Energy Spectrum of Quasigeostrophic Turbulence

We consider the energy spectrum of a quasigeostrophic model of forced, rotating turbulent flow. We provide a rigorous a priori bound [Formula presented] valid for wave numbers that are smaller than a wave number associated with the forcing injection scale. This upper bound separates this spectrum from the Kolmogorov-Kraichnan [Formula presented] energy spectrum that is expected in a two-dimensional Navier-Stokes inverse cascade. Our bound provides theoretical support for the [Formula presented] spectrum observed in recent experiments.