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The modulation of short gravity waves by long waves or currents

Published online by Cambridge University Press:  17 February 2009

R. Grimshaw
R. Grimshaw
Affiliation:
School of Mathematics, University of New South Wales, P.O. Box 1, Kensington, NSW 2033, Australia.
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Abstract

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The modulation of short gravity waves by long waves or currents is described for the situation when the flow is irrotational and when the short waves are described by linearised equations. Two cases are distinguished depending on whether the basic flow can be characterised as a deep-water current, or a shallow-water current. In both cases the basic flow has a current which has finite amplitude, while in the first case the free surface slope of the basic flow can be finite, but in the second case is small. The modulation equations are the local dispersion relation of the short waves, the kinematic equation for conservation of wave crests and the wave action equation. The results incorporate and extend the earlier work of Longuet-Higgins and Stewart [10, 11].

Type
Research Article
Information
The ANZIAM Journal , Volume 29 , Issue 4 , April 1988 , pp. 410 - 429
Copyright
Copyright © Australian Mathematical Society 1988

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