A Model of Large-Scale Instabilities in the Jovian Troposphere: 2. Quasi-linear Model

In a companion paper (Y. Orsolini and C. B. Leovy 1993, Icarus 106, 392-405, we developed a linear model to test the possible role of large-scale instabilities of zonal jets in the jovian upper troposphere. A quasi-linear model is now used to investigate how an initially barotropically unstable flow develops a quasi-steady shear zone in the lower scale heights of the model domain, as a result of the action of the eddy fluxes. The barotropic instabilities are then acting as a drag term, the nonlinear evolution of the instability enhancing an initially small vertical shear as in the strongly truncated spectral model of J. A. Pirraglia (1989, Icarus 79, 196-207). In the absence of radiative damping or of forcing mechanisms, a quasi-neutral state is reached at the end of the equilibration stage characterized by an eddy-to-mean flow kinetic energy ratio of about 20% for westward jets and of less than 1% for eastward jets. For adjacent eastward and westward jets, unstable modes can propagate meridionally and contribute to the decay of both jets. In another set of simulations, we introduce a Rayleigh drag, forcing the mean flow back to its unstable state, while the eddies are damped radiatively. When the forcing time scale is the same as the radiative damping time, an asymmetric life-cycle type of behavior develops, with the eddy energy growing quickly to saturation and decaying slowly. For stronger zonal flow forcings, the eddy energy can be steady, and there are time-averaged eddy fluxes which drive meridional circulations.