Pattern generation by convection in spherical shells

Abstract

The problem of pattern selection by thermal convection in thin spherical shells with nearly insulating boundaries is investigated for both non-singular and singular cases where the Rayleigh number attains its minimum value for a single and double values of the degreel of spherical harmonics, respectively. The number of distinct solutions for the singular case is found to be substantially larger than the number of distinct solutions for the non-singular case. While there is at least one stable solution for the non-singular case, there is an additional stable mixed mode solution in the singular case as is shown in the casel=1 andl*=2.