Numerical simulations of supergranular scales of convection in shallow spherical shells

The differential rotation of the sun, as deduced from helioseismology, exhibits a prominent radial shear layer near the top of the convection zone. Supergranulation and related scales of turbulent convection are likely to play a significant role in the maintenance of strong radial gradients in angular velocity which vary with latitude near the surface. We present results from 3-D numerical simulations of such turbulent convection in shallow spherical shells, using the anelastic spherical harmonic (ASH) code running on massively parallel computers to study the effects of rotation and compressibility on the resulting highly nonlinear convection. Convection of supergranular nature is driven by imposing the solar heat flux at the bottom of a shallow spherical shell located near the top of the convection zone which is rotating at the mean solar rate. The angular momentum balance in the shell is studied for cases where a solar-like differential rotation profile is imposed at the lower boundary. Convection spanning a large range of horizontal scales is driven within the shell, especially near the top of the domain. The resulting radial angular velocity gradient is negative for all latitudes, suggesting that fluid parcels partially conserve their angular momentum while moving radially.