Convective Spherical Shell: II. With Rotation

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Abstract
The problem of a convective, rotating spherical shell is considered in Herring's approximation. The temperature is expanded in spherical harmonics, , and the velocity field in basic poloidal and toroidal vectors. The scalar , together with , defines a basic poloidal [toroidal] vector. The equations for and with different L's are coupled by the Taylor number and two types of solutions are possible: symmetric or antisymmetric about the equator. For the case of axial symmetry and for a Rayleigh number equal to 1500, we calculate the convective steady-state solution with rotation by successively increasing the Taylor number from zero, its value for no rotation. Using free surface boundary conditions, the relevant equations determine the radial and time-dependent parts of the temperature and velocity field, with the exception of , the lowest toroidal component of the axisymmetric solution having equatorial symmetry. The conservation of the total angular momentum in the direction of the axis of rotation then determines . The stabilizing effect of rotation on axisymmetric convection is specially important at the equator. For Taylor numbers larger than ∼502, axisymmetric convection is completely inhibited and the spherical shell rotates as a solid body.

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