Inverse cascade in stably stratified rotating turbulence

Stably stratified rotating turbulence is numerically investigated both with energy injection at small scales and in a freely decaying situation. To discriminate between the turbulent geostrophic part of the motion and the component associated with the inertial-gravity waves two decompositions are used. The first is based upon the fact that the wave field has no potential vorticity, and the second consists of a normal-mode decomposition. Both in the forced and freely decaying cases, the regime of small Froude and Rossby numbers is characterized by an inverse cascade of geostrophic energy towards the large scales whereas the wave energy propagates towards the dissipative scales. In the forced case, the inverse cascade corresponds to a well-defined k(-5/3) spectral range for both the kinetic and available potential energy spectra. The applications to the observed mesoscale atmospheric spectrum are discussed.