ONSET OF CONVECTION IN A RAPIDLY ROTATING FLUID SPHERE.
Technical rept. no. 57,
BROWN UNIV PROVIDENCE R I DIV OF APPLIED MATHEMATICS
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The nature of the constraint imposed by rapid rotation on convective motions at their onset in a plane liquid layer can be found out from an exact solution of the problem. Here we use the physical insight derived from the simpler problem to formulate an asymptotic approximation to the equations governing the analogous problem in a sphere. The solutions we obtain for the asymptotic equations provide an asymptotic approximation of the dependence of the critical Rayleigh number for the onset of convection on the Taylor number. Author