  We present an investigation of rapidly rotating (small Rossby number $Ro\ll
1$) and stratified turbulence where the stratification strength is varied from
weak (large Froude number $Fr\gg1$) to strong ($Fr\ll1$). The investigation is
set in the context of a reduced model derived from the Boussinesq equations
that efficiently retains anisotropic inertia-gravity waves with order-one
frequencies and highlights a regime of wave-eddy interactions. Numerical
simulations of the reduced model are performed where energy is injected by a
stochastic forcing of vertical velocity, which forces wave modes only. The
simulations reveal two regimes characterized by the presence of well-formed,
persistent and thin turbulent layers of locally-weakened stratification at
small Froude numbers, and by the absence of layers at large Froude numbers.
Both regimes are characterized by a large-scale barotropic dipole enclosed by
small-scale turbulence. When the Reynolds number is not too large a direct
cascade of barotropic kinetic energy is observed, leading to total energy
equilibration. We examine net energy exchanges that occur through vortex
stretching and vertical buoyancy flux and diagnose the horizontal scales active
in these exchanges. We find that the baroclinic motions inject energy directly
to the largest scales of the barotropic mode, implying that the large-scale
barotropic dipole is not the end result of an inverse cascade within the
barotropic mode.
