Effects of temperature-dependent viscosity on thermal convection in a spherical shell

A numerical investigation is presented of the effects of a strongly temperature-dependent viscosity on the radial structure, horizontal planform, and heat transfer characteristics of a thermally convecting, infinite Prandtl number, Boussinesq fluid in a spherical shell. Basal and mixed-mode heating are considered wherein viscosity varies with temperature according to a linearized Arrhenius theology. Three-dimensional, fully nonlinear calculations are performed and compared to the predictions of linear theory. For basal heating, three convective regimes (mobile lid, sluggish lid, and stagnant lid) are observed in accord with theoretical and numerical studies in cartesian geometry. Solutions starred with similar initial conditions and comparable convective vigor result in distinct horizontal planforms which correspond to these three regimes. In the mobile-lid regime, planforms with moderate horizontal length scales are characterized by linear downwelling sheets and quasi-cylindrical upwelling plumes. Sluggish-lid flow assumes a much longer wavelength with linear bands of upwelling plumes and large cylindrical downflows. Stagnant-lid flow is characterized by very small-scale flow patterns with upwelling plumes embedded in a network of cold, stiff fluid. Mobile-lid and sluggish-lid regimes are also observed in the mixed-mode heating calculations with changes in horizontal length scales similar to those in the basally-heated cases.