I examine the geostrophic turbulence field in equilibrium with a horizontally uniform mean zonal flow driven by solar heating. The equilibrium mean vertical shear is highly supercritical, and the turbulence field has its maximum in kinetic energy at wavenumbers smaller than the wavenumbers of fastest growth predicted by linear stability theory. Wavenumber spectra obtained by averaging lengthy numerical integrations of the two-level quasi-geostrophic equations agree well with the predictions of a simple Markovian turbulence model. Analysis of the turbulence model suggests that the most energetic wavenumbers equilibrate from scattering of the temperature perturbations into higher wavenumbers by the barotropic adverting field. In the higher unstable wavenumbers, including the most supercritical, linear instability is offset chiefly by local rotations of the unstable structures by larger, more energetic eddies.