Hydrodynamic stability constraints on the three-dimensional structure of planetary vortices

Observations by the Juno spacecraft have inspired new 3D models of the Jovian vortices, including the Great Red Spot. However, these models are heuristic and not stable equilibria of Euler’s equation. Stability with respect to convection is a concern because anticyclones always locally de-stratify the fluid, and we consistently find that if a vortex is locally unstable at any height with respect to convection, it breaks apart and does not reform. Using the anelastic approximation, we compute families of 3D vortices embedded in a Jovian-like stratified shear flow. We show that a vortex’s horizontal cross-sectional area must decrease to zero at the top and bottom of the vortex, while the vertical vorticity must be nearly uniform as a function of height. Otherwise, the vortex will shear apart or look non-physical. For vortices in which the vertical vorticity, or potential vorticity is nearly uniform over in the horizontal directions, (e.g., one with solid-body rotation or the Jovian Red Oval), we have found only family of vortices that is stable with respect to convective and shear instabilities. We have developed a simple analytic approximation of these vortices that agrees well with the numerical simulations and captures the 3D vertical structure of this stable family of vortices.