Scaling of Mid-latitude Jets in Jupiter and Saturn's Atmospheres

Despite Jupiter and Saturn's similar radii, compositions, rotation rates and atmospheric structures, the characteristics of the off-equatorial jets in their atmospheres are very different. In particular, Jupiter has 15 - 20 off-equatorial jets with speeds of about 20 m/ s, while Saturn only has 5 -10 off-equatorial jets with speeds of about 100 m/s. Here we show that the observed differences in the jets can be explained by different strengths of the magnetohydrodynamic (MHD) drag produced by the planetary magnetic fields in the interiors of the planets.

In the off-equatorial regions of Jupiter's and Saturn's atmospheres, baroclinic eddies induced by the differential solar heating transport angular momentum out of retrograde jets and into prograde jets, which leads to the formation of the jets. In the statistical steady state, this angular momentum transfer by eddies must be balanced by the dissipation produced by the MHD drag in the planetary interior. To investigate the effect produced by MHD drag, we use a general circulation model, which is a thin-shell approximation of Jupiter's upper atmosphere with imposed Rayleigh drag in the bottom of the domain. The strength, width, and spacing of the jets depend on the drag at the bottom. The energy-containing eddy length scale varies weakly with latitude, controls the jet width and spacing, and is similar to the Rossby deformation radius and the Rhines scale. As the bottom drag decreases, both the eddy length and the eddy kinetic energy increase. Thus, the jets become stronger and wider, with increased interjet spacings. Saturn's magnetic field is much weaker than Jupiter's, which indicates that the generated MHD drag in Saturn's atmosphere is weaker. This may be the reason that the off-equatiorial jets in Saturn's atmosphere are stronger and have wider interjet spacings.

In the statistically steady state of the simulations, the generation rate of potential energy balances the conversion rate from potential energy to kinetic energy, and the energy conversion rate from eddy kinetic energy to zonal mean kinetic energy balances the energy dissipation by Rayleigh drag. For a wide range of the imposed Rayleigh drag parameters, the energy generation rates, the energy conversion rates and the energy dissipation rates remain remarkably constant, which implies that the efficiency of Jupiter and Saturn's atmosphere is not sensitive to the drag in the interiors.