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Convective motions in a spherical shell

Published online by Cambridge University Press:  20 April 2006

Abdelfattah Zebib ,
Atul K. Goyal  and
Gerald Schubert
Abdelfattah Zebib
Affiliation:
Department of Mechanical and Aerospace Engineering. Rutgers University, New Brunswick, NJ 08903
Atul K. Goyal
Affiliation:
Department of Mechanical and Aerospace Engineering. Rutgers University, New Brunswick, NJ 08903
Gerald Schubert
Affiliation:
Department of Earth and Space Science, University of California, Los Angeles, CA 90024
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Abstract

We compute the axisymmetric convective motions that exist in a spherical shell heated from below with inner to outer radius ratio equal to 0.5. The boundaries are stress-free and gravity is directly proportional to radius. Accurate solutions at large Rayleigh numbers (O(105)) are made feasible by a spectral method that employs diagonal-mode truncation. By examining the stability of axisymmetric motions we conclude that the preferred form of convection varies dramatically according to the value of the Rayleigh number. While axisymmetric motions with different patterns may exist for modestly nonlinear convection, only a single motion persists at sufficiently large values of the Rayleigh number. This circulation is symmetric about the equator and has two meridional cells with rising motion at the poles. Instability of this single axisymmetric motion determines that the preferred pattern of three-dimensional convection has one azimuthal wave.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 152 , March 1985 , pp. 39 - 48
Copyright
© 1985 Cambridge University Press

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