Differential rotation in giant planets maintained by density-stratified turbulent convection

Abstract

The zonal winds on the surfaces of giant planets vary with latitude. Jupiter and Saturn, for example, have several bands of alternating eastward (prograde) and westward (retrograde) jets relative to the angular velocity of their global magnetic fields. These surface wind profiles are likely manifestations of the variations in depth and latitude of angular velocity deep within the liquid interiors of these planets. Two decades ago it was proposed that this differential rotation could be maintained by vortex stretching of convective fluid columns that span the interiors of these planets from the northern hemisphere surface to the southern hemisphere surface. This now classic mechanism explains the differential rotation seen in laboratory experiments and in computer simulations of, at best, weakly turbulent convection in rotating constant-density fluid spheres. However, these experiments and simulations are poor approximations for the density-stratified strongly-turbulent interiors of giant planets. The long thin global convective columns predicted by the classic geostrophic theory for these planets would likely not develop. Here we propose a much more robust mechanism for maintaining differential rotation in radius based on the local generation of vorticity as rising plumes expand and sinking plumes contract. Our high-resolution two-dimensional computer simulations demonstrate how this mechanism could maintain either prograde or retrograde surface winds in the equatorial region of a giant planet depending on how the density scale height varies with depth.