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Steady nonlinear diffusion-driven flow

Published online by Cambridge University Press:  15 June 2009

M. A. PAGE  and
E. R. JOHNSON
M. A. PAGE*
Affiliation:
School of Mathematical Sciences, Monash University, Clayton, Victoria 3800, Australia
E. R. JOHNSON
Affiliation:
Department of Mathematics, University College London, Gower Street, London WC1E 6BT, UK
*
†Email address for correspondence: [email protected]
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Abstract

An imposed normal temperature gradient on a sloping surface in a viscous stratified fluid can generate a slow steady flow along a thin ‘buoyancy layer’ against that surface, and in a contained fluid the associated mass flux leads to a broader-scale ‘outer flow’. Previous analysis for small values of the Wunsch–Phillips parameter R is extended to the nonlinear case in a contained fluid, when the imposed temperature gradient is comparable with the background temperature gradient. As for the linear case, a compatibility condition relates the buoyancy-layer mass flux along each sloping boundary to the outer-flow temperature gradient. This condition allows the leading-order flow to be determined throughout the container for a variety of configurations.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 629 , 25 June 2009 , pp. 299 - 309
Copyright
Copyright © Cambridge University Press 2009

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