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The axisymmetric convective regime for a rigidly bounded rotating annulus

Published online by Cambridge University Press:  28 March 2006

Michael E. Mcintyre
Michael E. Mcintyre
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge
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Abstract

The axisymmetric flow of liquid in a rigidly bounded annular container of height H, rotating with angular velocity Ω and subjected to a temperature difference ΔT between its vertical cylindrical perfectly conducting side walls, whose distance apart is L, is analysed in the boundary-layer approximation for small Ekman number v/2ΩL2, with gαΔTHv/4Ω2L2K ∼ 1. The heat transfer across the annulus is then convection-dominated, as is characteristic of the experimentally observed ‘upper symmetric regime’. The Prandtl number v/k is assumed large, and H is restricted to be less than about 2L. The side wall boundary-layer equations are the same as in (non-rotating) convection in a rectangular cavity. The horizontal boundary layers are Ekman layers and the four boundary layers, together with certain spatial averages in the interior, are determined independently of the interior flow details. The determination of the latter comprises a ‘secondary’ problem in which viscosity and heat conduction are important throughout the interior; the meridional streamlines are not necessarily parallel to the isotherms. The secondary problem is discussed qualitatively but not solved. The theory agrees fairly well with an available numerical experiment in the upper symmetric regime, for v/k [bumpe ] 7, after finite-Ekmannumber effects such as finite boundary-layer thickness are allowed for heuris-tically.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 32 , Issue 4 , 18 June 1968 , pp. 625 - 655
Copyright
© 1968 Cambridge University Press

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