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On the subharmonic instabilities of steady three-dimensional deep water waves

Published online by Cambridge University Press:  26 April 2006

Mansour Ioualalen  and
Christian Kharif
Mansour Ioualalen
Affiliation:
Institut de Mécanique Statistique de la Turbulence, 12 avenue de Général Leclerc, 13003 Marseilles, France Present address: ORSTOM BP A5, Nouméa Cedex, New Caledonia, France.
Christian Kharif
Affiliation:
Institut de Mécanique Statistique de la Turbulence, 12 avenue de Général Leclerc, 13003 Marseilles, France
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Abstract

A numerical procedure has been developed to study the linear stability of nonlinear three-dimensional progressive gravity waves on deep water. The three-dimensional patterns considered herein are short-crested waves which may be produced by two progressive plane waves propagating at an oblique angle, γ, to each other. It is shown that for moderate wave steepness the dominant resonances are sideband-type instabilities in the direction of propagation and, depending on the value of γ, also in the transverse direction. It is also shown that three-dimensional progressive gravity waves are less unstable than two-dimensional progressive gravity waves.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 262 , 3 October 1994 , pp. 265 - 291
Copyright
© 1994 Cambridge University Press

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