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A rational model for Langmuir circulations

Published online by Cambridge University Press:  29 March 2006

A. D. D. Craik  and
S. Leibovich
A. D. D. Craik
Affiliation:
Department of Applied Mathematics, University of St Andrews, Fife, Scotland
S. Leibovich
Affiliation:
Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, New York 14850
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Abstract

A realistic theoretical model of steady Langmuir circulations is constructed. Vorticity in the wind direction is generated by the Stokes drift of the gravity-wave field acting upon spanwise vorticity deriving from the wind-driven current. We believe that the steady Langmuir circulations represent a balance between this generating mechanism and turbulent dissipation.

Nonlinear equations governing the motion are derived under fairly general conditions. Analytical and numerical solutions are sought for the case of a directional wave spectrum consisting of a single pair of gravity waves propagating at equal and opposite angles to the wind direction. Also, a statistical analysis, based on linearized equations, is developed for more general directional wave spectra. This yields an estimate of the average spacing of windrows associated with Langmuir circulations. The latter analysis is applied to a particular example with simple properties, and produces an expected windrow spacing of rather more than twice the length of the dominant gravity waves.

The relevance of our model is assessed with reference to known observational features, and the evidence supporting its applicability is promising.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 73 , Issue 3 , 10 February 1976 , pp. 401 - 426
Copyright
© 1976 Cambridge University Press

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