Emergence of Jets from Turbulence in the Shallow-Water Equations on an Equatorial Beta Plane

Coherent jets, such as the Jovian banded winds, are a prominent feature of rotating turbulence. Shallowwater turbulence models capture the essential mechanism of jet formation, which is systematic eddy momentum flux directed up the mean velocity gradient. Understanding how this systematic eddy flux convergence is maintained and how the mean zonal flow and the eddy field mutually adjust to produce the observed jet structure constitutes a fundamental theoretical problem. In this work a shallow-water equatorial betaplane model implementation of stochastic structural stability theory (SSST) is used to study the mechanism of zonal jet formation. In SSST a stochastic model for the ensemble-mean turbulent eddy fluxes is coupled with an equation for the mean jet dynamics to produce a nonlinear model of the mutual adjustment between the field of turbulent eddies and the zonal jets. In weak turbulence, and for parameters appropriate to Jupiter, both prograde and retrograde equatorial jets are found to be stable solutions of the SSST system, but only the prograde equatorial jet remains stable in strong turbulence. In addition to the equatorial jet, multiple midlatitude zonal jets are also maintained in these stable SSST equilibria. These midlatitude jets have structure and spacing in agreement with observed zonal jets and exhibit the observed robust reversals in sign of both absolute and potential vorticity gradient.