Thermal Wind Balance of Fluid Planets: The Effects of Oblateness, Centrifugal Forces, and Self-Gravitation

The nature of the flow below the cloud-level of Jupiter and Saturn is still unknown. Relating the flow on these planets to perturbations in their density field is key to the analysis of the high-precision gravity measurements expected from both the Juno (Jupiter, ongoing) and Cassini (Saturn, starting May 2017) spacecrafts. Both missions will provide latitude-dependent gravity fields, which in principle could be inverted to calculate the vertical structure of the observed cloud-level zonal flow on these planets. Given the size of these planets and their fast spin, simplifying assumptions, standardly made in the study of large-scale fluid motions on Earth, might not hold due to several physical processes. Those include the deviation from spherical symmetry, the centrifugal force due to density perturbations, and self-gravitational effects of the density perturbations themselves. Recent studies attempted to include some of these neglected terms, but lacked an overall approach that includes all effects in a self-consistent manner.

Here we introduce a full self-consistent perturbation approach to the vorticity balance that incorporates all physical effects, and apply it to several examples of gas giant wind structures, both barotropic and baroclinic. The contribution of each term is analyzed, and the results are compared in the barotropic limit to those of potential theory. We find that to-leading-order thermal wind gives a good estimate for the relation between the wind shear and density perturbations, which can be used for calculation of the gravity moments. Yet, it is found that the additional terms in the vorticity balance can become important for the higher gravitational moments and should be take into consideration when a higher-order analysis is desired.

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