Mechanisms for Limiting the Depth of Zonal Winds in the Gas Giant Planets

Abstract

Gravity signatures observed by the Juno and Cassini missions that are associated with the strong zonal winds in Jupiter’s and Saturn’s outer envelopes suggest that these flows extend for several thousand kilometers into the interior. It has been noted that the winds seem to abate at a depth where electrical conductivity becomes significant, suggesting that electromagnetic effects play a key role for confining the winds to the outer weakly conducting region. Here, we explore the possible mechanisms for braking the zonal flow at depth in two model setups with depth-dependent conductivity and forced jet flow, i.e., in axisymmetric shell models and in more simple linearized box models that allow the exploration of a wide parameter range. Braking of the winds directly by Lorentz forces does not reduce their speed in the conducting region enough to be compatible with the inferred secular variation of Jupiter’s field. Stable stratification above the depth where conductivity becomes significant can solve the problem. Electromagnetic forces drive a weak meridional circulation that perturbs the density distribution in the stable region such that the wind speed decreases strongly with depth, due to a thermal wind balance. For this mechanism to be effective, the stable layer must extend upward into a region of low conductivity. Applying the results of the linearized calculations to Jupiter suggests that the dissipation associated with the zonal winds can be limited to a fraction of the internal heat flow and that the jets may drop off over a depth range of 150–300 km.

Theory of Figures to the Seventh Order and the Interiors of Jupiter and Saturn

“…A superadiabatic temperature profile may result from stable stratification. Christensen et al (2020) showed that meridional flows in a stably stratified, slightly conducting region slow down the strong zonal flows and suggested the existence of such a region in Jupiter as an explanation for the truncation of the zonal flows, which, according to recent combined analysis of magnetic field and gravity field data, occurs rather sharply at 0.97 R Jup ).…”

Influence of reference states on Jupiter’s dynamo simulations

“…Secondly, although different density and temperature profiles are employed in this study, we assume that the whole simulation domain is convectively unstable. Stably stratified layers may exist within giant planets; if so, they could change the magnetohydrodynamics significantly (Stevenson, 1982b; Cao and Stevenson, 2017; Christensen et al, 2020). Finally, our numerical simulations are limited to a small range of control parameters with moderate Ekman numbers.…”

Acoustic and inertial modes in planetary-like rotating ellipsoids

“…However, the generation of geostrophic motions is a long-standing issue in the theory of rotating fluids even in the incompressible regime [74]. The observed zonal winds at Jupiter's surface could be also related to deep geostrophic flows [75,76], but different physical scenarios are highly disputed in light of recent high-precision data [77][78][79]. To assess the robustness of the deep scenario, the polynomial formulation might be used directly to solve dynamical problem (5.1) without any prior computations of the normal modes (as for incompressible theories [80,81]).…”