Successes and failures of shallow-water interpretations of Voyager wind data

Studying the dynamics of Jupiter's atmosphere is a rewarding experience, in part because the planet's cloud-top circulations are easy to track from space, the jet streams flow in straight lines eastward or westward, and there is enough room for the vortices to usually keep out of each other's way. Earth, in contrast, is a planet with global circulations that are not easy to track from space, with jet streams that make wide, fluctuating arcs as they negotiate mountain ranges, and with vortices that are constantly jostling against each other in a cramped environment. But we know a great deal more about the vertical structure of Earth's atmosphere than of Jupiter's. In order to make headway on the Jovian problem, researchers have turned to the shallow-water model as a guide to interpreting the Voyager wind data. The shallow-water model matches the character of the data because it combines high-resolution horizontal dynamics with low-resolution vertical structure, but there is no guarantee that it captures the character of Jupiter's atmosphere itself. Remarkably, the model does well at reproducing the Great Red Spot, and it has revealed that Jupiter is clever about how it manages its vorticity by arranging its zonal winds to be neutrally stable with respect to Arnol'd's second stability theorem. We discuss reasons why the shallow-water model works for Jupiter and point out the limitations that are motivating researchers to develop more realistic models.