Emergence of intense jets and Jupiter Great Red Spot as maximum entropy structures

We explain the emergence and robustness of intense jets in highly turbulent planetary atmospheres, like on Jupiter, by a general approach of statistical mechanics of potential vorticity patches. The idea is that potential vorticity mixing leads to the formation of a steady organized coarse grained flow, corresponding to the statistical equilibrium state. Our starting point is the quasi-geostrophic 1-1/2 layer model, and we consider the relevant limit of a small Rossby radius of deformation. Then narrow jets are obtained, scaling like the Rossby radius of deformation. These jets can be either zonal, or closed into a ring bounding a vortex. Taking into account the effect of the beta effect and a sublayer deep shear flow, we predict an organization of the turbulent atmospheric layer into an oval-shaped vortex amidst a background shear. Such an isolated vortex is centered over an extremum of the equivalent topography (determined by the deep shear flow and beta-effect). This prediction is in agreement with analysis of wind data in major Jovian vortices (Great Red Spot and Oval BC).