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W.B. Hubbard (UAz)
Groundbased and spacecraft-based measurements of Jupiter's atmospheric motions show a pattern of zonal flows which persists over decades. The flows alternate strongly with latitude and show partial north-south symmetry. Peak zonal cloud speeds with respect to the System III frame are about 100 m/s; Galileo Probe data at latitude 6.6 deg N show even higher wind speeds at pressures up to 21 bars. If such zonal flows persist to sufficiently high pressures and mass densities, they can be detectable in Jupiter's external gravity field.
I bound the effects of zonal flow on Jupiter's external gravity by considering two extreme models. For the first model, I assume that Jupiter's interior has constant specific entropy, and is thus barotropic, such that the planet rotates differentially on cylinders. In the second model, I assume that zonal flows are confined to a very shallow atmospheric region of negligible mass and thus have no effect on the gravity. In both models, the mass distribution is obtained from the solution to the steady-state Euler equation ({\bf v}\cdot \nabla){\bf v}+(\nabla P)/\rho-{\bf g}=0, where {\bf v} is the fluid velocity vector due to System III rotation plus differential flow (if any), P is the pressure, \rho is the mass density, and {\bf g} is the gravity vector.
The difference in predicted gravity for the two models is about 30 mgal at the equator, as measured by an orbiter at an altitude of 1000 km. Gravity anomalies above the 10th degree are almost entirely determined by the zonal flow field, tend to be anticorrelated with eastward wind speeds, and have an amplitude on the order of a milligal. The maximum gravity anomalies should occur if the zonal flows persist to a depth about 1000 km below the cloud layers (corresponding to a pressure of about 10 kbar). Such gravity anomalies would be readily detectable by a low Jupiter orbiter equipped with Galileo-level orbit-tracking technology.