  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.
