Turbulent Convection under the Influence of Rotation: Sustaining a Strong Differential Rotation
The intense turbulence present in the solar convection zone is a major challenge to both theory and simulation as one tries to understand the origins of the striking differential rotation profile with radius and latitude that has been revealed by helioseismology. The differential rotation must be an essential element in the operation of the solar magnetic dynamo and its cycles of activity, yet there are many aspects of the interplay between convection, rotation, and magnetic fields that are still unclear. We have here carried out a series of three-dimensional numerical simulations of turbulent convection within deep spherical shells using our anelastic spherical harmonic (ASH) code on massively parallel supercomputers. These studies of the global dynamics of the solar convection zone concentrate on how the differential rotation and meridional circulation are established. We have addressed two issues raised by previous simulations with ASH. First, can solutions be obtained that possess the apparent solar property that the angular velocity Ω continues to decrease significantly with latitude as the pole is approached? Prior simulations had most of their rotational slowing with latitude confined to the interval from the equator to about 45°. Second, can a strong latitudinal angular velocity contrast ΔΩ be sustained as the convection becomes increasingly more complex and turbulent? There was a tendency for ΔΩ to diminish in some of the turbulent solutions that also required the emerging energy flux to be invariant with latitude. In responding to these questions, five cases of increasingly turbulent convection coupled with rotation have been studied along two paths in parameter space. We have achieved in one case the slow pole behavior comparable to that deduced from helioseismology and have retained in our more turbulent simulations a consistently strong ΔΩ. We have analyzed the transport of angular momentum in establishing such differential rotation and clarified the roles played by Reynolds stresses and the meridional circulation in this process. We have found that the Reynolds stresses are crucial in transporting angular momentum toward the equator. The effects of baroclinicity (thermal wind) have been found to have a modest role in the resulting mean zonal flows. The simulations have produced differential rotation profiles within the bulk of the convection zone that make reasonable contact with ones inferred from helioseismic inversions, namely, possessing a fast equator, an angular velocity difference of about 30% from equator to pole, and some constancy along radial lines at midlatitudes. Future studies must address the implications of the tachocline at the base of the convection zone, and the near-surface shear layer, on that differential rotation.