The Big Effects of Small Vertical Velocities on the Structures of 3D Rapidly-Rotating, Stratified Planetary Vortices

Vortices in rapidly-rotating, stratified flows are often computed with 2D quasigeostrophic or shallow-water equations. However when the Rossby number is small and/or N/ω_z is large, the vertical velocity v_z of the vortex can strongly affect vertical vorticity ω_z of the vortex and the log of the temperature field of the vortex because their temporal derivatives are proportional to f v_z/Λ and v_z N/g, respectively, where N is the Brunt-Vaisala frequency, g the acceleration of gravity, f the Coriolis parameter, and Λ the vertical density scale height. Here, we present some of the consequences of v_z for anticyclones computed with a 3D, high-resolution spectral code used to simulate the Jovian vortices. We show how v_z produces the bright warm rings observed around many of Jupiter’s anticyclones, such as the Great Red Spot, and how v_z increases the longevities of the large Jovian anticyclones to tens or hundreds of years -- far greater than the vortex turn-around times and the local atmosphere’s radiative decay time. We present a new analytic scaling relation for the magnitude of v_z in terms of the vortex's Rossby number and its vertical aspect ratio (i.e., its vertical scale height divided by the horizontal scale height of the pressure anomaly of the vortex) for vortices in which the vertical scale-heights of the vertical and horizontal components are of the same order.