Gravity Signatures of Stable, Equilibrial 3D Great Red Spot Solutions Consistent with Observed Cloud-Level Velocities

Recent gravity measurements from the Juno mission provided indirect evidence of the 3D structure of the Great Red Spot (GRS). Parisi et al. (2021) concluded from the gravity observations that GRS could extend into the convective layer. However, their model is not a solution to the full equations of motion. In addition, such a vortex is likely to be unstable to shear or convection.

To create true equilibrial GRS models and to assess their stability, we explore the following questions regarding the 3D structure (i.e., the three-dimensional distribution of vorticity) of the planetary vortices. First, what 3D vortex structures are simultaneously dynamically stable and consistent with cloud-level observations as well as the Juno gravity data? Second, is the vorticity primarily aligned with the planet's rotational axis or the gravity direction?

In order to address those questions, we adopt the following numerical strategy. We construct a thermal background profile that is consistent with Jovian observations. We then compute a family of GRS models based on the thermal background and the observed cloud-level velocity. We run initial value simulations using the anelastic approximation allowing the vortex to converge to statistically-stable 3D equilibrium. The gravity is then expanded in terms of the Slepian functions similarly to Galanti et al. (2019). Based on the Slepian projection coefficients, we provide a mapping between the vortex properties (such as its orientation, the 3D distribution of the vortex area and vorticity) and the resulting expected gravity signature and cloud-level velocity field.