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.

Saturn Atmospheric Structure and Dynamics

“…The advantage of this mechanism over the topographic β effect is that it is local and does not require convective columns to span the entire planet as a Taylor column. Evonuk andGlatzmaier (2006, 2007), Evonuk (2008), andGlatzmaier et al (2009) presented 2D numerical simulations in the equatorial plane to confirm these qualitative arguments. However, a possible stumbling block for this mechanism is that it would also predict equatorial superrotation on Uranus and Neptune, where equatorial subrotation is observed instead.…”

“…This mechanism, which can be viewed as a ``topographic'' β effect, requires convective rolls that act as coherent Taylor columns (i.e., the convective rolls must remain coherent along their entire length from the northern to the southern boundary). As Glatzmaier et al (2009) point out, current 3D convection studies are relatively laminar (a result of the low resolution necessary in a 3D study), which -combined with the fact that the simulated convective structures are relatively large-scale -promotes such columnar coherence. In reality, convective plumes are probably much narrower than current models can resolve; because of their small scales, such plumes are less likely to be geostrophic and thus may not exhibit the columnar structure necessary for the topographic β effect to occur.…”

“…In reality, convective plumes are probably much narrower than current models can resolve; because of their small scales, such plumes are less likely to be geostrophic and thus may not exhibit the columnar structure necessary for the topographic β effect to occur. Instead, Glatzmaier et al (2009) propose that equatorial superrotation on Jupiter and Saturn results from the interaction of convection with the radial density gradient (an effect that is ignored in the Boussinesq models). On Jupiter and Saturn, the density varies by a factor of ~1000 from the cloud layer to the deep interior, and most of this density variation occurs near 2…”

“…As a rising plume expands, it spins up anticyclonically, leading to a wavelike behavior that propagates eastward, with faster eastward propagation for fluid elements farther from the rotation axis. This radial dependence of the eastward propagation speed causes an eastward tilt in ascending convective plumes and a westward tilt in descending convective plumes (Glatzmaier et al 2009). The Reynolds stresses acting on such tilted convective columns transport eastward momentum radially outward and westward momentum radially inward (Busse 2002;Vasavada and Showman 2005;Glatzmaier et al 2009), leading to differential rotation with a superrotating jet at the equatorial surface.…”

“…This radial dependence of the eastward propagation speed causes an eastward tilt in ascending convective plumes and a westward tilt in descending convective plumes (Glatzmaier et al 2009). The Reynolds stresses acting on such tilted convective columns transport eastward momentum radially outward and westward momentum radially inward (Busse 2002;Vasavada and Showman 2005;Glatzmaier et al 2009), leading to differential rotation with a superrotating jet at the equatorial surface. The advantage of this mechanism over the topographic β effect is that it is local and does not require convective columns to span the entire planet as a Taylor column.…”