Energy Spectrum of Quasi-Geostrophic Turbulence

Abstract

We consider the energy spectrum of a quasi-geostrophic model of forced, rotating turbulent flow. We provide a rigorous a priori bound E(k) <= Ck^{-2} valid for wave numbers that are smaller than a wave number associated to the forcing injection scale. This upper bound separates this spectrum from the Kolmogorov-Kraichnan k^{-{5/3}} energy spectrum that is expected in a two-dimensional Navier-Stokes inverse cascade. Our bound provides theoretical support for the k^{-2} spectrum observed in recent experiments.