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Fourth-order nonlinear evolution equations for surface gravity waves in the presence of a thin thermocline

Published online by Cambridge University Press:  17 February 2009

Sudebi Bhattacharyya  and
K. P. Das
Sudebi Bhattacharyya
Affiliation:
Department of Applied Mathematics, University of Calcutta, 92 Acharya Prafulla Chandra Road, Calcutta 700009, INDIA
K. P. Das
Affiliation:
Department of Applied Mathematics, University of Calcutta, 92 Acharya Prafulla Chandra Road, Calcutta 700009, INDIA
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Abstract

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Two coupled nonlinear evolution equations correct to fourth order in wave steepness are derived for a three-dimensional wave packet in the presence of a thin thermocline. These two coupled equations are reduced to a single equation on the assumption that the space variation of the amplitudes takes place along a line making an arbitrary fixed angle with the direction of propagation of the wave. This single equation is used to study the stability of a uniform wave train. Expressions for maximum growth rate of instability and wave number at marginal stability are obtained. Some of the results are shown graphically. It is found that a thin thermocline has a stabilizing influence and the maximum growth rate of instability decreases with the increase of thermocline depth.

Type
Research Article
Information
The ANZIAM Journal , Volume 39 , Issue 2 , October 1997 , pp. 214 - 229
Copyright
Copyright © Australian Mathematical Society 1997

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