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.
Publisher
Cambridge University Press (CUP)
Subject
Mechanical Engineering,Mechanics of Materials,Condensed Matter Physics
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