scholarly journals NONLINEAR OBLIQUE INTERACTION OF LARGE AMPLITUDE INTERNAL SOLITARY WAVES

2012 ◽  
Vol 1 (33) ◽  
pp. 19
Author(s):  
Keisuke Nakayama ◽  
Taro Kakinuma ◽  
Hidekazu Tsuji ◽  
Masayuki Oikawa
Keyword(s):  
Solitary Waves ◽  
Water Waves ◽  
Large Amplitude ◽  
Numerical Study ◽  
Incident Angle ◽  
Resonant Interaction ◽  
Internal Solitary Waves ◽  
Weakly Nonlinear ◽  
Wave Angle ◽  
The One

Solitary waves are typical nonlinear long waves in the ocean. The two-dimensional interaction of solitary waves has been shown to be essentially different from the one-dimensional case and can be related to generation of large amplitude waves (including ‘freak waves’). Concerning surface-water waves, Miles (1977) theoretically analyzed interaction of three solitary waves, which is called “resonant interaction” because of the relation among parameters of each wave. Weakly-nonlinear numerical study (Funakoshi, 1980) and fully-nonlinear one (Tanaka, 1993) both clarified the formation of large amplitude wave due to the interaction (“stem” wave) at the wall and its dependency of incident angle. For the case of internal waves, analyses using weakly nonlinear model equation (ex. Tsuji and Oikawa, 2006) suggest also qualitatively similar result. Therefore, the aim of this study is to investigate the strongly nonlinear interaction of internal solitary waves; especially whether the resonant behavior is found or not. As a result, it is found that the amplified internal wave amplitude becomes about three times as much as the original amplitude. In contrast, a "stem" was not found to occur when the incident wave angle was more than the critical angle, which has been demonstrated in the previous studies.

scholarly journals Interactions of large amplitude solitary waves in viscous fluid conduits

2014 ◽  
Vol 750 ◽  
pp. 372-384 ◽  
Author(s):  
Nicholas K. Lowman ◽  
M. A. Hoefer ◽  
G. A. El
Keyword(s):  
Solitary Wave ◽  
Viscous Fluid ◽  
Solitary Waves ◽  
Water Waves ◽  
Large Amplitude ◽  
Wave Interactions ◽  
Weakly Nonlinear ◽  
Strongly Nonlinear ◽  
Nonlinear Solitary Waves

AbstractThe 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 behaviour 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.

scholarly journals Anomalous width variation of rarefactive ion acoustic solitary waves in the context of auroral plasmas

2004 ◽  
Vol 11 (2) ◽  
pp. 219-228 ◽  
Author(s):  
S. S. Ghosh ◽  
G. S. Lakhina
Keyword(s):  
Solitary Waves ◽  
Nonlinear Theory ◽  
Acoustic Waves ◽  
Large Amplitude ◽  
Magnetized Plasma ◽  
Amplitude Variation ◽  
Fully Nonlinear ◽  
Weakly Nonlinear ◽  
Ion Acoustic Solitary Waves ◽  
Ion Acoustic

Abstract. The presence of dynamic, large amplitude solitary waves in the auroral regions of space is well known. Since their velocities are of the order of the ion acoustic speed, they may well be considered as being generated from the nonlinear evolution of ion acoustic waves. However, they do not show the expected width-amplitude correlation for K-dV solitons. Recent POLAR observations have actually revealed that the low altitude rarefactive ion acoustic solitary waves are associated with an increase in the width with increasing amplitude. This indicates that a weakly nonlinear theory is not appropriate to describe the solitary structures in the auroral regions. In the present work, a fully nonlinear analysis based on Sagdeev pseudopotential technique has been adopted for both parallel and oblique propagation of rarefactive solitary waves in a two electron temperature multi-ion plasma. The large amplitude solutions have consistently shown an increase in the width with increasing amplitude. The width-amplitude variation profile of obliquely propagating rarefactive solitary waves in a magnetized plasma have been compared with the recent POLAR observations. The width-amplitude variation pattern is found to fit well with the analytical results. It indicates that a fully nonlinear theory of ion acoustic solitary waves may well explain the observed anomalous width variations of large amplitude structures in the auroral region.

scholarly journals Optimal transient growth in thin-interface internal solitary waves

2018 ◽  
Vol 840 ◽  
pp. 342-378 ◽  
Author(s):  
Pierre-Yves Passaggia ◽  
Karl R. Helfrich ◽  
Brian L. White
Keyword(s):  
Solitary Waves ◽  
Carrier Frequency ◽  
Large Amplitude ◽  
Stokes Equations ◽  
Normal Growth ◽  
Energy Gain ◽  
Wkb Approximation ◽  
Internal Solitary Waves ◽  
Transient Growth ◽  
Optimal Disturbances

The dynamics of perturbations to large-amplitude internal solitary waves (ISWs) in two-layered flows with thin interfaces is analysed by means of linear optimal transient growth methods. Optimal perturbations are computed through direct–adjoint iterations of the Navier–Stokes equations linearized around inviscid, steady ISWs obtained from the Dubreil-Jacotin–Long (DJL) equation. Optimal perturbations are found as a function of the ISW phase velocity $c$ (alternatively amplitude) for one representative stratification. These disturbances are found to be localized wave-like packets that originate just upstream of the ISW self-induced zone (for large enough $c$) of potentially unstable Richardson number, $Ri<0.25$. They propagate through the base wave as coherent packets whose total energy gain increases rapidly with $c$. The optimal disturbances are also shown to be relevant to DJL solitary waves that have been modified by viscosity representative of laboratory experiments. The optimal disturbances are compared to the local Wentzel–Kramers–Brillouin (WKB) approximation for spatially growing Kelvin–Helmholtz (K–H) waves through the $Ri<0.25$ zone. The WKB approach is able to capture properties (e.g. carrier frequency, wavenumber and energy gain) of the optimal disturbances except for an initial phase of non-normal growth due to the Orr mechanism. The non-normal growth can be a substantial portion of the total gain, especially for ISWs that are weakly unstable to K–H waves. The linear evolution of Gaussian packets of linear free waves with the same carrier frequency as the optimal disturbances is shown to result in less energy gain than found for either the optimal perturbations or the WKB approximation due to non-normal effects that cause absorption of disturbance energy into the leading face of the wave. Two-dimensional numerical calculations of the nonlinear evolution of optimal disturbance packets leads to the generation of large-amplitude K–H billows that can emerge on the leading face of the wave and that break down into turbulence in the lee of the wave. The nonlinear calculations are used to derive a slowly varying model of ISW decay due to repeated encounters with optimal or free wave packets. Field observations of unstable ISW by Moum et al. (J. Phys. Oceanogr., vol. 33 (10), 2003, pp. 2093–2112) are consistent with excitation by optimal disturbances.

scholarly journals The transformation of an interfacial solitary wave of elevation at a bottom step

2009 ◽  
Vol 16 (1) ◽  
pp. 33-42 ◽  
Author(s):  
V. Maderich ◽  
T. Talipova ◽  
R. Grimshaw ◽  
E. Pelinovsky ◽  
B. H. Choi ◽  
...  
Keyword(s):  
Solitary Wave ◽  
Solitary Waves ◽  
Numerical Study ◽  
Nonlinear Effects ◽  
Ocean Model ◽  
Gardner Equation ◽  
Fully Nonlinear ◽  
Layer Flow ◽  
The One ◽  
Bottom Step

Abstract. In this paper we study the transformation of an internal solitary wave at a bottom step in the framework of two-layer flow, for the case when the interface lies close to the bottom, and so the solitary waves are elevation waves. The outcome is the formation of solitary waves and dispersive wave trains in both the reflected and transmitted fields. We use a two-pronged approach, based on numerical simulations of the fully nonlinear equations using a version of the Princeton Ocean Model on the one hand, and a theoretical and numerical study of the Gardner equation on the other hand. In the numerical experiments, the ratio of the initial wave amplitude to the layer thickness is varied up one-half, and nonlinear effects are then essential. In general, the characteristics of the generated solitary waves obtained in the fully nonlinear simulations are in reasonable agreement with the predictions of our theoretical model, which is based on matching linear shallow-water theory in the vicinity of a step with solutions of the Gardner equation for waves far from the step.

Numerical Study of the Motions in Shallow Water Waves of Floating Bodies Elastically Linked to Bottom

2009 ◽  
Author(s):  
Marcio Michiharu Tsukamoto ◽  
Liang-Yee Cheng ◽  
Kazuo Nishimoto
Keyword(s):  
Shallow Water ◽  
Water Waves ◽  
Large Amplitude ◽  
Numerical Study ◽  
Numerical Approach ◽  
Floating Bodies ◽  
Restoring Force ◽  
Hydrodynamic Loads ◽  
Elastic Links ◽  
Analytical Approaches

The motion of floating bodies linked elastically to the bottom of seas and waterways is of great interest in the analysis of the wave suppressing devices, such as wave breakers, and the behaviors of the floating structures, such as buoys and tension leg platforms (TLP). For the modeling of the dynamics, the coupling between the hydrodynamic loads due to waves and the restoring forces due to the elastic link must be considered. In some simpler cases, the analytical approaches are available. However, in case of large amplitude waves and floating bodies with complex geometries, the analytical solutions do not give accurate results. In the present study, a numerical model based on MPS (moving particle semi-implicit method) for the hydrodynamic loads coupled with the Hook’s Law for the restoring force is adopted to analyze the motion of floating bodies with one or several elastic links to the bottom of shallow water under large amplitude waves. Initially, the results of 2D numerical simulation of simple oscillating buoys are compared with the analytical and experimental ones to validate the numerical approach. After that, the approach is applied to the study of the shallow water wave supressing devices. Heave, surge and pitching motions of the floaters are assessed as well as the hydrodynamic coefficients to show the effect of the elastic links in the nonlinear wave hydrodynamics.

scholarly journals NUMERICAL STUDY OF ROSENAU-KDV EQUATION USING FINITE ELEMENT METHOD BASED ON COLLOCATION APPROACH

2017 ◽  
Vol 22 (3) ◽  
pp. 373-388 ◽  
Author(s):  
Turgut Ak ◽  
Sharanjeet Dhawan ◽  
S. Battal Gazi Karakoc ◽  
Samir K. Bhowmik ◽  
Kamal R. Raslan
Keyword(s):  
Solitary Waves ◽  
Water Waves ◽  
Numerical Study ◽  
Kdv Equation ◽  
Uniform Mesh ◽  
Shallow Water Waves ◽  
Undular Bore ◽  
Von Neumann ◽  
B Spline ◽  
Collocation Approach

In the present paper, a numerical method is proposed for the numerical solution of Rosenau-KdV equation with appropriate initial and boundary conditions by using collocation method with septic B-spline functions on the uniform mesh points. The method is shown to be unconditionally stable using von-Neumann technique. To check accuracy of the error norms L2 and L∞ are computed. Interaction of two and three solitary waves are used to discuss the effect of the behavior of the solitary waves during the interaction. Furthermore, evolution of solitons is illustrated by undular bore initial condition. These results show that the technique introduced here is suitable to investigate behaviors of shallow water waves.

A numerical study of generation and propagation of type-a and type-b internal solitary waves in the northern South China Sea

2019 ◽  
Vol 38 (11) ◽  
pp. 20-30
Author(s):  
Zhi Zeng ◽  
Xueen Chen ◽  
Chunxin Yuan ◽  
Shengquan Tang ◽  
Lequan Chi
Keyword(s):  
South China Sea ◽  
Solitary Waves ◽  
South China ◽  
Numerical Study ◽  
Northern South China Sea ◽  
Type A ◽  
Internal Solitary Waves ◽  
Type B ◽  
China Sea
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