scholarly journals Transformation of envelope solitons on a bottom step

2021 ◽  
Vol 33 (6) ◽  
pp. 066606
Author(s):  
G. Ducrozet ◽  
A. V. Slunyaev ◽  
Y. A. Stepanyants
Keyword(s):  
Envelope Solitons ◽  
Bottom Step

scholarly journals Transformation of envelope solitons propagating over a bottom step

2020 ◽  
Author(s):  
Alexey Slunyaev ◽  
Guillaume Ducrozet ◽  
Yury Stepanyants
Keyword(s):  
Surface Waves ◽  
Russian Federation ◽  
Wave Transformation ◽  
Approximate Theory ◽  
Envelope Soliton ◽  
Envelope Solitons ◽  
Approximate Analytical Solutions ◽  
The Russian Federation ◽  
The University ◽  
Bottom Step

<p>The problem of the weakly nonlinear wave transformation on a bottom step is studied analytically and numerically by means of the direct simulation of the Euler equation. It is assumed that the quasi-linear wave packets can be described by the nonlinear Schrödinger equation for surface waves in finite-depth water. The process of wave transformation in the vicinity of the bottom step can be described within the framework of the linear theory and the transformation coefficients (the transmission and reflection coefficients) can be determined by the approximate formula suggested in [1]. The fate of transmitted and reflected wave trains emerging from the incident envelope soliton can be determined with the help of the Inverse Scattering Technique [2, 3].</p><p>The parameters of secondary envelope solitons (their number, amplitudes, and speeds) asymptotically forming in the far-field zone are obtained analytically and compared against the numerically calculated ones, as the functions of the depth drop <em>h</em><sub>2</sub>/<em>h</em><sub>1</sub>, where <em>h</em><sub>1</sub> and <em>h</em><sub>2</sub> are the undisturbed water depths in front of and behind the bottom step, respectively. It is shown that the wave amplitudes can notably increase when the envelope soliton travels from the relatively shallow to much deeper water. The amplitudes of secondary solitons can exceed more than twice the amplitude of the incident wave.</p><p>The direct numerical simulation of envelope soliton transformation was undertaken by means of the High Order Spectral Method [4, 5]. The comparison of approximate analytical solutions with the results of numerical simulations reveals the domains of very good agreement between the data where the approximate theory is applicable. In the meantime, the noticeable disagreement between the approximate nonlinear theory and the direct simulations is found when the theory is inapplicable.</p><p>The research by A.S. is supported by the RFBR grant No. 18-02-00042; he also acknowledges the support from the International Visitor Program of the University of Sydney and is grateful for the hospitality of the University of Southern Queensland. The research of Y.S. was support by the grant of the President of the Russian Federation for State support of scientific research of leading scientific Schools of the Russian Federation NSh-2485.2020.5.</p><p>[1] Kurkin, A.A., Semin, S.V., and Stepanyants, Yu.A., Transformation of Surface Waves over a Bottom Step. Izvestiya, Atmospheric and Oceanic Physics, 2015, Vol. 51, 214–223.</p><p>[2] Zakharov, V.E., Shabat, A.B., Exact theory of two-dimensional self-focussing and one-dimensional self-modulation of waves in nonlinear media. Sov. Phys. JETP, 1972, Vol. 34, 62-69.</p><p>[3] Slunyaev, A., Klein, M., Clauss, G.F., Laboratory and numerical study of intense envelope solitons of water waves: generation, reflection from a wall and collisions. Physics of Fluids, 2017, Vol. 29, 047103.</p><p>[4] West, B.J., Brueckner, K.A., Janda, R.S., Milder, D.M., Milton, R.L., A new numerical method for surface hydrodynamics. J. Geophys. Res., 1987, Vol. 92, 11803-11824.</p><p>[5] Ducrozet, G., Gouin, M., Influence of varying bathymetry in rogue wave occurrence within unidirectional and directional sea-states. J. Ocean Eng. Mar. Energy, 2017, Vol. 3, 309-324.</p>

Spin-wave envelope solitons in periodically modulated magnetic films

1992 ◽  
Vol 28 (5) ◽  
pp. 3306-3308 ◽  
Author(s):  
N.-N. Chen ◽  
A.N. Slavin ◽  
M.G. Cottom
Keyword(s):  
Spin Wave ◽  
Magnetic Films ◽  
Envelope Solitons

Envelope Solitons versus Solitons

2002 ◽  
Vol 65 (6) ◽  
pp. 502-508 ◽  
Author(s):  
Renato Fedele
Keyword(s):  
Envelope Solitons

scholarly journals Travelling and standing envelope solitons in discrete non-linear cyclic structures

2016 ◽  
Vol 81 ◽  
pp. 75-87 ◽  
Author(s):  
Aurelien Grolet ◽  
Norbert Hoffmann ◽  
Fabrice Thouverez ◽  
Christoph Schwingshackl
Keyword(s):  
Envelope Solitons ◽  
Non Linear

Quantum and Relativistic Effects on the KdV and Envelope Solitons in Ion-Plasma Waves

2021 ◽  
pp. 1-14
Author(s):  
Himangshu Sahoo ◽  
Chinmay Das ◽  
Swarniv Chandra ◽  
Basudev Ghosh ◽  
Kalyan Kumar Mondal
Keyword(s):  
Relativistic Effects ◽  
Plasma Waves ◽  
Envelope Solitons ◽  
Ion Plasma

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.

Bottom step enlarging horizontal momentum flux of dam break flow

2020 ◽  
Vol 214 ◽  
pp. 107729
Author(s):  
Xiantao Zhang ◽  
Xinliang Tian ◽  
Xiaoxian Guo ◽  
Xin Li ◽  
Longfei Xiao
Keyword(s):  
Momentum Flux ◽  
Dam Break ◽  
Dam Break Flow ◽  
Horizontal Momentum ◽  
Bottom Step
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