From gas to ice giants: A unified mechanism for equatorial jets

Abstract

The equatorial jets dominating the dynamics of the Jovian planets exhibit two distinct types of zonal flows: strongly eastward in the gas giants (superrotation) and strongly westward in the ice giants (subrotation). Existing theories propose different mechanisms for these patterns, but no single mechanism has successfully explained both. However, the planetary parameters of the four Solar System giant planets suggest that a fundamentally different mechanism is unlikely. In this study, we show that convection-driven columnar structures can account for both eastward and westward equatorial jets, framing the phenomenon as a bifurcation. Consequently, both superrotation and subrotation emerge as stable branches of the same mechanistic solution. Our analysis of these solutions uncovers similarities in the properties of equatorial waves and the leading-order momentum balance. This study suggests that the fundamental dynamics governing equatorial jet formation may be more broadly applicable across the Jovian planets than previously believed, offering a unified explanation for their two distinct zonal wind patterns.

Figures (5)

• Figure 1: Measurements of zonal wind profiles of the Jovian planets. Zonally averaged zonal cloud-level winds $\left[{\rm m\,s^{-1}}\right]$ of (A) Jupiter Tollefson2017, (B) Saturn garcia2011, (C) Uranus Hammel2001Hammel2005Sromovsky2005, and (D) Neptune Sromovsky1993Sromovsky2001a. Saturn's wind field incorporates recent estimations of the planet's rotation rate mankovich2019. The winds on Uranus and Neptune were measured by Voyager 2 (circles) and HST (squares), and are presented along with a polynomial fit of the data (line).
• Figure 2: Schematics of tilted convection columns. The tilt driving to either outward (superrotation, red) or inward (subrotation, blue) transport of positive angular momentum with convex boundaries (dashed envelope). In the subrotation case, the columns have a concave structure while existing within a convex-boundary system. $\hat{\Omega}$ is the direction of the rotation axis, $\hat{r}_\perp$ is the direction perpendicular to the rotation axis, and $\hat{\varphi}$ is the zonal direction. $\bar{u}$ is the mean flow and $u^\prime v^{\prime}_\perp$ is the eddy momentum flux directed perpendicular to the rotation axis.
• Figure 3: Results from two simulations with identical physical parameters, initiated from rest with random entropy noise. (A) Zonally averaged zonal wind $\left[{\rm cm\,s^{-1}}\right]$ (left side of the sphere) and zonal wind (right side of the sphere) of a convection-driven simulation, showing a superrotating equatorial jet flanked by two retrograde higher-latitude jets. The right side also displays convection columns tilted in the prograde direction. Outer shell is shown for $r=r_{o}$ and inside the slice values are shown for $r=r_{i}$ ($\mu=\frac{r_{i}}{r_{o}}=0.92$). (B) Similar setup but with reversed patterns: the equatorial jet is subrotating, the higher-latitude jets are in the prograde direction, and the convection columns are tilted in the retrograde direction.
• Figure 4: Zonal wind and eddy fluxes in superrotation and subrotation. Superrotation in the upper panels and subrotation in the lower panels. (A, E) Zonally-averaged zonal wind $\left[{\rm cm\,s^{-1}}\right]$ (shown are latitudes -30° to 30° ), (B, F) Zonally-averaged eddy fluxes in the direction perpendicular to the axis of rotation $\left[{\rm cm^{2}\,s^{-2}}\right]$, where the black dashed lines emphasize the curvature of the cylinder at the bottom, (C, G) Snapshot of eddy fluxes in the equatorial plane $\left[{\rm cm^{2}\,s^{-2}}\right]$, and (D, H) Snapshot of the zonal wind velocity at mid-shell depth $\left[{\rm cm\,s^{-1}}\right]$. Both simulations have identical physical parameters and were initiated from random noise. The geometric orientation of the different panels is shown between the upper and lower rows.
• Figure 5: 38 simulations revealing a back-to-back saddle-node bifurcation. Two initial conditions are studied: a superrotating case (red dots, with the red dashed line indicating the initial mean velocity value) and a subrotating case (blue dots, with the blue dashed line indicating the initial mean velocity value). For each normalized inner radius ($\mu=\frac{r_{i}}{r_{o}}$), two simulations were performed with both sets of initial conditions. All the simulations are in a statistical steady state, with the mean zonal value and error bars, representing one SD, are averaged over the last 100 rotations (mostly notable around the bifurcation nodes, elsewhere the SD is smaller than the circle). The figure reveals four different regions based on $\mu$: A normalized inner radius smaller than $\mu<0.88$ cannot maintain a concave structure of columns, resulting in a reversion to the superrotation condition (orange shade). Depths in the range $\left(0.88<\mu<0.97\right)$ can support both convex (red shade) and concave (blue shade) columnar structures. Depths associated with $\mu>0.97$ are presented with open circles and dotted lines as the results are less conclusive (see main text). In this regime (grey shade), only subrotation persists.