Infinite Prandtl number spherical-shell convection.

Presents an overview of numerical simulations of thermal convection for constant viscosity, infinite Prandtl number fluids in a spherical shell, with mantle convection being the main application. We have monitored the transitions from steady state to the onset of oscillatory time-dependent convection. This occurs at a Rayleigh number which is around 30 times the critical for an inner to outer radii of .62. Additional bifurcations are found with increasing strength of convection. This process culminates in chaotic convection. A large scale circulation, dominated by the degree n = 2 component is found to coexist with aperiodic boundary layer instabilities, mainly starting from the bottom. Spectral analysis of the power associated with the thermal anomalies reveals an upward cascade of energy from n = 2 to n = 4 to 6 at the bottom boundary. This last signature agrees well with recent seismic findings at the core-mantle boundary.-from Authors