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An analysis of near-marginal, mildly penetrative convection with heat flux prescribed on the boundaries

Published online by Cambridge University Press:  20 April 2006

A. J. Roberts
A. J. Roberts
Affiliation:
Department of Applied Mathematics and Theoretical Physics, Silver Street, Cambridge CB3 9EW Permanent address: Department of Applied Mathematics, University of Adelaide, G.P.O. Box 498, Adelaide, South Australia 5001.
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Abstract

The model penetrative-convection problem of ice–water convection is considered. Analytical progress is made through the remarkable simplification that horizontally long convection cells are preferred when the heat flux is fixed on the boundaries (Chapman & Proctor 1980). However, a linear analysis shows that long horizontal scales are preferred only when the convection is mildly penetrative (i.e. the overlying layer of stable fluid is not deep). A straightforward nonlinear asymptotic analysis of the convection only provides the relatively uninteresting information that the convection is subcritical. Using the technique of reconstitution (Roberts 1985) to provide higher-order corrections to the asymptotic theory, flow properties at larger amplitudes are calculated and predictions about the extent of the subcriticality are made.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 158 , September 1985 , pp. 71 - 93
Copyright
© 1985 Cambridge University Press

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