Modeling the stability of polygonal patterns of vortices at the poles of Jupiter as revealed by the Juno spacecraft

From its pole-to-pole orbit, the Juno spacecraft discovered arrays of cyclonic vortices in polygonal patterns around the poles of Jupiter. In the north, there are eight vortices around a central vortex, and in the south there are five. The patterns and the individual vortices that define them have been stable since August 2016. The azimuthal velocity profile vs. radius has been measured, but vertical structure is unknown. Here, we ask, what repulsive mechanism prevents the vortices from merging, given that cyclones drift poleward in atmospheres of rotating planets like Earth? What atmospheric properties distinguish Jupiter from Saturn, which has only one cyclone at each pole? We model the vortices using the shallow water equations, which describe a single layer of fluid that moves horizontally and has a free surface that moves up and down in response to fluid convergence and divergence. We find that the stability of the pattern depends mostly on shielding—an anticyclonic ring around each cyclone, but also on the depth. Too little shielding and small depth lead to merging and loss of the polygonal pattern. Too much shielding causes the cyclonic and anticyclonic parts of the vortices to fly apart. The stable polygons exist in between. Why Jupiter’s vortices occupy this middle range is unknown. The budget—how the vortices appear and disappear—is also unknown, since no changes, except for an intruder that visited the south pole briefly, have occurred at either pole since Juno arrived at Jupiter in 2016