Zhenya

2015-12-01

We study higher-order rogue wave (RW) solutions of the coupled integrable dispersive AB system (also called Pedlosky system), which describes the evolution of wave-packets in a marginally stable or unstable baroclinic shear flow in geophysical fluids. We propose its continuous-wave (CW) solutions and existent conditions for their modulation instability to form the rogue waves. A new generalized N-fold Darboux transformation (DT) is proposed in terms of the Taylor series expansion for the spectral parameter in the Darboux matrix and its limit procedure and applied to the CW solutions to generate multi-rogue wave solutions of the coupled AB system, which satisfy the general compatibility condition. The dynamical behaviors of these higher-order rogue wave solutions demonstrate both strong and weak interactions by modulating parameters, in which some weak interactions can generate the abundant triangle, pentagon structures, etc. Particularly, the trajectories of motion of peaks and depressions of profiles of the first-order RWs are explicitly analyzed. The generalized DT method used in this paper can be extended to other nonlinear integrable systems. These results may be useful for understanding the corresponding rogue-wave phenomena in fluid mechanics and related fields.

Trapping of high-energy electrons into regime of surfatron acceleration by electromagnetic waves in space plasma

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

Erokhin, A. N.; Erokhin, N. S.; Milant'ev, V. P.

2012-05-15

The phenomenon of trapping of weakly relativistic charged particles (with kinetic energies on the order of mc{sup 2}) into a regime of surfatron acceleration by an electromagnetic wave that propagates in plasma across a weak external magnetic field has been studied using nonlinear numerical calculations based on a solution of the relativistic equations of motion. Analysis showed that, for the wave amplitude above a certain threshold value and the initial wave phase outside the interval favorable for the surfing regime, the trajectory of a charged particle initially corresponds to its cyclotron rotation in the external magnetic field. For the initialmore » particle energies studied, the period of this rotation is relatively short. After a certain number (from several dozen to several thousand and above) of periods of rotation, the wave phase takes a value that is favorable for trapping of the charged particle on its trajectory by the electromagnetic wave, provided the Cherenkov resonance conditions are satisfied. As a result, the wave traps the charged particle and imparts it an ultrarelativistic acceleration. In momentum space, the region of trapping into the regime of surfing on an electromagnetic wave turns out to be rather large.« less

Nonlinear optics of fibre event horizons.

PubMed

Webb, Karen E; Erkintalo, Miro; Xu, Yiqing; Broderick, Neil G R; Dudley, John M; Genty, Goëry; Murdoch, Stuart G

2014-09-17

The nonlinear interaction of light in an optical fibre can mimic the physics at an event horizon. This analogue arises when a weak probe wave is unable to pass through an intense soliton, despite propagating at a different velocity. To date, these dynamics have been described in the time domain in terms of a soliton-induced refractive index barrier that modifies the velocity of the probe. Here we complete the physical description of fibre-optic event horizons by presenting a full frequency-domain description in terms of cascaded four-wave mixing between discrete single-frequency fields, and experimentally demonstrate signature frequency shifts using continuous wave lasers. Our description is confirmed by the remarkable agreement with experiments performed in the continuum limit, reached using ultrafast lasers. We anticipate that clarifying the description of fibre event horizons will significantly impact on the description of horizon dynamics and soliton interactions in photonics and other systems.

Reduction of LDI threshold by electron trapping

NASA Astrophysics Data System (ADS)

Rose, Harvey A.; Russell, David

2000-10-01

The effect of trapped electrons on the Langmuir wave decay instability (LDI), considered as a secondary instability to SRS, is twofold. First, for a given level of SRS, the Langmuir wave (LW) response, LW_0, may increase compared to that predicted by the linearized Vlasov equation because of electrons trapped by LW_0, and second, given LW_0, the threshold for LDI is lowered^* by electrons trapped in the LDI daughter wave, LW_1. When kλ D for LW0 is large, say greater than 0.30, then its harmonics, and those of LW_1, are very weakly excited and a complete catalog of nonlinear periodic solutions arising from the LDI is possible. Dependence of the nonlinear LDI threshold on kλ D for a CH plasma will be presented. *This possibility has also been discussed by D. Mourenas, Phys. Plasmas 6, 1258 (1999).

Assessing the performance of formulations for nonlinear feedback of surface gravity waves on ocean currents over coastal waters

NASA Astrophysics Data System (ADS)

Wang, Pengcheng; Sheng, Jinyu; Hannah, Charles

2017-08-01

This study presents applications of a two-way coupled wave-circulation modelling system over coastal waters, with a special emphasis of performance assessments of two different methods for nonlinear feedback of ocean surface gravity waves on three-dimensional (3D) ocean currents. These two methods are the vortex force (VF) formulation suggested by Bennis et al. (2011) and the latest version of radiation stress (RS) formulation suggested by Mellor (2015). The coupled modelling system is first applied to two idealized test cases of surf-zone scales to validate implementations of these two methods in the coupled wave-circulation system. Model results show that the latest version of RS has difficulties in producing the undertow over the surf zone. The coupled system is then applied to Lunenburg Bay (LB) of Nova Scotia during Hurricane Juan in 2003. The coupled system using both the VF and RS formulations generates much stronger and more realistic 3D circulation in the Bay during Hurricane Juan than the circulation-only model, demonstrating the importance of surface wave forces to the 3D ocean circulation over coastal waters. However, the RS formulation generates some weak unphysical currents outside the wave breaking zone due to a less reasonable representation for the vertical distribution of the RS gradients over a slopping bottom. These weak unphysical currents are significantly magnified in a two-way coupled system when interacting with large surface waves, degrading the model performance in simulating currents at one observation site. Our results demonstrate that the VF formulation with an appropriate parameterization of wave breaking effects is able to produce reasonable results for applications over coastal waters during extreme weather events. The RS formulation requires a complex wave theory rather than the linear wave theory for the approximation of a vertical RS term to improve its performance under both breaking and non-breaking wave conditions.

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

NASA Astrophysics Data System (ADS)

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

2017-10-01

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

The breakdown of the weakly-nonlinear regime for kinetic instabilities

NASA Astrophysics Data System (ADS)

Sanz-Orozco, David; Berk, Herbert; Wang, Ge

2017-10-01

The evolution of marginally-unstable waves that interact resonantly with populations of energetic particles is governed by a well-known cubic integro-differential equation for the mode amplitude. One of the outcomes predicted by the equation is the so-called ``explosive'' regime, where the amplitude grows indefinitely, eventually taking the equation outside of its domain of validity. Beyond this point, only full Vlasov simulations will accurately describe the evolution of the mode amplitude. In this work, we study the breakdown of the cubic equation in detail. We find that, while the cubic equation is still valid, the distribution function of the energetic particles locally flattens or ``folds'' in phase space. This feature is unexpected in view of the assumptions of the theory that are given in. We also derive fifth-order terms in the wave equation, which not only give us a more accurate description of the marginally-unstable modes, but they also allow us to predict the breakdown of the cubic equation. Our findings allow us to better understand the transition between weakly-nonlinear modes and the long-term chirping modes that ultimately emerge.

Characteristics of solitary waves in a relativistic degenerate ion beam driven magneto plasma

NASA Astrophysics Data System (ADS)

Deka, Manoj Kr.; Dev, Apul N.; Misra, Amar P.; Adhikary, Nirab C.

2018-01-01

The nonlinear propagation of a small amplitude ion acoustic solitary wave in a relativistic degenerate magneto plasma in the presence of an ion beam is investigated in detail. The nonlinear equations describing the evolution of a solitary wave in the presence of relativistic non-degenerate magnetized positive ions and ion beams including magnetized degenerate relativistic electrons are derived in terms of Zakharov-Kuznetsov (Z-K) equation for such plasma systems. The ion beams which are a ubiquitous ingredient in such plasma systems are found to have a decisive role in the propagation of a solitary wave in such a highly dense plasma system. The conditions of a wave, propagating with typical solitonic characteristics, are examined and discussed in detail under suitable conditions of different physical parameters. Both a subsonic and supersonic wave can propagate in such plasmas bearing different characteristics under different physical situations. A detailed analysis of waves propagating in subsonic and/or supersonic regime is carried out. The ion beam concentrations, magnetic field, as well as ion beam streaming velocity are found to play a momentous role on the control of the amplitude and width of small amplitude perturbation in both weakly (or non-relativistic) and relativistic plasmas.

Simulations of kinetic electrostatic electron nonlinear (KEEN) waves with variable velocity resolution grids and high-order time-splitting

NASA Astrophysics Data System (ADS)

Afeyan, Bedros; Casas, Fernando; Crouseilles, Nicolas; Dodhy, Adila; Faou, Erwan; Mehrenberger, Michel; Sonnendrücker, Eric

2014-10-01

KEEN waves are non-stationary, nonlinear, self-organized asymptotic states in Vlasov plasmas. They lie outside the precepts of linear theory or perturbative analysis, unlike electron plasma waves or ion acoustic waves. Steady state, nonlinear constructs such as BGK modes also do not apply. The range in velocity that is strongly perturbed by KEEN waves depends on the amplitude and duration of the ponderomotive force generated by two crossing laser beams, for instance, used to drive them. Smaller amplitude drives manage to devolve into multiple highly-localized vorticlets, after the drive is turned off, and may eventually succeed to coalesce into KEEN waves. Fragmentation once the drive stops, and potential eventual remerger, is a hallmark of the weakly driven cases. A fully formed (more strongly driven) KEEN wave has one dominant vortical core. But it also involves fine scale complex dynamics due to shedding and merging of smaller vortical structures with the main one. Shedding and merging of vorticlets are involved in either case, but at different rates and with different relative importance. The narrow velocity range in which one must maintain sufficient resolution in the weakly driven cases, challenges fixed velocity grid numerical schemes. What is needed is the capability of resolving locally in velocity while maintaining a coarse grid outside the highly perturbed region of phase space. We here report on a new Semi-Lagrangian Vlasov-Poisson solver based on conservative non-uniform cubic splines in velocity that tackles this problem head on. An additional feature of our approach is the use of a new high-order time-splitting scheme which allows much longer simulations per computational effort. This is needed for low amplitude runs. There, global coherent structures take a long time to set up, such as KEEN waves, if they do so at all. The new code's performance is compared to uniform grid simulations and the advantages are quantified. The birth pains associated with weakly driven KEEN waves are captured in these simulations. Canonical KEEN waves with ample drive are also treated using these advanced techniques. They will allow the efficient simulation of KEEN waves in multiple dimensions, which will be tackled next, as well as generalizations to Vlasov-Maxwell codes. These are essential for pursuing the impact of KEEN waves in high energy density plasmas and in inertial confinement fusion applications. More generally, one needs a fully-adaptive grid-in-phase-space method which could handle all small vorticlet dynamics whether pealing off or remerging. Such fully adaptive grids would have to be computed sparsely in order to be viable. This two-velocity grid method is a concrete and fruitful step in that direction. Contribution to the Topical Issue "Theory and Applications of the Vlasov Equation", edited by Francesco Pegoraro, Francesco Califano, Giovanni Manfredi and Philip J. Morrison.

Solitary waves in a peridynamic elastic solid

DOE PAGES

Silling, Stewart A.

2016-06-23

The propagation of large amplitude nonlinear waves in a peridynamic solid is ana- lyzed. With an elastic material model that hardens in compression, sufficiently large wave pulses propagate as solitary waves whose velocity can far exceed the linear wave speed. In spite of their large velocity and amplitude, these waves leave the material they pass through with no net change in velocity and stress. They are nondissipative and nondispersive, and they travel unchanged over large distances. An approximate solution for solitary waves is derived that reproduces the main features of these waves observed in computational simulations. We demonstrate, by numericalmore » studies, that waves interact only weakly with each other when they collide. Finally, we found that wavetrains composed of many non-interacting solitary waves form and propagate under certain boundary and initial conditions.« less

Oblique Propagation of Electrostatic Waves in a Magnetized Electron-Positron-Ion Plasma in the Presence of Heavy Particles

NASA Astrophysics Data System (ADS)

Sarker, M.; Hossen, M. R.; Shah, M. G.; Hosen, B.; Mamun, A. A.

2018-06-01

A theoretical investigation is carried out to understand the basic features of nonlinear propagation of heavy ion-acoustic (HIA) waves subjected to an external magnetic field in an electron-positron-ion plasma that consists of cold magnetized positively charged heavy ion fluids and superthermal distributed electrons and positrons. In the nonlinear regime, the Korteweg-de Vries (K-dV) and modified K-dV (mK-dV) equations describing the propagation of HIA waves are derived. The latter admits a solitary wave solution with both positive and negative potentials (for K-dV equation) and only positive potential (for mK-dV equation) in the weak amplitude limit. It is observed that the effects of external magnetic field (obliqueness), superthermal electrons and positrons, different plasma species concentration, heavy ion dynamics, and temperature ratio significantly modify the basic features of HIA solitary waves. The application of the results in a magnetized EPI plasma, which occurs in many astrophysical objects (e.g. pulsars, cluster explosions, and active galactic nuclei) is briefly discussed.

Soliton interactions, Bäcklund transformations, Lax pair for a variable-coefficient generalized dispersive water-wave system

NASA Astrophysics Data System (ADS)

Liu, Lei; Tian, Bo; Zhen, Hui-Ling; Liu, De-Yin; Xie, Xi-Yang

2018-04-01

Under investigation in this paper is a variable-coefficient generalized dispersive water-wave system, which can simulate the propagation of the long weakly non-linear and weakly dispersive surface waves of variable depth in the shallow water. Under certain variable-coefficient constraints, by virtue of the Bell polynomials, Hirota method and symbolic computation, the bilinear forms, one- and two-soliton solutions are obtained. Bäcklund transformations and new Lax pair are also obtained. Our Lax pair is different from that previously reported. Based on the asymptotic and graphic analysis, with different forms of the variable coefficients, we find that there exist the elastic interactions for u, while either the elastic or inelastic interactions for v, with u and v as the horizontal velocity field and deviation height from the equilibrium position of the water, respectively. When the interactions are inelastic, we see the fission and fusion phenomena.

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

NASA Astrophysics Data System (ADS)

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

2012-01-01

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

Nonlinear reflection of a spherically divergent N-wave from a plane surface: Optical interferometry measurements in air

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

Karzova, M., E-mail: masha@acs366.phys.msu.ru; Physics Faculty, Moscow State University, Leninskie Gory, 119991 Moscow; Yuldashev, P.

2015-10-28

Mach stem is a well-known structure typically observed in the process of strong (acoustic Mach numbers greater than 0.4) step-shock waves reflection from a rigid boundary. However, this phenomenon has been much less studied for weak shocks in nonlinear acoustic fields where Mach numbers are in the range from 0.001 to 0.01 and pressure waveforms have more complicated waveforms than step shocks. The goal of this work was to demonstrate experimentally how nonlinear reflection occurs in air for very weak spherically divergent acoustic spark-generated pulses resembling an N-wave. Measurements of reflection patterns were performed using a Mach-Zehnder interferometer. A thinmore » laser beam with sub-millimeter cross-section was used to obtain the time resolution of 0.4 µs, which is 6 times higher than the time resolution of the condenser microphones. Pressure waveforms were reconstructed using the inverse Abel transform applied to the phase of the signal measured by the interferometer. The Mach stem formation was observed experimentally as a result of collision of the incident and reflected shock pulses. It was shown that irregular reflection of the pulse occurred in a dynamic way and the length of the Mach stem increased linearly while the pulse propagated along the surface. Since the front shock of the spark-generated pulse was steeper than the rear shock, irregular type of reflection was observed only for the front shock of the pulse while the rear shock reflection occurred in a regular regime.« less

Design of a LiNbO(3) ribbon waveguide for efficient difference-frequency generation of terahertz wave in the collinear configuration.

PubMed

Takushima, Y; Shin, S Y; Chung, Y C

2007-10-29

We propose and investigate a ribbon waveguide for difference-frequency generation of terahertz (THz) wave from infrared light sources. The proposed ribbon waveguide is composed of a nonlinear optic crystal and has a thickness less than the wavelength of the THz wave to support the surface-wave mode in the THz region. By utilizing the waveguide dispersion of the surface-wave mode, the phase matching condition between infrared pump, idler and THz waves can be realized in the collinear configuration. Owing to the weak mode confinement of the THz wave, the absorption coefficient can also be reduced. We design the ribbon waveguide which uses LiNbO(3) crystal and discuss the phase-matching condition for DFG of THz wave. Highly efficient THz-wave generation is confirmed by numerical simulations.

Dispersive shock waves in Bose-Einstein condensates and nonlinear nano-oscillators in ferromagnetic thin films

NASA Astrophysics Data System (ADS)

Hoefer, Mark A.

This thesis examines nonlinear wave phenomena, in two physical systems: a Bose-Einstein condensate (BEC) and thin film ferromagnets where the magnetization dynamics are excited by the spin momentum transfer (SMT) effect. In the first system, shock waves generated by steep gradients in the BEC wavefunction are shown to be of the disperse type. Asymptotic and averaging methods are used to determine shock speeds and structure in one spatial dimension. These results are compared with multidimensional numerical simulations and experiment showing good, qualitative agreement. In the second system, a model of magnetization dynamics due to SMT is presented. Using this model, nonlinear oscillating modes---nano-oscillators---are found numerically and analytically using perturbative methods. These results compare well with experiment. A Bose-Einstein condensate (BEC) is a quantum fluid that gives rise to interesting shock wave nonlinear dynamics. Experiments depict a BEC that exhibits behavior similar to that of a shock wave in a compressible gas, e.g. traveling fronts with steep gradients. However, the governing Gross-Pitaevskii (GP) equation that describes the mean field of a BEC admits no dissipation hence classical dissipative shock solutions do not explain the phenomena. Instead, wave dynamics with small dispersion is considered and it is shown that this provides a mechanism for the generation of a dispersive shock wave (DSW). Computations with the GP equation are compared to experiment with excellent agreement. A comparison between a canonical 1D dissipative and dispersive shock problem shows significant differences in shock structure and shock front speed. Numerical results associated with laboratory experiments show that three and two-dimensional approximations are in excellent agreement and one dimensional approximations are in qualitative agreement. The interaction of two DSWs is investigated analytically and numerically. Using one dimensional DSW theory it is argued that the experimentally observed blast waves may be viewed as dispersive shock waves. A nonlinear mathematical model of spin-wave excitation using a point contact in a thin ferromagnetic film is introduced. This work incorporates a recently proposed spin-torque contribution to classical magnetodynamic theory with a variable coefficient terra in the magnetic torque equation. Large-amplitude magnetic solitary waves are computed, which help explain recent spin-torque experiments. Numerical simulations of the full nonlinear model predict excitation frequencies in excess of 0.2 THz for contact diameters smaller than 6 nm. Simulations also predict a saturation and red shift of the frequency at currents large enough to invert the magnetization tinder the point contact. In the weak nonlinear limit, the theory is approximated by a cubic complex Ginzburg-Landau type equation. The mode's nonlinear frequency shift is found by use of perturbation techniques, whose results agree with those of direct numerical simulations.

Non-linear analysis of wave progagation using transform methods and plates and shells using integral equations

NASA Astrophysics Data System (ADS)

Pipkins, Daniel Scott

Two diverse topics of relevance in modern computational mechanics are treated. The first involves the modeling of linear and non-linear wave propagation in flexible, lattice structures. The technique used combines the Laplace Transform with the Finite Element Method (FEM). The procedure is to transform the governing differential equations and boundary conditions into the transform domain where the FEM formulation is carried out. For linear problems, the transformed differential equations can be solved exactly, hence the method is exact. As a result, each member of the lattice structure is modeled using only one element. In the non-linear problem, the method is no longer exact. The approximation introduced is a spatial discretization of the transformed non-linear terms. The non-linear terms are represented in the transform domain by making use of the complex convolution theorem. A weak formulation of the resulting transformed non-linear equations yields a set of element level matrix equations. The trial and test functions used in the weak formulation correspond to the exact solution of the linear part of the transformed governing differential equation. Numerical results are presented for both linear and non-linear systems. The linear systems modeled are longitudinal and torsional rods and Bernoulli-Euler and Timoshenko beams. For non-linear systems, a viscoelastic rod and Von Karman type beam are modeled. The second topic is the analysis of plates and shallow shells under-going finite deflections by the Field/Boundary Element Method. Numerical results are presented for two plate problems. The first is the bifurcation problem associated with a square plate having free boundaries which is loaded by four, self equilibrating corner forces. The results are compared to two existing numerical solutions of the problem which differ substantially.

Layer contributions to the nonlinear acoustic radiation from stratified media.

PubMed

Vander Meulen, François; Haumesser, Lionel

2016-12-01

This study presents the thorough investigation of the second harmonic generation scenario in a three fluid layer system. An emphasis is on the evaluation of the nonlinear parameter B/A in each layer from remote measurements. A theoretical approach of the propagation of a finite amplitude acoustic wave in a multilayered medium is developed. In the frame of the KZK equation, the weak nonlinearity of the media, attenuation and diffraction effects are computed for the fundamental and second harmonic waves propagating back and forth in each of the layers of the system. The model uses a gaussian expansion to describe the beam propagation in order to quantitatively evaluate the contribution of each part of the system (layers and interfaces) to its nonlinearity. The model is validated through measurements on a water/aluminum/water system. Transmission as well as reflection configurations are studied. Good agreement is found between the theoretical results and the experimental data. The analysis of the second harmonic field sources measured by the transducers from outside the stratified medium highlights the factors that favor the cumulative effects. Copyright © 2016 Elsevier B.V. All rights reserved.

Experimental observations of nonlinearly enhanced 2omega-UH electromagnetic radiation excited by steady-state colliding electron beams

NASA Technical Reports Server (NTRS)

Intrator, T.; Hershkowitz, N.; Chan, C.

1984-01-01

Counterstreaming large-diameter electron beams in a steady-state laboratory experiment are observed to generate transverse radiation at twice the upper-hybrid frequency (2omega-UH) with a quadrupole radiation pattern. The electromagnetic wave power density is nonlinearly enhanced over the power density obtained from a single beam-plasma system. Electromagnetic power density scales exponentially with beam energy and increases with ion mass. Weak turbulence theory can predict similar (but weaker) beam energy scaling but not the high power density, or the predominance of the 2omega-UH radiation peak over the omega-UH peak. Significant noise near the upper-hybrid and ion plasma frequencies is also measured, with normalized electrostatic wave energy density W(ES)/n(e)T(e) approximately 0.01.

Simulations of neutral wind shear effect on the equatorial ionosphere irregularities

NASA Astrophysics Data System (ADS)

Kim, J.; Chagelishvili, G.; Horton, W.

2005-12-01

We present numerical calculations of the large-scale electron density driven by the gradient drift instability in the daytime equatorial electrojet. Under two-fluid theory the linear analysis for kilometer scale waves lead to the result that all the perturbations are transformed to small scales through linear convection by shear and then damped by diffusion. The inclusion of the nonlinearity enables inverse energy cascade to provide energy to long scale. The feedback between velocity shear and nonlinearity keeps waves growing and leads to the turbulence. In strongly turbulent regime, the nonlinear states are saturated [1]. Since the convective nonlinearities are isotropic while the interactions of velocity shear with waves are anisotropic, the feedback do not necessarily enable waves to grow. The growth of waves are highly variable on k-space configuration [2]. Our simulations show that the directional relationship between vorticity of irregularities and shear are one of key factors. Thus during the transient period, the irregularities show the anisotropy of the vorticity power spectrum. We report the evolution of the power spectrum of the vorticity and density of irregularties and its anistropic nature as observed. The work was supported in part by the Department of NSF Grant ATM-0229863 and ISTC Grant G-553. C. Ronchi, R.N. Sudan, and D.T. Farley. Numerical simulations of large-scale plasma turbulece in teh day time equatorial electrojet. J. Geophys. Res., 96:21263--21279, 1991. G.D. Chagelishvili, R.G. Chanishvili, T.S. Hristov, and J.G. Lominadze. A turbulence model in unbounded smooth shear flows : The weak turbulence approach. JETP, 94(2):434--445, 2002.

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.

Noncollinear wave mixing of attosecond XUV and few-cycle optical laser pulses in gas-phase atoms: Toward multidimensional spectroscopy involving XUV excitations

NASA Astrophysics Data System (ADS)

Cao, Wei; Warrick, Erika R.; Fidler, Ashley; Neumark, Daniel M.; Leone, Stephen R.

2016-11-01

Ultrafast nonlinear spectroscopy, which records transient wave-mixing signals in a medium, is a powerful tool to access microscopic information using light sources in the radio-frequency and optical regimes. The extension of this technique towards the extreme ultraviolet (XUV) or even x-ray regimes holds the promise to uncover rich structural or dynamical information with even higher spatial or temporal resolution. Here, we demonstrate noncollinear wave mixing between weak XUV attosecond pulses and a strong near-infrared (NIR) few-cycle laser pulse in gas phase atoms (one photon of XUV and two photons of NIR). In the noncollinear geometry the attosecond and either one or two NIR pulses interact with argon atoms. Nonlinear XUV signals are generated in a spatially resolved fashion as required by phase matching. Different transition pathways can be identified from these background-free nonlinear signals according to the specific phase-matching conditions. Time-resolved measurements of the spatially gated XUV signals reveal electronic coherences of Rydberg wave packets prepared by a single XUV photon or XUV-NIR two-photon excitation, depending on the applied pulse sequences. These measurements open possible applications of tabletop multidimensional spectroscopy to the study of dynamics associated with valence or core excitation with XUV photons.

Microwave phase conjugation using artificial nonlinear microwave surfaces

NASA Astrophysics Data System (ADS)

Chang, Yian

1997-09-01

A new technique is developed and demonstrated to simulate nonlinear materials in the microwave and millimeter wave regime. Such materials are required to extend nonlinear optical techniques into longer wavelength areas. Using an array of antenna coupled mixers as an artificial nonlinear surface, we have demonstrated two-dimensional free space microwave phase conjugation at 10 GHz. The basic concept is to replace the weak nonlinearity of electron distribution in a crystal with the strong nonlinear V-I response of a P-N junction. This demnstration uses a three-wave mixing method with the effective nonlinear susceptibility χ(2) provided by an artificial nonlinear surface. The pump signal at 2ω (20 GHz) can be injected to the mixing elements electrically or optically. Electrical injection was first used to prove the concept of artificial nonlinear surfaces. However, due to the loss and size of microwave components, electrical injection is not practical for an array of artificial nonlinear surfaces, as would be needed in a three-dimensional free space phase conjugation setup. Therefore optical injection was implemented to carry the 2ω microwave pump signal in phase to all mixing elements. In both cases, two-dimensional free space phase conjugation was observed by directly measuring the electric field amplitude and phase distribution. The electric field wavefronts exhibited retro-directivity and auto- correction characteristics of phase conjugation. This demonstration surface also shows a power gain of 10 dB, which is desired for potential communication applications.

Studies of large amplitude Alfvén waves and wave-wave interactions in LAPD

NASA Astrophysics Data System (ADS)

Carter, T. A.; Brugman, B.; Auerbach, D. W.

2006-10-01

Electromagnetic turbulence is thought to play an important role in plasmas in astrophysical settings (e.g. the interstellar medium, accretion disks) and in the laboratory (e.g. transport in magnetic fusion devices). From a weak turbulence point of view, nonlinear interactions between shear Alfvén waves are fundamental to the turbulent energy cascade in magnetic turbulence. An overview of experiments on large amplitude shear Alfvén waves in the Large Plasma Device (LAPD) will be presented. Large amplitude Alfvén waves (δB/B ˜1%) are generated either using a resonant cavity or loop antennas. Properties of Alfvén waves generated by these sources will be discussed, along with evidence of heating, background density modification and electron acceleration by the waves. An overview of experiments on wave-wave interactions will be given along with a discussion of future directions.

Nonlinear and dissipative constitutive equations for coupled first-order acoustic field equations that are consistent with the generalized Westervelt equation

NASA Astrophysics Data System (ADS)

Verweij, Martin D.; Huijssen, Jacob

2006-05-01

In diagnostic medical ultrasound, it has become increasingly important to evaluate the nonlinear field of an acoustic beam that propagates in a weakly nonlinear, dissipative medium and that is steered off-axis up to very wide angles. In this case, computations cannot be based on the widely used KZK equation since it applies only to small angles. To benefit from successful computational schemes from elastodynamics and electromagnetics, we propose to use two first-order acoustic field equations, accompanied by two constitutive equations, as an alternative basis. This formulation quite naturally results in the contrast source formalism, makes a clear distinction between fundamental conservation laws and medium behavior, and allows for a straightforward inclusion of any medium inhomogenities. This paper is concerned with the derivation of relevant constitutive equations. We take a pragmatic approach and aim to find those constitutive equations that represent the same medium as implicitly described by the recognized, full wave, nonlinear equations such as the generalized Westervelt equation. We will show how this is achieved by considering the nonlinear case without attenuation, the linear case with attenuation, and the nonlinear case with attenuation. As a result we will obtain surprisingly simple constitutive equations for the full wave case.

Seismic waves in a self-gravitating planet

NASA Astrophysics Data System (ADS)

Brazda, Katharina; de Hoop, Maarten V.; Hörmann, Günther

2013-04-01

The elastic-gravitational equations describe the propagation of seismic waves including the effect of self-gravitation. We rigorously derive and analyze this system of partial differential equations and boundary conditions for a general, uniformly rotating, elastic, but aspherical, inhomogeneous, and anisotropic, fluid-solid earth model, under minimal assumptions concerning the smoothness of material parameters and geometry. For this purpose we first establish a consistent mathematical formulation of the low regularity planetary model within the framework of nonlinear continuum mechanics. Using calculus of variations in a Sobolev space setting, we then show how the weak form of the linearized elastic-gravitational equations directly arises from Hamilton's principle of stationary action. Finally we prove existence and uniqueness of weak solutions by the method of energy estimates and discuss additional regularity properties.

Spatiotemporal Stochastic Resonance:Theory and Experiment

NASA Astrophysics Data System (ADS)

Peter, Jung

1996-03-01

The amplification of weak periodic signals in bistable or excitable systems via stochastic resonance has been studied intensively over the last years. We are going one step further and ask: Can noise enhance spatiotemporal patterns in excitable media and can this effect be observed in nature? To this end, we are looking at large, two dimensional arrays of coupled excitable elements. Due to the coupling, excitation can propagate through the array in form of nonlinear waves. We observe target waves, rotating spiral waves and other wave forms. If the coupling between the elements is below a critical threshold, any excitational pattern will die out in the absence of noise. Below this threshold, large scale rotating spiral waves - as they are observed above threshold - can be maintained by a proper level of the noise[1]. Furthermore, their geometric features, such as the curvature can be controlled by the homogeneous noise level[2]. If the noise level is too large, break up of spiral waves and collisions with spontaneously nucleated waves yields spiral turbulence. Driving our array with a spatiotemporal pattern, e.g. a rotating spiral wave, we show that for weak coupling the excitational response of the array shows stochastic resonance - an effect we have termed spatiotemporal stochastic resonance. In the last part of the talk I'll make contact with calcium waves, observed in astrocyte cultures and hippocampus slices[3]. A. Cornell-Bell and collaborators[3] have pointed out the role of calcium waves for long-range glial signaling. We demonstrate the similarity of calcium waves with nonlinear waves in noisy excitable media. The noise level in the tissue is characterized by spontaneous activity and can be controlled by applying neuro-transmitter substances[3]. Noise effects in our model are compared with the effect of neuro-transmitters on calcium waves. [1]P. Jung and G. Mayer-Kress, CHAOS 5, 458 (1995). [2]P. Jung and G. Mayer-Kress, Phys. Rev. Lett.62, 2682 (1995). [3] A. Cornell-Bell, Steven M. Finkbeiner, Mark.S. Cooper and Stephen J. Smith, SCIENCE, 247, 373 (1990).

Internal Gravity Waves Forced by an Isolated Mountain

NASA Astrophysics Data System (ADS)

Nikitina, L.; Campbell, L.

2009-12-01

Density-stratified fluid flow over topography such as mountains, hills and ridges may give rise to internal gravity waves which transport and distribute energy away from their source and have profound effects on the general circulation of the atmosphere and ocean. Much of our knowledge of internal gravity wave dynamics has been acquired from theoretical studies involving mathematical analyses of simplified forms of the governing equations, as well as numerical simulations at varying levels of approximation. In this study, both analytical and numerical methods are used to examine the nonlinear dynamics of gravity waves forced by an isolated mountain. The topography is represented by a lower boundary condition on a two-dimensional rectangular domain and the waves are represented as a perturbation to the background shear flow, thus allowing the use of weakly-nonlinear and multiple-scale asymptotic analyzes. The waves take the form of a packet, localized in the horizontal direction and comprising a continuous spectrum of horizontal wavenumbers centered at zero. For horizontally-localized wave packets, such as those forced by a mountain range with multiple peaks, there are generally two horizontal scales, the fast (short) scale which is defined by the oscillations within the packet and the slow (large) scale which is defined by the horizontal extent of the packet. In the case of an isolated mountain that we examine here, the multiple-scaling procedure is simplified by the absence of a fast spatial scale. The problem is governed by two small parameters that define the height and width of the mountain and approximate solutions are derived in terms of these parameters. Numerical solutions are also carried out to simulate nonlinear critical-level interactions such as the transfer of energy to the background flow by the wave packet, wave reflection and static instability and, eventually, wave breaking leading to turbulence. It is found that for waves forced by an isolated mountain the time frame within which these nonlinear effects become significant depends on both the mountain height and width and that they begin to occur at least an order of magnitude later and the configuration thus remains stable longer than in the case of waves forced by a mountain range of equivalent height.

Interesting features of nonlinear shock equations in dissipative pair-ion-electron plasmas

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

Masood, W.; National Centre for Physics; Rizvi, H.

2011-09-15

Two dimensional nonlinear electrostatic waves are studied in unmagnetized, dissipative pair-ion-electron plasmas in the presence of weak transverse perturbation. The dissipation in the system is taken into account by incorporating the kinematic viscosity of both positive and negative ions. In the linear case, a biquadratic dispersion relation is obtained, which yields the fast and slow modes in a pair-ion-electron plasma. It is shown that the limiting cases of electron-ion and pair-ion can be retrieved from the general biquadratic dispersion relation, and the differences in the characters of the waves propagating in both the cases are also highlighted. Using the smallmore » amplitude approximation method, the nonlinear Kadomtsev Petviashvili Burgers as well as Burgers-Kadomtsev Petviashvili equations are derived and their applicability for pair-ion-electron plasma is explained in detail. The present study may have relevance to understand the formation of two dimensional electrostatic shocks in laboratory produced pair-ion-electron plasmas.« less

On the coupled evolution of oceanic internal waves and quasi-geostrophic flow

NASA Astrophysics Data System (ADS)

Wagner, Gregory LeClaire

Oceanic motion outside thin boundary layers is primarily a mixture of quasi-geostrophic flow and internal waves with either near-inertial frequencies or the frequency of the semidiurnal lunar tide. This dissertation seeks a deeper understanding of waves and flow through reduced models that isolate their nonlinear and coupled evolution from the Boussinesq equations. Three physical-space models are developed: an equation that describes quasi-geostrophic evolution in an arbitrary and prescribed field of hydrostatic internal waves; a three-component model that couples quasi-geostrophic flow to both near-inertial waves and the near-inertial second harmonic; and a model for the slow evolution of hydrostatic internal tides in quasi-geostrophic flow of near-arbitrary scale. This slow internal tide equation opens the path to a coupled model for the energetic interaction of quasi-geostrophic flow and oceanic internal tides. Four results emerge. First, the wave-averaged quasi-geostrophic equation reveals that finite-amplitude waves give rise to a mean flow that advects quasi-geostrophic potential vorticity. Second is the definition of a new material invariant: Available Potential Vorticity, or APV. APV isolates the part of Ertel potential vorticity available for balanced-flow evolution in Eulerian frames and proves necessary in the separating waves and quasi-geostrophic flow. The third result, hashed out for near-inertial waves and quasi-geostrophic flow, is that wave-flow interaction leads to energy exchange even under conditions of weak nonlinearity. For storm-forced oceanic near-inertial waves the interaction often energizes waves at the expense of flow. We call this extraction of balanced quasi-geostrophic energy 'stimulated generation' since it requires externally-forced rather than spontaneously-generated waves. The fourth result is that quasi-geostrophic flow can encourage or 'catalyze' a nonlinear interaction between a near-inertial wave field and its second harmonic that transfers energy to the small near-inertial vertical scales of wave breaking and mixing.

Three-wave and four-wave interactions in gravity wave turbulence

NASA Astrophysics Data System (ADS)

Aubourg, Quentin; Campagne, Antoine; Peureux, Charles; Ardhuin, Fabrice; Sommeria, Joel; Viboud, Samuel; Mordant, Nicolas

2017-11-01

Weak-turbulence theory is a statistical framework to describe a large ensemble of nonlinearly interacting waves. The archetypal example of such system is the ocean surface that is made of interacting surface gravity waves. Here we describe a laboratory experiment dedicated to probe the statistical properties of turbulent gravity waves. We set up an isotropic state of interacting gravity waves in the Coriolis facility (13-m-diam circular wave tank) by exciting waves at 1 Hz by wedge wave makers. We implement a stereoscopic technique to obtain a measurement of the surface elevation that is resolved in both space and time. Fourier analysis shows that the laboratory spectra are systematically steeper than the theoretical predictions and the field observations in the Black Sea by Leckler et al. [F. Leckler et al., J. Phys. Oceanogr. 45, 2484 (2015), 10.1175/JPO-D-14-0237.1]. We identify a strong impact of surface dissipation on the scaling of the Fourier spectrum at the scales that are accessible in the experiments. We use bicoherence and tricoherence statistical tools in frequency and/or wave-vector space to identify the active nonlinear coupling. These analyses are also performed on the field data by Leckler et al. for comparison with the laboratory data. Three-wave coupling is characterized by and shown to involve mostly quasiresonances of waves with second- or higher-order harmonics. Four-wave coupling is not observed in the laboratory but is evidenced in the field data. We discuss temporal scale separation to explain our observations.

Electromagnetic radiation by parametric decay of upper hybrid waves in ionospheric modification experiments

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

Leyser, T.B.

1994-06-01

A nonlinear dispersion relation for the parametric decay of an electrostatic upper hybrid wave into an ordinary mode electromagnetic wave, propagating parallel to the ambient magnetic field, and an electrostatic low frequency wave, being either a lower hybrid wave or a high harmonic ion Bernstein wave, is derived. The coherent and resonant wave interaction is considered to take place in a weakly magnetized and collisionless Vlasov plasma. The instability growth rate is computed for parameter values typical of ionospheric modification experiments, in which a powerful high frequency electromagnetic pump wave is injected into the ionospheric F-region from ground-based transmitters. Themore » electromagnetic radiation which is excited by the decaying upper hybrid wave is found to be consistent with the prominent and commonly observed downshifted maximum (DM) emission in the spectrum of stimulated electromagnetic emission.« less

Gravitational Waves from Isolated Systems: Surprising Consequences of a Positive Cosmological Constant.

PubMed

Ashtekar, Abhay; Bonga, Béatrice; Kesavan, Aruna

2016-02-05

There is a deep tension between the well-developed theory of gravitational waves from isolated systems and the presence of a positive cosmological constant Λ, however tiny. In particular a generalization of Einstein's 1918 quadrupole formula that would allow a positive Λ is not yet available. We first explain the principal difficulties and then show that it is possible to overcome them in the weak field limit. These results also provide concrete hints for constructing the Λ>0 generalization of the Bondi-Sachs framework for full, nonlinear general relativity.

Gravitational Waves from Isolated Systems: Surprising Consequences of a Positive Cosmological Constant

NASA Astrophysics Data System (ADS)

Ashtekar, Abhay; Bonga, Béatrice; Kesavan, Aruna

2016-02-01

There is a deep tension between the well-developed theory of gravitational waves from isolated systems and the presence of a positive cosmological constant Λ , however tiny. In particular a generalization of Einstein's 1918 quadrupole formula that would allow a positive Λ is not yet available. We first explain the principal difficulties and then show that it is possible to overcome them in the weak field limit. These results also provide concrete hints for constructing the Λ >0 generalization of the Bondi-Sachs framework for full, nonlinear general relativity.

Multi-soliton solutions and Bäcklund transformation for a two-mode KdV equation in a fluid

NASA Astrophysics Data System (ADS)

Xiao, Zi-Jian; Tian, Bo; Zhen, Hui-Ling; Chai, Jun; Wu, Xiao-Yu

2017-01-01

In this paper, we investigate a two-mode Korteweg-de Vries equation, which describes the one-dimensional propagation of shallow water waves with two modes in a weakly nonlinear and dispersive fluid system. With the binary Bell polynomial and an auxiliary variable, bilinear forms, multi-soliton solutions in the two-wave modes and Bell polynomial-type Bäcklund transformation for such an equation are obtained through the symbolic computation. Soliton propagation and collisions between the two solitons are presented. Based on the graphic analysis, it is shown that the increase in s can lead to the increase in the soliton velocities under the condition of ?, but the soliton amplitudes remain unchanged when s changes, where s means the difference between the phase velocities of two-mode waves, ? and ? are the nonlinearity parameter and dispersion parameter respectively. Elastic collisions between the two solitons in both two modes are analyzed with the help of graphic analysis.

Interaction of the sonic boom with atmospheric turbulence

NASA Technical Reports Server (NTRS)

Rusak, Zvi; Cole, Julian D.

1994-01-01

Theoretical research was carried out to study the effect of free-stream turbulence on sonic boom pressure fields. A new transonic small-disturbance model to analyze the interactions of random disturbances with a weak shock was developed. The model equation has an extended form of the classic small-disturbance equation for unsteady transonic aerodynamics. An alternative approach shows that the pressure field may be described by an equation that has an extended form of the classic nonlinear acoustics equation that describes the propagation of sound beams with narrow angular spectrum. The model shows that diffraction effects, nonlinear steepening effects, focusing and caustic effects and random induced vorticity fluctuations interact simultaneously to determine the development of the shock wave in space and time and the pressure field behind it. A finite-difference algorithm to solve the mixed type elliptic-hyperbolic flows around the shock wave was also developed. Numerical calculations of shock wave interactions with various deterministic and random fluctuations will be presented in a future report.

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

PubMed

Akylas, T R; Cho, Yeunwoo

2008-08-13

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

Nonlinear theory for axisymmetric self-similar two-dimensional oscillations of electrons in cold plasma with constant proton background

NASA Astrophysics Data System (ADS)

Osherovich, V. A.; Fainberg, J.

2018-01-01

We consider simultaneous oscillations of electrons moving both along the axis of symmetry and also in the direction perpendicular to the axis. We derive a system of three nonlinear ordinary differential equations which describe self-similar oscillations of cold electrons in a constant proton density background (np = n0 = constant). These three equations represent an exact class of solutions. For weak nonlinear conditions, the frequency spectra of electric field oscillations exhibit split frequency behavior at the Langmuir frequency ωp0 and its harmonics, as well as presence of difference frequencies at low spectral values. For strong nonlinear conditions, the spectra contain peaks at frequencies with values ωp0(n +m √{2 }) , where n and m are integer numbers (positive and negative). We predict that both spectral types (weak and strong) should be observed in plasmas where axial symmetry may exist. To illustrate possible applications of our theory, we present a spectrum of electric field oscillations observed in situ in the solar wind by the WAVES experiment on the Wind spacecraft during the passage of a type III solar radio burst.

Spiral waves in driven dusty plasma medium: Generalized hydrodynamic fluid description

NASA Astrophysics Data System (ADS)

Kumar, Sandeep; Patel, Bhavesh; Das, Amita

2018-04-01

Spiral waves are observed in many natural phenomena. They have been extensively represented by the mathematical FitzHugh-Nagumo model [Barkley et al., Phys. Rev. A 42, 2489 (1990)] of excitable media. Also, in incompressible fluid simulations, the excitation of thermal spiral waves has been reported by Li et al. [Phys. of Fluids 22, 011701 (2010)]. In the present paper, the spatiotemporal development of spiral waves in the context of weak and strong coupling limits has been shown. While the weakly coupled medium has been represented by a simple fluid description, for strong coupling, a generalized visco-elastic fluid description has been employed. The medium has been driven by an external force in the form of a rotating electric field. It is shown that when the amplitude of force is small, the density perturbations in the medium are also small. In this case, the excitations do not develop as a spiral wave. Only when the amplitude of force is high so as to drive the density perturbations to nonlinear amplitudes does the spiral density wave formation occurs. The role of the forcing frequency and the effect of strong coupling and the sound velocity of medium in the formation and evolution of spiral waves have been investigated in detail.

FOCUSING OF HIGH POWER ULTRASOUND BEAMS AND LIMITING VALUES OF SHOCK WAVE PARAMETERS

PubMed Central

Bessonova, O.V.; Khokhlova, V.A.; Bailey, M.R.; Canney, M.S.; Crum, L.A.

2009-01-01

In this work, the influence of nonlinear and diffraction effects on amplification factors of focused ultrasound systems is investigated. The limiting values of acoustic field parameters obtained by focusing of high power ultrasound are studied. The Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation was used for the numerical modeling. Solutions for the nonlinear acoustic field were obtained at output levels corresponding to both pre- and post- shock formation conditions in the focal area of the beam in a weakly dissipative medium. Numerical solutions were compared with experimental data as well as with known analytic predictions. PMID:20161349

FOCUSING OF HIGH POWER ULTRASOUND BEAMS AND LIMITING VALUES OF SHOCK WAVE PARAMETERS.

PubMed

Bessonova, O V; Khokhlova, V A; Bailey, M R; Canney, M S; Crum, L A

2009-07-21

In this work, the influence of nonlinear and diffraction effects on amplification factors of focused ultrasound systems is investigated. The limiting values of acoustic field parameters obtained by focusing of high power ultrasound are studied. The Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation was used for the numerical modeling. Solutions for the nonlinear acoustic field were obtained at output levels corresponding to both pre- and post- shock formation conditions in the focal area of the beam in a weakly dissipative medium. Numerical solutions were compared with experimental data as well as with known analytic predictions.

Focusing of high power ultrasound beams and limiting values of shock wave parameters

NASA Astrophysics Data System (ADS)

Bessonova, O. V.; Khokhlova, V. A.; Bailey, M. R.; Canney, M. S.; Crum, L. A.

2009-10-01

In this work, the influence of nonlinear and diffraction effects on amplification factors of focused ultrasound systems is investigated. The limiting values of acoustic field parameters obtained by focusing of high power ultrasound are studied. The Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation was used for the numerical modeling. Solutions for the nonlinear acoustic field were obtained at output levels corresponding to both pre- and post-shock formation conditions in the focal area of the beam in a weakly dissipative medium. Numerical solutions were compared with experimental data as well as with known analytic predictions.

Rogue events in the group velocity horizon.

PubMed

Demircan, Ayhan; Amiranashvili, Shalva; Brée, Carsten; Mahnke, Christoph; Mitschke, Fedor; Steinmeyer, Günter

2012-01-01

The concept of rogue waves arises from a mysterious and potentially calamitous phenomenon of oceanic surfaces. There is mounting evidence that they are actually commonplace in a variety of different physical settings. A set of defining criteria has been advanced; this set is of great generality and therefore applicable to a wide class of systems. The question arises naturally whether there are generic mechanisms responsible for extreme events in different systems. Here we argue that under suitable circumstances nonlinear interaction between weak and strong waves results in intermittent giant waves with all the signatures of rogue waves. To obtain these circumstances only a few basic conditions must be met. Then reflection of waves at the so-called group-velocity horizon occurs. The connection between rogue waves and event horizons, seemingly unrelated physical phenomena, is identified as a feature common in many different physical systems.

Current structure of strongly nonlinear interfacial solitary waves

NASA Astrophysics Data System (ADS)

Semin, Sergey; Kurkina, Oxana; Kurkin, Andrey; Talipova, Tatiana; Pelinovsky, Efim; Churaev, Egor

2015-04-01

The characteristics of highly nonlinear solitary internal waves (solitons) in two-layer flow are computed within the fully nonlinear Navier-Stokes equations with use of numerical model of the Massachusetts Institute of Technology (MITgcm). The verification and adaptation of the model is based on the data from laboratory experiments [Carr & Davies, 2006]. The present paper also compares the results of our calculations with the computations performed in the framework of the fully nonlinear Bergen Ocean Model [Thiem et al, 2011]. The comparison of the computed soliton parameters with the predictions of the weakly nonlinear theory based on the Gardner equation is given. The occurrence of reverse flow in the bottom layer directly behind the soliton is confirmed in numerical simulations. The trajectories of Lagrangian particles in the internal soliton on the surface, on the interface and near the bottom are computed. The results demonstrated completely different trajectories at different depths of the model area. Thus, in the surface layer is observed the largest displacement of Lagrangian particles, which can be more than two and a half times larger than the characteristic width of the soliton. Located at the initial moment along the middle pycnocline fluid particles move along the elongated vertical loop at a distance of not more than one third of the width of the solitary wave. In the bottom layer of the fluid moves in the opposite direction of propagation of the internal wave, but under the influence of the reverse flow, when the bulk of the velocity field of the soliton ceases to influence the trajectory, it moves in the opposite direction. The magnitude of displacement of fluid particles in the bottom layer is not more than the half-width of the solitary wave. 1. Carr, M., and Davies, P.A. The motion of an internal solitary wave of depression over a fixed bottom boundary in a shallow, two-layer fluid. Phys. Fluids, 2006, vol. 18, No. 1, 1 - 10. 2. Thiem, O., Carr, M., Berntsen, J., and Davies, P.A. Numerical simulation of internal solitary wave-induced reverse flow and associated vortices in a shallow, two-layer fluid benthic boundary layer. Ocean Dynamics, 2011, vol. 61, No. 6, 857 - 872.

Simulation of wind wave growth with reference source functions

NASA Astrophysics Data System (ADS)

Badulin, Sergei I.; Zakharov, Vladimir E.; Pushkarev, Andrei N.

2013-04-01

We present results of extensive simulations of wind wave growth with the so-called reference source function in the right-hand side of the Hasselmann equation written as follows First, we use Webb's algorithm [8] for calculating the exact nonlinear transfer function Snl. Second, we consider a family of wind input functions in accordance with recent consideration [9] ( )s S = ?(k)N , ?(k) = ? ? ?- f (?). in k 0 ?0 in (2) Function fin(?) describes dependence on angle ?. Parameters in (2) are tunable and determine magnitude (parameters ?0, ?0) and wave growth rate s [9]. Exponent s plays a key role in this study being responsible for reference scenarios of wave growth: s = 4-3 gives linear growth of wave momentum, s = 2 - linear growth of wave energy and s = 8-3 - constant rate of wave action growth. Note, the values are close to ones of conventional parameterizations of wave growth rates (e.g. s = 1 for [7] and s = 2 for [5]). Dissipation function Sdiss is chosen as one providing the Phillips spectrum E(?) ~ ?5 at high frequency range [3] (parameter ?diss fixes a dissipation scale of wind waves) Sdiss = Cdissμ4w?N (k)θ(? - ?diss) (3) Here frequency-dependent wave steepness μ2w = E(?,?)?5-g2 makes this function to be heavily nonlinear and provides a remarkable property of stationary solutions at high frequencies: the dissipation coefficient Cdiss should keep certain value to provide the observed power-law tails close to the Phillips spectrum E(?) ~ ?-5. Our recent estimates [3] give Cdiss ? 2.0. The Hasselmann equation (1) with the new functions Sin, Sdiss (2,3) has a family of self-similar solutions of the same form as previously studied models [1,3,9] and proposes a solid basis for further theoretical and numerical study of wave evolution under action of all the physical mechanisms: wind input, wave dissipation and nonlinear transfer. Simulations of duration- and fetch-limited wind wave growth have been carried out within the above model setup to check its conformity with theoretical predictions, previous simulations [2,6,9], experimental parameterizations of wave spectra [1,4] and to specify tunable parameters of terms (2,3). These simulations showed realistic spatio-temporal scales of wave evolution and spectral shaping close to conventional parameterizations [e.g. 4]. An additional important feature of the numerical solutions is a saturation of frequency-dependent wave steepness μw in short-frequency range. The work was supported by the Russian government contract No.11.934.31.0035, Russian Foundation for Basic Research grant 11-05-01114-a and ONR grant N00014-10-1-0991. References [1] S. I. Badulin, A. V. Babanin, D. Resio, and V. Zakharov. Weakly turbulent laws of wind-wave growth. J. Fluid Mech., 591:339-378, 2007. [2] S. I. Badulin, A. N. Pushkarev, D. Resio, and V. E. Zakharov. Self-similarity of wind-driven seas. Nonl. Proc. Geophys., 12:891-946, 2005. [3] S. I. Badulin and V. E. Zakharov. New dissipation function for weakly turbulent wind-driven seas. ArXiv e-prints, (1212.0963), December 2012. [4] M. A. Donelan, J. Hamilton, and W. H. Hui. Directional spectra of wind-generated waves. Phil. Trans. Roy. Soc. Lond. A, 315:509-562, 1985. [5] M. A. Donelan and W. J. Pierson-jr. Radar scattering and equilibrium ranges in wind-generated waves with application to scatterometry. J. Geophys. Res., 92(C5):4971-5029, 1987. [6] E. Gagnaire-Renou, M. Benoit, and S. I. Badulin. On weakly turbulent scaling of wind sea in simulations of fetch-limited growth. J. Fluid Mech., 669:178-213, 2011. [7] R. L. Snyder, F. W. Dobson, J. A. Elliot, and R. B. Long. Array measurements of atmospheric pressure fluctuations above surface gravity waves. J. Fluid Mech., 102:1-59, 1981. [8] D. J. Webb. Non-linear transfers between sea waves. Deep Sea Res., 25:279-298, 1978. [9] V. E. Zakharov, D. Resio, and A. N. Pushkarev. New wind input term consistent with experimental, theoretical and numerical considerations. ArXiv e-prints, (1212.1069), December 2012.

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

Particle motions beneath irrotational water waves

NASA Astrophysics Data System (ADS)

Bakhoday-Paskyabi, Mostafa

2015-08-01

Neutral and buoyant particle motions in an irrotational flow are investigated under the passage of linear, nonlinear gravity, and weakly nonlinear solitary waves at a constant water depth. The developed numerical models for the particle trajectories in a non-turbulent flow incorporate particle momentum, size, and mass (i.e., inertial particles) under the influence of various surface waves such as Korteweg-de Vries waves which admit a three parameter family of periodic cnoidal wave solutions. We then formulate expressions of mass-transport velocities for the neutral and buoyant particles. A series of test cases suggests that the inertial particles possess a combined horizontal and vertical drifts from the locations of their release, with a fall velocity as a function of particle material properties, ambient flow, and wave parameters. The estimated solutions exhibit good agreement with previously explained particle behavior beneath progressive surface gravity waves. We further investigate the response of a neutrally buoyant water parcel trajectories in a rotating fluid when subjected to a series of wind and wave events. The results confirm the importance of the wave-induced Coriolis-Stokes force effect in both amplifying (destroying) the pre-existing inertial oscillations and in modulating the direction of the flow particles. Although this work has mainly focused on wave-current-particle interaction in the absence of turbulence stochastic forcing effects, the exercise of the suggested numerical models provides additional insights into the mechanisms of wave effects on the passive trajectories for both living and nonliving particles such as swimming trajectories of plankton in non-turbulent flows.

Pseudo-incompressible, finite-amplitude gravity waves: wave trains and stability

NASA Astrophysics Data System (ADS)

Schlutow, Mark; Klein, Rupert

2017-04-01

Based on weak asymptotic WKB-like solutions for two-dimensional atmospheric gravity waves (GWs) traveling wave solutions (wave trains) are derived and analyzed with respect to stability. A systematic multiple-scale analysis using the ratio of the dominant wavelength and the scale height as a scale separation parameter is applied on the fully compressible Euler equations. A distinguished limit favorable for GWs close to static instability, reveals that pseudo-incompressible rather than Boussinesq theory applies. A spectral expansion including a mean flow, combined with the additional WKB assumption of slowly varying phases and amplitudes, is used to find general weak asymptotic solutions. This ansatz allows for arbitrarily strong, non-uniform stratification and holds even for finite-amplitude waves. It is deduced that wave trains as leading order solutions can only exist if either some non-uniform background stratification is given but the wave train propagates only horizontally or if the wave train velocity vector is given but the background is isothermal. For the first case, general analytical solutions are obtained that may be used to model mountain lee waves. For the second case with the additional assumption of horizontal periodicity, upward propagating wave train fronts were found. These wave train fronts modify the mean flow beyond the non-acceleration theorem. Stability analysis reveal that they are intrinsically modulationally unstable. The range of validity for the scale separation parameter was tested with fully nonlinear simulations. Even for large values an excellent agreement with the theory was found.

Derivation of nonlinear wave equations for ultrasound beam in nonuniform bubbly liquids

NASA Astrophysics Data System (ADS)

Kanagawa, Tetsuya; Yano, Takeru; Kawahara, Junya; Kobayashi, Kazumichi; Watanabe, Masao; Fujikawa, Shigeo

2012-09-01

Weakly nonlinear propagation of diffracted ultrasound beams in a nonuniform bubbly liquid is theoretically studied based on the method of multiple scales with the set of scaling relations of some physical parameters. It is assumed that the spatial distribution of the number density of bubbles in an initial state at rest is a slowly varying function of space coordinates and the amplitude of its variation is small compared with a mean number density. As a result, a Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation with dispersion and nonuniform effects for a low frequency case and a nonlinear Schrödinger (NLS) equation with dissipation, diffraction, and nonuniform effects for a high frequency case, are derived from the basic equations of bubbly flows.

Acoustic instability driven by cosmic-ray streaming

NASA Technical Reports Server (NTRS)

Begelman, Mitchell C.; Zweibel, Ellen G.

1994-01-01

We study the linear stability of compressional waves in a medium through which cosmic rays stream at the Alfven speed due to strong coupling with Alfven waves. Acoustic waves can be driven unstable by the cosmic-ray drift, provided that the streaming speed is sufficiently large compared to the thermal sound speed. Two effects can cause instability: (1) the heating of the thermal gas due to the damping of Alfven waves driven unstable by cosmic-ray streaming; and (2) phase shifts in the cosmic-ray pressure perturbation caused by the combination of cosmic-ray streaming and diffusion. The instability does not depend on the magnitude of the background cosmic-ray pressure gradient, and occurs whether or not cosmic-ray diffusion is important relative to streaming. When the cosmic-ray pressure is small compared to the gas pressure, or cosmic-ray diffusion is strong, the instability manifests itself as a weak overstability of slow magnetosonic waves. Larger cosmic-ray pressure gives rise to new hybrid modes, which can be strongly unstable in the limits of both weak and strong cosmic-ray diffusion and in the presence of thermal conduction. Parts of our analysis parallel earlier work by McKenzie & Webb (which were brought to our attention after this paper was accepted for publication), but our treatment of diffusive effects, thermal conduction, and nonlinearities represent significant extensions. Although the linear growth rate of instability is independent of the background cosmic-ray pressure gradient, the onset of nonlinear eff ects does depend on absolute value of DEL (vector differential operator) P(sub c). At the onset of nonlinearity the fractional amplitude of cosmic-ray pressure perturbations is delta P(sub C)/P(sub C) approximately (kL) (exp -1) much less than 1, where k is the wavenumber and L is the pressure scale height of the unperturbed cosmic rays. We speculate that the instability may lead to a mode of cosmic-ray transport in which plateaus of uniform cosmic-ray pressure are separated by either laminar or turbulent jumps in which the thermal gas is subject to intense heating.

Light Meets Water in Nonlocal Media: Surface Tension Analogue in Optics

NASA Astrophysics Data System (ADS)

Horikis, Theodoros P.; Frantzeskakis, Dimitrios J.

2017-06-01

Shallow water wave phenomena find their analogue in optics through a nonlocal nonlinear Schrödinger (NLS) model in 2 +1 dimensions. We identify an analogue of surface tension in optics, namely, a single parameter depending on the degree of nonlocality, which changes the sign of dispersion, much like surface tension does in the shallow water wave problem. Using multiscale expansions, we reduce the NLS model to a Kadomtsev-Petviashvili (KP) equation, which is of the KPII (KPI) type, for strong (weak) nonlocality. We demonstrate the emergence of robust optical antidark solitons forming Y -, X -, and H -shaped wave patterns, which are approximated by colliding KPII line solitons, similar to those observed in shallow waters.

Light Meets Water in Nonlocal Media: Surface Tension Analogue in Optics.

PubMed

Horikis, Theodoros P; Frantzeskakis, Dimitrios J

2017-06-16

Shallow water wave phenomena find their analogue in optics through a nonlocal nonlinear Schrödinger (NLS) model in 2+1 dimensions. We identify an analogue of surface tension in optics, namely, a single parameter depending on the degree of nonlocality, which changes the sign of dispersion, much like surface tension does in the shallow water wave problem. Using multiscale expansions, we reduce the NLS model to a Kadomtsev-Petviashvili (KP) equation, which is of the KPII (KPI) type, for strong (weak) nonlocality. We demonstrate the emergence of robust optical antidark solitons forming Y-, X-, and H-shaped wave patterns, which are approximated by colliding KPII line solitons, similar to those observed in shallow waters.

Interaction of solitons for obliquely propagating magnetoacoustic waves in stellar atmosphere

NASA Astrophysics Data System (ADS)

Jahangir, R.; Masood, W.; Siddiq, M.; Batool, Nazia

2016-12-01

We study here the nonlinear oblique propagation of magnetoacoustic waves in dense plasmas with degenerate electrons by deriving Kadomtsev-Petviashvili (KP) equation for small but finite amplitude perturbations. The two soliton interaction has been studied by finding the solution of the KP equation using the Hirota bilinear formalism. For illustrative purposes, we have used the plasma parameters typically found in white dwarf stars for both the fast and slow modes of magnetoacoustic waves. It has been observed that the soliton interaction in the fast and slow modes is strongly influenced by the predominant and weak dispersive coefficients of the KP equation. The single soliton behavior has also been explained for the fast and slow magnetoacoustic modes.

Parametric resonant triad interactions in a free shear layer

NASA Technical Reports Server (NTRS)

Mallier, R.; Maslowe, S. A.

1993-01-01

We investigate the weakly nonlinear evolution of a triad of nearly-neutral modes superimposed on a mixing layer with velocity profile u bar equals Um + tanh y. The perturbation consists of a plane wave and a pair of oblique waves each inclined at approximately 60 degrees to the mean flow direction. Because the evolution occurs on a relatively fast time scale, the critical layer dynamics dominate the process and the amplitude evolution of the oblique waves is governed by an integro-differential equation. The long-time solution of this equation predicts very rapid (exponential of an exponential) amplification and we discuss the pertinence of this result to vortex pairing phenomena in mixing layers.

Acoustics of One-Dimensional Homogeneous Granular Chains

NASA Astrophysics Data System (ADS)

Starosvetsky, Yuli; Jayaprakash, K. R.; Hasan, Md. Arif; Vakakis, Alexander F.

The Chapter 1 provided a brief glimpse of the general ordered granular chain/lattices, their subtle features and the intricacies associated with their analysis. By now it should be clear that this class of highly-inhomogeneous and discontinuous systems poses new challenges in the form of strongly nonlinear behavior, bead separations, and twice (at most) differentiable interaction potential. It follows that the traditional analytical methodologies may need to be modified to effectively address these challenges. To begin with, we consider the simplest case of the homogeneous granular chains, wherein, the particles are identical and are perfectly in contact (no gaps) initially. We consider the case of both the uncompressed (strongly nonlinear) and the pre-compressed (weakly nonlinear) chains and elucidate the striking differences between their dynamical behaviors. In the latter case, the long wave/continuum approximation is invoked in this analysis thus precluding any bead separations. A landmark discovery in this class of systems is the realization of the solitary wave propagation [1-3]. These waves are highly localized spatially symmetric disturbances which propagate in the nonlinear medium. In general, it is well known that the linear nondispersive waves have a characteristic wave speed (property of the medium), and a disturbance of any amplitude or waveform propagates at the same speed undistorted. In contrast, the propagation velocity of the solitary waves in a nonlinear medium is a function of the wave amplitude (a general nonlinear behavior) and the physical properties of the medium. It is worth noting that any arbitrary disturbance set in motion in a homogeneous granular chain eventually disintegrates into a train of the solitary waves of varying amplitudes propagating at the proportional velocities (higher the amplitude, higher the propagation velocity). Although these waves are called solitary waves, they do not necessarily conform to the definition [4] provided in the previous chapter. In fact such a definition is applicable when the medium is a continuum and does not consist of a discrete set of particles. Thus such localized waves are alternatively given the name compactons as they span a limited spatial domain of about 6-7 beads or in other words they only require compact support in the media where they propagate (although the characterization as solitary wave is also common in the research community). We briefly dwell on the concept of the compactons [5] and the decaying characteristic [6] of these waves. An aspect that has interested many researchers is the interaction of these solitary waves with the mass defects/intruders (disparity in masses). Such defects, e.g., in the form of a large mass disparity, can lead to the discrete breathers that transiently entrap the energy in space. In the final part of this chapter we consider the effects of the periodic intruders on the wave propagation and the shock mitigation of pulse propagating in the granular chains.

Spectral evolution and extreme value analysis of non-linear numerical simulations of narrow band random surface gravity waves.

NASA Astrophysics Data System (ADS)

Socquet-Juglard, H.; Dysthe, K. B.; Trulsen, K.; Liu, J.; Krogstad, H. E.

2003-04-01

Numerical simulations of a narrow band gaussian spectrum of random surface gravity waves have been carried out in two and three spatial dimensions [7]. Different types of non-linear Schr&{uml;o}dinger equations, [1] and [4], have been used in these simulations. Simulations have now been carried with a JONSWAP spectrum associated with a spreading function of the type cosine-squared [5]. The evolution of the spectrum, skewness, kurtosis, ... will be presented. In addition, some results about stochastic properties of the surface will be shown. Based on the approach found in [2], [3] and [6], the results are presented in terms of deviations from linear Gaussian theory and the standard second order small slope perturbation theory. begin{thebibliography}{9} bibitem{kk96} Trulsen, K. &Dysthe, K. B. (1996). A modified nonlinear Schr&{uml;o}dinger equation for broader bandwidth gravity waves on deep water. Wave Motion, 24, pp. 281-289. bibitem{BK2000} Krogstad, H.E. and S.F. Barstow (2000). A uniform approach to extreme value analysis of ocean waves, Proc. ISOPE'2000, Seattle, USA, 3, pp. 103-108. bibitem{PRK} Prevosto, M., H. E. Krogstad and A. Robin (2000). Probability distributions for maximum wave and crest heights, Coast. Eng., 40, 329-360. bibitem{ketal} Trulsen, K., Kliakhandler, I., Dysthe, K. B. &Velarde, M. G. (2000) On weakly nonlinear modulation of waves on deep water, Phys. Fluids, 12, pp. L25-L28. bibitem{onorato} Onorato, M., Osborne, A.R. and Serio, M. (2002) Extreme wave events in directional, random oceanic sea states, Phys. Fluids, 14, pp. 2432-2437. bibitem{BK2002} Krogstad, H.E. and S.F. Barstow (2002). Analysis and Applications of Second Order Models for the Maximum Crest height, % Proc. 21nd Int. Conf. Offshore Mechanics and Arctic Engineering, Oslo. Paper no. OMAE2002-28479. bibitem{JFMP} Dysthe, K. B., Trulsen, K., Krogstad, H. E. and Socquet-Juglard, H. (2002, in press) Evolution of a narrow band spectrum of random surface gravity waves, J. Fluid Mech.

On the generation of internal wave modes by surface waves

NASA Astrophysics Data System (ADS)

Harlander, Uwe; Kirschner, Ian; Maas, Christian; Zaussinger, Florian

2016-04-01

Internal gravity waves play an important role in the ocean since they transport energy and momentum and the can lead to mixing when they break. Surface waves and internal gravity waves can interact. On the one hand, long internal waves imply a slow varying shear current that modifies the propagation of surface waves. Surface waves generated by the atmosphere can, on the other hand, excite internal waves by nonlinear interaction. Thereby a surface wave packet consisting of two close frequencies can resonate with a low frequency internal wave (Phillips, 1966). From a theoretical point of view, the latter has been studied intensively by using a 2-layer model, i.e. a surface layer with a strong density contrast and an internal layer with a comparable weak density contrast (Ball, 1964; Craig et al., 2010). In the present work we analyse the wave coupling for a continuously stratified fluid using a fully non-linear 2D numerical model (OpenFoam) and compare this with laboratory experiments (see Lewis et al. 1974). Surface wave modes are used as initial condition and the time development of the dominant surface and internal waves are studied by spectral and harmonic analysis. For the simple geometry of a box, the results are compared with analytical spectra of surface and gravity waves. Ball, F.K. 1964: Energy transfer between external and internal gravity waves. J. Fluid Mech. 19, 465. Craig, W., Guyenne, P., Sulem, C. 2010: Coupling between internal and surface waves. Natural Hazards 57, 617-642. Lewis, J.E., Lake, B.M., Ko, D.R.S 1974: On the interaction of internal waves and surfacr gravity waves, J. Fluid Mech. 63, 773-800. Phillips, O.M. 1966: The dynamics of the upper ocean, Cambridge University Press, 336pp.

A new (2+1) dimensional integrable evolution equation for an ion acoustic wave in a magnetized plasma

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

Mukherjee, Abhik, E-mail: abhik.mukherjee@saha.ac.in; Janaki, M. S., E-mail: ms.janaki@saha.ac.in; Kundu, Anjan, E-mail: anjan.kundu@saha.ac.in

2015-07-15

A new, completely integrable, two dimensional evolution equation is derived for an ion acoustic wave propagating in a magnetized, collisionless plasma. The equation is a multidimensional generalization of a modulated wavepacket with weak transverse propagation, which has resemblance to nonlinear Schrödinger (NLS) equation and has a connection to Kadomtsev-Petviashvili equation through a constraint relation. Higher soliton solutions of the equation are derived through Hirota bilinearization procedure, and an exact lump solution is calculated exhibiting 2D structure. Some mathematical properties demonstrating the completely integrable nature of this equation are described. Modulational instability using nonlinear frequency correction is derived, and the correspondingmore » growth rate is calculated, which shows the directional asymmetry of the system. The discovery of this novel (2+1) dimensional integrable NLS type equation for a magnetized plasma should pave a new direction of research in the field.« less

Monitoring stress related velocity variation in concrete with a 2 x 10(-5) relative resolution using diffuse ultrasound.

PubMed

Larose, Eric; Hall, Stephen

2009-04-01

Ultrasonic waves propagating in solids have stress-dependent velocities. The relation between stress (or strain) and velocity forms the basis of non-linear acoustics. In homogeneous solids, conventional time-of-flight techniques have measured this dependence with spectacular precision. In heterogeneous media such as concrete, the direct (ballistic) wave around 500 kHz is strongly attenuated and conventional techniques are less efficient. In this manuscript, the effect of weak stress changes on the late arrivals constituting the acoustic diffuse coda is tracked. A resolution of 2 x 10(-5) in relative velocity change is attained which corresponds to a sensitivity to stress change of better than 50 kPa. Therefore, the technique described here provides an original way to measure the non-linear parameter with stress variations on the order of tens of kPa.

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.

Rogue events in the group velocity horizon

PubMed Central

Demircan, Ayhan; Amiranashvili, Shalva; Brée, Carsten; Mahnke, Christoph; Mitschke, Fedor; Steinmeyer, Günter

2012-01-01

The concept of rogue waves arises from a mysterious and potentially calamitous phenomenon of oceanic surfaces. There is mounting evidence that they are actually commonplace in a variety of different physical settings. A set of defining criteria has been advanced; this set is of great generality and therefore applicable to a wide class of systems. The question arises naturally whether there are generic mechanisms responsible for extreme events in different systems. Here we argue that under suitable circumstances nonlinear interaction between weak and strong waves results in intermittent giant waves with all the signatures of rogue waves. To obtain these circumstances only a few basic conditions must be met. Then reflection of waves at the so-called group-velocity horizon occurs. The connection between rogue waves and event horizons, seemingly unrelated physical phenomena, is identified as a feature common in many different physical systems. PMID:23152941

Dispersion relation in oscillatory reaction-diffusion systems with self-consistent flow in true slime mold.

PubMed

Yamada, H; Nakagaki, T; Baker, R E; Maini, P K

2007-06-01

In the large amoeboid organism Physarum, biochemical oscillators are spatially distributed throughout the organism and their collective motion exhibits phase waves, which carry physiological signals. The basic nature of this wave behaviour is not well-understood because, to date, an important effect has been neglected, namely, the shuttle streaming of protoplasm which accompanies the biochemical rhythms. Here we study the effects of self-consistent flow on the wave behaviour of oscillatory reaction-diffusion models proposed for the Physarum plasmodium, by means of numerical simulation for the dispersion relation and weakly nonlinear analysis for derivation of the phase equation. We conclude that the flow term is able to increase the speed of phase waves (similar to elongation of wave length). We compare the theoretical consequences with real waves observed in the organism and also point out the physiological roles of these effects on control mechanisms of intracellular communication.

Lower Hybrid Oscillations in Multicomponent Space Plasmas Subjected to Ion Cyclotron Waves

NASA Technical Reports Server (NTRS)

Khazanov, G. V.; Krivorutsky, E. N.; Moore, T. E.; Liemohn, M. W.; Horwitz, J. L.

1997-01-01

It is found that in multicomponent plasmas subjected to Alfven or fast magnetosonic waves, such as are observed in regions of the outer plasmasphere and ring current-plasmapause overlap, lower hybrid oscillations are generated. The addition of a minor heavy ion component to a proton-electron plasma significantly lowers the low-frequency electric wave amplitude needed for lower hybrid wave excitation. It is found that the lower hybrid wave energy density level is determined by the nonlinear process of induced scattering by ions and electrons; hydrogen ions in the region of resonant velocities are accelerated; and nonresonant particles are weakly heated due to the induced scattering. For a given example, the light resonant ions have an energy gain factor of 20, leading to the development of a high-energy tail in the H(+) distribution function due to low-frequency waves.

Sonic boom interaction with turbulence

NASA Technical Reports Server (NTRS)

Rusak, Zvi; Giddings, Thomas E.

1994-01-01

A recently developed transonic small-disturbance model is used to analyze the interactions of random disturbances with a weak shock. The model equation has an extended form of the classic small-disturbance equation for unsteady transonic aerodynamics. It shows that diffraction effects, nonlinear steepening effects, focusing and caustic effects and random induced vorticity fluctuations interact simultaneously to determine the development of the shock wave in space and time and the pressure field behind it. A finite-difference algorithm to solve the mixed-type elliptic hyperbolic flows around the shock wave is presented. Numerical calculations of shock wave interactions with various deterministic vorticity and temperature disturbances result in complicate shock wave structures and describe peaked as well as rounded pressure signatures behind the shock front, as were recorded in experiments of sonic booms running through atmospheric turbulence.

Electron acoustic-Langmuir solitons in a two-component electron plasma

NASA Astrophysics Data System (ADS)

McKenzie, J. F.

2003-04-01

We investigate the conditions under which ‘high-frequency’ electron acoustic Langmuir solitons can be constructed in a plasma consisting of protons and two electron populations: one ‘cold’ and the other ‘hot’. Conservation of total momentum can be cast as a structure equation either for the ‘cold’ or ‘hot’ electron flow speed in a stationary wave using the Bernoulli energy equations for each species. The linearized version of the governing equations gives the dispersion equation for the stationary waves of the system, from which follows the necessary but not sufficient conditions for the existence of soliton structures; namely that the wave speed must be less than the acoustic speed of the ‘hot’ electron component and greater than the low-frequency compound acoustic speed of the two electron populations. In this wave speed regime linear waves are ‘evanescent’, giving rise to the exponential growth or decay, which readily can give rise to non-linear effects that may balance dispersion and allow soliton formation. In general the ‘hot’ component must be more abundant than the ‘cold’ one and the wave is characterized by a compression of the ‘cold’ component and an expansion in the ‘hot’ component necessitating a potential dip. Both components are driven towards their sonic points; the ‘cold’ from above and the ‘hot’ from below. It is this transonic feature which limits the amplitude of the soliton. If the ‘hot’ component is not sufficiently abundant the window for soliton formation shrinks to a narrow speed regime which is quasi-transonic relative to the ‘hot’ electron acoustic speed, and it is shown that smooth solitons cannot be constructed. In the special case of a very cold electron population (i.e. ‘highly supersonic’) and the other population being very hot (i.e. ‘highly subsonic’) with adiabatic index 2, the structure equation simplifies and can be integrated in terms of elementary transcendental functions that provide the fully non-linear counterpart to the weakly non-linear sech(2) -type solitons. In this case the limiting soliton is comprised of an infinite compression in the cold component, a weak rarefaction in the ‘hot’ electrons and a modest potential dip.

Experimental Observation and Theoretical Description of Multisoliton Fission in Shallow Water

NASA Astrophysics Data System (ADS)

Trillo, S.; Deng, G.; Biondini, G.; Klein, M.; Clauss, G. F.; Chabchoub, A.; Onorato, M.

2016-09-01

We observe the dispersive breaking of cosine-type long waves [Phys. Rev. Lett. 15, 240 (1965)] in shallow water, characterizing the highly nonlinear "multisoliton" fission over variable conditions. We provide new insight into the interpretation of the results by analyzing the data in terms of the periodic inverse scattering transform for the Korteweg-de Vries equation. In a wide range of dispersion and nonlinearity, the data compare favorably with our analytical estimate, based on a rigorous WKB approach, of the number of emerging solitons. We are also able to observe experimentally the universal Fermi-Pasta-Ulam recurrence in the regime of moderately weak dispersion.

Interaction of a weak shock wave with a discontinuous heavy-gas cylinder

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

Wang, Xiansheng; Yang, Dangguo; Wu, Junqiang

2015-06-15

The interaction between a cylindrical inhomogeneity and a weak planar shock wave is investigated experimentally and numerically, and special attention is given to the wave patterns and vortex dynamics in this scenario. A soap-film technique is realized to generate a well-controlled discontinuous cylinder (SF{sub 6} surrounded by air) with no supports or wires in the shock-tube experiment. The symmetric evolving interfaces and few disturbance waves are observed in a high-speed schlieren photography. Numerical simulations are also carried out for a detailed analysis. The refracted shock wave inside the cylinder is perturbed by the diffracted shock waves and divided into threemore » branches. When these shock branches collide, the shock focusing occurs. A nonlinear model is then proposed to elucidate effects of the wave patterns on the evolution of the cylinder. A distinct vortex pair is gradually developing during the shock-cylinder interaction. The numerical results show that a low pressure region appears at the vortex core. Subsequently, the ambient fluid is entrained into the vortices which are expanding at the same time. Based on the relation between the vortex motion and the circulation, several theoretical models of circulation in the literature are then checked by the experimental and numerical results. Most of these theoretical circulation models provide a reasonably good prediction of the vortex motion in the present configuration.« less

Two-photon excited fluorescence from a pseudoisocyanine-attached gold-coated tip via a thin tapered fiber under a weak continuous wave excitation.

PubMed

Ren, Fang; Takashima, Hideaki; Tanaka, Yoshito; Fujiwara, Hideki; Sasaki, Keiji

2013-11-18

A simple tapered fiber based photonic-plasmonic hybrid nanostructure composed of a thin tapered fiber and a pseudoisocyanine (PIC)-attached Au-coated tip was demonstrated. Using this simple hybrid nanostructure, we succeeded in observing two-photon excited fluorescence from the PIC dye molecules under a weak continuous wave excitation condition. From the results of the tip-fiber distance dependence and excitation polarization dependence, we found that using a thin tapered fiber and an Au-coated tip realized efficient coupling of the incident light (~95%) and LSP excitation at the Au-coated tip, suggesting the possibility of efficiently inducing two-photon excited fluorescence from the PIC dye molecules attached on the Au-coated tip. This simple photonic-plasmonic hybrid system is one of the promising tools for single photon sources, highly efficient plasmonic sensors, and integrated nonlinear plasmonic devices.

Nonlinear propagation of ion-acoustic waves in electron-positron-ion plasma with trapped electrons

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

Alinejad, H.; Sobhanian, S.; Mahmoodi, J.

2006-01-15

A theoretical investigation has been made for ion-acoustic waves in an unmagnetized electron-positron-ion plasma. A more realistic situation in which plasma consists of a negatively charged ion fluid, free positrons, and trapped as well as free electrons is considered. The properties of stationary structures are studied by the reductive perturbation method, which is valid for small but finite amplitude limit, and by pseudopotential approach, which is valid for large amplitude. With an appropriate modified form of the electron number density, two new equations for the ion dynamics have been found. When deviations from isothermality are finite, the modified Korteweg-deVries equationmore » has been found, and for the case that deviations from isothermality are small, calculations lead to a generalized Korteweg-deVries equation. It is shown from both weakly and highly nonlinear analysis that the presence of the positrons may allow solitary waves to exist. It is found that the effect of the positron density changes the maximum value of the amplitude and M (Mach number) for which solitary waves can exist. The present theory is applicable to analyze arbitrary amplitude ion-acoustic waves associated with positrons which may occur in space plasma.« less

Stability of matter-wave solitons in optical lattices

NASA Astrophysics Data System (ADS)

Ali, Sk. Golam; Roy, S. K.; Talukdar, B.

2010-08-01

We consider localized states of both single- and two-component Bose-Einstein condensates (BECs) confined in a potential resulting from the superposition of linear and nonlinear optical lattices and make use of Vakhitov-Kolokolov criterion to investigate the effect of nonlinear lattice on the stability of the soliton solutions in the linear optical lattice (LOL). For the single-component case we show that a weak nonlinear lattice has very little effect on the stability of such solitons while sufficiently strong nonlinear optical lattice (NOL) squeezes them to produce narrow bound states. For two-component condensates we find that when the strength of the NOL (γ1) is less than that of the LOL (V0) a relatively weak intra-atomic interaction (IAI) has little effect on the stability of the component solitons. This is true for both attractive and repulsive IAI. A strong attractive IAI, however, squeezes the BEC solitons while a similar repulsive IAI makes the component solitons wider. For γ1 > V0, only a strong attractive IAI squeezes the BEC solitons but the squeezing effect is less prominent than that found for γ1 < V0. We make useful checks on the results of our semianalytical stability analysis by solving the appropriate Gross-Pitaevskii equations numerically.

Linear and nonlinear stability of the Blasius boundary layer

NASA Technical Reports Server (NTRS)

Bertolotti, F. P.; Herbert, TH.; Spalart, P. R.

1992-01-01

Two new techniques for the study of the linear and nonlinear instability in growing boundary layers are presented. The first technique employs partial differential equations of parabolic type exploiting the slow change of the mean flow, disturbance velocity profiles, wavelengths, and growth rates in the streamwise direction. The second technique solves the Navier-Stokes equation for spatially evolving disturbances using buffer zones adjacent to the inflow and outflow boundaries. Results of both techniques are in excellent agreement. The linear and nonlinear development of Tollmien-Schlichting (TS) waves in the Blasius boundary layer is investigated with both techniques and with a local procedure based on a system of ordinary differential equations. The results are compared with previous work and the effects of non-parallelism and nonlinearity are clarified. The effect of nonparallelism is confirmed to be weak and, consequently, not responsible for the discrepancies between measurements and theoretical results for parallel flow.

Application of Huang-Hilbert Transforms to Geophysical Datasets

NASA Technical Reports Server (NTRS)

Duffy, Dean G.

2003-01-01

The Huang-Hilbert transform is a promising new method for analyzing nonstationary and nonlinear datasets. In this talk I will apply this technique to several important geophysical datasets. To understand the strengths and weaknesses of this method, multi- year, hourly datasets of the sea level heights and solar radiation will be analyzed. Then we will apply this transform to the analysis of gravity waves observed in a mesoscale observational net.

Observation of three-photon bound states in a quantum nonlinear medium

NASA Astrophysics Data System (ADS)

Liang, Qi-Yu; Venkatramani, Aditya V.; Cantu, Sergio H.; Nicholson, Travis L.; Gullans, Michael J.; Gorshkov, Alexey V.; Thompson, Jeff D.; Chin, Cheng; Lukin, Mikhail D.; Vuletić, Vladan

2018-02-01

Bound states of massive particles, such as nuclei, atoms, or molecules, constitute the bulk of the visible world around us. By contrast, photons typically only interact weakly. We report the observation of traveling three-photon bound states in a quantum nonlinear medium where the interactions between photons are mediated by atomic Rydberg states. Photon correlation and conditional phase measurements reveal the distinct bunching and phase features associated with three-photon and two-photon bound states. Such photonic trimers and dimers possess shape-preserving wave functions that depend on the constituent photon number. The observed bunching and strongly nonlinear optical phase are described by an effective field theory of Rydberg-induced photon-photon interactions. These observations demonstrate the ability to realize and control strongly interacting quantum many-body states of light.

Filamentation of plasma in the auroral region by an ion-ion instability: A process for the formation of bidimensional potential structures

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

Mottez, F.; Chanteur, G.; Roux, A.

1992-07-01

A two-dimensional, explicit, electrostatic particle code is used to investigate the nonlinear behavior of electrostatic ion waves generated by an ion beam flowing through a thermal ion and electron background in a strongly magnetized plasma ({omega}{sub ce} {much gt} {omega}{sub pe} where {omega}{sub ce} and {omega}{sub pe} are the electron gyrofrequency and the plasma frequency). To follow the nonlinear evolution of these ions waves, a long-lasting simulation is run with a large simulation grid: 128 {times} 512{lambda}{sub d}. Beam ions are shown to generate oblique waves. The nonlinear beatings between these oblique waves produce purely transverse waves, which leads tomore » a strong modulation of the density and of the electric potential in a direction transverse to the magnetic field. The transverse scale of these essentially field-aligned filaments is L{sub {perpendicular}} = 10 {rho}{sub i} where {rho}{sub i} is the ion Larmor radius of beam ions. Within these filaments, relatively stable field-aligned density and potential structures develop. The typical size, along the magnetic field, of these structures is L{sub {parallel}} = 10 {lambda}{sub d}, the density is modulated by 30%, and the electric potential is as large as T{sub e} within these structures. Unlike the potential structures that develop in a two-component plasma with downgoing electrons, these structures move upward. These characteristics are in good agreement with the weak double layers recently detected by Viking.« less

Three-dimensional site response at KiK-net downhole arrays

USGS Publications Warehouse

Thompson, Eric M.; Tanaka, Yasuo; Baise, Laurie G.; Kayen, Robert E.

2010-01-01

Ground motions at two Kiban-Kyoshin Network (KiK-net) strong motion downhole array sites in Hokkaido, Japan (TKCH08 in Taiki and TKCH05 in Honbetsu) illustrate the importance of three-dimensional (3D) site effects. These sites recorded the M8.0 2003 Tokachi-Oki earthquake, with recorded accelerations above 0.4 g at both sites as well as numerous ground motions from smaller events. Weak ground motions indicate that site TKCH08 is well modeled with the assumption of plane SH waves traveling through a 1D medium (SH1D), while TKCH05 is characteristic of a poor fit to the SH1D theoretical response. We hypothesized that the misfit at TKCH05results from the heterogeneity of the subsurface. To test this hypothesis, we measured four S-wave velocity profiles in the vicinity (< 300 m) of each site with the spectral analysis of surface waves (SASW) method. This KiK-net site pair is ideal for assessing the relative importance of 3D site effects and nonlinear site effects. The linear ground motions at TKCH05 isolate the 3D site effects, as we hypothesized from the linear ground motions and confirmed with our subsequent SASW surveys. The Tokachi-Oki time history at TKCH08 isolates the effects of nonlinearity from spatial heterogeneity because the 3D effects are negligible. The Tokachi-Oki time history at TKCH05 includes both nonlinear and 3D site effects. Comparisons of the accuracy of the SH1D model predictions of these surface time histories from the downhole time histories indicates that the 3D site effects are at least as important as nonlinear effects in this case. The errors associated with the assumption of a 1D medium and 1D wave propagation will be carried into a nonlinear analysis that relies on these same assumptions. Thus, the presence of 3D effects should be ruled out prior to a 1D nonlinear analysis. The SH1D residuals show that 3D effects can be mistaken for nonlinear effects.

Generation of long subharmonic internal waves by surface waves

NASA Astrophysics Data System (ADS)

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

2016-10-01

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

The effect of rotation on shoaling of large amplitude internal solitary waves in the northern South China Sea

NASA Astrophysics Data System (ADS)

Guo, C.; Vlasenko, V.

2012-12-01

The propagation of large amplitude internal solitary waves (ISWs) in the northern South China Sea (SCS) is simulated using the fully nonlinear, nonhydrostatic MIT general circulation model (MITgcm). Special attention is paid to the effects of rotation and the shoaling three-dimensional topography. It is found that for the conditions of the northern SCS, a propagating ISW continuously loses its energy under the action of rotation by shedding inertia-gravity waves backwards, which further become steepened and form a new ISW. Such a decay-reemergence process repeats itself in a similar way as discussed by Helfrich (2007) with the only difference that, instead of the formation of a final localized wave packet, the frontal waves constantly attenuate by repeatedly shedding inertia-gravity waves backwards. Under the action of rotation and variable topography, the shoaling ISWs attenuate severely and disintegrate after passing through the continental slope. Wave polarity starts to reverse at the depth of about 130 m, which is consistent with the prediction of weakly nonlinear theories. It is also found that the rotational effects are more pronounced in combination with the topographic effects in the three-dimensional realistic context. Discrepancies between the wave profiles obtained with and without rotation are small in the deep part of the ocean but eventually turn out to be significant when going upon the shelf, addressing the crucial roles played by the rotation in the northern SCS.

Local control of globally competing patterns in coupled Swift-Hohenberg equations

NASA Astrophysics Data System (ADS)

Becker, Maximilian; Frenzel, Thomas; Niedermayer, Thomas; Reichelt, Sina; Mielke, Alexander; Bär, Markus

2018-04-01

We present analytical and numerical investigations of two anti-symmetrically coupled 1D Swift-Hohenberg equations (SHEs) with cubic nonlinearities. The SHE provides a generic formulation for pattern formation at a characteristic length scale. A linear stability analysis of the homogeneous state reveals a wave instability in addition to the usual Turing instability of uncoupled SHEs. We performed weakly nonlinear analysis in the vicinity of the codimension-two point of the Turing-wave instability, resulting in a set of coupled amplitude equations for the Turing pattern as well as left- and right-traveling waves. In particular, these complex Ginzburg-Landau-type equations predict two major things: there exists a parameter regime where multiple different patterns are stable with respect to each other and that the amplitudes of different patterns interact by local mutual suppression. In consequence, different patterns can coexist in distinct spatial regions, separated by localized interfaces. We identified specific mechanisms for controlling the position of these interfaces, which distinguish what kinds of patterns the interface connects and thus allow for global pattern selection. Extensive simulations of the original SHEs confirm our results.

Modulated amplitude waves in collisionally inhomogeneous Bose Einstein condensates

NASA Astrophysics Data System (ADS)

Porter, Mason A.; Kevrekidis, P. G.; Malomed, Boris A.; Frantzeskakis, D. J.

2007-05-01

We investigate the dynamics of an effectively one-dimensional Bose-Einstein condensate (BEC) with scattering length a subjected to a spatially periodic modulation, a=a(x)=a(x+L). This “collisionally inhomogeneous” BEC is described by a Gross-Pitaevskii (GP) equation whose nonlinearity coefficient is a periodic function of x. We transform this equation into a GP equation with a constant coefficient and an additional effective potential and study a class of extended wave solutions of the transformed equation. For weak underlying inhomogeneity, the effective potential takes a form resembling a superlattice, and the amplitude dynamics of the solutions of the constant-coefficient GP equation obey a nonlinear generalization of the Ince equation. In the small-amplitude limit, we use averaging to construct analytical solutions for modulated amplitude waves (MAWs), whose stability we subsequently examine using both numerical simulations of the original GP equation and fixed-point computations with the MAWs as numerically exact solutions. We show that “on-site” solutions, whose maxima correspond to maxima of a(x), are more robust and likely to be observed than their “off-site” counterparts.

Three-dimensional freak waves and higher-order wave-wave resonances

NASA Astrophysics Data System (ADS)

Badulin, S. I.; Ivonin, D. V.; Dulov, V. A.

2012-04-01

Quite often the freak wave phenomenon is associated with the mechanism of modulational (Benjamin-Feir) instability resulted from resonances of four waves with close directions and scales. This weakly nonlinear model reflects some important features of the phenomenon and is discussing in a great number of studies as initial stage of evolution of essentially nonlinear water waves. Higher-order wave-wave resonances attract incomparably less attention. More complicated mathematics and physics explain this disregard partially only. The true reason is a lack of adequate experimental background for the study of essentially three-dimensional water wave dynamics. We start our study with the classic example of New Year Wave. Two extreme events: the famous wave 26.5 meters and one of smaller 18.5 meters height (formally, not freak) of the same record, are shown to have pronounced features of essentially three-dimensional five-wave resonant interactions. The quasi-spectra approach is used for the data analysis in order to resolve adequately frequencies near the spectral peak fp ≈ 0.057Hz and, thus, to analyze possible modulations of the dominant wave component. In terms of the quasi-spectra the above two anomalous waves show co-existence of the peak harmonic and one at frequency f5w = 3/2fp that corresponds to maximum of five-wave instability of weakly nonlinear waves. No pronounced marks of usually discussed Benjamin-Feir instability are found in the record that is easy to explain: the spectral peak frequency fp corresponds to the non-dimensional depth parameter kD ≈ 0.92 (k - wavenumber, D ≈ 70 meters - depth at the Statoil platform Draupner site) that is well below the shallow water limit of the instability kD = 1.36. A unique data collection of wave records of the Marine Hydrophysical Institute in the Katsiveli platform (Black Sea) has been analyzed in view of the above findings of possible impact of the five-wave instability on freak wave occurrence. The data cover period October 14 - November 6, 2009 almost continuously. Antenna of 6 resistance wave gauges (a pentagon with one center gauge) is used to gain information on wave directions. Wave conditions vary from perfect still to storms with significant wave heights up to Hs = 1.7 meters and wind speeds 15m/s. Measurements with frequency 10Hz for dominant frequencies 0.1 - 0.2Hz fixed 40 freak wave events (criterium H/Hs > 2) and showed no dependence on Hs definitely. Data processing within frequency quasi-spectra approach and directional spectra reconstructions found pronounced features of essentially three-dimensional anomalous waves. All the events are associated with dramatic widening of instant frequency spectra in the range fp - f5w and stronger directional spreading. On the contrary, the classic Benjamin-Feir modulations show no definite links with the events and can be likely treated as dynamically neutral part of wave field. The apparent contradiction with the recent study (Saprykina, Dulov, Kuznetsov, Smolov, 2010) based on the same data collection can be explained partially by features of data processing. Physical roots of the inconsistency should be detailed in further studies. The work was supported by the Russian government contract 11.G34.31.0035 (signed 25 November 2010), Russian Foundation for Basic Research grant 11-05-01114-a, Ukrainian State Agency of Science, Innovations and Information under Contract M/412-2011 and ONR grant N000141010991. Authors gratefully acknowledge continuing support of these foundations.

Directed electromagnetic wave propagation in 1D metamaterial: Projecting operators method

NASA Astrophysics Data System (ADS)

Ampilogov, Dmitrii; Leble, Sergey

2016-07-01

We consider a boundary problem for 1D electrodynamics modeling of a pulse propagation in a metamaterial medium. We build and apply projecting operators to a Maxwell system in time domain that allows to split the linear propagation problem to directed waves for a material relations with general dispersion. Matrix elements of the projectors act as convolution integral operators. For a weak nonlinearity we generalize the linear results still for arbitrary dispersion and derive the system of interacting right/left waves with combined (hybrid) amplitudes. The result is specified for the popular metamaterial model with Drude formula for both permittivity and permeability coefficients. We also discuss and investigate stationary solutions of the system related to some boundary regimes.

Fluctuations and discrete particle noise in gyrokinetic simulation of drift waves

NASA Astrophysics Data System (ADS)

Jenkins, Thomas G.; Lee, W. W.

2007-03-01

The relevance of the gyrokinetic fluctuation-dissipation theorem (FDT) to thermal equilibrium and nonequilibrium states of the gyrokinetic plasma is explored, with particular focus being given to the contribution of weakly damped normal modes to the fluctuation spectrum. It is found that the fluctuation energy carried in the normal modes exhibits the proper scaling with particle count (as predicted by the FDT in thermal equilibrium) even in the presence of drift waves, which grow linearly and attain a nonlinearly saturated steady state. This favorable scaling is preserved, and the saturation amplitude of the drift wave unaffected, for parameter regimes in which the normal modes become strongly damped and introduce a broad spectrum of discreteness-induced background noise in frequency space.

Three-dimensional Hybrid Simulation Study of Anisotropic Turbulence in the Proton Kinetic Regime

NASA Astrophysics Data System (ADS)

Vasquez, Bernard J.; Markovskii, Sergei A.; Chandran, Benjamin D. G.

2014-06-01

Three-dimensional numerical hybrid simulations with particle protons and quasi-neutralizing fluid electrons are conducted for a freely decaying turbulence that is anisotropic with respect to the background magnetic field. The turbulence evolution is determined by both the combined root-mean-square (rms) amplitude for fluctuating proton bulk velocity and magnetic field and by the ratio of perpendicular to parallel wavenumbers. This kind of relationship had been considered in the past with regard to interplanetary turbulence. The fluctuations nonlinearly evolve to a turbulent phase whose net wave vector anisotropy is usually more perpendicular than the initial one, irrespective of the initial ratio of perpendicular to parallel wavenumbers. Self-similar anisotropy evolution is found as a function of the rms amplitude and parallel wavenumber. Proton heating rates in the turbulent phase vary strongly with the rms amplitude but only weakly with the initial wave vector anisotropy. Even in the limit where wave vectors are confined to the plane perpendicular to the background magnetic field, the heating rate remains close to the corresponding case with finite parallel wave vector components. Simulation results obtained as a function of proton plasma to background magnetic pressure ratio β p in the range 0.1-0.5 show that the wave vector anisotropy also weakly depends on β p .

Lagrangian description of warm plasmas

NASA Technical Reports Server (NTRS)

Kim, H.

1970-01-01

Efforts are described to extend the averaged Lagrangian method of describing small signal wave propagation and nonlinear wave interaction, developed by earlier workers for cold plasmas, to the more general conditions of warm collisionless plasmas, and to demonstrate particularly the effectiveness of the method in analyzing wave-wave interactions. The theory is developed for both the microscopic description and the hydrodynamic approximation to plasma behavior. First, a microscopic Lagrangian is formulated rigorously, and expanded in terms of perturbations about equilibrium. Two methods are then described for deriving a hydrodynamic Lagrangian. In the first of these, the Lagrangian is obtained by velocity integration of the exact microscopic Lagrangian. In the second, the expanded hydrodynamic Lagrangian is obtained directly from the expanded microscopic Lagrangian. As applications of the microscopic Lagrangian, the small-signal dispersion relations and the coupled mode equations are derived for all possible waves in a warm infinite, weakly inhomogeneous magnetoplasma, and their interactions are examined.

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

Ro, Stephen; Matzner, Christopher D., E-mail: ro@astro.utoronto.ca

Wave-driven outflows and non-disruptive explosions have been implicated in pre-supernova outbursts, supernova impostors, luminous blue variable eruptions, and some narrow-line and superluminous supernovae. To model these events, we investigate the dynamics of stars set in motion by strong acoustic pulses and wave trains, focusing on nonlinear wave propagation, shock formation, and an early phase of the development of a weak shock. We identify the shock formation radius, showing that a heuristic estimate based on crossing characteristics matches an exact expansion around the wave front and verifying both with numerical experiments. Our general analytical condition for shock formation applies to one-dimensionalmore » motions within any static environment, including both eruptions and implosions. We also consider the early phase of shock energy dissipation. We find that waves of super-Eddington acoustic luminosity always create shocks, rather than damping by radiative diffusion. Therefore, shock formation is integral to super-Eddington outbursts.« less

A Boussinesq-scaled, pressure-Poisson water wave model

NASA Astrophysics Data System (ADS)

Donahue, Aaron S.; Zhang, Yao; Kennedy, Andrew B.; Westerink, Joannes J.; Panda, Nishant; Dawson, Clint

2015-02-01

Through the use of Boussinesq scaling we develop and test a model for resolving non-hydrostatic pressure profiles in nonlinear wave systems over varying bathymetry. A Green-Nagdhi type polynomial expansion is used to resolve the pressure profile along the vertical axis, this is then inserted into the pressure-Poisson equation, retaining terms up to a prescribed order and solved using a weighted residual approach. The model shows rapid convergence properties with increasing order of polynomial expansion which can be greatly improved through the application of asymptotic rearrangement. Models of Boussinesq scaling of the fully nonlinear O (μ2) and weakly nonlinear O (μN) are presented, the analytical and numerical properties of O (μ2) and O (μ4) models are discussed. Optimal basis functions in the Green-Nagdhi expansion are determined through manipulation of the free-parameters which arise due to the Boussinesq scaling. The optimal O (μ2) model has dispersion accuracy equivalent to a Padé [2,2] approximation with one extra free-parameter. The optimal O (μ4) model obtains dispersion accuracy equivalent to a Padé [4,4] approximation with two free-parameters which can be used to optimize shoaling or nonlinear properties. In comparison to experimental results the O (μ4) model shows excellent agreement to experimental data.

The effect of shear stress on solitary waves in arteries.

PubMed

Demiray, H

1997-09-01

In the present work, we study the propagation of solitary waves in a prestressed thick walled elastic tube filled with an incompressible inviscid fluid. In order to include the geometric dispersion in the analysis the wall inertia and shear deformation effects are taken into account for the inner pressure-cross-sectional area relation. Using the reductive perturbation technique, the propagation of weakly non-linear waves in the long-wave approximation is examined. It is shown that, contrary to thin tube theories, the present approach makes it possible to have solitary waves even for a Mooney-Rivlin (M-R) material. Due to dependence of the coefficients of the governing Korteweg-deVries equation on initial deformation, the solution profile changes with inner pressure and the axial stretch. The variation of wave profiles for a class of elastic materials are depicted in graphic forms. As might be seen from these illustrations, with increasing thickness ratio, the profile of solitary wave is steepened for a M-R material but it is broadened for biological tissue.

Tollmien-Schlichting/vortex interactions in compressible boundary layer flows

NASA Technical Reports Server (NTRS)

Blackaby, Nicholas D.

1993-01-01

The weakly nonlinear interaction of oblique Tollmien-Schlichting waves and longitudinal vortices in compressible, high Reynolds number, boundary-layer flow over a flat plate is considered for all ranges of the Mach number. The interaction equations comprise of equations for the vortex which is indirectly forced by the waves via a boundary condition, whereas a vortex term appears in the amplitude equation for the wave pressure. The downstream solution properties of interaction equations are found to depend on the sign of an interaction coefficient. Compressibility is found to have a significant effect on the interaction properties; principally through its impact on the waves and their governing mechanism, the triple-deck structure. It is found that, in general, the flow quantities will grow slowly with increasing downstream co-ordinate; i.e. in general, solutions do not terminate in abrupt, finite-distance 'break-ups'.

Linear and nonlinear instability in vertical counter-current laminar gas-liquid flows

NASA Astrophysics Data System (ADS)

Schmidt, Patrick; Ó Náraigh, Lennon; Lucquiaud, Mathieu; Valluri, Prashant

2016-04-01

We consider the genesis and dynamics of interfacial instability in vertical gas-liquid flows, using as a model the two-dimensional channel flow of a thin falling film sheared by counter-current gas. The methodology is linear stability theory (Orr-Sommerfeld analysis) together with direct numerical simulation of the two-phase flow in the case of nonlinear disturbances. We investigate the influence of two main flow parameters on the interfacial dynamics, namely the film thickness and pressure drop applied to drive the gas stream. To make contact with existing studies in the literature, the effect of various density contrasts is also examined. Energy budget analyses based on the Orr-Sommerfeld theory reveal various coexisting unstable modes (interfacial, shear, internal) in the case of high density contrasts, which results in mode coalescence and mode competition, but only one dynamically relevant unstable interfacial mode for low density contrast. A study of absolute and convective instability for low density contrast shows that the system is absolutely unstable for all but two narrow regions of the investigated parameter space. Direct numerical simulations of the same system (low density contrast) show that linear theory holds up remarkably well upon the onset of large-amplitude waves as well as the existence of weakly nonlinear waves. For high density contrasts, corresponding more closely to an air-water-type system, linear stability theory is also successful at determining the most-dominant features in the interfacial wave dynamics at early-to-intermediate times. Nevertheless, the short waves selected by the linear theory undergo secondary instability and the wave train is no longer regular but rather exhibits chaotic motion. The same linear stability theory predicts when the direction of travel of the waves changes — from downwards to upwards. We outline the practical implications of this change in terms of loading and flooding. The change in direction of the wave propagation is represented graphically in terms of a flow map based on the liquid and gas flow rates and the prediction carries over to the nonlinear regime with only a small deviation.

Linear and nonlinear instability in vertical counter-current laminar gas-liquid flows

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

Schmidt, Patrick; Lucquiaud, Mathieu; Valluri, Prashant, E-mail: prashant.valluri@ed.ac.uk

We consider the genesis and dynamics of interfacial instability in vertical gas-liquid flows, using as a model the two-dimensional channel flow of a thin falling film sheared by counter-current gas. The methodology is linear stability theory (Orr-Sommerfeld analysis) together with direct numerical simulation of the two-phase flow in the case of nonlinear disturbances. We investigate the influence of two main flow parameters on the interfacial dynamics, namely the film thickness and pressure drop applied to drive the gas stream. To make contact with existing studies in the literature, the effect of various density contrasts is also examined. Energy budget analysesmore » based on the Orr-Sommerfeld theory reveal various coexisting unstable modes (interfacial, shear, internal) in the case of high density contrasts, which results in mode coalescence and mode competition, but only one dynamically relevant unstable interfacial mode for low density contrast. A study of absolute and convective instability for low density contrast shows that the system is absolutely unstable for all but two narrow regions of the investigated parameter space. Direct numerical simulations of the same system (low density contrast) show that linear theory holds up remarkably well upon the onset of large-amplitude waves as well as the existence of weakly nonlinear waves. For high density contrasts, corresponding more closely to an air-water-type system, linear stability theory is also successful at determining the most-dominant features in the interfacial wave dynamics at early-to-intermediate times. Nevertheless, the short waves selected by the linear theory undergo secondary instability and the wave train is no longer regular but rather exhibits chaotic motion. The same linear stability theory predicts when the direction of travel of the waves changes — from downwards to upwards. We outline the practical implications of this change in terms of loading and flooding. The change in direction of the wave propagation is represented graphically in terms of a flow map based on the liquid and gas flow rates and the prediction carries over to the nonlinear regime with only a small deviation.« less

Effects of discrete-electrode arrangement on traveling-wave electroosmotic pumping

NASA Astrophysics Data System (ADS)

Liu, Weiyu; Shao, Jinyou; Ren, Yukun; Wu, Yupan; Wang, Chunhui; Ding, Haitao; Jiang, Hongyuan; Ding, Yucheng

2016-09-01

Traveling-wave electroosmotic (TWEO) pumping arises from the action of an imposed traveling-wave (TW) electric field on its own induced charge in the diffuse double layer, which is formed on top of an electrode array immersed in electrolyte solutions. Such a traveling field can be merely realized in practice by a discrete electrode array upon which the corresponding voltages of correct phase are imposed. By employing the theory of linear and weakly nonlinear double-layer charging dynamics, a physical model incorporating both the nonlinear surface capacitance of diffuse layer and Faradaic current injection is developed herein in order to quantify the changes in TWEO pumping performance from a single-mode TW to discrete electrode configuration. Benefiting from the linear analysis, we investigate the influence of using discrete electrode array to create the TW signal on the resulting fluid motion, and several approaches are suggested to improve the pumping performance. In the nonlinear regime, our full numerical analysis considering the intervening isolation spacing indicates that a practical four-phase discrete electrode configuration of equal electrode and gap width exhibits stronger nonlinearity than expected from the idealized pump applied with a single-mode TW in terms of voltage-dependence of the ideal pumping frequency and peak flow rate, though it has a much lower pumping performance. For model validation, pumping of electrolytes by TWEO is achieved over a confocal spiral four-phase electrode array covered by an insulating microchannel; measurement of flow velocity indicates the modified nonlinear theory considering moderate Faradaic conductance is indeed a more accurate physical description of TWEO. These results offer useful guidelines for designing high-performance TWEO microfluidic pumps with discrete electrode array.

Oblique propagation of solitary waves in weakly relativistic magnetized plasma with kappa distributed electrons in the presence of negative ions

NASA Astrophysics Data System (ADS)

Salmanpoor, H.; Sharifian, M.; Gholipour, S.; Borhani Zarandi, M.; Shokri, B.

2018-03-01

The oblique propagation of nonlinear ion acoustic solitary waves (solitons) in magnetized collisionless and weakly relativistic plasma with positive and negative ions and super thermal electrons has been examined by using reduced perturbation method to obtain the Korteweg-de Vries equation that admits an obliquely propagating soliton solution. We have investigated the effects of plasma parameters like negative ion density, electrons temperature, angle between wave vector and magnetic field, ions velocity, and k (spectral index in kappa distribution) on the amplitude and width of solitary waves. It has been found out that four modes exist in our plasma model, but the analysis of the results showed that only two types of ion acoustic modes (fast and slow) exist in the plasma and in special cases only one mode could be propagated. The parameters of plasma for these two modes (or one mode) determine which one is rarefactive and which one is compressive. The main parameter is negative ions density (β) indicating which mode is compressive or rarefactive. The effects of the other plasma parameters on amplitude and width of the ion acoustic solitary waves have been studied. The main conclusion is that the effects of the plasma parameters on amplitude and width of the solitary wave strongly depend on the value of the negative ion density.

A Landau fluid model for dispersive magnetohydrodynamics

NASA Astrophysics Data System (ADS)

Passot, T.; Sulem, P. L.

2004-11-01

A monofluid model with Landau damping is presented for strongly magnetized electron-proton collisionless plasmas whose distribution functions are close to bi-Maxwellians. This description that includes dynamical equations for the gyrotropic components of the pressure and heat flux tensors, extends the Landau-fluid model of Snyder, Hammett, and Dorland [Phys. Plasmas 4, 3974 (1997)] by retaining Hall effect and finite Larmor radius corrections. It accurately reproduces the weakly nonlinear dynamics of dispersive Alfvén waves whose wavelengths are large compared to the ion inertial length, whatever their direction of propagation, and also the rapid Landau dissipation of long magnetosonic waves in a warm plasma.

REVIEWS OF TOPICAL PROBLEMS: Generation of large-scale eddies and zonal winds in planetary atmospheres

NASA Astrophysics Data System (ADS)

Onishchenko, O. G.; Pokhotelov, O. A.; Astafieva, N. M.

2008-06-01

The review deals with a theoretical description of the generation of zonal winds and vortices in a turbulent barotropic atmosphere. These large-scale structures largely determine the dynamics and transport processes in planetary atmospheres. The role of nonlinear effects on the formation of mesoscale vortical structures (cyclones and anticyclones) is examined. A new mechanism for zonal wind generation in planetary atmospheres is discussed. It is based on the parametric generation of convective cells by finite-amplitude Rossby waves. Weakly turbulent spectra of Rossby waves are considered. The theoretical results are compared to the results of satellite microwave monitoring of the Earth's atmosphere.

Kinetic theory for the ion humps at the foot of the Earth's bow shock

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

Jovanovic, D.; Krasnoselskikh, V. V.

2009-10-15

The nonlinear kinetic theory is presented for the ion acoustic perturbations at the foot of the Earth's quasiperpendicular bow shock, that is characterized by weakly magnetized electrons and unmagnetized ions. The streaming ions, due to the reflection of the solar wind ions from the shock, provide the free energy source for the linear instability of the acoustic wave. In the fully nonlinear regime, a coherent localized solution is found in the form of a stationary ion hump, which is traveling with the velocity close to the phase velocity of the linear mode. The structure is supported by the nonlinearities comingmore » from the increased population of the resonant beam ions, trapped in the self-consistent potential. As their size in the direction perpendicular to the local magnetic field is somewhat smaller that the electron Larmor radius and much larger that the Debye length, their spatial properties are determined by the effects of the magnetic field on weakly magnetized electrons. These coherent structures provide a theoretical explanation for the bipolar electric pulses, observed upstream of the shock by Polar and Cluster satellite missions.« less

Supermodes in Coupled Multi-Core Waveguide Structures

DTIC Science & Technology

2016-04-01

and therefore can be treated as linear polarization (LP) modes. In essence, the LP modes are scalar approximations of the vector mode fields and contain...field, including the discovery of optical discrete solitons , Bragg and vector solitons in fibers, nonlinear surface waves, and the discovery of self...increased for an isolated core, it can guide high-order modes. For optical fibers with low re- fractive index contrast, the vector modes are weakly guided

Magnetospheric Multiscale Observations of an Ion Diffusion Region With Large Guide Field at the Magnetopause: Current System, Electron Heating, and Plasma Waves

NASA Astrophysics Data System (ADS)

Zhou, M.; Berchem, J.; Walker, R. J.; El-Alaoui, M.; Goldstein, M. L.; Lapenta, G.; Deng, X.; Li, J.; Le Contel, O.; Graham, D. B.; Lavraud, B.; Paterson, W. R.; Giles, B. L.; Burch, J. L.; Torbert, R. B.; Russell, C. T.; Strangeway, R. J.; Zhao, C.; Ergun, R. E.; Lindqvist, P.-A.; Marklund, G.

2018-03-01

We report Magnetospheric Multiscale (MMS) observations of a reconnecting current sheet in the presence of a weak density asymmetry with large guide field at the dayside magnetopause. An ion diffusion region (IDR) was detected associated with this current sheet. Parallel current dominated over the perpendicular current in the IDR, as found in previous studies of component reconnection. Electrons were preferentially heated parallel to the magnetic field within the IDR. The heating was manifested as a flattop distribution below 400 eV. Two types of electromagnetic electron whistler waves were observed within the regions where electrons were heated. One type of whistler wave was associated with nonlinear structures in E|| with amplitudes up to 20 mV/m. The other type was not associated with any structures in E||. Poynting fluxes of these two types of whistler waves were directed away from the X-line. We suggest that the nonlinear evolution of the oblique whistler waves gave rise to the solitary structures in E||. There was a perpendicular super-Alfvénic outflow jet that was carried by magnetized electrons. Intense electrostatic lower hybrid drift waves were localized in the current sheet center and were probably driven by the super-Alfvénic electron jet, the velocity of which was approximately equal to the diamagnetic drift of demagnetized ions. Our observations suggest that the guide field significantly modified the structures (Hall electromagnetic fields and current system) and wave properties in the IDR.

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

NASA Astrophysics Data System (ADS)

Kurkina, Oxana; Talipova, Tatiana; Kurkin, Andrey; Naumov, Alexander; Rybin, Artem

2017-04-01

Kinematic parameters of second-mode internal waves (in the framework of weakly nonlinear model of the Gardner equation) are calculated for the region of the South China Sea on a base of GDEM climatology. The prognostic parameters of the model include phase speed of long linear waves, coefficients of dispersion, quadratic and cubic nonlinearity, location (in vertical) of minimum, zero and maximum of the second vertical baroclinic mode and the ratio of its maximal and minimal values. All the parameters are presented in the form of geographical maps for winter (January) and summer (July) seasons. Frequence (in the sense of occurrence) histograms and scatter plots with depth are also given for all the parameters. Special attention is paid to the conditions of normalizing for internal waves of the second mode, as it possesses two extremes. Here some freedom exists, but for correct further modeling of internal waves within the Gardner model one has to fix and keep the same normalization (at maximum or at minimum) for whole a basin. Constructed arrays of prognostic parameters of second-mode internal waves are necessary for the estimations of shape and width (at fixed amplitude) of internal solitary and breather-like waves, limiting amplitudes of internal solitary waves of different families, for assessment of near-bed and near-surface flows induced by such waves, and for evaluation of transport distance for dissolved and suspended matter. The presented results of research are obtained with the support of the Russian Foundation for Basic Research grant 16-05-00049.

Adiabatic decay of internal solitons due to Earth's rotation within the framework of the Gardner-Ostrovsky equation

NASA Astrophysics Data System (ADS)

Obregon, Maria; Raj, Nawin; Stepanyants, Yury

2018-03-01

The adiabatic decay of different types of internal wave solitons caused by the Earth's rotation is studied within the framework of the Gardner-Ostrovsky equation. The governing equation describing such processes includes quadratic and cubic nonlinear terms, as well as the Boussinesq and Coriolis dispersions: (ut + c ux + α u ux + α1 u2 ux + β uxxx)x = γ u. It is shown that at the early stage of evolution solitons gradually decay under the influence of weak Earth's rotation described by the parameter γ. The characteristic decay time is derived for different types of solitons for positive and negative coefficients of cubic nonlinearity α1 (both signs of that parameter may occur in the oceans). The coefficient of quadratic nonlinearity α determines only a polarity of solitary wave when α1 < 0 or the asymmetry of solitary waves of opposite polarity when α1 > 0. It is found that the adiabatic theory describes well the decay of solitons having bell-shaped profiles. In contrast to that, large amplitude table-top solitons, which can exist when α1 is negative, are structurally unstable. Under the influence of Earth's rotation, they transfer first to the bell-shaped solitons, which decay then adiabatically. Estimates of the characteristic decay time of internal solitons are presented for the real oceanographic conditions.

Semiconductor quantum well irradiated by a two-mode electromagnetic field as a terahertz emitter

NASA Astrophysics Data System (ADS)

Mandal, S.; Liew, T. C. H.; Kibis, O. V.

2018-04-01

We study theoretically the nonlinear optical properties of a semiconductor quantum well (QW) irradiated by a two-mode electromagnetic wave consisting of a strong resonant dressing field and a weak off-resonant driving field. In the considered strongly coupled electron-field system, the dressing field opens dynamic Stark gaps in the electron energy spectrum of the QW, whereas the driving field induces electron oscillations in the QW plane. Since the gapped electron spectrum restricts the amplitude of the oscillations, the emission of a frequency comb from the QW appears. Therefore, the doubly driven QW operates as a nonlinear optical element which can be used, particularly, for optically controlled generation of terahertz radiation.

Nonlinear Gap Junctions Enable Long-Distance Propagation of Pulsating Calcium Waves in Astrocyte Networks

PubMed Central

Goldberg, Mati; De Pittà, Maurizio; Volman, Vladislav; Berry, Hugues; Ben-Jacob, Eshel

2010-01-01

A new paradigm has recently emerged in brain science whereby communications between glial cells and neuron-glia interactions should be considered together with neurons and their networks to understand higher brain functions. In particular, astrocytes, the main type of glial cells in the cortex, have been shown to communicate with neurons and with each other. They are thought to form a gap-junction-coupled syncytium supporting cell-cell communication via propagating Ca2+ waves. An identified mode of propagation is based on cytoplasm-to-cytoplasm transport of inositol trisphosphate (IP3) through gap junctions that locally trigger Ca2+ pulses via IP3-dependent Ca2+-induced Ca2+ release. It is, however, currently unknown whether this intracellular route is able to support the propagation of long-distance regenerative Ca2+ waves or is restricted to short-distance signaling. Furthermore, the influence of the intracellular signaling dynamics on intercellular propagation remains to be understood. In this work, we propose a model of the gap-junctional route for intercellular Ca2+ wave propagation in astrocytes. Our model yields two major predictions. First, we show that long-distance regenerative signaling requires nonlinear coupling in the gap junctions. Second, we show that even with nonlinear gap junctions, long-distance regenerative signaling is favored when the internal Ca2+ dynamics implements frequency modulation-encoding oscillations with pulsating dynamics, while amplitude modulation-encoding dynamics tends to restrict the propagation range. As a result, spatially heterogeneous molecular properties and/or weak couplings are shown to give rise to rich spatiotemporal dynamics that support complex propagation behaviors. These results shed new light on the mechanisms implicated in the propagation of Ca2+ waves across astrocytes and the precise conditions under which glial cells may participate in information processing in the brain. PMID:20865153

Numerical Simulations of Upstream Propagating Solitary Waves and Wave Breaking In A Stratified Fjord

NASA Astrophysics Data System (ADS)

Stastna, M.; Peltier, W. R.

In this talk we will discuss ongoing numerical modeling of the flow of a stratified fluid over large scale topography motivated by observations in Knight Inlet, a fjord in British Columbia, Canada. After briefly surveying the work done on the topic in the past we will discuss our latest set of simulations in which we have observed the gener- ation and breaking of three different types of nonlinear internal waves in the lee of the sill topography. The first type of wave observed is a large lee wave in the weakly strat- ified main portion of the water column, The second is an upward propagating internal wave forced by topography that breaks in the strong, near-surface pycnocline. The third is a train of upstream propagating solitary waves that, in certain circumstances, form as breaking waves consisting of a nearly solitary wave envelope and a highly unsteady core near the surface. Time premitting, we will comment on the implications of these results for our long term goal of quantifying tidally driven mixing in Knight Inlet.

Marine natural hazards in coastal zone: observations, analysis and modelling (Plinius Medal Lecture)

NASA Astrophysics Data System (ADS)

Didenkulova, Ira

2010-05-01

Giant surface waves approaching the coast frequently cause extensive coastal flooding, destruction of coastal constructions and loss of lives. Such waves can be generated by various phenomena: strong storms and cyclones, underwater earthquakes, high-speed ferries, aerial and submarine landslides. The most famous examples of such events are the catastrophic tsunami in the Indian Ocean, which occurred on 26 December 2004 and hurricane Katrina (28 August 2005) in the Atlantic Ocean. The huge storm in the Baltic Sea on 9 January 2005, which produced unexpectedly long waves in many areas of the Baltic Sea and the influence of unusually high surge created by long waves from high-speed ferries, should also be mentioned as examples of regional marine natural hazards connected with extensive runup of certain types of waves. The processes of wave shoaling and runup for all these different marine natural hazards (tsunami, coastal freak waves, ship waves) are studied based on rigorous solutions of nonlinear shallow-water theory. The key and novel results presented here are: i) parameterization of basic formulas for extreme runup characteristics for bell-shape waves, showing that they weakly depend on the initial wave shape, which is usually unknown in real sea conditions; ii) runup analysis of periodic asymmetric waves with a steep front, as such waves are penetrating inland over large distances and with larger velocities than symmetric waves; iii) statistical analysis of irregular wave runup demonstrating that wave nonlinearity nearshore does not influence on the probability distribution of the velocity of the moving shoreline and its moments, and influences on the vertical displacement of the moving shoreline (runup). Wave runup on convex beaches and in narrow bays, which allow abnormal wave amplification is also discussed. Described analytical results are used for explanation of observed extreme runup of tsunami, freak (sneaker) waves and ship waves on different coasts along different bottom profiles.

Gravitational-Wave Tests of General Relativity with Ground-Based Detectors and Pulsar-Timing Arrays.

PubMed

Yunes, Nicolás; Siemens, Xavier

2013-01-01

This review is focused on tests of Einstein's theory of general relativity with gravitational waves that are detectable by ground-based interferometers and pulsar-timing experiments. Einstein's theory has been greatly constrained in the quasi-linear, quasi-stationary regime, where gravity is weak and velocities are small. Gravitational waves will allow us to probe a complimentary, yet previously unexplored regime: the non-linear and dynamical strong-field regime . Such a regime is, for example, applicable to compact binaries coalescing, where characteristic velocities can reach fifty percent the speed of light and gravitational fields are large and dynamical. This review begins with the theoretical basis and the predicted gravitational-wave observables of modified gravity theories. The review continues with a brief description of the detectors, including both gravitational-wave interferometers and pulsar-timing arrays, leading to a discussion of the data analysis formalism that is applicable for such tests. The review ends with a discussion of gravitational-wave tests for compact binary systems.

Vorticity Transport and Wave Emission In A Protoplanetary Disk

NASA Technical Reports Server (NTRS)

Davis, S. S.; Davis, Sanford (Technical Monitor)

2002-01-01

Higher order numerical algorithms (4th order in time, 3rd order in space) are applied to the Euler equations and are used to examine vorticity transport and wave motion in a non-self gravitating, initially isentropic Keplerian disk. In this talk we will examine the response of the disk to an isolated vortex with a circulation about equal to the rotation rate of Jupiter. The vortex is located on the 4 AU circle and the nebula is simulated from 1 to 24 AU. We show that the vortex emits pressure-supported density and Rossby-type wave packets before it decays within a few orbits. The acoustic density waves evolve into weak (non entropy preserving) shock waves that propagate over the entire disk. The Rossby waves remain in the vicinity of the initial vortex disturbance, but are rapidly damped. Temporal frequencies and spatial wavenumbers are derived from the nonlinear simulation data and correlated with analytical dispersion relations from the linearized Euler and energy equations.

4-wave dynamics in kinetic wave turbulence

NASA Astrophysics Data System (ADS)

Chibbaro, Sergio; Dematteis, Giovanni; Rondoni, Lamberto

2018-01-01

A general Hamiltonian wave system with quartic resonances is considered, in the standard kinetic limit of a continuum of weakly interacting dispersive waves with random phases. The evolution equation for the multimode characteristic function Z is obtained within an ;interaction representation; and a perturbation expansion in the small nonlinearity parameter. A frequency renormalization is performed to remove linear terms that do not appear in the 3-wave case. Feynman-Wyld diagrams are used to average over phases, leading to a first order differential evolution equation for Z. A hierarchy of equations, analogous to the Boltzmann hierarchy for low density gases is derived, which preserves in time the property of random phases and amplitudes. This amounts to a general formalism for both the N-mode and the 1-mode PDF equations for 4-wave turbulent systems, suitable for numerical simulations and for investigating intermittency. Some of the main results which are developed here in detail have been tested numerically in a recent work.

Nonlinear waves in viscoelastic magnetized complex astroplasmas with polarized dust-charge variations

NASA Astrophysics Data System (ADS)

Das, Papari; Karmakar, Pralay Kumar

2018-01-01

A nonextensive nonthermal magnetized viscoelastic astrofluid, compositionally containing nonthermal electrons and ions together with massive polarized dust micro-spherical grains of variable electric charge, is allowed to endure weakly nonlinear perturbation around its equilibrium. The nonextensivity originating from the large-scale non-local effects is included via the Tsallis thermo-statistical distribution laws describing the lighter species. Assuming the equilibrium as a homogeneous hydrostatic one, the dust polarization effects are incorporated via the conventional homogeneous polarization force law. The perturbed fluid model evolves as a unique conjugate pair of coupled extended Korteweg-de Vries (e-KdV) equations. A constructed numerical tapestry shows the collective excitations of a new pair of distinct classes of nonlinear mode structures in new parametric space. The first family indicates periodic electrostatic compressive eigenmodes in the form of soliton-chains. Likewise, the second one reveals gravitational rarefactive solitary patterns. Their microphysical multi-parametric dependencies of the eigen-patterns are illustratively analyzed and bolstered. The paper ends up with some promising implications and applications in the astro-cosmo-plasmic context of wave-induced accretive triggering processes responsible for gravitationally bounded (gravito-condensed) astro-structure formation, such as stellesimals, planetsimals, etc.

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

Stringent limitations on reductive perturbation studies of nonplanar acoustic solitons in plasmas

NASA Astrophysics Data System (ADS)

Verheest, Frank; Hellberg, Manfred A.

2016-06-01

More than fifty years ago, the Korteweg-de Vries equation was shown to describe not only solitary surface waves on shallow water, but also nonlinear ion-acoustic waves. Because of the algorithmic ease of using reductive perturbation theory, intensive research followed on a wide range of wave types. Soon, the formalism was extended to nonplanar modes by introducing a stretching designed to accommodate spherically and cylindrically symmetric ion-acoustic waves. Over the last two decades many authors followed this approach, but almost all have ignored the severe restrictions in parameter space imposed by the Ansatz. In addition, for other steps in the formalism, the justification is often not spelled out, leading to effects that are physically undesirable or ambiguous. Hence, there is a need to critically assess this approach to nonplanar modes and to use it with the utmost care, respecting the restrictions on its validity. Only inward propagation may be meaningfully studied and respect for weak nonlinearities of at most 1/10 implies that one cannot get closer to the axis or centre of symmetry than about 30 Debye lengths. Thus, one is in a regime where the modes are quasi-planar and not particularly interesting. Most papers disregard these constraints and hence reach questionable conclusions.

Electron beam-plasma interaction and electron-acoustic solitary waves in a plasma with suprathermal electrons

NASA Astrophysics Data System (ADS)

Danehkar, A.

2018-06-01

Suprathermal electrons and inertial drifting electrons, so called electron beam, are crucial to the nonlinear dynamics of electrostatic solitary waves observed in several astrophysical plasmas. In this paper, the propagation of electron-acoustic solitary waves (EAWs) is investigated in a collisionless, unmagnetized plasma consisting of cool inertial background electrons, hot suprathermal electrons (modeled by a κ-type distribution), and stationary ions. The plasma is penetrated by a cool electron beam component. A linear dispersion relation is derived to describe small-amplitude wave structures that shows a weak dependence of the phase speed on the electron beam velocity and density. A (Sagdeev-type) pseudopotential approach is employed to obtain the existence domain of large-amplitude solitary waves, and investigate how their nonlinear structures depend on the kinematic and physical properties of the electron beam and the suprathermality (described by κ) of the hot electrons. The results indicate that the electron beam can largely alter the EAWs, but can only produce negative polarity solitary waves in this model. While the electron beam co-propagates with the solitary waves, the soliton existence domain (Mach number range) becomes narrower (nearly down to nil) with increasing the beam speed and the beam-to-hot electron temperature ratio, and decreasing the beam-to-cool electron density ratio in high suprathermality (low κ). It is found that the electric potential amplitude largely declines with increasing the beam speed and the beam-to-cool electron density ratio for co-propagating solitary waves, but is slightly decreased by raising the beam-to-hot electron temperature ratio.

Realization of a twin beam source based on four-wave mixing in Cesium

NASA Astrophysics Data System (ADS)

Adenier, G.; Calonico, D.; Micalizio, S.; Samantaray, N.; Degiovanni, I. P.; Berchera, I. Ruo

2016-05-01

Four-wave mixing (4WM) is a known source of intense non-classical twin beams. It can be generated when an intense laser beam (the pump) and a weak laser beam (the seed) overlap in a χ(3) medium (here Cesium vapor), with frequencies close to resonance with atomic transitions. The twin beams generated by 4WM have frequencies naturally close to atomic transitions, and can be intense (gain ≫1) even in the CW pump regime, which is not the case for PDC χ(2) phenomenon in nonlinear crystals. So, 4WM is well suited for atom-light interaction and atom-based quantum-protocols. Here, we present the first realization of a source of 4-wave mixing exploiting D2 line of Cesium atoms.

Small data global solutions for the Camassa–Choi equations

NASA Astrophysics Data System (ADS)

Harrop-Griffiths, Benjamin; Marzuola, Jeremy L.

2018-05-01

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

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.

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

NASA Astrophysics Data System (ADS)

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

2014-05-01

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

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

NASA Astrophysics Data System (ADS)

Benoit, Michel

2017-04-01

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

Measuring the linear and nonlinear elastic properties of brain tissue with shear waves and inverse analysis.

PubMed

Jiang, Yi; Li, Guoyang; Qian, Lin-Xue; Liang, Si; Destrade, Michel; Cao, Yanping

2015-10-01

We use supersonic shear wave imaging (SSI) technique to measure not only the linear but also the nonlinear elastic properties of brain matter. Here, we tested six porcine brains ex vivo and measured the velocities of the plane shear waves induced by acoustic radiation force at different states of pre-deformation when the ultrasonic probe is pushed into the soft tissue. We relied on an inverse method based on the theory governing the propagation of small-amplitude acoustic waves in deformed solids to interpret the experimental data. We found that, depending on the subjects, the resulting initial shear modulus [Formula: see text] varies from 1.8 to 3.2 kPa, the stiffening parameter [Formula: see text] of the hyperelastic Demiray-Fung model from 0.13 to 0.73, and the third- [Formula: see text] and fourth-order [Formula: see text] constants of weakly nonlinear elasticity from [Formula: see text]1.3 to [Formula: see text]20.6 kPa and from 3.1 to 8.7 kPa, respectively. Paired [Formula: see text] test performed on the experimental results of the left and right lobes of the brain shows no significant difference. These values are in line with those reported in the literature on brain tissue, indicating that the SSI method, combined to the inverse analysis, is an efficient and powerful tool for the mechanical characterization of brain tissue, which is of great importance for computer simulation of traumatic brain injury and virtual neurosurgery.

Modelling strong seismic ground motion: three-dimensional loading path versus wavefield polarization

NASA Astrophysics Data System (ADS)

Santisi d'Avila, Maria Paola; Lenti, Luca; Semblat, Jean-François

2012-09-01

Seismic waves due to strong earthquakes propagating in surficial soil layers may both reduce soil stiffness and increase the energy dissipation into the soil. To investigate seismic wave amplification in such cases, past studies have been devoted to one-directional shear wave propagation in a soil column (1D-propagation) considering one motion component only (1C-polarization). Three independent purely 1C computations may be performed ('1D-1C' approach) and directly superimposed in the case of weak motions (linear behaviour). This research aims at studying local site effects by considering seismic wave propagation in a 1-D soil profile accounting for the influence of the 3-D loading path and non-linear hysteretic behaviour of the soil. In the proposed '1D-3C' approach, the three components (3C-polarization) of the incident wave are simultaneously propagated into a horizontal multilayered soil. A 3-D non-linear constitutive relation for the soil is implemented in the framework of the Finite Element Method in the time domain. The complex rheology of soils is modelled by mean of a multisurface cyclic plasticity model of the Masing-Prandtl-Ishlinskii-Iwan type. The great advantage of this choice is that the only data needed to describe the model is the modulus reduction curve. A parametric study is carried out to characterize the changes in the seismic motion of the surficial layers due to both incident wavefield properties and soil non-linearities. The numerical simulations show a seismic response depending on several parameters such as polarization of seismic waves, material elastic and dynamic properties, as well as on the impedance contrast between layers and frequency content and oscillatory character of the input motion. The 3-D loading path due to the 3C-polarization leads to multi-axial stress interaction that reduces soil strength and increases non-linear effects. The non-linear behaviour of the soil may have beneficial or detrimental effects on the seismic response at the free surface, depending on the energy dissipation rate. Free surface time histories, stress-strain hysteresis loops and in-depth profiles of octahedral stress and strain are estimated for each soil column. The combination of three separate 1D-1C non-linear analyses is compared to the proposed 1D-3C approach, evidencing the influence of the 3C-polarization and the 3-D loading path on strong seismic motions.

Variational modelling of extreme waves through oblique interaction of solitary waves: application to Mach reflection

NASA Astrophysics Data System (ADS)

Gidel, Floriane; Bokhove, Onno; Kalogirou, Anna

2017-01-01

In this work, we model extreme waves that occur due to Mach reflection through the intersection of two obliquely incident solitary waves. For a given range of incident angles and amplitudes, the Mach stem wave grows linearly in length and amplitude, reaching up to 4 times the amplitude of the incident waves. A variational approach is used to derive the bidirectional Benney-Luke equations, an asymptotic equivalent of the three-dimensional potential-flow equations modelling water waves. This nonlinear and weakly dispersive model has the advantage of allowing wave propagation in two horizontal directions, which is not the case with the unidirectional Kadomtsev-Petviashvili (KP) equation used in most previous studies. A variational Galerkin finite-element method is applied to solve the system numerically in Firedrake with a second-order Störmer-Verlet temporal integration scheme, in order to obtain stable simulations that conserve the overall mass and energy of the system. Using this approach, we are able to get close to the 4-fold amplitude amplification predicted by Miles.

Pressure wave propagation in fluid-filled co-axial elastic tubes. Part 1: Basic theory.

PubMed

Berkouk, K; Carpenter, P W; Lucey, A D

2003-12-01

Our work is motivated by ideas about the pathogenesis of syringomyelia. This is a serious disease characterized by the appearance of longitudinal cavities within the spinal cord. Its causes are unknown, but pressure propagation is probably implicated. We have developed an inviscid theory for the propagation of pressure waves in co-axial, fluid-filled, elastic tubes. This is intended as a simple model of the intraspinal cerebrospinal-fluid system. Our approach is based on the classic theory for the propagation of longitudinal waves in single, fluid-filled, elastic tubes. We show that for small-amplitude waves the governing equations reduce to the classic wave equation. The wave speed is found to be a strong function of the ratio of the tubes' cross-sectional areas. It is found that the leading edge of a transmural pressure pulse tends to generate compressive waves with converging wave fronts. Consequently, the leading edge of the pressure pulse steepens to form a shock-like elastic jump. A weakly nonlinear theory is developed for such an elastic jump.

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

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.

Modulated optical phase conjugation in rhodamine 110 doped boric acid glass saturable absorber thin films

NASA Astrophysics Data System (ADS)

Sharma, Ramesh C.; Waigh, Thomas A.; Singh, Jagdish P.

2008-03-01

The optical phase conjugation signal in nearly nondegenerate four wave mixing was studied using a rhodamine 110 doped boric acid glass saturable absorber nonlinear medium. We have demonstrated a narrow band optical filter (2.56±0.15Hz) using an optical phase conjugation signal in the frequency modulation of a weak probe beam in the presence of two strong counterpropagating pump beams in rhodamine 110 doped boric acid glass thin films (10-4m). Both the pump beams and the probe beam are at a wavelength of 488nm (continuous-wave Ar+ laser). The probe beam frequency was detuned with a ramp signal using a piezoelectric transducer mirror.

Van Allen Probes observations of structured whistler mode activity and coincident electron Landau acceleration inside a remnant plasmaspheric plume

NASA Astrophysics Data System (ADS)

Woodroffe, J. R.; Jordanova, V. K.; Funsten, H. O.; Streltsov, A. V.; Bengtson, M. T.; Kletzing, C. A.; Wygant, J. R.; Thaller, S. A.; Breneman, A. W.

2017-03-01

We present observations from the Van Allen Probes spacecraft that identify a region of intense whistler mode activity within a large density enhancement outside of the plasmasphere. We speculate that this density enhancement is part of a remnant plasmaspheric plume, with the observed wave being driven by a weakly anisotropic electron injection that drifted into the plume and became nonlinearly unstable to whistler emission. Particle measurements indicate that a significant fraction of thermal (<100 eV) electrons within the plume were subject to Landau acceleration by these waves, an effect that is naturally explained by whistler emission within a gradient and high-density ducting inside a density enhancement.

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

Passot, T.; Sulem, P. L., E-mail: passot@oca.eu, E-mail: sulem@oca.eu

A phenomenological turbulence model for kinetic Alfvén waves in a magnetized collisionless plasma that is able to reproduce the non-universal power-law spectra observed at the sub-ion scales in the solar wind and the terrestrial magnetosphere is presented. The process of temperature homogenization along distorted magnetic field lines, induced by Landau damping, affects the turbulence transfer time and results in a steepening of the sub-ion power-law spectrum of critically balanced turbulence, whose exponent is sensitive to the ratio between the Alfvén wave period and the nonlinear timescale. Transition from large-scale weak turbulence to smaller scale strong turbulence is captured and nonlocalmore » interactions, relevant in the case of steep spectra, are accounted for.« less

Observation of Tropical Cyclone-Induced Shallow Water Currents in Taiwan Strait

NASA Astrophysics Data System (ADS)

Shen, Junqiang; Qiu, Yun; Zhang, Shanwu; Kuang, Fangfang

2017-06-01

The data from three stations equipped with Acoustic Doppler Current Profilers (ADCPs) deployed in the shallow water of the Taiwan Strait (TWS) were used to study the shallow coastal ocean response to five quasi-continuous tropical cyclone (TC) events in the late summer 2006. We revealed that, in the forced stage, when the large and strong TC (Bilis) transited, the geostrophic currents were formed which dominated the whole event, while the strong but relatively small one (Saomai) or the weak one (Bopha) primarily leaded to the generation of Ekman currents. In the relaxation stage, the barotropic subinertial waves and/or the baroclinic near-inertial oscillations (NIOs) were triggered. Typically, during the transit of the Saomai, subinertial waves were induced which demonstrated a period of 2.8-4.1 days and a mean alongshore phase velocity of 14.9 ± 3.2 m/s in the form of free-barotropic continental shelf waves. However, the NIOs are only notable in the area in which the water column is stably stratified and also where the wind stress is dominated by the clockwise component and accompanied by high-frequency (near-inertial) variations. We also demonstrated that, due to the damping effects, the nonlinear wave-wave interaction (e.g., between NIO and semidiurnal tide in our case), together with the well-known bottom friction, led to the rapid decay of the observed TC-induced near-inertial currents, giving a typical e-folding time scale of 1-3 inertial periods. Moreover, such nonlinear wave-wave interaction was even found to play a major role during the spring tide in TWS.

Small nanoparticles, surface geometry and contact forces.

PubMed

Takato, Yoichi; Benson, Michael E; Sen, Surajit

2018-03-01

In this molecular dynamics study, we examine the local surface geometric effects of the normal impact force between two approximately spherical nanoparticles that collide in a vacuum. Three types of surface geometries-(i) crystal facets, (ii) sharp edges, and (iii) amorphous surfaces of small nanoparticles with radii R <10 nm-are considered. The impact forces are compared with their macroscopic counterparts described by nonlinear contact forces based on Hertz contact mechanics. In our simulations, edge and amorphous surface contacts with weak surface energy reveal that the average impact forces are in excellent agreement with the Hertz contact force. On the other hand, facet collisions show a linearly increasing force with increasing compression. Our results suggest that the nearly spherical nanoparticles are likely to enable some nonlinear dynamic phenomena, such as breathers and solitary waves observed in granular materials, both originating from the nonlinear contact force.

Mathematical problems arising in interfacial electrohydrodynamics

NASA Astrophysics Data System (ADS)

Tseluiko, Dmitri

In this work we consider the nonlinear stability of thin films in the presence of electric fields. We study a perfectly conducting thin film flow down an inclined plane in the presence of an electric field which is uniform in its undisturbed state, and normal to the plate at infinity. In addition, the effect of normal electric fields on films lying above, or hanging from, horizontal substrates is considered. Systematic asymptotic expansions are used to derive fully nonlinear long wave model equations for the scaled interface motion and corresponding flow fields. For the case of an inclined plane, higher order terms are need to be retained to regularize the problem in the sense that the long wave approximation remains valid for long times. For the case of a horizontal plane the fully nonlinear evolution equation which is derived at the leading order, is asymptotically correct and no regularization procedure is required. In both physical situations, the effect of the electric field is to introduce a non-local term which arises from the potential region above the liquid film, and enters through the electric Maxwell stresses at the interface. This term is always linearly destabilizing and produces growth rates proportional to the cubic power of the wavenumber - surface tension is included and provides a short wavelength cut-off, that is, all sufficiently short waves are linearly stable. For the case of film flow down an inclined plane, the fully nonlinear equation can produce singular solutions (for certain parameter values) after a finite time, even in the absence of an electric field. This difficulty is avoided at smaller amplitudes where the weakly nonlinear evolution is governed by an extension of the Kuramoto-Sivashinsky (KS) equation. Global existence and uniqueness results are proved, and refined estimates of the radius of the absorbing ball in L2 are obtained in terms of the parameters of the equations for a generalized class of modified KS equations. The established estimates are compared with numerical solutions of the equations which in turn suggest an optimal upper bound for the radius of the absorbing ball. A scaling argument is used to explain this, and a general conjecture is made based on extensive computations. We also carry out a complete study of the nonlinear behavior of competing physical mechanisms: long wave instability above a critical Reynolds number, short wave damping due to surface tension and intermediate growth due to the electric field. Through a combination of analysis and extensive numerical experiments, we elucidate parameter regimes that support non-uniform travelling waves, time-periodic travelling waves and complex nonlinear dynamics including chaotic interfacial oscillations. It is established that a sufficiently high electric field will drive the system to chaotic oscillations, even when the Reynolds number is smaller than the critical value below which the non-electrified problem is linearly stable. A particular case of this is Stokes flow, which is known to be stable for this class of problems (an analogous statement holds for horizontally supported films also). Our theoretical results indicate that such highly stable flows can be rendered unstable by using electric fields. This opens the way for possible heat and mass transfer applications which can benefit significantly from interfacial oscillations and interfacial turbulence. For the case of a horizontal plane, a weakly nonlinear theory is not possible due to the absence of the shear flow generated by the gravitational force along the plate when the latter is inclined. We study the fully nonlinear equation, which in this case is asymptotically correct and is obtained at the leading order. The model equation describes both overlying and hanging films - in the former case gravity is stabilizing while in the latter it is destabilizing. The numerical and theoretical analysis of the fully nonlinear evolution is complicated by the fact that the coefficients of the highest order terms (surface tension in this instance) are nonlinear. We implement a fully implicit two level numerical scheme and perform numerical experiments. We also prove global boundedness of positive periodic smooth solutions, using an appropriate energy functional. This global boundedness result is seen in all our numerical results. Through a combination of analysis and extensive numerical experiments we present evidence for global existence of positive smooth solutions. This means, in turn, that the film does not touch the wall in finite time but asymptotically at infinite time. Numerical solutions are presented to support such phenomena.

Quasi-monoenergetic ion beam acceleration by laser-driven shock and solitary waves in near-critical plasmas

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

Zhang, W. L.; Qiao, B., E-mail: bqiao@pku.edu.cn; Huang, T. W.

2016-07-15

Ion acceleration in near-critical plasmas driven by intense laser pulses is investigated theoretically and numerically. A theoretical model has been given for clarification of the ion acceleration dynamics in relation to different laser and target parameters. Two distinct regimes have been identified, where ions are accelerated by, respectively, the laser-induced shock wave in the weakly driven regime (comparatively low laser intensity) and the nonlinear solitary wave in the strongly driven regime (comparatively high laser intensity). Two-dimensional particle-in-cell simulations show that quasi-monoenergetic proton beams with a peak energy of 94.6 MeV and an energy spread 15.8% are obtained by intense laser pulsesmore » at intensity I{sub 0} = 3 × 10{sup 20 }W/cm{sup 2} and pulse duration τ = 0.5 ps in the strongly driven regime, which is more advantageous than that got in the weakly driven regime. In addition, 233 MeV proton beams with narrow spread can be produced by extending τ to 1.0 ps in the strongly driven regime.« 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.

Wakes and precursor soliton excitations by a moving charged object in a plasma

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

Kumar Tiwari, Sanat, E-mail: sanat-tiwari@uiowa.edu; Department of Physics and Astronomy, University of Iowa, Iowa City, Iowa 52242; Sen, Abhijit, E-mail: senabhijit@gmail.com

2016-02-15

We study the evolution of nonlinear ion acoustic wave excitations due to a moving charged source in a plasma. Our numerical investigations of the full set of cold fluid equations go beyond the usual weak nonlinearity approximation and show the existence of a rich variety of solutions including wakes, precursor solitons, and “pinned” solitons that travel with the source velocity. These solutions represent a large amplitude generalization of solutions obtained in the past for the forced Korteweg deVries equation and can find useful applications in a variety of situations in the laboratory and in space, wherever there is a largemore » relative velocity between the plasma and a charged object.« less

Critical time for acoustic wavesin weakly nonlinear poroelastic materials

NASA Astrophysics Data System (ADS)

Wilmanski, K.

2005-05-01

The final time of existence (critical time) of acoustic waves is a characteristic feature of nonlinear hyperbolic models. We consider such a problem for poroelastic saurated materials of which the material properties are described by Signorini-type constitutitve relations for stresses in the skeleton, and whose material parameters depend on the current porosity. In the one-dimensional case under consideration, the governing set of equations describes changes of extension of the skeleton, a mass density of the fluid, partial velocities of the skeleton and of the fluid and a porosity. We rely on a second order approximation. Relations of the critical time to an initial porosity and to an initial amplitude are discussed. The connection to the threshold of liquefaction is indicated.

Parametric decay of current-driven Langmuir oscillations and wave packet formation in plateau plasmas: Relevance to type III bursts

NASA Astrophysics Data System (ADS)

Sauer, K.; Malaspina, D.; Pulupa, M.

2016-12-01

Instead of starting with an unstable electron beam, our focus is directed on the nonlinear response of Langmuir oscillations which are driven after beam stabilization by the still persisting current of the (stable) two-electron plasma. The velocity distribution function of the second population forms a plateau with weak damping over a more or less extended wave number range k. As shown by PIC simulations, this so-called plateau plasma drives primarily Langmuir oscillations at the plasma frequency ωe with k=0 over long times without remarkable change of the distribution function. The Langmuir oscillations, however, act as pump wave for parametric decay by which an electron-acoustic wave slightly below ωe and a counter-streaming ion-acoustic wave are generated. Both high-frequency waves have nearly the same amplitude which is simply given by the product of plateau density and velocity. Beating of these two wave types leads to pronounced Langmuir amplitude modulation, in good agreement with solar wind and foreshock WIND observations where waveforms and electron distribution functions have simultaneously been analyzed.

Amplitude-dependent topological edge states in nonlinear phononic lattices

NASA Astrophysics Data System (ADS)

Pal, Raj Kumar; Vila, Javier; Leamy, Michael; Ruzzene, Massimo

2018-03-01

This work investigates the effect of nonlinearities on topologically protected edge states in one- and two-dimensional phononic lattices. We first show that localized modes arise at the interface between two spring-mass chains that are inverted copies of each other. Explicit expressions derived for the frequencies of the localized modes guide the study of the effect of cubic nonlinearities on the resonant characteristics of the interface, which are shown to be described by a Duffing-like equation. Nonlinearities produce amplitude-dependent frequency shifts, which in the case of a softening nonlinearity cause the localized mode to migrate to the bulk spectrum. The case of a hexagonal lattice implementing a phononic analog of a crystal exhibiting the quantum spin Hall effect is also investigated in the presence of weakly nonlinear cubic springs. An asymptotic analysis provides estimates of the amplitude dependence of the localized modes, while numerical simulations illustrate how the lattice response transitions from bulk-to-edge mode-dominated by varying the excitation amplitude. In contrast with the interface mode of the first example studies, this occurs both for hardening and softening springs. The results of this study provide a theoretical framework for the investigation of nonlinear effects that induce and control topologically protected wave modes through nonlinear interactions and amplitude tuning.

Color Memory: A Yang-Mills Analog of Gravitational Wave Memory.

PubMed

Pate, Monica; Raclariu, Ana-Maria; Strominger, Andrew

2017-12-29

A transient color flux across null infinity in classical Yang-Mills theory is considered. It is shown that a pair of test "quarks" initially in a color singlet generically acquire net color as a result of the flux. A nonlinear formula is derived for the relative color rotation of the quarks. For a weak color flux, the formula linearizes to the Fourier transform of the soft gluon theorem. This color memory effect is the Yang-Mills analog of the gravitational memory effect.

Color Memory: A Yang-Mills Analog of Gravitational Wave Memory

NASA Astrophysics Data System (ADS)

Pate, Monica; Raclariu, Ana-Maria; Strominger, Andrew

2017-12-01

A transient color flux across null infinity in classical Yang-Mills theory is considered. It is shown that a pair of test "quarks" initially in a color singlet generically acquire net color as a result of the flux. A nonlinear formula is derived for the relative color rotation of the quarks. For a weak color flux, the formula linearizes to the Fourier transform of the soft gluon theorem. This color memory effect is the Yang-Mills analog of the gravitational memory effect.

A Numerical Solution of the Second-Order-Nonlinear Acoustic Wave Equation in One and in Three Dimensions.

DTIC Science & Technology

1981-01-08

95 Limits of Applicability of Weak-Finite- Amplitude Theory ... ............ 100 Near- Field Calibration of Parametric Sources...concerning the amount of energy that may be trans- mitted to the far field by various types of signals. CPOIi eslu er 06]i C) 3O d SIM aC NOI.LjZI’IS...ducers at finite amplitudes, conclusions are presented concerning the amount of energy that may be transmitted to the far field by various types of

Characterization of nonequilibrium states of trapped Bose–Einstein condensates

NASA Astrophysics Data System (ADS)

Yukalov, V. I.; Novikov, A. N.; Bagnato, V. S.

2018-06-01

The generation of different nonequilibrium states in trapped Bose–Einstein condensates is studied by numerically solving the nonlinear Schrödinger equation. Inducing nonequilibrium states by shaking a trap creates the following states: weak nonequilibrium, the state of vortex germs, the state of vortex rings, the state of straight vortex lines, the state of deformed vortices, vortex turbulence, grain turbulence, and wave turbulence. A characterization of nonequilibrium states is advanced by introducing effective temperature, Fresnel number, and Mach number.

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

NASA Astrophysics Data System (ADS)

Tsuji, Hidekazu; Yufu, Kei; Marubayashi, Kenji

2012-11-01

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

On the nonlinear forced response of the North Atlantic atmosphere to meridional shifts of the Gulf Stream path

NASA Astrophysics Data System (ADS)

Seo, H.; Kwon, Y. O.; Joyce, T. M.; Ummenhofer, C.

2016-12-01

This study examines the North Atlantic atmospheric circulation response to the meridional shift of Gulf Stream path using a large-ensemble, high-resolution, and hemispheric-scale WRF simulations. The model is forced with wintertime SST anomalies derived from a wide range of Gulf Stream shift scenarios. The key result of the model experiments, supported in part by an independent analysis of a reanalysis data set, is that the large-scale, quasi-steady North Atlantic circulation response is unambiguously nonlinear about the sign and amplitude of chosen SST anomalies. This nonlinear response prevails over the weak linear response and resembles the negative North Atlantic Oscillation, the leading intrinsic mode of variability in the model and the observations. Further analysis of the associated dynamics reveals that the nonlinear responses are accompanied by the anomalous southward shift of the North Atlantic eddy-driven jet stream, which is reinforced nearly equally by the high-frequency transient eddy feedback and the low-frequency high-latitude wave breaking events. The result highlights the importance of the intrinsically nonlinear transient eddy dynamics and eddy-mean flow interactions in generating the nonlinear forced response to the meridional shift in the Gulf Stream.

Quantitative and qualitative characterization of zigzag spatiotemporal chaos in a system of amplitude equations for nematic electroconvection.

PubMed

Oprea, Iuliana; Triandaf, Ioana; Dangelmayr, Gerhard; Schwartz, Ira B

2007-06-01

It has been suggested by experimentalists that a weakly nonlinear analysis of the recently introduced equations of motion for the nematic electroconvection by M. Treiber and L. Kramer [Phys. Rev. E 58, 1973 (1998)] has the potential to reproduce the dynamics of the zigzag-type extended spatiotemporal chaos and localized solutions observed near onset in experiments [M. Dennin, D. S. Cannell, and G. Ahlers, Phys. Rev. E 57, 638 (1998); J. T. Gleeson (private communication)]. In this paper, we study a complex spatiotemporal pattern, identified as spatiotemporal chaos, that bifurcates at the onset from a spatially uniform solution of a system of globally coupled complex Ginzburg-Landau equations governing the weakly nonlinear evolution of four traveling wave envelopes. The Ginzburg-Landau system can be derived directly from the weak electrolyte model for electroconvection in nematic liquid crystals when the primary instability is a Hopf bifurcation to oblique traveling rolls. The chaotic nature of the pattern and the resemblance to the observed experimental spatiotemporal chaos in the electroconvection of nematic liquid crystals are confirmed through a combination of techniques including the Karhunen-Loeve decomposition, time-series analysis of the amplitudes of the dominant modes, statistical descriptions, and normal form theory, showing good agreement between theory and experiments.

Another look at zonal flows: Resonance, shearing, and frictionless saturation

NASA Astrophysics Data System (ADS)

Li, J. C.; Diamond, P. H.

2018-04-01

We show that shear is not the exclusive parameter that represents all aspects of flow structure effects on turbulence. Rather, wave-flow resonance enters turbulence regulation, both linearly and nonlinearly. Resonance suppresses the linear instability by wave absorption. Flow shear can weaken the resonance, and thus destabilize drift waves, in contrast to the near-universal conventional shear suppression paradigm. Furthermore, consideration of wave-flow resonance resolves the long-standing problem of how zonal flows (ZFs) saturate in the limit of weak or zero frictional drag, and also determines the ZF scale. We show that resonant vorticity mixing, which conserves potential enstrophy, enables ZF saturation in the absence of drag, and so is effective at regulating the Dimits up-shift regime. Vorticity mixing is incorporated as a nonlinear, self-regulation effect in an extended 0D predator-prey model of drift-ZF turbulence. This analysis determines the saturated ZF shear and shows that the mesoscopic ZF width scales as LZ F˜f3 /16(1-f ) 1 /8ρs5/8l03 /8 in the (relevant) adiabatic limit (i.e., τckk‖2D‖≫1 ). f is the fraction of turbulence energy coupled to ZF and l0 is the base state mixing length, absent ZF shears. We calculate and compare the stationary flow and turbulence level in frictionless, weakly frictional, and strongly frictional regimes. In the frictionless limit, the results differ significantly from conventionally quoted scalings derived for frictional regimes. To leading order, the flow is independent of turbulence intensity. The turbulence level scales as E ˜(γL/εc) 2 , which indicates the extent of the "near-marginal" regime to be γL<εc , for the case of avalanche-induced profile variability. Here, εc is the rate of dissipation of potential enstrophy and γL is the characteristic linear growth rate of fluctuations. The implications for dynamics near marginality of the strong scaling of saturated E with γL are discussed.

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.

Analog gravity by an optical vortex: Resonance enhancement of Hawking radiation

NASA Astrophysics Data System (ADS)

Ornigotti, Marco; Bar-Ad, Shimshon; Szameit, Alexander; Fleurov, Victor

2018-01-01

Propagation of coherent light in a Kerr nonlinear medium can be mapped onto a flow of an equivalent fluid. Here we use this mapping to model the conditions in the vicinity of a rotating black hole as a Laguerre-Gauss vortex beam. We describe weak fluctuations of the phase and amplitude of the electric field by wave equations in curved space, with a metric that is similar to the Kerr metric. We find the positions of event horizons and ergoregion boundaries, and the conditions for the onset of superradiance, which are simultaneously the conditions for a resonance in the analog Hawking radiation. The resonance strongly enhances the otherwise exponentially weak Hawking radiation at certain frequencies and makes its experimental observation feasible.

The Kadomtsev-Petviashvili equation under rapid forcing

NASA Astrophysics Data System (ADS)

Moroz, Irene M.

1997-06-01

We consider the initial value problem for the forced Kadomtsev-Petviashvili equation (KP) when the forcing is assumed to be fast compared to the evolution of the unforced equation. This suggests the introduction of two time scales. Solutions to the forced KP are sought by expanding the dependent variable in powers of a small parameter, which is inversely related to the forcing time scale. The unforced system describes weakly nonlinear, weakly dispersive, weakly two-dimensional wave propagation and is studied in two forms, depending upon whether gravity dominates surface tension or vice versa. We focus on the effect that the forcing has on the one-lump solution to the KPI equation (where surface tension dominates) and on the one- and two-line soliton solutions to the KPII equation (when gravity dominates). Solutions to second order in the expansion are computed analytically for some specific choices of the forcing function, which are related to the choice of initial data.

Wave Tank Studies of Strong Modulation of Wind Ripples Due To Long Waves

NASA Astrophysics Data System (ADS)

Ermakov, S.; Sergievskaya, I.; Shchegolkov, Yu.

Modulation of wind capillary-gravity ripples due to long waves has been studied in wave tank experiment at low wind speeds using Ka-band radar. The experiments were carried out both for clean water and the water surface covered with surfactant films. It is obtained that the modulation of radar signals is quite strong and can increase with surfactant concentration and fetch. It is shown that the hydrodynamic Modulation Transfer Function (MTF) calculated for free wind ripples and taking into account the kinematic (straining) effect, variations of the wind stress and variations of surfactant concentration strongly underestimates experimental MTF-values. The effect of strong modulation is assumed to be connected with nonlinear harmonics of longer dm-cm- scale waves - bound waves ("parasitic ripples"). The intensity of bound waves depends strongly on the amplitude of decimetre-scale waves, therefore even weak modulation of the dm-scale waves due to long waves results to strong ("cascade") modulation of bound waves. Modulation of the system of "free/bound waves" is estimated using results of wave tank studies of bound waves generation and is shown to be in quali- tative agreement with experiment. This work was supported by MOD, UK via DERA Winfrith (Project ISTC 1774P) and by RFBR (Project 02-05-65102).

The fluid-dynamic paradigm of the dust-acoustic soliton

NASA Astrophysics Data System (ADS)

McKenzie, J. F.

2002-06-01

In most studies, the properties of dust-acoustic solitons are derived from the first integral of the Poisson equation, in which the shape of the pseudopotential determines both the conditions in which a soliton may exist and its amplitude. Here this first integral is interpreted as conservation of total momentum, which, along with the Bernoulli-like energy equations for each species, may be cast as the structure equation for the dust (or heavy-ion) speed in the wave. In this fluid-dynamic picture, the significance of the sonic points of each species becomes apparent. In the wave, the heavy-ion (or dust) flow speed is supersonic (relative to its sound speed), whereas the protons and electrons are subsonic (relative to their sound speeds), and the dust flow is driven towards its sonic point. It is this last feature that limits the strength (amplitude) of the wave, since the equilibrium point (the centre of the wave) must be reached before the dust speed becomes sonic. The wave is characterized by a compression in the heavies and a compression (rarefaction) in the electrons and a rarefaction (compression) in the protons if the heavies have positive (negative) charge, and the corresponding potential is a hump (dip). These features are elucidated by an exact analytical soliton, in a special case, which provides the fully nonlinear counterpoint to the weakly nonlinear sech2-type solitons associated with the Korteweg de Vries equation, and indicates the parameter regimes in which solitons may exist.

Spatio-temporal dynamics induced by competing instabilities in two asymmetrically coupled nonlinear evolution equations.

PubMed

Schüler, D; Alonso, S; Torcini, A; Bär, M

2014-12-01

Pattern formation often occurs in spatially extended physical, biological, and chemical systems due to an instability of the homogeneous steady state. The type of the instability usually prescribes the resulting spatio-temporal patterns and their characteristic length scales. However, patterns resulting from the simultaneous occurrence of instabilities cannot be expected to be simple superposition of the patterns associated with the considered instabilities. To address this issue, we design two simple models composed by two asymmetrically coupled equations of non-conserved (Swift-Hohenberg equations) or conserved (Cahn-Hilliard equations) order parameters with different characteristic wave lengths. The patterns arising in these systems range from coexisting static patterns of different wavelengths to traveling waves. A linear stability analysis allows to derive a two parameter phase diagram for the studied models, in particular, revealing for the Swift-Hohenberg equations, a co-dimension two bifurcation point of Turing and wave instability and a region of coexistence of stationary and traveling patterns. The nonlinear dynamics of the coupled evolution equations is investigated by performing accurate numerical simulations. These reveal more complex patterns, ranging from traveling waves with embedded Turing patterns domains to spatio-temporal chaos, and a wide hysteretic region, where waves or Turing patterns coexist. For the coupled Cahn-Hilliard equations the presence of a weak coupling is sufficient to arrest the coarsening process and to lead to the emergence of purely periodic patterns. The final states are characterized by domains with a characteristic length, which diverges logarithmically with the coupling amplitude.

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.

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

Chacon, Luis; Stanier, Adam John

Here, we demonstrate a scalable fully implicit algorithm for the two-field low-β extended MHD model. This reduced model describes plasma behavior in the presence of strong guide fields, and is of significant practical impact both in nature and in laboratory plasmas. The model displays strong hyperbolic behavior, as manifested by the presence of fast dispersive waves, which make a fully implicit treatment very challenging. In this study, we employ a Jacobian-free Newton–Krylov nonlinear solver, for which we propose a physics-based preconditioner that renders the linearized set of equations suitable for inversion with multigrid methods. As a result, the algorithm ismore » shown to scale both algorithmically (i.e., the iteration count is insensitive to grid refinement and timestep size) and in parallel in a weak-scaling sense, with the wall-clock time scaling weakly with the number of cores for up to 4096 cores. For a 4096 × 4096 mesh, we demonstrate a wall-clock-time speedup of ~6700 with respect to explicit algorithms. The model is validated linearly (against linear theory predictions) and nonlinearly (against fully kinetic simulations), demonstrating excellent agreement.« less

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.

Optical Sidebands Multiplier

NASA Technical Reports Server (NTRS)

Strekalov, Dmitry V.; Yu, Nan

2010-01-01

Optical sidebands have been generated with relative frequency tens to hundreds of GHz by using optical sidebands that are generated in a cascade process in high-quality optical resonators with Kerr nonlinearity, such as whispering gallery mode (WGM) resonators. For this purpose, the WGM resonator needs to be optically pumped at two frequencies matching its resonances. These two optical components can be one or several free spectral ranges (FSRs), equal to approximately 12 GHz, in this example, apart from each other, and can be easily derived from a monochromatic pump with an ordinary EOM (electro-optic modulation) operating at half the FSR frequency. With sufficient nonlinearity, an optical cascade process will convert the two pump frequencies into a comb-like structure extending many FSRs around the carrier frequency. This has a demonstratively efficient frequency conversion of this type with only a few milliwatt optical pump power. The concept of using Kerr nonlinearity in a resonator for non-degenerate wave mixing has been discussed before, but it was a common belief that this was a weak process requiring very high peak powers to be observable. It was not thought possible for this approach to compete with electro-optical modulators in CW applications, especially those at lower optical powers. By using the high-Q WGM resonators, the effective Kerr nonlinearity can be made so high that, using even weak seeding bands available from a conventional EOM, one can effectively multiply the optical sidebands, extending them into an otherwise inaccessible frequency range.

Theory of multinonlinear media and its application to the soliton processes in ferrite–ferroelectric structures

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

Cherkasskii, M. A., E-mail: macherkasskii@hotmail.com; Nikitin, A. A.; Kalinikos, B. A.

A theory is developed to describe the wave processes that occur in waveguide media having several types of nonlinearity, specifically, multinonlinear media. It is shown that the nonlinear Schrödinger equation can be used to describe the general wave process that occurs in such media. The competition between the electric wave nonlinearity and the magnetic wave nonlinearity in a layered multinonlinear ferrite–ferroelectric structure is found to change a total repulsive nonlinearity into a total attractive nonlinearity.

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.

Book review: Modern Plasma Physics, Vol. I: Physical Kinetics of Turbulent Plasmas, by Patrick H. Diamond, Sanae-I. Itoh and Kimitaka Itoh, Cambridge University Press, Cambridge (UK), 2010, IX, 417 p., ISBN 978-0-521-86920-1 (Hardback)

NASA Astrophysics Data System (ADS)

Somov, B. V.

If you want to learn not only the most fundamental things about the physics of turbulent plasmas but also the current state of the problem including the most recent results in theoretical and experimental investigations - and certainly many physicists and astrophysicists do - this series of three excellent monographs is just for you. The first volume "Physical Kinetics of Turbulent Plasmas" develops the kinetic theory of turbulence through a focus on quasi-particle models and dynamics. It discusses the concepts and theoretical methods for describing weak and strong fluid and phase space turbulence in plasma systems far from equilibrium. The core material includes fluctuation theory, self-similar cascades and transport, mean field theory, resonance broadening and nonlinear wave-particle interaction, wave-wave interaction and wave turbulence, strong turbulence theory and renormalization. The book gives readers a deep understanding of the fields under consideration and builds a foundation for future applications to multi-scale processes of self-organization in tokamaks and other confined plasmas. In spite of a short pedagogical introduction, the book is addressed mainly to well prepared readers with a serious background in plasma physics, to researchers and advanced graduate students in nonlinear plasma physics, controlled fusions and related fields such as cosmic plasma physics

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 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.

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.

The application of the constants of motion to nonlinear stationary waves in complex plasmas: a unified fluid dynamic viewpoint

NASA Astrophysics Data System (ADS)

McKenzie, J. F.; Dubinin, E.; Sauer, K.; Doyle, T. B.

2004-08-01

Perturbation reductive procedures, as used to analyse various weakly nonlinear plasma waves (solitons and periodic waves), normally lead to the dynamical system being described by KdV, Burgers' or a nonlinear Schrödinger-type equation, with properties that can be deduced from an array of mathematical techniques. Here we develop a fully nonlinear theory of one-dimensional stationary plasma waves, which elucidates the common nature of various diverse wave phenomena. This is accomplished by adopting an essentially fluid dynamic viewpoint. In this unified treatment the constants of the motion (for mass, momentum and energy) lead naturally to the construction of the wave structure equations. It is shown, for example, that electrostatic, Hall magnetohydrodynamic and ion cyclotron acoustic nonlinear waves all obey first-order differential equations of the same generic type for the longitudinal flow field of the wave. The equilibrium points, which define the soliton amplitude, are given by the compressive and/or rarefactive roots of a total plasma ‘energy’ or ‘momentum’ function characterizing the wave type. This energy function, which is an algebraic combination of the Bernoulli momentum and energy functions for the longitudinal flow field, is the fluid dynamic counterpart of the pseudo-potentials, which are characteristic of system structure equations formulated in other than fluid variables. Another general feature of the structure equation is the phenomenon of choked flow, which occurs when the flow speed becomes sonic. It is this trans-sonic property that limits the soliton amplitudes and defines the critical collective Mach numbers of the waves. These features are also obtained in multi-component plasmas where, for example, in a bi-ion plasma, momentum exchanges between protons and heavier ions are mediated by the Maxwell magnetic stresses. With a suitable generalization of the concept of a sonic point in a bi-ion system and the corresponding choked flow feature, the wave structures, although now more complicated, can also be understood within this overall fluid framework. Particularly useful tools in this context are the momentum hodograph (an algebraic relation between the bi-ion speeds and the electron speed, or magnetic field, which follows from the conservation of mass, momentum and charge-neutrality) and a generalized Bernoulli energy density for each species. Analysis shows that the bi-ion solitons are essentially compressive, but contain the remarkable feature of the presence of a proton rarefactive core. A new type of soliton, called an ‘oscilliton’ because embedded spatial oscillations are superimposed on the classical soliton, is also described and discussed. A necessary condition for the existence of this type of wave is that the linear phase velocity must exhibit an extremum where the phase speed matches the group speed. The remarkable properties of this wave are illustrated for the case of both whistler waves and bi-ion waves where, for the latter, the requisite condition is met near the cross-over frequencies. In the case of the whistler oscilliton, which propagates at speeds in excess of one half of the Alfvén speed (based on the electrons), an analytic solution has been constructed through a phase-portrait integral of the system in which the proton and electron dynamics must be placed on the same footing. The relevance of the different wave structures to diverse space environments is briefly discussed in relation to recently available high-time and spatial resolution data from satellite observations.

Non linear shock wave propagation in heterogeneous fluids: a numerical approach beyond the parabolic approximation with application to sonic boom.

NASA Astrophysics Data System (ADS)

Dagrau, Franck; Coulouvrat, François; Marchiano, Régis; Héron, Nicolas

2008-06-01

Dassault Aviation as a civil aircraft manufacturer is studying the feasibility of a supersonic business jet with the target of an "acceptable" sonic boom at the ground level, and in particular in case of focusing. A sonic boom computational process has been performed, that takes into account meteorological effects and aircraft manoeuvres. Turn manoeuvres and aircraft acceleration create zones of convergence of rays (caustics) which are the place of sound amplification. Therefore two elements have to be evaluated: firstly the geometrical position of the caustics, and secondly the noise level in the neighbourhood of the caustics. The modelling of the sonic boom propagation is based essentially on the assumptions of geometrical acoustics. Ray tracing is obtained according to Fermat's principle as paths that minimise the propagation time between the source (the aircraft) and the receiver. Wave amplitude and time waveform result from the solution of the inviscid Burgers' equation written along each individual ray. The "age variable" measuring the cumulative nonlinear effects is linked to the ray tube area. Caustics are located as the place where the ray tube area vanishes. Since geometrical acoustics does not take into account diffraction effects, it breaks down in the neighbourhood of caustics where it would predict unphysical infinite pressure amplitude. The aim of this study is to describe an original method for computing the focused noise level. The approach involves three main steps that can be summarised as follows. The propagation equation is solved by a forward marching procedure split into three successive steps: linear propagation in a homogeneous medium, linear perturbation due to the weak heterogeneity of the medium, and non-linear effects. The first step is solved using an "exact" angular spectrum algorithm. Parabolic approximation is applied only for the weak perturbation due to the heterogeneities. Finally, non linear effects are performed by solving the in-viscid Burgers' equation. As this one is valid for a plane wave, the direction of this last one is not prescribed a priori, but is computed in a self-adaptative way using an efficient numerical solver of the non-linear eikonal equation (Fast Marching Method).

Regular and Chaotic Spatial Distribution of Bose-Einstein Condensed Atoms in a Ratchet Potential

NASA Astrophysics Data System (ADS)

Li, Fei; Xu, Lan; Li, Wenwu

2018-02-01

We study the regular and chaotic spatial distribution of Bose-Einstein condensed atoms with a space-dependent nonlinear interaction in a ratchet potential. There exists in the system a space-dependent atomic current that can be tuned via Feshbach resonance technique. In the presence of the space-dependent atomic current and a weak ratchet potential, the Smale-horseshoe chaos is studied and the Melnikov chaotic criterion is obtained. Numerical simulations show that the ratio between the intensities of optical potentials forming the ratchet potential, the wave vector of the laser producing the ratchet potential or the wave vector of the modulating laser can be chosen as the controlling parameters to result in or avoid chaotic spatial distributional states.

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

Strong plasma turbulence in the earth's electron foreshock

NASA Technical Reports Server (NTRS)

Robinson, P. A.; Newman, D. L.

1991-01-01

A quantitative model is developed to account for the distribution in magnitude and location of the intense plasma waves observed in the earth's electron foreshock given the observed rms levels of waves. In this model, nonlinear strong-turbulence effects cause solitonlike coherent wave packets to form and decouple from incoherent background beam-excited weak turbulence, after which they convect downstream with the solar wind while collapsing to scales as short as 100 m and fields as high as 2 V/m. The existence of waves with energy densities above the strong-turbulence wave-collapse threshold is inferred from observations from IMP 6 and ISEE 1 and quantitative agreement is found between the predicted distribution of fields in an ensemble of such wave packets and the actual field distribution observed in situ by IMP 6. Predictions for the polarization of plasma waves and the bandwidth of ion-sound waves are also consistent with the observations. It is shown that strong-turbulence effects must be incorporated in any comprehensive theory of the propagation and evolution of electron beams in the foreshock. Previous arguments against the existence of strong turbulence in the foreshock are refuted.

The role of the complete Coriolis force in weakly stratified oceanic flows

NASA Astrophysics Data System (ADS)

Tort, M.; Winters, K. B.; Ribstein, B.; Zeitlin, V.

2016-02-01

Ocean dynamics is usually described using the primitive equations based on the so-called traditional approximation (TA), where the Coriolis force associated with the horizontal component of the planetary rotation is neglected (also called non-traditional (NT) part proportional to cosΦ, see Fig 1.). However, recent studies have shown that the NT part of the Coriolis force plays a non-negligible dynamical role in some particular oceanic flows (see Gerkema et al., 2008 for an extensive review of NT effects for geophysical and astrophysical flows). Here we explore the relevance of including the NT component of the Coriolis force in ocean models, by presenting particular results regarding two different mid-latitude flow configurations after relaxing the TA: Propagation of wind-induced near-inertial waves (NIWs). Under the TA, NIWs propagate toward the equator, the inertially poleward propagation being internally reflected at a depth-independent critical latitude. The combined effects of the NT Coriolis force and weak stratification in the deep ocean leads to the existence of waveguides for sub-inertial waves, which get trapped and propagate further poleward (Winters et al., 2011). Here we consider storm-induced NIWs and their evolution in a non-linear Boussinesq model on the β-plane in the NT approximation. Preliminary results are presented concerning the behavior of the waves in a weakly stratified mixed-layer, where NT effects are expected to be significant. Inertial instability. A detailed linear stability analysis of the Bickley jet at large Rossby numbers in the NT approximation on the f-plane is performed for long waves in a continuously stratified Boussinesq model. For a sufficiently weak stratification, both symmetric and asymmetric inertial instabilities have substantially higher growth rates than in the TA while no discernible differences between the two approximations are observed for strong enough stratifications (Tort et al., 2015).

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.

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

Field measurements and modeling of wave propagation and subsequent weak layer failure in snow due to explosive loading

NASA Astrophysics Data System (ADS)

Simioni, Stephan; Sidler, Rolf; Dual, Jürg; Schweizer, Jürg

2015-04-01

Avalanche control by explosives is among the key temporary preventive measures. Yet, little is known about the mechanism involved in releasing avalanches by the effect of an explosion. Here, we test the hypothesis that the stress induced by acoustic waves exceeds the strength of weak snow layers. Consequently the snow fails and the onset of rapid crack propagation might finally lead to the release of a snow slab avalanche. We performed experiments with explosive charges over a snowpack. We installed microphones above the snowpack to measure near-surface air pressure and accelerometers within three snow pits. We also recorded pit walls of each pit with high speed cameras to detect weak layer failure. Empirical relationships and a priori information from ice and air were used to characterize a porous layered model from density measurements of snow profiles in the snow pits. This model was used to perform two-dimensional numerical simulations of wave propagation in Biot-type porous material. Locations of snow failure were identified in the simulation by comparing the axial and deviatoric stress field of the simulation to the corresponding snow strength. The identified snow failure locations corresponded well with the observed failure locations in the experiment. The acceleration measured in the snowpack best correlated with the modeled acceleration of the fluid relative to the ice frame. Even though the near field of the explosion is expected to be governed by non-linear effects as for example the observed supersonic wave propagation in the air above the snow surface, the results of the linear poroelastic simulation fit well with the measured air pressure and snowpack accelerations. The results of this comparison are an important step towards quantifying the effectiveness of avalanche control by explosives.

K-P-Burgers equation in negative ion-rich relativistic dusty plasma including the effect of kinematic viscosity

NASA Astrophysics Data System (ADS)

Dev, A. N.; Deka, M. K.; Sarma, J.; Saikia, D.; Adhikary, N. C.

2016-10-01

The stationary solution is obtained for the K-P-Burgers equation that describes the nonlinear propagations of dust ion acoustic waves in a multi-component, collisionless, un-magnetized relativistic dusty plasma consisting of electrons, positive and negative ions in the presence of charged massive dust grains. Here, the Kadomtsev-Petviashvili (K-P) equation, three-dimensional (3D) Burgers equation, and K-P-Burgers equations are derived by using the reductive perturbation method including the effects of viscosity of plasma fluid, thermal energy, ion density, and ion temperature on the structure of a dust ion acoustic shock wave (DIASW). The K-P equation predictes the existences of stationary small amplitude solitary wave, whereas the K-P-Burgers equation in the weakly relativistic regime describes the evolution of shock-like structures in such a multi-ion dusty plasma.

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.

Investigation of focused and unfocused transducer beam patterns in moderately nonlinear absorbing media

NASA Astrophysics Data System (ADS)

Kharin, Nikolay A.

2001-05-01

The novel solution of the KZK equation for acoustic pressure of the second harmonic in slightly focused beam of a circular transducer was obtained in a closed form for moderately nonlinear absorbing media (Gol'dberg numbers ~ 1). The solution is based on the method of slowly changing wave profile in combination with the method of successive approximations. Two pairs of transducers (Valpey-Fisher Corp.) Were compared to investigate the influence of focusing on the applicability of the moderate nonlinearity approach. The first pair was of 0.25' diameter and the second was of 0.5' diameter. Both pairs has one transducer with flat surface and the other geometrically focused at 4'. The central frequency for all transducers was 5 MHz. Measurements were undertaken in the blood-mimicking solution of water and glycerine. The results demonstrated that for slightly focused transducers with circular apertures, the moderate nonlinearity approach is still valid, as it was proved for flat sources with the same source level, despite the higher pressures in the focal region. The peak pressure for the weakly focused system occurs at a shorter range than focal length.

Nonlinear cross-field coupling on the route to broadband turbulence

NASA Astrophysics Data System (ADS)

Brandt, Christian; Thakur, Saikat C.; Cui, Lang; Gosselin, Jordan J.; Negrete, Jose, Jr.; Holland, Chris; Tynan, George R.

2013-10-01

In the linear magnetized plasma device CSDX (Controlled Shear De-correlation eXperiment) drift interchange modes are studied coexisting on top of a weak turbulence driven azimuthally symmetric, radially sheared plasma flow. In helicon discharges (helicon antenna diameter 15 cm) with increasing magnetic field (B <= 0 . 24 T) the system can be driven to fully developed broadband turbulence. Fast imaging using a refractive telescope setup is applied to study the dynamics in the azimuthal-radial cross-section. The image data is supported by Langmuir probe measurements. In the present study we examine the development of nonlinear transfer as the fully developed turbulence emerges. Nonlinear cross-field coupling between eigenmodes at different radial positions is investigated using Fourier decomposition of azimuthal eigenmodes. The coupling strength between waves at different radial positions is inferred to radial profiles and cross-field transport between adjacent magnetic flux surfaces. Nonlinear effects like synchronization, phase slippages, phase pulling and periodic pulling are observed. The effects of mode coupling and the stability of modes is compared to the dynamics of a coupled chain of Kuramoto oscillators.

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

Manipulating acoustic wave reflection by a nonlinear elastic metasurface

NASA Astrophysics Data System (ADS)

Guo, Xinxin; Gusev, Vitalyi E.; Bertoldi, Katia; Tournat, Vincent

2018-03-01

The acoustic wave reflection properties of a nonlinear elastic metasurface, derived from resonant nonlinear elastic elements, are theoretically and numerically studied. The metasurface is composed of a two degree-of-freedom mass-spring system with quadratic elastic nonlinearity. The possibility of converting, during the reflection process, most of the fundamental incoming wave energy into the second harmonic wave is shown, both theoretically and numerically, by means of a proper design of the nonlinear metasurface. The theoretical results from the harmonic balance method for a monochromatic source are compared with time domain simulations for a wave packet source. This protocol allows analyzing the dynamics of the nonlinear reflection process in the metasurface as well as exploring the limits of the operating frequency bandwidth. The reported methodology can be applied to a wide variety of nonlinear metasurfaces, thus possibly extending the family of exotic nonlinear reflection processes.

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.

Thermal Non-Equilibrium Flows in Three Space Dimensions

NASA Astrophysics Data System (ADS)

Zeng, Yanni

2016-01-01

We study the equations describing the motion of a thermal non-equilibrium gas in three space dimensions. It is a hyperbolic system of six equations with a relaxation term. The dissipation mechanism induced by the relaxation is weak in the sense that the Shizuta-Kawashima criterion is violated. This implies that a perturbation of a constant equilibrium state consists of two parts: one decays in time while the other stays. In fact, the entropy wave grows weakly along the particle path as the process is irreversible. We study thermal properties related to the well-posedness of the nonlinear system. We also obtain a detailed pointwise estimate on the Green's function for the Cauchy problem when the system is linearized around an equilibrium constant state. The Green's function provides a complete picture of the wave pattern, with an exact and explicit leading term. Comparing with existing results for one dimensional flows, our results reveal a new feature of three dimensional flows: not only does the entropy wave not decay, but the velocity also contains a non-decaying part, strongly coupled with its decaying one. The new feature is supported by the second order approximation via the Chapman-Enskog expansions, which are the Navier-Stokes equations with vanished shear viscosity and heat conductivity.

Three-dimensional wave evolution on electrified falling films

NASA Astrophysics Data System (ADS)

Tomlin, Ruben; Papageorgiou, Demetrios; Pavliotis, Greg

2016-11-01

We consider the full three-dimensional model for a thin viscous liquid film completely wetting a flat infinite solid substrate at some non-zero angle to the horizontal, with an electric field normal to the substrate far from the flow. Thin film flows have applications in cooling processes. Many studies have shown that the presence of interfacial waves increases heat transfer by orders of magnitude due to film thinning and convection effects. A long-wave asymptotics procedure yields a Kuramoto-Sivashinsky equation with a non-local term to model the weakly nonlinear evolution of the interface dynamics for overlying film arrangements, with a restriction on the electric field strength. The non-local term is always linearly destabilising and produces growth rates proportional to the cube of the magnitude of the wavenumber vector. A sufficiently strong electric field is able promote non-trivial dynamics for subcritical Reynolds number flows where the flat interface is stable in the absence of an electric field. We present numerical simulations where we observe rich dynamical behavior with competing attractors, including "snaking" travelling waves and other fully three-dimensional wave formations. EPSRC studentship (RJT).

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.

Physics of Alfvén waves and energetic particles in burning plasmas

NASA Astrophysics Data System (ADS)

Chen, Liu; Zonca, Fulvio

2016-01-01

Dynamics of shear Alfvén waves and energetic particles are crucial to the performance of burning fusion plasmas. This article reviews linear as well as nonlinear physics of shear Alfvén waves and their self-consistent interaction with energetic particles in tokamak fusion devices. More specifically, the review on the linear physics deals with wave spectral properties and collective excitations by energetic particles via wave-particle resonances. The nonlinear physics deals with nonlinear wave-wave interactions as well as nonlinear wave-energetic particle interactions. Both linear as well as nonlinear physics demonstrate the qualitatively important roles played by realistic equilibrium nonuniformities, magnetic field geometries, and the specific radial mode structures in determining the instability evolution, saturation, and, ultimately, energetic-particle transport. These topics are presented within a single unified theoretical framework, where experimental observations and numerical simulation results are referred to elucidate concepts and physics processes.

Directional asymmetry of the nonlinear wave phenomena in a three-dimensional granular phononic crystal under gravity.

PubMed

Merkel, A; Tournat, V; Gusev, V

2014-08-01

We report the experimental observation of the gravity-induced asymmetry for the nonlinear transformation of acoustic waves in a noncohesive granular phononic crystal. Because of the gravity, the contact precompression increases with depth inducing space variations of not only the linear and nonlinear elastic moduli but also of the acoustic wave dissipation. We show experimentally and explain theoretically that, in contrast to symmetric propagation of linear waves, the amplitude of the nonlinearly self-demodulated wave depends on whether the propagation of the waves is in the direction of the gravity or in the opposite direction. Among the observed nonlinear processes, we report frequency mixing of the two transverse-rotational modes belonging to the optical band of vibrations and propagating with negative phase velocities, which results in the excitation of a longitudinal wave belonging to the acoustic band of vibrations and propagating with positive phase velocity. We show that the measurements of the gravity-induced asymmetry in the nonlinear acoustic phenomena can be used to compare the in-depth distributions of the contact nonlinearity and of acoustic absorption.

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.

Spatio-temporal dynamics induced by competing instabilities in two asymmetrically coupled nonlinear evolution equations

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

Schüler, D.; Alonso, S.; Bär, M.

2014-12-15

Pattern formation often occurs in spatially extended physical, biological, and chemical systems due to an instability of the homogeneous steady state. The type of the instability usually prescribes the resulting spatio-temporal patterns and their characteristic length scales. However, patterns resulting from the simultaneous occurrence of instabilities cannot be expected to be simple superposition of the patterns associated with the considered instabilities. To address this issue, we design two simple models composed by two asymmetrically coupled equations of non-conserved (Swift-Hohenberg equations) or conserved (Cahn-Hilliard equations) order parameters with different characteristic wave lengths. The patterns arising in these systems range from coexistingmore » static patterns of different wavelengths to traveling waves. A linear stability analysis allows to derive a two parameter phase diagram for the studied models, in particular, revealing for the Swift-Hohenberg equations, a co-dimension two bifurcation point of Turing and wave instability and a region of coexistence of stationary and traveling patterns. The nonlinear dynamics of the coupled evolution equations is investigated by performing accurate numerical simulations. These reveal more complex patterns, ranging from traveling waves with embedded Turing patterns domains to spatio-temporal chaos, and a wide hysteretic region, where waves or Turing patterns coexist. For the coupled Cahn-Hilliard equations the presence of a weak coupling is sufficient to arrest the coarsening process and to lead to the emergence of purely periodic patterns. The final states are characterized by domains with a characteristic length, which diverges logarithmically with the coupling amplitude.« less

Reflection and Transmission of a Focused Finite Amplitude Sound Beam Incident on a Curved Interface

NASA Astrophysics Data System (ADS)

Makin, Inder Raj Singh

Reflection and transmission of a finite amplitude focused sound beam at a weakly curved interface separating two fluid-like media are investigated. The KZK parabolic wave equation, which accounts for thermoviscous absorption, diffraction, and nonlinearity, is used to describe the high intensity focused beam. The first part of the work deals with the quasilinear analysis of a weakly nonlinear beam after its reflection and transmission from a curved interface. A Green's function approach is used to define the field integrals describing the primary and the nonlinearly generated second harmonic beam. Closed-form solutions are obtained for the primary and second harmonic beams when a Gaussian amplitude distribution at the source is assumed. The second part of the research uses a numerical frequency domain solution of the KZK equation for a fully nonlinear analysis of the reflected and transmitted fields. Both piston and Gaussian sources are considered. Harmonic components generated in the medium due to propagation of the focused beam are evaluated, and formation of shocks in the reflected and transmitted beams is investigated. A finite amplitude focused beam is observed to be modified due to reflection and transmission from a curved interface in a manner distinct from that in the case of a small signal beam. Propagation curves, beam patterns, phase plots and time waveforms for various parameters defining the source and media pairs are presented, highlighting the effect of the interface curvature on the reflected and transmitted beams. Relevance of the current work to biomedical applications of ultrasound is discussed.

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.

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.

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).

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.

Sediment transport under wave groups: Relative importance between nonlinear waveshape and nonlinear boundary layer streaming

USGS Publications Warehouse

Yu, X.; Hsu, T.-J.; Hanes, D.M.

2010-01-01

Sediment transport under nonlinear waves in a predominately sheet flow condition is investigated using a two-phase model. Specifically, we study the relative importance between the nonlinear waveshape and nonlinear boundary layer streaming on cross-shore sand transport. Terms in the governing equations because of the nonlinear boundary layer process are included in this one-dimensional vertical (1DV) model by simplifying the two-dimensional vertical (2DV) ensemble-averaged two-phase equations with the assumption that waves propagate without changing their form. The model is first driven by measured time series of near-bed flow velocity because of a wave group during the SISTEX99 large wave flume experiment and validated with the measured sand concentration in the sheet flow layer. Additional studies are then carried out by including and excluding the nonlinear boundary layer terms. It is found that for the grain diameter (0.24 mm) and high-velocity skewness wave condition considered here, nonlinear waveshape (e.g., skewness) is the dominant mechanism causing net onshore transport and nonlinear boundary layer streaming effect only causes an additional 36% onshore transport. However, for conditions of relatively low-wave skewness and a stronger offshore directed current, nonlinear boundary layer streaming plays a more critical role in determining the net transport. Numerical experiments further suggest that the nonlinear boundary layer streaming effect becomes increasingly important for finer grain. When the numerical model is driven by measured near-bed flow velocity in a more realistic surf zone setting, model results suggest nonlinear boundary layer processes may nearly double the onshore transport purely because of nonlinear waveshape. Copyright 2010 by the American Geophysical Union.

Electrostatic shocks and solitons in pair-ion plasmas in a two-dimensional geometry

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

Masood, W.; Mahmood, S.; Imtiaz, N.

2009-12-15

Nonlinear electrostatic waves are studied in unmagnetized, dissipative pair-ion plasmas in the presence of weak transverse perturbations. The dissipation in the system is taken into account by incorporating the kinematic viscosity of both positive and negative ions in plasmas. The Kadomtsev-Petviashvili-Burger equation is derived using the small amplitude expansion method. The Kadomtsev-Petviashvili equation for pair-ion plasmas is also presented by ignoring the dissipative effects. Both compressive and rarefactive shocks and solitary waves are found to exist in pair-ion plasmas. The dependence of compression and rarefaction on the temperature ratios between the ion species is numerically shown. The present study maymore » have relevance to the understanding of the formation of electrostatic shocks and solitons in laboratory produced pair-ion plasmas.« less

Poincaré analysis of wave motion in ultrarelativistic electron-ion plasmas.

PubMed

Lehmann, G; Spatschek, K H

2011-03-01

Based on a relativistic Maxwell-fluid description, the existence of ultrarelativistic laser-induced periodic waves in an electron-ion plasma is investigated. Within a one-dimensional propagation geometry nonlinear coupling of the electromagnetic and electrostatic components occurs that makes the fourth-order problem nonintegrable. A Hamiltonian description is derived, and the manifolds of periodic solutions are studied by Poincaré section plots. The influence of ion motion is investigated in different intensity regimes. For ultrarelativistic laser intensities the phase-space structures change significantly compared to the weakly relativistic case. Ion motion becomes very important such that finally electron-ion plasmas in the far-ultrarelativistic regime behave similarly to electron-positron plasmas. The characteristic new types of periodic solutions of the system are identified and discussed.

The Evolution of Modulated Wavetrains Into Turbulent Spots

NASA Technical Reports Server (NTRS)

Gaster, M.

2007-01-01

Experiment are being carried out to study the process by which th almost periodic disturbance waves generated naturally by the freestream evolve into turbulence. The boundary layer on a flat plate has been used for this study. The novelty of the approach is in the form of artificial excitation that is used. In this work the flow is excited artificially by deterministic white noise. The weak T-S wave created develops down stream, becomes nonlinear and blows up locally onto a highly distorted flow. These large local distortions of the mean flow allow very high frequency disturbances to grow and form into small turbulent spots. The spots arise from the excitation, and if the same noise sequence is repeated a spot will form at the same position and time instant relative to the excitation.

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

Weak wind-wave/tide interaction over fixed and moveable bottoms: a formulation and some preliminary results

NASA Astrophysics Data System (ADS)

Kagan, B. A.; Alvarez, O.; Izquierdo, A.

2005-05-01

The formulation of weak wind-wave/low-frequency current interaction is discussed comprehensively as applied to fixed- and moveable-bottom cases. It involves (1) a dependence of the drag coefficient on the ratio between wave and current bottom friction velocity amplitudes, (2) the resistance law for the oscillatory, rough, turbulent bottom boundary layer (BBL) which accounts for the usually neglected effects of rotation and the phase difference between the bottom stress and the friction-free current velocity, (3) the expression for the BBL depth in terms of the bottom Rossby number and (4) the bottom roughness predictor of Grant and Madsen (J. Geophys. Res., 87 (1982) 469) in the version of Tolman (J. Phys. Oceanogr., 24 (1994) 994). The formulation is implemented in the UCA (University of Cadiz) 2D nonlinear, high-resolution, hydrodynamic model and used to study the influence of wind-wave/tide interaction, bottom mobility and the improved flow-resistance description on the M 2 tidal dynamics of Cadiz Bay. The inclusion of either of the first two factors can cause the drag coefficient to increase significantly over its reference value. If the third factor is included, changes in the drag coefficient are quite moderate. This is because the effect of rotation is opposite in sign to the effect of phase difference, so that these effects taken together very nearly balance. The reason why bottom mobility has such an important influence on shallow-water tidal dynamics as wind-wave/tide interaction has, is the occurrence of the large irregular variations in the drag coefficient that accompany sediment motion.

Nonlinear spin conductance of yttrium iron garnet thin films driven by large spin-orbit torque

NASA Astrophysics Data System (ADS)

Thiery, N.; Draveny, A.; Naletov, V. V.; Vila, L.; Attané, J. P.; Beigné, C.; de Loubens, G.; Viret, M.; Beaulieu, N.; Ben Youssef, J.; Demidov, V. E.; Demokritov, S. O.; Slavin, A. N.; Tiberkevich, V. S.; Anane, A.; Bortolotti, P.; Cros, V.; Klein, O.

2018-02-01

We report high power spin transfer studies in open magnetic geometries by measuring the spin conductance between two nearby Pt wires deposited on top of an epitaxial yttrium iron garnet thin film. Spin transport is provided by propagating spin waves that are generated and detected by direct and inverse spin Hall effects. We observe a crossover in spin conductance from a linear transport dominated by exchange magnons (low current regime) to a nonlinear transport dominated by magnetostatic magnons (high current regime). The latter are low-damping magnetic excitations, located near the spectral bottom of the magnon manifold, with a sensitivity to the applied magnetic field. This picture is supported by microfocus Brillouin light-scattering spectroscopy. Our findings could be used for the development of controllable spin conductors by variation of relatively weak magnetic fields.

On the generation and evolution of internal solitary waves in the southern Red Sea

NASA Astrophysics Data System (ADS)

Guo, Daquan; Zhan, Peng; Kartadikaria, Aditya; Akylas, Triantaphyllos; Hoteit, Ibrahim

2015-04-01

Satellite observations recently revealed the existence of trains of internal solitary waves in the southern Red Sea between 16.0°N and 16.5°N, propagating from the centre of the domain toward the continental shelf [Da silva et al., 2012]. Given the relatively weak tidal velocity in this area and their generation in the central of the domain, Da Silva suggested three possible mechanisms behind the generation of the waves, namely Resonance and disintegration of interfacial tides, Generation of interfacial tides by impinging, remotely generated internal tidal beams and for geometrically focused and amplified internal tidal beams. Tide analysis based on tide stations data and barotropic tide model in the Red Sea shows that tide is indeed very weak in the centre part of the Red Sea, but it is relatively strong in the northern and southern parts (reaching up to 66 cm/s). Together with extreme steep slopes along the deep trench, it provides favourable conditions for the generation of internal solitary in the southern Red Sea. To investigate the generation mechanisms and study the evolution of the internal waves in the off-shelf region of the southern Red Sea we have implemented a 2-D, high-resolution and non-hydrostatic configuration of the MIT general circulation model (MITgcm). Our simulations reproduce well that the generation process of the internal solitary waves. Analysis of the model's output suggests that the interaction between the topography and tidal flow with the nonlinear effect is the main mechanism behind the generation of the internal solitary waves. Sensitivity experiments suggest that neither tidal beam nor the resonance effect of the topography is important factor in this process.

Scaling properties of weakly nonlinear coefficients in the Faraday problem.

PubMed

Skeldon, A C; Porter, J

2011-07-01

Interesting and exotic surface wave patterns have regularly been observed in the Faraday experiment. Although symmetry arguments provide a qualitative explanation for the selection of some of these patterns (e.g., superlattices), quantitative analysis is hindered by mathematical difficulties inherent in a time-dependent, free-boundary Navier-Stokes problem. More tractable low viscosity approximations are available, but these do not necessarily capture the moderate viscosity regime of the most interesting experiments. Here we focus on weakly nonlinear behavior and compare the scaling results derived from symmetry arguments in the low viscosity limit with the computed coefficients of appropriate amplitude equations using both the full Navier-Stokes equations and a reduced set of partial differential equations due to Zhang and Vinãls. We find the range of viscosities over which one can expect "low viscosity" theories to hold. We also find that there is an optimal viscosity range for locating superlattice patterns experimentally-large enough that the region of parameters giving stable patterns is not impracticably small, yet not so large that crucial resonance effects are washed out. These results help explain some of the discrepancies between theory and experiment.

A scalable, fully implicit algorithm for the reduced two-field low-β extended MHD model

DOE PAGES

Chacon, Luis; Stanier, Adam John

2016-12-01

Here, we demonstrate a scalable fully implicit algorithm for the two-field low-β extended MHD model. This reduced model describes plasma behavior in the presence of strong guide fields, and is of significant practical impact both in nature and in laboratory plasmas. The model displays strong hyperbolic behavior, as manifested by the presence of fast dispersive waves, which make a fully implicit treatment very challenging. In this study, we employ a Jacobian-free Newton–Krylov nonlinear solver, for which we propose a physics-based preconditioner that renders the linearized set of equations suitable for inversion with multigrid methods. As a result, the algorithm ismore » shown to scale both algorithmically (i.e., the iteration count is insensitive to grid refinement and timestep size) and in parallel in a weak-scaling sense, with the wall-clock time scaling weakly with the number of cores for up to 4096 cores. For a 4096 × 4096 mesh, we demonstrate a wall-clock-time speedup of ~6700 with respect to explicit algorithms. The model is validated linearly (against linear theory predictions) and nonlinearly (against fully kinetic simulations), demonstrating excellent agreement.« less

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.

Kolmogorov Turbulence Defeated by Anderson Localization for a Bose-Einstein Condensate in a Sinai-Oscillator Trap

NASA Astrophysics Data System (ADS)

Ermann, Leonardo; Vergini, Eduardo; Shepelyansky, Dima L.

2017-08-01

We study the dynamics of a Bose-Einstein condensate in a Sinai-oscillator trap under a monochromatic driving force. Such a trap is formed by a harmonic potential and a repulsive disk located in the center vicinity corresponding to the first experiments of condensate formation by Ketterle and co-workers in 1995. We allow that the external driving allows us to model the regime of weak wave turbulence with the Kolmogorov energy flow from low to high energies. We show that in a certain regime of weak driving and weak nonlinearity such a turbulent energy flow is defeated by the Anderson localization that leads to localization of energy on low energy modes. This is in a drastic contrast to the random phase approximation leading to energy flow to high modes. A critical threshold is determined above which the turbulent flow to high energies becomes possible. We argue that this phenomenon can be studied with ultracold atoms in magneto-optical traps.

Kolmogorov Turbulence Defeated by Anderson Localization for a Bose-Einstein Condensate in a Sinai-Oscillator Trap.

PubMed

Ermann, Leonardo; Vergini, Eduardo; Shepelyansky, Dima L

2017-08-04

We study the dynamics of a Bose-Einstein condensate in a Sinai-oscillator trap under a monochromatic driving force. Such a trap is formed by a harmonic potential and a repulsive disk located in the center vicinity corresponding to the first experiments of condensate formation by Ketterle and co-workers in 1995. We allow that the external driving allows us to model the regime of weak wave turbulence with the Kolmogorov energy flow from low to high energies. We show that in a certain regime of weak driving and weak nonlinearity such a turbulent energy flow is defeated by the Anderson localization that leads to localization of energy on low energy modes. This is in a drastic contrast to the random phase approximation leading to energy flow to high modes. A critical threshold is determined above which the turbulent flow to high energies becomes possible. We argue that this phenomenon can be studied with ultracold atoms in magneto-optical traps.

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.

Sheared Layers in the Continental Crust: Nonlinear and Linearized inversion for Ps receiver functions

NASA Astrophysics Data System (ADS)

Park, J. J.

2017-12-01

Sheared Layers in the Continental Crust: Nonlinear and Linearized inversion for Ps receiver functions Jeffrey Park, Yale University The interpretation of seismic receiver functions (RFs) in terms of isotropic and anisotropic layered structure can be complex. The relationship between structure and body-wave scattering is nonlinear. The anisotropy can involve more parameters than the observations can readily constrain. Finally, reflectivity-predicted layer reverberations are often not prominent in data, so that nonlinear waveform inversion can search in vain to match ghost signals. Multiple-taper correlation (MTC) receiver functions have uncertainties in the frequency domain that follow Gaussian statistics [Park and Levin, 2016a], so grid-searches for the best-fitting collections of interfaces can be performed rapidly to minimize weighted misfit variance. Tests for layer-reverberations can be performed in the frequency domain without reflectivity calculations, allowing flexible modelling of weak, but nonzero, reverberations. Park and Levin [2016b] linearized the hybridization of P and S body waves in an anisotropic layer to predict first-order Ps conversion amplitudes at crust and mantle interfaces. In an anisotropic layer, the P wave acquires small SV and SH components. To ensure continuity of displacement and traction at the top and bottom boundaries of the layer, shear waves are generated. Assuming hexagonal symmetry with an arbitrary symmetry axis, theory confirms the empirical stacking trick of phase-shifting transverse RFs by 90 degrees in back-azimuth [Shiomi and Park, 2008; Schulte-Pelkum and Mahan, 2014] to enhance 2-lobed and 4-lobed harmonic variation. Ps scattering is generated by sharp interfaces, so that RFs resemble the first derivative of the model. MTC RFs in the frequency domain can be manipulated to obtain a first-order reconstruction of the layered anisotropy, under the above modeling constraints and neglecting reverberations. Examples from long-running continental stations will be discussed. Park, J., and V. Levin, 2016a. doi:10.1093/gji/ggw291. Park, J., and V. Levin, 2016b. doi:10.1093/gji/ggw323. Schulte-Pelkum, V., and Mahan, K. H., 2014. doi:10.1007/s00024-014-0853-4. Shiomi, K., & Park, J., 2008. doi:10.1029/2007JB005535.

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.

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.

Effect of Local Thermal Equilibrium Misbalance on Long-wavelength Slow Magnetoacoustic Waves

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

Nakariakov, V. M.; Afanasyev, A. N.; Kumar, S.

Evolution of slow magnetoacoustic waves guided by a cylindrical magnetic flux tube that represents a coronal loop or plume, is modeled accounting for the effects of finite gas pressure, weak nonlinearity, dissipation by thermal conduction and viscosity, and the misbalance between the cooling by optically thin radiation and unspecified heating of the plasma. An evolutionary equation of the Burgers–Malthus type is derived. It is shown that the cooling/heating misbalance, determined by the derivatives of the combined radiative cooling and heating function, with respect to the density, temperature, and magnetic field at the thermal equilibrium affect the wave rather strongly. Thismore » effect may either cause additional damping, or counteract it, or lead to the gradual amplification of the wave. In the latter case, the coronal plasma acts as an active medium for the slow magnetoacoustic waves. The effect of the cooling/heating misbalance could be important for coronal slow waves, and could be responsible for certain discrepancies between theoretical results and observations, in particular, the increased or decreased damping lengths and times, detection of the waves at certain heights only, and excitation of compressive oscillations. The results obtained open up a possibility for the diagnostics of the coronal heating function by slow magnetoacoustic waves.« less

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

Roles Played by Electrostatic Waves in Producing Radio Emissions

NASA Technical Reports Server (NTRS)

Cairns, Iver H.

2000-01-01

Processes in which electromagnetic radiation is produced directly or indirectly via intermediate waves are reviewed. It is shown that strict theoretical constraints exist for electrons to produce nonthermal levels of radiation directly by the Cerenkov or cyclotron resonances. In contrast, indirect emission processes in which intermediary plasma waves are converted into radiation are often favored on general and specific grounds. Four classes of mechanisms involving the conversion of electrostatic waves into radiation are linear mode conversion, hybrid linear/nonlinear mechanisms, nonlinear wave-wave and wave-particle processes, and radiation from localized wave packets. These processes are reviewed theoretically and observational evidence summarized for their occurrence. Strong evidence exists that specific nonlinear wave processes and mode conversion can explain quantitatively phenomena involving type III solar radio bursts and ionospheric emissions. On the other hand, no convincing evidence exists that magnetospheric continuum radiation is produced by mode conversion instead of nonlinear wave processes. Further research on these processes is needed.

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.

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.

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.

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.

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.

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].

Interaction of Kelvin waves and nonlocality of energy transfer in superfluids

NASA Astrophysics Data System (ADS)

Laurie, Jason; L'Vov, Victor S.; Nazarenko, Sergey; Rudenko, Oleksii

2010-03-01

We argue that the physics of interacting Kelvin Waves (KWs) is highly nontrivial and cannot be understood on the basis of pure dimensional reasoning. A consistent theory of KW turbulence in superfluids should be based upon explicit knowledge of their interactions. To achieve this, we present a detailed calculation and comprehensive analysis of the interaction coefficients for KW turbuelence, thereby, resolving previous mistakes stemming from unaccounted contributions. As a first application of this analysis, we derive a local nonlinear (partial differential) equation. This equation is much simpler for analysis and numerical simulations of KWs than the Biot-Savart equation, and in contrast to the completely integrable local induction approximation (in which the energy exchange between KWs is absent), describes the nonlinear dynamics of KWs. Second, we show that the previously suggested Kozik-Svistunov energy spectrum for KWs, which has often been used in the analysis of experimental and numerical data in superfluid turbulence, is irrelevant, because it is based upon an erroneous assumption of the locality of the energy transfer through scales. Moreover, we demonstrate the weak nonlocality of the inverse cascade spectrum with a constant particle-number flux and find resulting logarithmic corrections to this spectrum.

Spectral characterization of a supercontinuum source based on nonlinear broadening in an aqueous K_2ZnCl_4 salt solution

DOE PAGES

Robinson, Timothy S.; Patankar, Siddharth; Floyd, Emma; ...

2017-01-01

We report on investigations concerning the shot-to-shot spectral stability properties of a supercontinuum source based on nonlinear processes such as self-phase modulation and optical wave-breaking in a highly concentrated K 2ZnCl 4 double salt solution. The use of a liquid medium offers both damage resistance and high third-order optical nonlinearity. Approximately 40 μJ pulses spanning a spectral range between 390 and 960 nm were produced with 3.8% RMS energy stability, using infrared input pulses of 500±50 fs FWHM durations and 2.42±0.04 mJ energies with an RMS stability of 2%. The spectral stability was quantified via acquiring single-shot spectra and studyingmore » shot-to-shot variation across a spectral range of 200–1100 nm, as well as by considering spectral correlations. The regional spectral correlation variations were indicative of nonlinear processes leading to sideband generation. Spectral stability and efficiency of energy transfer into the supercontinuum were found to weakly improve with increasing driver pulse energy, suggesting that the nonlinear broadening processes are more stable when driven more strongly, or that self-guiding effects in a filament help to stabilize the supercontinuum generation.« less

Spectral characterization of a supercontinuum source based on nonlinear broadening in an aqueous K_2ZnCl_4 salt solution

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

Robinson, Timothy S.; Patankar, Siddharth; Floyd, Emma

We report on investigations concerning the shot-to-shot spectral stability properties of a supercontinuum source based on nonlinear processes such as self-phase modulation and optical wave-breaking in a highly concentrated K 2ZnCl 4 double salt solution. The use of a liquid medium offers both damage resistance and high third-order optical nonlinearity. Approximately 40 μJ pulses spanning a spectral range between 390 and 960 nm were produced with 3.8% RMS energy stability, using infrared input pulses of 500±50 fs FWHM durations and 2.42±0.04 mJ energies with an RMS stability of 2%. The spectral stability was quantified via acquiring single-shot spectra and studyingmore » shot-to-shot variation across a spectral range of 200–1100 nm, as well as by considering spectral correlations. The regional spectral correlation variations were indicative of nonlinear processes leading to sideband generation. Spectral stability and efficiency of energy transfer into the supercontinuum were found to weakly improve with increasing driver pulse energy, suggesting that the nonlinear broadening processes are more stable when driven more strongly, or that self-guiding effects in a filament help to stabilize the supercontinuum generation.« less

Controllable nonlinearity in a dual-coupling optomechanical system under a weak-coupling regime

NASA Astrophysics Data System (ADS)

Zhu, Gui-Lei; Lü, Xin-You; Wan, Liang-Liang; Yin, Tai-Shuang; Bin, Qian; Wu, Ying

2018-03-01

Strong quantum nonlinearity gives rise to many interesting quantum effects and has wide applications in quantum physics. Here we investigate the quantum nonlinear effect of an optomechanical system (OMS) consisting of both linear and quadratic coupling. Interestingly, a controllable optomechanical nonlinearity is obtained by applying a driving laser into the cavity. This controllable optomechanical nonlinearity can be enhanced into a strong coupling regime, even if the system is initially in the weak-coupling regime. Moreover, the system dissipation can be suppressed effectively, which allows the appearance of phonon sideband and photon blockade effects in the weak-coupling regime. This work may inspire the exploration of a dual-coupling optomechanical system as well as its applications in modern quantum science.

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.

The excitation of spiral density waves through turbulent fluctuations in accretion discs - II. Numerical simulations with MRI-driven turbulence

NASA Astrophysics Data System (ADS)

Heinemann, T.; Papaloizou, J. C. B.

2009-07-01

We present fully three-dimensional local simulations of compressible magneto-rotational instability (MRI) turbulence with the object of studying and elucidating the excitation of the non-axisymmetric spiral density waves that are observed to always be present in such simulations. They are potentially important for affecting protoplanetary migration through the action of associated stochastic gravitational forces and producing residual transport in MHD inactive regions through which they may propagate. The simulations we perform are with zero net flux and produce mean activity levels corresponding to the Shakura & Syunyaev α ~ 5 × 10-3, being at the lower end of the range usually considered in accretion disc modelling. We reveal the nature of the mechanism responsible for the excitation of these waves by determining the time-dependent evolution of the Fourier transforms of the participating state variables. The dominant waves are found to have no vertical structure and to be excited during periodically repeating swings in which they change from leading to trailing. The initial phase of the evolution of such a swing is found to be in excellent agreement with that expected from the WKBJ theory developed in a preceding paper by Heinemann & Papaloizou. However, shortly after the attainment of the expected maximum wave amplitude, the waves begin to be damped on account of the formation of weak shocks. As expected from the theory, the waves are seen to shorten in radial wavelength as they propagate. This feature enables non-linear dissipation to continue in spite of amplitude decrease. As a consequence, the waves are almost always seen to be in the non-linear regime. We demonstrate that the important source terms causing excitation of the waves are related to a quantity that reduces to the potential vorticity for small perturbations from the background state with no vertical dependence. We find that the root mean square density fluctuations associated with the waves are positively correlated with both this quantity and the general level of hydromagnetic turbulence. The mean angular momentum transport associated with spiral density waves generated in our simulations is estimated to be a significant fraction of that associated with the turbulent Reynolds stress.

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.

Non-degenerate two-photon absorption in silicon waveguides. Analytical and experimental study

DOE PAGES

Zhang, Yanbing; Husko, Chad; Lefrancois, Simon; ...

2015-06-22

We theoretically and experimentally investigate the nonlinear evolution of two optical pulses in a silicon waveguide. We provide an analytic solution for the weak probe wave undergoing non-degenerate two-photon absorption (TPA) from the strong pump. At larger pump intensities, we employ a numerical solution to study the interplay between TPA and photo-generated free carriers. We develop a simple and powerful approach to extract and separate out the distinct loss contributions of TPA and free-carrier absorption from readily available experimental data. Our analysis accounts accurately for experimental results in silicon photonic crystal waveguides.

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

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

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.

Exact result in strong wave turbulence of thin elastic plates

NASA Astrophysics Data System (ADS)

Düring, Gustavo; Krstulovic, Giorgio

2018-02-01

An exact result concerning the energy transfers between nonlinear waves of a thin elastic plate is derived. Following Kolmogorov's original ideas in hydrodynamical turbulence, but applied to the Föppl-von Kármán equation for thin plates, the corresponding Kármán-Howarth-Monin relation and an equivalent of the 4/5 -Kolmogorov's law is derived. A third-order structure function involving increments of the amplitude, velocity, and the Airy stress function of a plate, is proven to be equal to -ɛ ℓ , where ℓ is a length scale in the inertial range at which the increments are evaluated and ɛ the energy dissipation rate. Numerical data confirm this law. In addition, a useful definition of the energy fluxes in Fourier space is introduced and proven numerically to be flat in the inertial range. The exact results derived in this Rapid Communication are valid for both weak and strong wave turbulence. They could be used as a theoretical benchmark of new wave-turbulence theories and to develop further analogies with hydrodynamical turbulence.

An Intense Traveling Airglow Front in the Upper Mesosphere-Lower Thermosphere with Characteristic of a Turbulent Bore Observed over Alice Springs, Australia

NASA Astrophysics Data System (ADS)

Walterscheid, R. L.; Hecht, J. H.; Hickey, M. P.; Gelinas, L. J.; Vincent, R. A.; Reid, I. M.; Woithe, J.

2010-12-01

The Aerospace Corporation’s Nightglow Imager observed a large step-function change in airglow in the form of a traveling front in the OH and O2 airglow emissions over Alice Springs Australia on February 2, 2003. The front exhibited a stepwise increase of nearly a factor two in the OH brightness and a stepwise decrease in the O2 brightness. The change in brightness in each layer was associated with a strong leading disturbance followed by a train of weak barely visible waves. The OH airglow brightness behind the front was the brightness night for 02 at Alice Springs that we have measured in seven years of observations. The OH brightness was among the five brightest. The event was associated with a strong phase-locked two-day wave (TDW).We have analyzed the stability conditions for the upper mesosphere and lower thermosphere and found that the airglow layers were found in a region of strong ducting. The thermal structure was obtained from combining data from the SABER instrument on the TIMED satellite and the NRLMSISE-00 model. The wind profile was obtained by combining the HWM07 model and MF radar winds from Buckland Park Australia. We found that the TDW-disturbed profile was significantly more effective in supporting a high degree of ducting than a profile based only on HWM07 winds. Dramatic wall events have been interpreted as manifestations of undular bores (e.g., Smith et al. [2003]). Undular bores are nonlinear high Froude number events that must generate an ever increasing train of waves to carry the excess energy away from the bore front. Only a very weak wave train behind the initial disturbance was seen for the Alice Springs event. The form of the amplitude ordering was not typical of a nonlinear wave train. Therefore a bore interpretation requires another means of energy dissipation, namely turbulent dissipation. We suggest that a reasonable interpretation of the observed event is a turbulent bore. We are unaware of any previous event having characteristics of a turbulent bore. Smith, S. M., et al., A multidiagnostic investigation of the mesospheric bore phenomenon, J. Geophys. Res., 108, 2003

Parametric instability, inverse cascade and the range of solar-wind turbulence

NASA Astrophysics Data System (ADS)

Chandran, Benjamin D. G.

2018-02-01

In this paper, weak-turbulence theory is used to investigate the nonlinear evolution of the parametric instability in three-dimensional low- plasmas at wavelengths much greater than the ion inertial length under the assumption that slow magnetosonic waves are strongly damped. It is shown analytically that the parametric instability leads to an inverse cascade of Alfvén wave quanta, and several exact solutions to the wave kinetic equations are presented. The main results of the paper concern the parametric decay of Alfvén waves that initially satisfy +\\gg e-$ , where +$ and -$ are the frequency ( ) spectra of Alfvén waves propagating in opposite directions along the magnetic field lines. If +$ initially has a peak frequency 0$ (at which +$ is maximized) and an `infrared' scaling p$ at smaller with , then +$ acquires an -1$ scaling throughout a range of frequencies that spreads out in both directions from 0$ . At the same time, -$ acquires an -2$ scaling within this same frequency range. If the plasma parameters and infrared +$ spectrum are chosen to match conditions in the fast solar wind at a heliocentric distance of 0.3 astronomical units (AU), then the nonlinear evolution of the parametric instability leads to an +$ spectrum that matches fast-wind measurements from the Helios spacecraft at 0.3 AU, including the observed -1$ scaling at -4~\\text{Hz}$ . The results of this paper suggest that the -1$ spectrum seen by Helios in the fast solar wind at -4~\\text{Hz}$ is produced in situ by parametric decay and that the -1$ range of +$ extends over an increasingly narrow range of frequencies as decreases below 0.3 AU. This prediction will be tested by measurements from the Parker Solar Probe.

Matter-wave solitons in nonlinear optical lattices

NASA Astrophysics Data System (ADS)

Sakaguchi, Hidetsugu; Malomed, Boris A.

2005-10-01

We introduce a dynamical model of a Bose-Einstein condensate based on the one-dimensional (1D) Gross-Pitaevskii equation (GPE) with a nonlinear optical lattice (NOL), which is represented by the cubic term whose coefficient is periodically modulated in the coordinate. The model describes a situation when the atomic scattering length is spatially modulated, via the optically controlled Feshbach resonance, in an optical lattice created by interference of two laser beams. Relatively narrow solitons supported by the NOL are predicted by means of the variational approximation (VA), and an averaging method is applied to broad solitons. A different feature is a minimum norm (number of atoms), N=Nmin , necessary for the existence of solitons. The VA predicts Nmin very accurately. Numerical results are chiefly presented for the NOL with the zero spatial average value of the nonlinearity coefficient. Solitons with values of the amplitude A larger than at N=Nmin are stable. Unstable solitons with smaller, but not too small, A rearrange themselves into persistent breathers. For still smaller A , the soliton slowly decays into radiation without forming a breather. Broad solitons with very small A are practically stable, as their decay is extremely slow. These broad solitons may freely move across the lattice, featuring quasielastic collisions. Narrow solitons, which are strongly pinned to the NOL, can easily form stable complexes. Finally, the weakly unstable low-amplitude solitons are stabilized if a cubic term with a constant coefficient, corresponding to weak attraction, is included in the GPE.

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.

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.

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.

Fibre multi-wave mixing combs reveal the broken symmetry of Fermi-Pasta-Ulam recurrence

NASA Astrophysics Data System (ADS)

Mussot, Arnaud; Naveau, Corentin; Conforti, Matteo; Kudlinski, Alexandre; Copie, Francois; Szriftgiser, Pascal; Trillo, Stefano

2018-05-01

In optical fibres, weak modulations can grow at the expense of a strong pump to form a triangular comb of sideband pairs, until the process is reversed. Repeated cycles of such conversion and back-conversion constitute a manifestation of the universal nonlinear phenomenon known as Fermi-Pasta-Ulam recurrence. However, it remains a major challenge to observe the coexistence of different types of recurrences owing to the spontaneous symmetry-breaking nature of such a phenomenon. Here, we implement a novel non-destructive technique that allows the evolution in amplitude and phase of frequency modes to be reconstructed via post-processing of the fibre backscattered light. We clearly observe how control of the input modulation seed results in different recursive behaviours emerging from the phase-space structure dictated by the spontaneously broken symmetry. The proposed technique is an important tool to characterize other mixing processes and new regimes of rogue-wave formation and wave turbulence in fibre optics.

Dynamics of the seasonal variation of the North Equatorial Current bifurcation

NASA Astrophysics Data System (ADS)

Chen, Zhaohui; Wu, Lixin

2011-02-01

The dynamics of the seasonal variation of the North Equatorial Current (NEC) bifurcation is studied using a 1.5-layer nonlinear reduced-gravity Pacific basin model and a linear, first-mode baroclinic Rossby wave model. The model-simulated bifurcation latitude exhibits a distinct seasonal cycle with the southernmost latitude in June and the northernmost latitude in November, consistent with observational analysis. It is found that the seasonal migration of the NEC bifurcation latitude (NBL) not only is determined by wind locally in the tropics, as suggested in previous studies, but is also significantly intensified by the extratropical wind through coastal Kelvin waves. The model further demonstrates that the amplitude of the NEC bifurcation is also associated with stratification. A strong (weak) stratification leads to a fast (slow) phase speed of first-mode baroclinic Rossby waves, and thus large (small) annual range of the bifurcation latitude. Therefore, it is expected that in a warm climate the NBL should have a large range of annual migration.

Altimeter Observations of Baroclinic Oceanic Inertia-Gravity Wave Turbulence

NASA Technical Reports Server (NTRS)

Glazman, R. E.; Cheng, B.

1996-01-01

For a wide range of nonlinear wave processes - from capillary to planetary waves - theory predicts the existence of Kolmogorov-type spectral cascades of energy and other conserved quantities occuring via nonlinear resonant wave-wave interactions. So far, observations of wave turbulence (WT) have been limited to small-scale processes such as surface gravity and capillary-gravity waves.

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.

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

NONLINEAR REFLECTION PROCESS OF LINEARLY POLARIZED, BROADBAND ALFVÉN WAVES IN THE FAST SOLAR WIND

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

Shoda, M.; Yokoyama, T., E-mail: shoda@eps.s.u-tokyo.ac.jp

2016-04-01

Using one-dimensional numerical simulations, we study the elementary process of Alfvén wave reflection in a uniform medium, including nonlinear effects. In the linear regime, Alfvén wave reflection is triggered only by the inhomogeneity of the medium, whereas in the nonlinear regime, it can occur via nonlinear wave–wave interactions. Such nonlinear reflection (backscattering) is typified by decay instability. In most studies of decay instabilities, the initial condition has been a circularly polarized Alfvén wave. In this study we consider a linearly polarized Alfvén wave, which drives density fluctuations by its magnetic pressure force. For generality, we also assume a broadband wavemore » with a red-noise spectrum. In the data analysis, we decompose the fluctuations into characteristic variables using local eigenvectors, thus revealing the behaviors of the individual modes. Different from the circular-polarization case, we find that the wave steepening produces a new energy channel from the parent Alfvén wave to the backscattered one. Such nonlinear reflection explains the observed increasing energy ratio of the sunward to the anti-sunward Alfvénic fluctuations in the solar wind with distance against the dynamical alignment effect.« less

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.

Numerical study of heterogeneous mean temperature and shock wave in a resonator

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

Yano, Takeru

2015-10-28

When a frequency of gas oscillation in an acoustic resonator is sufficiently close to one of resonant frequencies of the resonator, the amplitude of gas oscillation becomes large and hence the nonlinear effect manifests itself. Then, if the dissipation effects due to viscosity and thermal conductivity of the gas are sufficiently small, the gas oscillation may evolve into the acoustic shock wave, in the so-called consonant resonators. At the shock front, the kinetic energy of gas oscillation is converted into heat by the dissipation process inside the shock layer, and therefore the temperature of the gas in the resonator rises.more » Since the acoustic shock wave travels in the resonator repeatedly over and over again, the temperature rise becomes noticeable in due course of time even if the shock wave is weak. We numerically study the gas oscillation with shock wave in a resonator of square cross section by solving the initial and boundary value problem of the system of three-dimensional Navier-Stokes equations with a finite difference method. In this case, the heat conduction across the boundary layer on the wall of resonator causes a spatially heterogeneous distribution of mean (time-averaged) gas temperature.« less

Modelling of Charles Darwin's tsunami reports

NASA Astrophysics Data System (ADS)

Galiev, Shamil

2010-05-01

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

Dynamics of coupled mode solitons in bursting neural networks

NASA Astrophysics Data System (ADS)

Nfor, N. Oma; Ghomsi, P. Guemkam; Moukam Kakmeni, F. M.

2018-02-01

Using an electrically coupled chain of Hindmarsh-Rose neural models, we analytically derived the nonlinearly coupled complex Ginzburg-Landau equations. This is realized by superimposing the lower and upper cutoff modes of wave propagation and by employing the multiple scale expansions in the semidiscrete approximation. We explore the modified Hirota method to analytically obtain the bright-bright pulse soliton solutions of our nonlinearly coupled equations. With these bright solitons as initial conditions of our numerical scheme, and knowing that electrical signals are the basis of information transfer in the nervous system, it is found that prior to collisions at the boundaries of the network, neural information is purely conveyed by bisolitons at lower cutoff mode. After collision, the bisolitons are completely annihilated and neural information is now relayed by the upper cutoff mode via the propagation of plane waves. It is also shown that the linear gain of the system is inextricably linked to the complex physiological mechanisms of ion mobility, since the speeds and spatial profiles of the coupled nerve impulses vary with the gain. A linear stability analysis performed on the coupled system mainly confirms the instability of plane waves in the neural network, with a glaring example of the transition of weak plane waves into a dark soliton and then static kinks. Numerical simulations have confirmed the annihilation phenomenon subsequent to collision in neural systems. They equally showed that the symmetry breaking of the pulse solution of the system leaves in the network static internal modes, sometime referred to as Goldstone modes.

Computational study of the interaction between a shock and a near-wall vortex using a weighted compact nonlinear scheme

NASA Astrophysics Data System (ADS)

Zuo, Zhifeng; Maekawa, Hiroshi

2014-02-01

The interaction between a moderate-strength shock wave and a near-wall vortex is studied numerically by solving the two-dimensional, unsteady compressible Navier-Stokes equations using a weighted compact nonlinear scheme with a simple low-dissipation advection upstream splitting method for flux splitting. Our main purpose is to clarify the development of the flow field and the generation of sound waves resulting from the interaction. The effects of the vortex-wall distance on the sound generation associated with variations in the flow structures are also examined. The computational results show that three sound sources are involved in this problem: (i) a quadrupolar sound source due to the shock-vortex interaction; (ii) a dipolar sound source due to the vortex-wall interaction; and (iii) a dipolar sound source due to unsteady wall shear stress. The sound field is the combination of the sound waves produced by all three sound sources. In addition to the interaction of the incident shock with the vortex, a secondary shock-vortex interaction is caused by the reflection of the reflected shock (MR2) from the wall. The flow field is dominated by the primary and secondary shock-vortex interactions. The generation mechanism of the third sound, which is newly discovered, due to the MR2-vortex interaction is presented. The pressure variations generated by (ii) become significant with decreasing vortex-wall distance. The sound waves caused by (iii) are extremely weak compared with those caused by (i) and (ii) and are negligible in the computed sound field.

Dynamics of coupled mode solitons in bursting neural networks.

PubMed

Nfor, N Oma; Ghomsi, P Guemkam; Moukam Kakmeni, F M

2018-02-01

Using an electrically coupled chain of Hindmarsh-Rose neural models, we analytically derived the nonlinearly coupled complex Ginzburg-Landau equations. This is realized by superimposing the lower and upper cutoff modes of wave propagation and by employing the multiple scale expansions in the semidiscrete approximation. We explore the modified Hirota method to analytically obtain the bright-bright pulse soliton solutions of our nonlinearly coupled equations. With these bright solitons as initial conditions of our numerical scheme, and knowing that electrical signals are the basis of information transfer in the nervous system, it is found that prior to collisions at the boundaries of the network, neural information is purely conveyed by bisolitons at lower cutoff mode. After collision, the bisolitons are completely annihilated and neural information is now relayed by the upper cutoff mode via the propagation of plane waves. It is also shown that the linear gain of the system is inextricably linked to the complex physiological mechanisms of ion mobility, since the speeds and spatial profiles of the coupled nerve impulses vary with the gain. A linear stability analysis performed on the coupled system mainly confirms the instability of plane waves in the neural network, with a glaring example of the transition of weak plane waves into a dark soliton and then static kinks. Numerical simulations have confirmed the annihilation phenomenon subsequent to collision in neural systems. They equally showed that the symmetry breaking of the pulse solution of the system leaves in the network static internal modes, sometime referred to as Goldstone modes.

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.

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.

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.

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.

Exact modelling of the optical bistability in ferroelectics via two-wave mixing: A system with full nonlinearity

NASA Astrophysics Data System (ADS)

Khushaini, Muhammad Asif A.; Ibrahim, Abdel-Baset M. A.; Choudhury, P. K.

2018-05-01

In this paper, we provide a complete mathematical model of the phenomenon of optical bistability (OB) resulting from the degenerate two-wave mixing (TWM) process of laser beams interacting with a single nonlinear layer of ferroelectric material. Starting with the electromagnetic wave equation for optical wave propagating in nonlinear media, a nonlinear coupled wave (CW) system with both self-phase modulation (SPM) and cross-phase modulation (XPM) sources of nonlinearity are derived. The complete CW system with full nonlinearity is solved numerically and a comparison between both the cases of with and without SPM at various combinations of design parameters is given. Furthermore, to provide a reliable theoretical model for the OB via TWM process, the results obtained theoretically are compared with the available experimental data. We found that the nonlinear system without SPM fails to predict the bistable response at lower combinations of the input parameters. However, at relatively higher values, the solution without SPM shows a reduction in the switching contrast and period in the OB response. A comparison with the experimental results shows better agreement with the system with full nonlinearity.

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.

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.

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.

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.

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.

The Weakly Nonlinear Magnetorotational Instability in a Global, Cylindrical Taylor–Couette Flow

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

Clark, S. E.; Oishi, Jeffrey S., E-mail: seclark@astro.columbia.edu

We conduct a global, weakly nonlinear analysis of the magnetorotational instability (MRI) in a Taylor–Couette flow. This is a multiscale, perturbative treatment of the nonideal, axisymmetric MRI near threshold, subject to realistic radial boundary conditions and cylindrical geometry. We analyze both the standard MRI, initialized by a constant vertical background magnetic field, and the helical MRI, with an azimuthal background field component. This is the first weakly nonlinear analysis of the MRI in a global Taylor–Couette geometry, as well as the first weakly nonlinear analysis of the helical MRI. We find that the evolution of the amplitude of the standardmore » MRI is described by a real Ginzburg–Landau equation (GLE), whereas the amplitude of the helical MRI takes the form of a complex GLE. This suggests that the saturated state of the helical MRI may itself be unstable on long spatial and temporal scales.« less

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.

Inverse four-wave-mixing and self-parametric amplification effect in optical fibre

PubMed Central

Turitsyn, Sergei K.; Bednyakova, Anastasia E.; Fedoruk, Mikhail P.; Papernyi, Serguei B.; Clements, Wallace R.L.

2015-01-01

An important group of nonlinear processes in optical fibre involves the mixing of four waves due to the intensity dependence of the refractive index. It is customary to distinguish between nonlinear effects that require external/pumping waves (cross-phase modulation and parametric processes such as four-wave mixing) and self-action of the propagating optical field (self-phase modulation and modulation instability). Here, we present a new nonlinear self-action effect, self-parametric amplification (SPA), which manifests itself as optical spectrum narrowing in normal dispersion fibre, leading to very stable propagation with a distinctive spectral distribution. The narrowing results from an inverse four-wave mixing, resembling an effective parametric amplification of the central part of the spectrum by energy transfer from the spectral tails. SPA and the observed stable nonlinear spectral propagation with random temporal waveform can find applications in optical communications and high power fibre lasers with nonlinear intra-cavity dynamics. PMID:26345290

Oscillations of a standing shock wave generated by the Richtmyer-Meshkov instability

NASA Astrophysics Data System (ADS)

Mikaelian, Karnig O.

2016-07-01

In a typical Richtmyer-Meshkov experiment a fast moving flat shock strikes a stationary perturbed interface between fluids A and B creating a transmitted and a reflected shock, both of which are perturbed. We propose shock tube experiments in which the reflected shock is stationary in the laboratory. Such a standing perturbed shock undergoes well-known damped oscillations. We present the conditions required for producing such a standing shock wave, which greatly facilitates the measurement of the oscillations and their rate of damping. We define a critical density ratio Rcritical, in terms of the adiabatic indices of the two fluids, and a critical Mach number Mscritical of the incident shock wave, which produces a standing reflected wave. If the initial density ratio R of the two fluids is less than Rcritical then a standing shock wave is possible at Ms=Mscritical . Otherwise a standing shock is not possible and the reflected wave always moves in the direction opposite the incident shock. Examples are given for present-day operating shock tubes with sinusoidal or inclined interfaces. We consider the effect of viscosity, which affects the damping rate of the oscillations. We point out that nonlinear bubble and spike amplitudes depend relatively weakly on the viscosity of the fluids and that the interface area is a better diagnostic.

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.

Weakly nonlinear behavior of a plate thickness-mode piezoelectric transformer.

PubMed

Yang, Jiashi; Chen, Ziguang; Hu, Yuantai; Jiang, Shunong; Guo, Shaohua

2007-04-01

We analyzed the weakly nonlinear behavior of a plate thickness-shear mode piezoelectric transformer near resonance. An approximate analytical solution was obtained. Numerical results based on the analytical solution are presented. It is shown that on one side of the resonant frequency the input-output relation becomes nonlinear, and on the other side the output voltage experiences jumps.

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