UC Berkeley

Coherent vortices are one of the most common structures in geophysical and astrophysical fluid systems. On Earth, geostrophic eddies play important roles in the ocean kinetic energy balance (Ferrari & Wunsch, 2009). On Jupiter, the Great Red Spot (GRS) and other vortices have been observed for hundreds of years (Hooke, 1665; Dawes, 1857). On Saturn, its polar vortex shapes the hexagonal patterns at the north pole (Rostami et al., 2017). On Neptune, observations show dark spots emerging and fading away over the past 25 years (Wong et al., 2022).This dissertation focuses on the fluid dynamics of the Jovian vortices, given their abundance (Li et al., 2004; Sankar et al., 2022) and long observation history(Hooke, 1665; Cassini, 1666; Dawes, 1857). To study Jovian vortices, we develop a three-dimensional pseudo-spectral code, the Pseudo-spectraL ANElastic Three-dimensional Simulator (PLANETS), to simulate the anelastic equations of motion. Modeling planetary vortices is computationally challenging because the timestep dt is constrained by fast-dynamics (gravity waves, planetary rotation, zonal shear). We improve the semi-analytic method proposed by Barranco & Marcus (2006) to handle the complex environment of the Jovian atmosphere. We demonstrate that the code can efficiently model the fast-dynamics using a relatively large timestep dt without losing accuracy. More details of our equations of motion and numerical methods can be found in Chapter 2. Using the PLANETS, we systematically study the three-dimensional structure of Jovian vortices. We show that the model used in previous studies, characterized by a similar area and changing vorticity as a function of depth, is not a stable equilibrium. Instead, our findings indicate that a stable 3D Jovian vortex should feature a varying area and similar vorticity throughout its depth. We discuss the scaling analysis of the flow field based on our numerical simulations and present a semi-analytic relation of the shape of the vortices and how the convection zone of the lower layer affects the stability of the vortex. The study on the three-dimensional structure of Jovian vortices has been published in the Journal of Fluid Mechanics. We also use simulations to constrain the vertical structure of the Great Red Spot (GRS). Despite the long observational history, we have very little knowledge about the vertical structure of the GRS. We quantitatively reproduce vortices in quasi-equilibrium, consistent with the wind velocities observed by the Hubble Space Telescope (HST). We show that the new observational constraints from the temperature and velocity observations with the James Webb Space Telescope (JWST) severely reduce the possible range of allowable vortices that are stable solutions to the equations of motion and that also quantitatively fit the new and old observations. The allowable solutions provide precise values, with small uncertainties, for the heights of the top of the Jovian convection zone, the HST and JWST cloud decks from which velocities are extracted, and the top and bottom of the GRS, along with its strength and vertical structure. We also show that our calculations are consistent with the gravity anomalies probed by the Juno mission.