Freak Wave in High-Order Weakly Nonlinear Wave Evolution with Bottom Topography Change

2021 ◽  
pp. 103918
Author(s):  
Zuorui Lyu ◽  
Nobuhito Mori ◽  
Hiroaki Kashima
Keyword(s):  
Nonlinear Wave ◽  
Bottom Topography ◽  
High Order ◽  
Freak Wave ◽  
Weakly Nonlinear ◽  
Wave Evolution

scholarly journals HIGH ORDER NONLINEAR WAVE INTERACTIONS FROM DEEP TO FINITE WATER DEPTH WITH BOTTOM TOPOGRAPHY CHANGE

2020 ◽  
pp. 24
Author(s):  
Zuorui Lyu ◽  
Hiroaki Kashima ◽  
Nobuhito Mori
Keyword(s):  
Nonlinear Wave ◽  
Water Depth ◽  
Deep Water ◽  
Modulational Instability ◽  
High Order ◽  
Long Distance ◽  
Freak Wave ◽  
Wave Evolution ◽  
Finite Water Depth ◽  
Skewness And Kurtosis

In recent years, freak wave/rouge wave has become an important problem in science and engineering. Modulational instability is considered to be an important factor leading to freak wave in the wave evolution of deep water, and Janssen (2003) defined Benjamin-Feir index (BFI) to reflect it. Mori and Janssen (2006) gave the occurrence probability of freak waves based on a weakly non-Gaussian theory, and distribution of wave height is determined by skewness and kurtosis of surface elevation to a considerable extent in deep water. According to observational record, freak wave has not only been found in deep water in the ocean, but also been observed in shallow water and coastal areas. In the process of water wave entering continental shelf, water depth is changing with mild slope after a long distance propagation. This study focus on investigating how water depth affect skewness and kurtosis in the high order nonlinear wave evolution from deep water to finite water depth in two-dimension.Recorded Presentation from the vICCE (YouTube Link): https://youtu.be/a8LiJvXWRrw

Wave evolution over a gradual slope with turbulent friction

1983 ◽  
Vol 133 ◽  
pp. 207-216 ◽  
Author(s):  
John W. Miles
Keyword(s):  
Friction Coefficient ◽  
Gravity Wave ◽  
Solitary Waves ◽  
Periodic Sequence ◽  
Relative Amplitude ◽  
Sinusoidal Wave ◽  
Turbulent Friction ◽  
Weakly Nonlinear ◽  
Wave Evolution

The evolution of a weakly nonlinear, weakly dispersive gravity wave in water of depth d over a bottom of gradual slope δ and Chezy friction coefficient Cf is studied. It is found that an initially sinusoidal wave evolves into a periodic sequence of solitary waves with relative amplitude a/d = α1 = 15δ/4Cf if α1 < αb, where αb is the relative amplitude above which breaking occurs. This prediction is supported by observations (Wells 1978) of the evolution of swell over mudflats.

Chaos in positive ion–negative ion magnetized plasmas

2020 ◽  
Vol 86 (6) ◽  
Author(s):  
Samiran Ghosh ◽  
Biplab Maity ◽  
Swarup Poria
Keyword(s):  
Nonlinear Wave ◽  
Low Frequency ◽  
Negative Ions ◽  
Dynamical Behaviour ◽  
Negative Ion ◽  
Sound Waves ◽  
Weakly Nonlinear ◽  
Positive Ions ◽  
Experimental Parameters ◽  
Map Analysis

The dynamical behaviour of weakly nonlinear, low-frequency sound waves are investigated in a plasma composed of only positive and negative ions incorporating the effects of a weak external uniform magnetic field. In the plasma model the mass (temperature) of the positive ions is smaller (larger) than that of the negative ions. The dynamics of the nonlinear wave is shown to be governed by a novel nonlinear equation. The stationary plane wave (analytical and numerical) nonlinear analysis on the basis of experimental parameters reveals that the nonlinear wave does have quasi-periodic and chaotic solutions. The Poincarè return map analysis confirms these observed complex structures.

Dissipative effects on the resonant flow of a stratified fluid over topography

1988 ◽  
Vol 192 ◽  
pp. 287-312 ◽  
Author(s):  
N. F. Smyth
Keyword(s):  
Bottom Topography ◽  
Stratified Fluid ◽  
Flow Speed ◽  
Resonant Condition ◽  
Weakly Nonlinear ◽  
Dissipative Effects ◽  
Long Wave ◽  
Near Resonance ◽  
Wave Limit ◽  
Wave Modes

The effect of dissipation on the flow of a stratified fluid over topography is considered in the weakly nonlinear, long-wave limit for the case when the flow is near resonance, i.e. the basic flow speed is close to a linear long-wave speed for one of the long-wave modes. The two types of dissipation considered are the dissipation due to viscosity acting in boundary layers and/or interfaces and the dissipation due to viscosity acting in the fluid as a whole. The effect of changing bottom topography on the flow produced by a force moving at a resonant velocity is also considered. In this case, the resonant condition is that the force velocity is close to a linear long-wave velocity for one of the long-wave modes. It is found that in most cases, these extra effects result in the formation of a steady state, in contrast to the flow without these effects, which remains unsteady for all time. The flow resulting under the action of boundary-layer dissipation is compared with recent experimental results.

scholarly journals Hamiltonian description of wave dynamics in nonequilibrium media

1994 ◽  
Vol 1 (4) ◽  
pp. 234-248 ◽  
Author(s):  
N. N. Romanova
Keyword(s):  
Nonlinear Wave ◽  
Evolution Equations ◽  
Normal Modes ◽  
Weak Nonlinearity ◽  
Hamiltonian Description ◽  
Weakly Nonlinear ◽  
Wave Dynamics ◽  
Canonical Variables ◽  
Stable Points ◽  
Stable Area

Abstract. We consider Hamiltonian description of weakly nonlinear wave dynamics in unstable and nonequilibrium media. We construct the appropriate canonical variables in the whole wavenumber space. The essentially new element is the construction of canonical variables in a vicinity of marginally stable points where two normal modes coalesce. The commonly used normal variables are not appropriate in this domain. The mater is that the approximation of weak nonlinearity breaks down when the dynamical system is written in terms of these variables. In this case we introduce the canonical variables based on the linear combination of modes belonging to the two different branches of dispersion curve. As an example of one of the possible applications of presented results the evolution equations for weakly nonlinear wave packets in the marginally stable area are derived. These equations cannot be derived if we deal with the commonly used normal variables.

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