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Convection in a rapidly rotating spherical shell with an imposed laterally varying thermal boundary condition

Published online by Cambridge University Press:  10 December 2009

CHRISTOPHER J. DAVIES ,
DAVID GUBBINS  and
PETER K. JIMACK
CHRISTOPHER J. DAVIES*
Affiliation:
School of Earth and Environment, University of Leeds, Leeds LS2 9JT, UK
DAVID GUBBINS
Affiliation:
School of Earth and Environment, University of Leeds, Leeds LS2 9JT, UK
PETER K. JIMACK
Affiliation:
School of Computing, University of Leeds, Leeds LS2 9JT, UK
*
†Email address for correspondence: [email protected]
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Abstract

We investigate thermally driven convection in a rotating spherical shell subject to inhomogeneous heating on the outer boundary, extending previous results to more rapid rotation rates and larger amplitudes of the boundary heating. The analysis explores the conditions under which steady flows can be obtained, and the stability of these solutions, for two boundary heating modes: first, when the scale of the boundary heating corresponds to the most unstable mode of the homogeneous problem; second, when the scale is larger. In the former case stable steady solutions exhibit a two-layer flow pattern at moderate rotation rates, but at very rapid rotation rates no steady solutions exist. In the latter case, stable steady solutions are always possible, and unstable solutions show convection rolls that cluster into nests that are out of phase with the boundary anomalies and remain trapped for many thermal diffusion times.

JFM classification

Convection: Convection
Type
Papers
Information
Journal of Fluid Mechanics , Volume 641 , 25 December 2009 , pp. 335 - 358
Copyright
Copyright © Cambridge University Press 2009

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References

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