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On the boundary layer structure of differentially heated cavity flow in a stably stratified porous medium

Published online by Cambridge University Press:  14 August 2007

P. G. DANIELS
P. G. DANIELS*
Affiliation:
Centre for Mathematical Science, City University, Northampton Square, London EC1V 0HB, UK
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Abstract

This paper considers two-dimensional flow generated in a stably stratified porous medium by monotonic differential heating of the upper surface. For a rectangular cavity with thermally insulated sides and a constant-temperature base, the flow near the upper surface in the high-Darcy–Rayleigh-number limit is shown to consist of a double horizontal boundary layer structure with descending motion confined to the vicinity of the colder sidewall. Here there is a vertical boundary layer structure that terminates at a finite depth on the scale of the outer horizontal layer. Below the horizontal boundary layers the motion consists of a series of weak, uniformly stratified counter-rotating convection cells. Asymptotic results are compared with numerical solutions for the cavity flow at finite values of the Darcy–Rayleigh number.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 586 , 10 September 2007 , pp. 347 - 370
Copyright
Copyright © Cambridge University Press 2007

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