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Large-scale Langmuir circulation and double-diffusive convection: evolution equations and flow transitions

Published online by Cambridge University Press:  26 April 2006

Stephen M. Cox  and
Sidney Leibovich
Stephen M. Cox
Affiliation:
Department of Applied Mathematics, The University of Adelaide, Adelaide 5005, Australia
Sidney Leibovich
Affiliation:
Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, NY, USA
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Abstract

Two-dimensional Langmuir circulation in a layer of stably stratified water and the mathematically analogous problem of double-diffusive convection are studied with mixed boundary conditions. When the Biot numbers that occur in the mechanical boundary conditions are small and the destabilizing factors are large enough, the system will be unstable to perturbations of large horizontal length. The instability may be either direct or oscillatory depending on the control parameters. Evolution equations are derived here to account for both cases and for the transition between them. These evolution equations are not limited to small disturbances of the nonconvective basic velocity and temperature fields, provided the spatial variations in the horizontal remain small. The direct bifurcation may be supercritical or subcritical, while in the case of oscillatory motions, stable finite-amplitude travelling waves emerge. At the transition, travelling waves, standing waves, and modulated travelling waves all are stable in sub-regimes.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 276 , 10 October 1994 , pp. 189 - 210
Copyright
© 1994 Cambridge University Press

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