Influence of penetration depth on jets on giant planets: equatorial jet direction, jet numbers, and jet energy fraction

Abstract

It remains puzzling why, despite their similar nature, Jupiter and Saturn possess a prograde equatorial jet, whereas Uranus and Neptune have a retrograde one. To understand this discrepancy, we use a two-dimensional quasi-geostrophic model to explore how the jet penetration depth, regulated by Ohmic dissipation, influences the structure and organization of jet patterns. When jets penetrate deeply into the planetary interior, the effective planetary vorticity gradient $\beta$ becomes negative near the equator and decreases equatorward due to spherical geometry. This $\beta$ profile favors dynamical modes that transport eastward momentum toward the equator, producing a prograde equatorial jet, as observed on Jupiter and Saturn. In contrast, relatively shallow systems favor a retrograde equatorial jet. In our simulations, the equatorial jet direction is primarily controlled by the gradient of $\beta$, as predicted by Stochastic Structural Stability Theory, rather than by its sign, as suggested by Potential Vorticity mixing. If this mechanism applies to Uranus and Neptune, the observed jet structure may suggest the presence of a stratified or Ohmic dissipation layer near their surfaces. At mid-latitudes, jet widths are constrained by the Rhines scale, yielding a scaling that explains the presence of multiple jets on Jupiter and Saturn and a single jet per hemisphere on Uranus and Neptune. Lastly, we examine how planetary parameters influence the partitioning of energy between jets and eddies. Stronger energy input, faster rotation, smaller planetary radius, or weaker large-scale damping lead to a larger fraction of the total energy in zonal jets, resulting in smoother jet structures.