Large fully nonlinear internal solitary waves: The effect of background current

<p>Previous studies have suggested that fully nonlinear internal solitary waves (ISWs) are very soliton-like as the interaction of two ISWs results in only very small changes in amplitude of the interacting ISWs and in the production of a very small amplitude wave train. Previous studies have, however, considered ISWs with the polarity predicted by the sign of the quadratic nonlinear coefficient of the KdV equation. The Gardner equation, which is an extension of the KdV equation that includes a cubic nonlinear term, has ISWs of two polarities (i.e., waves of depression and elevation) when the cubic coefficient of the Gardner equation is positive. These waves are soliton solutions of the Gardner equations. &#160;In this talk I will discuss the interaction of ISWs of opposite polarity in continuous asymmetric three layer stratifications. Regions in parameter space where ISWs of opposite polarity exist will be discussed and I will demonstrate via fully nonlinear numerical simulations that the interaction of ISWs of opposite polarity waves are far from soliton-like: their interaction can result in very large changes in wave amplitude and may produce a very complicated wave field with multiple large ISWs, a large linear wave field and breather-like waves.<span>&#160;</span></p>

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Internal solitary waves with subsurface cores

Journal of Fluid Mechanics ◽

10.1017/jfm.2019.407 ◽

2019 ◽

Vol 873 ◽

pp. 1-17 ◽

Cited By ~ 3

Author(s):

Yangxin He ◽

Kevin G. Lamb ◽

Ren-Chieh Lien

Keyword(s):

Numerical Simulation ◽

South China Sea ◽

Solitary Wave ◽

Solitary Waves ◽

Internal Solitary Waves ◽

Two Dimensional ◽

Background Current ◽

Near Surface ◽

Nonlinear Solutions ◽

Surface Background

Large internal solitary waves with subsurface cores have recently been observed in the South China Sea. Here fully nonlinear solutions of the Dubreil–Jacotin–Long equation are used to study the conditions under which such cores exist. We find that the location of the cores, either at the surface or below the surface, is largely determined by the sign of the vorticity of the near-surface background current. The results of a numerical simulation of a two-dimensional shoaling internal solitary wave are presented which illustrate the formation of a subsurface core.

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The effect of strong shear on internal solitary-like waves

10.5194/npg-2021-16 ◽

2021 ◽

Author(s):

Marek Stastna ◽

Aaron Coutino ◽

Ryan Walter

Keyword(s):

Solitary Waves ◽

Large Amplitude ◽

Initial Conditions ◽

Theoretical Calculations ◽

Mathematical Proof ◽

Internal Solitary Waves ◽

Algebraic Complexity ◽

Background Current ◽

Variable Environment ◽

Strong Shear

Abstract. Large amplitude internal waves in the ocean propagate in a dynamic, highly variable environment with changes in background current, local depth, and stratification. The Dubreil-Jacotin-Long, or DJL, theory of exact internal solitary waves can account for a background shear, doing so at a cost of algebraic complexity and a lack of a mathematical proof of algorithm convergence. Waves in the presence of shear that is strong enough to preclude theoretical calculations have been reported in observations. We report on high resolution simulations of stratified adjustment in the presence of strong shear currents. We find instances of large amplitude solitary-like waves with recirculating cores in parameter regimes for which DJL theory fails, and of wave types that are completely different in shape from classical internal solitary waves. Both are spontaneously generated from general initial conditions. Some of the waves observed are associated with critical layers, but others exhibit a propagation speed that is very near the background current maximum. As such they are not freely propagating solitary waves, and a DJL theory would not apply. We thus provide a partial reconciliation between observations and theory.

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