Barotropic theory for the velocity profile of Jupiter turbulent jets: an example for an exact turbulent closure
We model the dynamics of Jupiter's jets by averaging the dynamics of eddies, in a barotropic beta-plane model, and explicitly predicting the balance between Reynolds' stresses and dissipation, thus predicting the average velocity profile explicitly.In order to obtain this result, we adopt a non-equilibrium statistical mechanics approach. We consider a relevant limit for Jupiter troposphere, of a time scale separation between inertial dynamics on one hand, and stochastic forcing and dissipation on the other hand. We assume that the forcing acts on scales much smaller than the jet scale, and we obtain a very simple explicit relation between the Reynolds stress, the energy injection rate, and the average velocity shear, valid far from the jet edges (extrema of zonal velocity). A specific asymptotic expansion close to jet edges unravel an asymmetry between eastward and westward, velocity extrema. We recover Jupiter's jet specificities: a cusp on eastward jets and a smooth parabola on westward jets.