Inhibiting shear instability induced by large amplitude internal solitary waves in two-layer flows with a free surface

Document Type

Article

Publication Date

1-1-2009

Abstract

We consider a strongly nonlinear long wave model for large amplitude internal waves in two-layer flows with the top free surface. It is shown that the model suffers from the Kelvin-Helmholtz (KH) instability so that any given shear (even if arbitrarily small) between the layers makes short waves unstable. Because a jump in tangential velocity is induced when the interface is deformed, the applicability of the model to describe the dynamics of internal waves is expected to remain rather limited. To overcome this major difficulty, the model is written in terms of the horizontal velocities at the bottom and the interface, instead of the depth-averaged velocities, which makes the system linearly stable for perturbations of arbitrary wavelengths as long as the shear does not exceed a certain critical value. © 2009 by the Massachusetts Institute of Technology.

Identifier

63849131759 (Scopus)

Publication Title

Studies in Applied Mathematics

External Full Text Location

https://doi.org/10.1111/j.1467-9590.2009.00436.x

e-ISSN

14679590

ISSN

00222526

First Page

325

Last Page

346

Issue

3

Volume

122

This document is currently not available here.

Share

COinS