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Asymptotic solutions of convection in rapidly rotating non-slip spheres

Published online by Cambridge University Press:  26 April 2007

KEKE ZHANG ,
XINHAO LIAO  and
F. H. BUSSE
KEKE ZHANG
Affiliation:
Department of Mathematical Sciences, University of Exeter, EX4 4QE, UK
XINHAO LIAO
Affiliation:
Shanghai Astronomical Observatory, Chinese Academy of Sciences, Shanghai 200030, China
F. H. BUSSE
Affiliation:
Institute of Physics, University of Bayreuth, D-95440 Bayreuth, Germany
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Abstract

Asymptotic solutions describing the onset of convection in rotating, self-gravitating Boussinesq fluid spheres with no-slip boundary conditions, valid for asymptotically small Ekman numbers and for all values of the Prandtl number, are derived. Central to the asymptotic analysis is the assumption that the leading-order convection can be represented, dependent on the size of the Prandtl number, by either a single quasi-geostrophic-inertial-wave mode or by a combination of several quasi-geostrophic-inertial-wave modes, and is controlled or influenced by the effect of the oscillatory Ekman boundary layer. Comparisons between the asymptotic solutions and the corresponding fully numerical simulations show a satisfactory quantitative agreement.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 578 , 10 May 2007 , pp. 371 - 380
Copyright
Copyright © Cambridge University Press 2007

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References

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