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The stability of continental shelf waves I. Side band instability and long wave resonance

Published online by Cambridge University Press:  17 February 2009

R. Grimshaw
R. Grimshaw
Affiliation:
Department of Mathematics, University of Melbourne, Parkville, Vic. 3052, Australia
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Abstract

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Continental shelf waves are examined for side band instability. It is shown that a modulated shelf wave is described by a nonlinear Schrödinger equation, from which the stability criterion is derived. Long shelf waves are stable to side band modulations, but as the wavenumber is increased there are regions of instability (in wavenumber space). A change of stability occurs at each long wave resonance, defined by the condition that the group velocity of the shelf wave equals a long wave speed. Equations describing the long wave resonance are derived.

Type
Research Article
Information
The ANZIAM Journal , Volume 20 , Issue 1 , June 1977 , pp. 13 - 30
Copyright
Copyright © Australian Mathematical Society 1977

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