Barotropic theory for the velocity profile of Jupiter turbulent jets: an example for an exact turbulent closure

TL;DR

This paper develops a barotropic model for Jupiter's turbulent jets using non-equilibrium statistical mechanics, explicitly predicting the velocity profile and jet asymmetries based on energy and stress balances.

Contribution

It introduces an explicit relation between Reynolds stress, energy injection, and velocity shear for Jupiter's jets, incorporating asymmetries near jet edges.

Findings

Reveals a cusp structure on eastward jets.

Shows a smooth parabola on westward jets.

Predicts asymmetry between eastward and westward jet extrema.

Abstract

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.