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Convection in a rotating spherical fluid shell with an inhomogeneous temperature boundary condition at infinite Prandtl number

Published online by Cambridge University Press:  26 April 2006

Keke Zhang  and
David Gubbins
Keke Zhang
Affiliation:
Department of Earth Sciences, University of Leeds, Leeds, LS2 9JT, UK Present address: Department of Mathematics, University of Exeter, Exeter, EX4 4QJ, UK.
David Gubbins
Affiliation:
Department of Earth Sciences, University of Leeds, Leeds, LS2 9JT, UK
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Abstract

We examine thermal convection in a rotating spherical shell with a spatially non-uniformly heated outer surface, concentrating on three distinct heating modes: first, with wavelength and symmetry corresponding to the most unstable mode of the uniformly heated problem; secondly, with the critical wavelength but opposite equatorial symmetry; and thirdly, with wavelength much larger than that of the most unstable mode. Analysis is focused on boundary-locked convection, the associated spatial resonance phenomena, the stability properties of the resonance solution, and time-dependent secondary convection. A number of new forms of instability and convection are found: the most interesting is perhaps the saddle-node bifurcation, which is the first to be found for realistic fluid systems governed by partial differential equations. An analogous Landau amplitude equation is also analysed, providing an important mathematical framework for understanding the complicated numerical solutions.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 250 , May 1993 , pp. 209 - 232
Copyright
© 1993 Cambridge University Press

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