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Interction of a short-wave field with a dominant long wave in deep water: derivation form Zakharov's spectral formulation

Published online by Cambridge University Press:  17 February 2009

A. D. D. Craik
A. D. D. Craik
Affiliation:
Mathematical Institute, University of St. Andrews, St. Andrews Fife KY16 9SS, Scotland.
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Abstract

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The leading-order interaction of short gravity waves with a dominant long-wave swell is calculated by means of Zakharov's [7] spectral formulation. Results are obtained both for a discrete train of short waves and for a localised wave packet comprising a spectrum of short waves.

The results for a discrete wavetrain agree with previous work of Longuet-Higgins & Stewart [5], and general agreement is found with parallel work of Grimshaw [4] which employed a very different wave-action approach.

Type
Research Article
Information
The ANZIAM Journal , Volume 29 , Issue 4 , April 1988 , pp. 430 - 439
Copyright
Copyright © Australian Mathematical Society 1988

References

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