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The generation of Langmuir circulations by an instability mechanism

Published online by Cambridge University Press:  12 April 2006

A. D. D. Craik
A. D. D. Craik
Affiliation:
Department of Applied Mathematics, University of St Andrews, Fife KY16 9SS, Scotland
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Abstract

Equations governing the current system in the upper layers of oceans and lakes were derived by Craik & Leibovich (1976). These incorporate the dominant effects of both wind and waves. Solutions comprising the mean wind-driven current and a system of ‘Langmuir’ cells aligned parallel to the wind were found for cases in which the wave field consisted of just a pair of plane waves. However, it was not clear that such cellular motions would persist for the more realistic case of a continuous wave spectrum.

The present paper shows that, in the latter case, infinitesimal spanwise periodic perturbations will grow on account of an instability mechanism. Mathematically, the instability is closely similar to the onset of thermal convection in horizontal fluid layers. Physically, the mechanism is governed by kinematical processes involving the mean (Eulerian) wind-driven current and the (Lagrangian) Stokes drift associated with the waves. The relationship of this mechanism to instability models of Garrett and Gammelsrød is clarified.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 81 , Issue 2 , 24 June 1977 , pp. 209 - 223
Copyright
© 1977 Cambridge University Press

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