Title:

The thermal shallow water equations, their quasigeostrophic limit, and equatorial superrotation in Jovian atmospheres

Observations of Jupiter show a superrotating (prograde) equatorial jet that has persisted for decades. Shallow water simulations run in the Jovian parameter regime reproduce the mixture of robust vortices and alternating zonal jets observed on Jupiter, but the equatorial jet is invariably subrotating (retrograde). Recent work has obtained superrotating equatorial jets by extending the standard shallow water equations to relax the height field towards its mean value. This Newtonian coolinglike term is intended to model radiative cooling to space, but its addition breaks key conservation properties for mass and momentum. In this thesis the radiatively damped thermal shallow water equations are proposed as an alternative model for Jovian atmospheres. They extend standard shallow water theory by permitting horizontal variations of the thermodynamic properties of the fluid. The additional temperature equation allows a Newtonian cooling term to be included while conserving mass and momentum. Simulations reproduce equatorial jets in the correct directions for both Jupiter and Neptune (which subrotates). Quasigeostrophic theory filters out rapidly moving inertiagravity waves. A local quasigeostrophic theory of the radiatively damped thermal shallow water equations is derived, and then extended to cover whole planets. Simulations of this global thermal quasigeostrophic theory show the same transition, from sub to superrotating equatorial jets, seen in simulations of the original thermal shallow water model as the radiative time scale is decreased. Thus the mechanism responsible for setting the direction of the equatorial jet must exist within quasigeostrophic theory. Such a mechanism is developed by calculating the competing effects of Newtonian cooling and Rayleigh friction upon the zonal mean zonal acceleration induced by equatorially trapped Rossby waves. These waves transport no momentum in the absence of dissipation. Dissipation by Newtonian cooling creates an eastward zonal mean zonal acceleration, consistent with the formation of superrotating equatorial jets in simulations, while the corresponding acceleration is westward for dissipation by Rayleigh friction.
