On stabilizing the strongly nonlinear internal wave model

Document Type

Article

Publication Date

1-1-2008

Abstract

A strongly nonlinear asymptotic model describing the evolution of large amplitude internal waves in a two-layer system is studied numerically. While the steady model has been demonstrated to capture correctly the characteristics of large amplitude internal solitary waves, a local stability analysis shows that the time-dependent inviscid model suffers from the Kelvin-Helmholtz instability due to a tangential velocity discontinuity across the interface accompanied by the interfacial deformation. An attempt to represent the viscous effect that is missing in the model is made with eddy viscosity, but this simple ad hoc model is shown to fail to suppress unstable short waves. Alternatively, when a smooth low-pass Fourier filter is applied, it is found that a large amplitude internal solitary wave propagates stably without change of form, and mass and energy are conserved well. The head-on collision of two counter-propagating solitary waves is studied using the filtered strongly nonlinear model and its numerical solution is compared with the weakly nonlinear asymptotic solution. © 2008 by the Massachusetts Institute of Technology.

Identifier

36849070404 (Scopus)

Publication Title

Studies in Applied Mathematics

External Full Text Location

https://doi.org/10.1111/j.1467-9590.2007.00393.x

e-ISSN

14679590

ISSN

00222526

First Page

65

Last Page

85

Issue

1

Volume

120

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