Convective Spherical Shell: II. With Rotation

Abstract

Abstract The problem of a convective, rotating spherical shell is considered in Herring's approximation. The temperature is expanded in spherical harmonics, YLm(θ,Φ), and the velocity field in basic poloidal pLm(r,t) and toroidal tLm(r,t) vectors. The scalar pLm(r,t) [tLm(r,t)], together with YLm(θ,Φ), defines a basic poloidal [toroidal] vector. The equations for pLm(r,t) and tLm(r,t) 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 t10(r), the lowest toroidal component of the axisymmetric solution having equatorial symmetry. The conse...