Compressible Convection in a Rotating Spherical Shell

Abstract

Giant cell stellar convection is modeled by solving the fluid equations for a compressible, rotating, spherical, fluid shell. A large part of the motivation is to understand the maintenance of the two major ingredients in solar dynamo theory, that is helicity and differential rotation. An anelastic approximation filters out sound waves but permits the investigation of the effects of large density stratifications in slightly superadiabatic stellar envelopes. Various rotation rates, convection zone depths, density stratifications, boundary conditions, viscosities, and conductivities are considered. The results of first order numerical calculations for the onset of convection are discussed with emphasis on the structure of the most unstable modes. Left (right) handed helical motion dominates in the northern (southern) hemisphere. Also, as the stratification increases, the horizontal dimension of the most unstable modes decreases, the prograde phase velocity increases, and the buoyancy force does more negative work in the upper part of the convection zone. Differential rotation is maintained by the transport of longitudinal momentum and by the coriolis forces acting on the meridional circulation. Second order numerical calculations provide profiles of the differential rotation and meridional circulation induced by the first order perturbations. Results of these calculations for the most unstable modes show that either equatorial acceleration, as observed on the sun, or equatorial deceleration can be maintained depending on the rotation rate, density stratification, viscosity, and conductivity. Small viscous diffusion relative to thermal diffusion is required for equatorial acceleration in rapidly rotating, highly stratified convection zones.