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Inertial convection at low Prandtl number

Published online by Cambridge University Press:  12 April 2006

Michael R. E. Proctor
Michael R. E. Proctor
Affiliation:
Department of Mathematics, Massachusetts Institute of Technology, Cambridge
Present address: Department of Applied Mathematics and Theoretical Physics, University of Cambridge.
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Abstract

The problem of Rayleigh-Bénard convection at low Prandtl number σ is investigated in a circular geometry. Jones, Moore & Weiss (1976) have formulated, but not solved analytically, an asymptotic nonlinear problem in the limit σ → 0 at small velocities. It is shown that the problem they posed can be solved exactly in this geometry. The solutions are extended by means of expansions in the amplitude ε and the reciprocal of the Reynolds number σε−1, both assumed small. The problem is related to one that occurs in nonlinear mean-field dynamo theory (Malkus & Proctor 1975) and it is surmised that similar problems may be expected to appear in a variety of physical situations.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 82 , Issue 1 , 19 August 1977 , pp. 97 - 114
Copyright
© 1977 Cambridge University Press

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