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On steady linear diffusion-driven flow

Published online by Cambridge University Press:  10 July 2008

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
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Abstract

Wunsch (1970) and Phillips (1970) (Deep-Sea Res. vol. 17, pp. 293, 435) showed that a temperature flux condition on a sloping non-slip surface in a stratified fluid can generate a slow steady upward flow along a thin ‘buoyancy layer’. Their analysis is extended here to the more-general case of steady flow in a contained fluid where buoyancy layers may expel or entrain fluid from their outer edge. A compatibility condition that relates the mass flux and temperature gradient along that edge is derived, and this allows the fluid recirculation and temperature perturbation to be determined in the broader-scale ‘outer flow’ region. The analysis applies when the Wunsch–Phillips parameter R is small, in the linear case for which the density variations are dominated by a constant vertical gradient.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 606 , 10 July 2008 , pp. 433 - 443
Copyright
Copyright © Cambridge University Press 2008

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