A regularized model for strongly nonlinear internal solitary waves

Document Type

Article

Publication Date

1-1-2009

Abstract

The strongly nonlinear long-wave model for large amplitude internal waves in a two-layer system is regularized to eliminate shear instability due to the wave-induced velocity jump across the interface. The model is written in terms of the horizontal velocities evaluated at the top and bottom boundaries instead of the depth-averaged velocities, and it is shown through local stability analysis that internal solitary waves are locally stable to perturbations of arbitrary wavelengths if the wave amplitudes are smaller than a critical value. For a wide range of depth and density ratios pertinent to oceanic conditions, the critical wave amplitude is close to the maximum wave amplitude and the regularized model is therefore expected to be applicable to the strongly nonlinear regime. The regularized model is solved numerically using a finite-difference method and its numerical solutions support the results of our linear stability analysis. It is also shown that the solitary wave solution of the regularized model, found numerically using a time-dependent numerical model, is close to the solitary wave solution of the original model, confirming that the two models are asymptotically equivalent. © 2009 Cambridge University Press.

Identifier

67650904801 (Scopus)

Publication Title

Journal of Fluid Mechanics

External Full Text Location

https://doi.org/10.1017/S0022112009006594

e-ISSN

14697645

ISSN

00221120

First Page

73

Last Page

85

Volume

629

Grant

DMS-0620832

Fund Ref

Inha University

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