Zonal flow formation in the presence of ambient mean shear

The effect of mean shear flows on zonal flow formation is considered in the contexts of plasma drift wave turbulence and quasi-geostrophic turbulence models. The generation of zonal flows by modulational instability in the presence of large-scale mean shear flows is studied using the method of characteristics as applied to the wave kinetic equation. It is shown that mean shear flows reduce the modulational instability growth rate by shortening the coherency time of the wave spectrum with the zonal shear. The scalings of zonal flow growth rate and turbulent vorticity flux with mean shear are determined in the strong shear limit.