Convective Models of Jupiter’s Zonal Jets with Realistic and Hyper-Energetic Excitation Source

Abstract

Numerical simulations of Jupiter’s zonal jets are presented, which are generated with realistic and hyper energetic source. The models are three dimensional and nonlinear, applied to a gas that is convective, stratified and compressible. Two solutions are presented, one for a shallow 0.6% envelope, the other one 5% deep. For the shallow model (SM), Jupiter’s small energy flux was applied with low kinematic viscosity. For the deep model (DM), the energy source and viscosity had to be much larger to obtain a solution with manageable computer time. Alternating zonal winds are generated of order 100 m/s, and the models reproduce the observed width of the prograde equatorial jet and adjacent retrograde jets at 20 ° latitude. But the height variations of the zonal winds differ markedly. In SM the velocities vary radially with altitude, but in DM Taylor columns are formed. The dynamical properties of these divergent model results are discussed in light of the computed meridional wind velocities. With large planetary rotation rate Ω , the zonal winds are close to geostrophic, and a quantitative measure of that property is the meridional Rossby number, Ro m . In the meridional momentum balance, the ratio between inertial and Coriolis forces produces Ro m = V 2 / Ω LU, U zonal, V meridional winds, L horizontal length scale. Our analysis shows that the meridional winds vary with the viscosity like ν 1/2 . With much larger viscosity and meridional winds, the Rossby number for DM is much larger, Ro m (DM) >> Ro m (SM). Compared to the shallow model with zonal winds varying radially, the deeper and more viscous model with Taylor columns is much less geostrophic. The zonal winds of numerical models in the literature tend to be independent of the energy source, in agreement with the present results. With 10 4 times larger energy flux, the zonal winds for DM only increase by a factor of 3, and the answer is provided by the zonal momentum budget with meridional winds, VU/L = Ω V, yielding U = Ω L, independent of the source. The same relationship produces the zonal Rossby number, Roz = U/ Ω L, of Order 1, which is commonly used as a dimensionless measure of the zonal wind velocities.