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Resonant gravity-wave interactions in a shear flow

Published online by Cambridge University Press:  28 March 2006

Alex. D. D. Craik
Alex. D. D. Craik
Affiliation:
Department of Applied Mathematics, University of St Andrews, Fife, Scotland
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Abstract

Among a triad of gravity waves in a uniform shear flow, a remarkably powerful second-order resonant interaction may take place. This interaction is characterized by large growth rates of waves which propagate in directions oblique to that of the primary flow, and by a systematic transfer of energy from the primary flow to such waves. Most of the energy transfer takes place in the vicinity of a ‘critical layer’, where viscous forces are dominant.

Provided the resonance condition may be satisfied, a uniform shear flow which is perturbed by a two-dimensional wave of small but finite amplitude may be unstable, owing to the growth of two initially infinitesimal oblique waves which complete the resonant triad.

Information

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 34 , Issue 3 , 2 December 1968, pp. 531 - 549
Copyright
© 1968 Cambridge University Press

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