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On the observability of finite-depth short-crested water waves

Published online by Cambridge University Press:  26 April 2006

M. Ioualalen ,
A. J. Roberts  and
C. Kharif
M. Ioualalen
Affiliation:
Groupe SURTROPAC, Institute Francais de Recherche Scientifique pour le Développement en Coopération (ORSTOM), BP A5, Nounmé, New-Caledonia Present address: Laboratoire d'Océanographie Dynamique et de Climatologie, LODYC, 4 place Jussieu, 75252 Paris, Cedex 05, France.
A. J. Roberts
Affiliation:
Department of Mathematics and Computing, University of Southern Queensland, Toowoomba, Queensland, 4350 Australia
C. Kharif
Affiliation:
Institut de Recherche sur les Phénomènes Hors Equilibre, LIOA, 163 avenue de Luminy, Case 903, 13288 Marseille cedex 9, France
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Abstract

A numerical study of the superharmonic instabilities of short-crested waves on water of finite depth is performed in order to measure their time scales. It is shown that these superharmonic instabilities can be significant-unlike the deep-water case-in parts of the parameter regime. New resonances associated with the standing wave limit are studied closely. These instabilities ‘contaminate’ most of the parameter space, excluding that near two-dimensional progressive waves; however, they are significant only near the standing wave limit. The main result is that very narrow bands of both short-crested waves ‘close’ to two-dimensional standing waves, and of well developed short-crested waves, perturbed by superharmonic instabilities, are unstable for depths shallower than approximately a non-dimensional depth d= 1; the study is performed down to depth d= 0.5 beyond which the computations do not converge sufficiently. As a corollary, the present study predicts that these very narrow sub-domains of short-crested wave fields will not be observable, although most of the short-crested wave fields will be.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 322 , 10 September 1996 , pp. 1 - 19
Copyright
© 1996 Cambridge University Press

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