Stably stratified rotating turbulence is numerically investigated both
with energy injection at small scales and in a freely decaying situat
ion. To discriminate between the turbulent geostrophic part of the mot
ion and the component associated with the inertial-gravity waves two d
ecompositions 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 inve
rse 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) spectr
al range for both the kinetic and available potential energy spectra.
The applications to the observed mesoscale atmospheric spectrum are di
scussed.