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Resonant wave interactions near a critical level in a stratified shear flow

Published online by Cambridge University Press:  26 April 2006

R. Grimshaw
R. Grimshaw
Affiliation:
Department of Mathematics, Monash University, Clayton VIC 3168, Australia
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Abstract

Resonant interactions between internal gravity waves propagating in a stratified shear flow are considered for the case when the background density and shear flow vary slowly with respect to the waves. In Grimshaw (1988) triad resonances were considered, and interaction equations derived for the case when the resonance conditions are met only on certain space-time surfaces, being resonance sites. Here this analysis is extended to include higher-order resonances, with the aim of studying resonant wave interactions near a critical level. It is shown that a secondary resonant interaction between two incoming waves, in which two harmonic components of one incoming wave interact with a single harmonic component of another incoming wave, produces a reflected wave. This result is shown to agree with the study of Brown & Stewartson (1980, 1982a, b) who obtained this same result by a different approach.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 269 , 25 June 1994 , pp. 1 - 22
Copyright
© 1994 Cambridge University Press

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