Linear Simulations of Boussinesq Convection in a Deep Rotating Spherical Shell

Abstract

Abstract We present extensive linear numerical simulations of Boussinesq convection in a rotating spherical shell of finite depth. The motivation for the study is the problem of general circulation of the solar convection zone. We solve the marching equations on a staggered grid in the meridian plane for the amplitudes of the most unstable Fourier mode of longitudinal wavenumber m between 0 and 24, for Taylor number T between 0 and 106, at a Prandtl number P=1, for a shell of depth 20% of the outer radius. Stress-free, fixed-temperature boundary conditions are used at the inner and outer bounding surfaces. Modes of two symmetries, symmetric and antisymmetric about the equator, are studied. The principal results are as follows: Increasing Taylor number T splits the most unstable solutions for each m into two classes: a broad band of high m solutions which peak at or near the equator, and a small number of low m solutions which peak at or near the poles. The equatorial modes are unstable at lower Rayleigh n...