Deriving circumpolar cyclones from zonal flow with a simplified multi-layer fluid model

A zonal flow pattern is well-established for Jupiter's lower latitudes. At high latitudes, this patterm breaks down as observed in visible-light, infrared, and much of the radio-wave spectrum.  But around each pole, Juno's instruments observe a cluster of circumpolar cyclones (CPC) that appears to remain essentially stable over at least six years. A heavily simplified multilayer fluid dynamical model suggests that such a pattern may be able to form in overlying atmospheric layers from an underlying zonal flow pattern.

Juno's wide-angle visible-light imager, JunoCam, continues to observe Jupiter's north polar region on a regular basis during each perijove flyby. As it is now northern summer on Jupiter, JunoCam with its wide field of view can see a little more than half of the northern CPCs. While locally the CPCs can change substantially, the overall octagonal pattern remains mostly stable.

An attempt to model such a CPC pattern with an incompressible 2D Euler flow numerical model can maintain such a pattern temporarily. But it shows several caveats in detail. Several questions remain: Why is the northern CPC pattern octagonal? Why is it stable? How did it form? Why are there counter-rotating cores in some of the CPCs? Why are many of the CPCs of an almost circular shape? Why are there two distinct morphologies, i.e., filled and spiral?  

Friction with an underlying steady flow can modify a 2D Euler flow in such a way that anticyclonic vorticity can form inside a cyclone. But explaing the CPC pattern itself appears hard with such a two-layer model.  However, the approach can be generalized in a computationally feasible way: Couple the 2D Euler flow tightly enough to the underlying steady flow such that it converges to a steady flow itself, and start with this new steady flow iteratively the same way. In this way, only one 2D fluid layer requires to be simulated at a time, but still an arbitrary number of layers can be simulated.

This approach turns out to morph an axially symmetrical steady zonal flow with only small fluctuations into a CPC pattern when traversing the layers from bottom to top. Since each layer becomes essentially a steady flow, the CPC pattern ends up stable for any given modelled fluid layer of interest. We can think of portions of the time axis being translated into the vertical z-axis. It is those portions that change the flow pattern.  A more chaotic flow can be achieved by reducing the coupling between layers. 
The simplification to the one-way effect of the coupling between layers is assumed to be justified by the density gradient.