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Stability analysis from fourth order evolution equation for small but finite amplitude interfacial waves in the presence of a basic current shear

Published online by Cambridge University Press:  17 February 2009

A. K. Dhar  and
K. P. Das
A. K. Dhar
Affiliation:
Department of Mathematics, Mahishadal Raj College, Midnapore, India.
K. P. Das
Affiliation:
Department of Applied Mathematics, University of Calcutta, Calcutta 700009, India.
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Abstract

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A fourth-order nonlinear evolution equation is derived for a wave propagating at the interface of two superposed fluids of infinite depths in the presence of a basic current shear. On the basis of this equation a stability analysis is made for a uniform wave train. Discussions are given for both an air-water interface and a Boussinesq approximation. Significant deviations are noticed from the results obtained from the third-order evolution equation, which is the nonlinear Schrödinger equation. In the Boussinesq approximation, it has been possible to compare the present results with the exact numerical analysis of Pullin and Grimshaw [12], and they are found to agree rather favourably.

Type
Research Article
Information
The ANZIAM Journal , Volume 35 , Issue 3 , January 1994 , pp. 348 - 365
Copyright
Copyright © Australian Mathematical Society 1994

References

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