  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.
