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.

[1] We have applied, for the first time in geodynamical flows, the Particle Level Set method for advecting compositional fields with sharp discontinuities. This robust and efficient Eulerian-Lagrangian technique is based on the concept of Implicit Surfaces, which allows the use of high order accurate numerical schemes in the vicinity of discontinuities. We have tested the Particle Level Set method against the robust and popular Tracer-in-Cell method on well-known 2D thermochemical benchmarks and typical 3D convective flows. The use of Lagrangian tracers in the Particle Level Set method yields accurate solutions of purely advective transport, where sub-grid scale features can be resolved. In every case we ran we found that the Particle Level Set method accuracy equals or is better than the popular Tracer-in-Cell method, and can lead to significantly smaller computational cost, in particular in three-dimensional flows, where the reduction of computational time for modeling advection processes is most needed.

No abstract

Local generation of vorticity occurs in rotating density-stratified fluids as fluid parcels move radially, expanding or contracting with respect to the background density stratification. Thermal convection in rotating 2D equatorial simulations demonstrates this mechanism. The convergence of the vorticity into zonal flow structures as a function of radius depends on the shape of the density profile, with the prograde jet forming in the region of the disk where the greatest number of density scale heights occurs. The number of stable jets that form in the fluid increases with decreasing Ekman number and decreases with increasing thermal driving. This local form of vorticity generation via the density stratification is likely to be of great importance in bodies that are quickly rotating, highly turbulent, and have large density changes, such as Jovian planets. However, it is likely to be of lesser importance in the interiors of planets such as the Earth, which have smaller density stratifications and are less turbulent.

No abstract