Axisymmetric convection in a rotating sphere: Part 2. Non-slip surface

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Abstract
This paper reports numerical experiments on large-scale nonlinear thermal convection in a rotating self-gravitating sphere of Boussinesq fluid containitrg a uniform distribution of heat sources. Solutions are obtained for Taylor numbers in the range 0≦Δ< 105, Rayleigh numbers in the range Rc≦R≲10Rc , and Prandtl numbers in the range 0.1≦P≦10. The present solutions, which are dynamically possible, have a similar form to that which seems to be required by some kinematic models of the earth's hydromagnetic dynamo. The flows with nearly uniform angular momentum and the sustained overstable oscillations, both of which occur when the outer surface is stress-free, are found to be inhibited by a non-slip surface. Most of the solutions qualitatively resemble those predicted by the linear stability equations, with wavenumber increasing with R and A, but other modes, sometimes including a sustained non-linear oscillation, can be produced by different initial conditions. The effect of Prandtl number is small, except when A = O, in which case the kinetic energy of the flow is proportional to P. for P<1.

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