Solar differential rotation influenced by latitudinal entropy variations in the tachocline

Three-dimensional simulations of solar convection in spherical shells are used to evaluate the differential rotation that results as thermal boundary conditions are varied. In some simulations a latitudinal entropy variation is imposed at the lower boundary in order to take into account the coupling between the convective envelope and the radiative interior through thermal wind balance in the tachocline. The issue is whether the baroclinic forcing arising from tachocline-induced entropy variations can break the tendency for numerical simulations of convection to yield cylindrical rotation profiles, unlike the conical profiles deduced from helioseismology. As the amplitude of the imposed variation is increased, cylindrical rotation profiles do give way to more conical profiles that exhibit nearly radial angular velocity contours at midlatitudes. Conical rotation profiles are maintained primarily by the resolved convective heat flux, which transmits entropy variations from the lower boundary into the convective envelope, giving rise to baroclinic forcing. The relative amplitude of the imposed entropy variations is of order 10(-5), corresponding to a latitudinal temperature variation of about 10 K. The role of thermal wind balance and tachocline-induced entropy variations in maintaining the solar differential rotation is discussed.