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We study the numerical simulations of 3-D inifinite Prandtl number convection with temperature-dependent viscosity in a spherical shell. Control volume method coupled with SIMPLE algorithm is used to solve the basic equations. Both constant and temperature-dependent viscosity cases are studied under the condition that the ratio of the inner to the outer shell radius is 0.55, which is appropriate for mantle convection of the Earth, with only basal heating. For the case of constant viscosity, when the Rayleigh number (Ra) is less than 105, steady state solutions (both cubic and tetrahedral types) are obtained. However, for Ra = 106, we find only a time-dependent solution. For the temperature-dependent viscosity case, we assume that the viscosity changes with temperature exponentially and we can successfully obtain solutions with the viscosity variation up to 10000. For the viscosity contrast of 1000 times and the surface Rayleigh number of Ra0 = 5 × 103, we get the flow patterns which consist of the sheet-like downwelling and small upwellings.

Three-Dimensional Infinite Prandtl Number Convection in a Spherical Shell with Temperature-Dependent Viscosity.