The stability of continental shelf waves I. Side band instability and long wave resonance
Open Access
- 1 June 1977
- journal article
- research article
- Published by Cambridge University Press (CUP) in The Journal of the Australian Mathematical Society. Series B. Applied Mathematics
- Vol. 20 (1) , 13-30
- https://doi.org/10.1017/s0334270000001417
Abstract
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.Keywords
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