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

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, Rom. In the meridional momentum balance, the ratio between inertial and Coriolis forces produces Rom = V2/ΩLU, U zonal, V meridional winds, L horizontal length scale. Our analysis shows that the meridional winds vary with the viscosity like ν1/2. With much larger viscosity and meridional winds, the Rossby number for DM is much larger, Rom(DM) >> Rom(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 104 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 = ΩV, yielding U = ΩL, independent of the source. The same relationship produces the zonal Rossby number, Roz = U/ΩL, of Order 1, which is commonly used as a dimensionless measure of the zonal wind velocities.

Meridional Circulation with Latitude Bands of Long-Lived Cyclones in Jupiter’s Convective Atmosphere

Mayr et al. [1] proposed that the vertical velocities in the global scale meridional circulation can produce distinct latitude bands where Jovian vortices like the white and brown are observed, and we present here a brief review of the mechanism. The observed life times of the ovals are much longer than the estimated spin-down times, which indicates that the vortices must be sustained through the release of internal energy. Like Jupiter’s Great Red Spot (GRS), the white/brown ovals are treated like terrestrial hurricanes or cyclones, which are generated by convection. The planetary energy Jupiter emits is transferred by convection, and under this condition the upward motions in the meridional circulation, around the equator for example, release energy from below and decrease the convective instability to suppress the formation of cyclones. But the downward motions in the circulation, near 20° latitude for example, carry energy down so that the convective instability is amplified to produce a dynamical environment that is favorable for the development of cyclones like the GRS and white/brown ovals. This picture is supported by an analysis of results from a numerical model of Jupiter’s alternating jets (Chan and Mayr [2]). Generated by alternating vertical winds in the meridional circulation, the vertical temperature variations reveal distinct latitude bands with enhanced convective instability, most prominent at high latitudes where long-lived circumpolar cyclones are observed from the Juno spacecraft.