We study anisotropic statistics in rotating stratified flows. The toroidal/poloidal decomposition exhibits two limits: 2D modes with horizontal wavevectors, and 1D vertically sheared horizontal modes, with only vertical wavevectors. For rotation, both toroidal and poloidal components are affected by inertial waves, thus anisotropic phase mixing is responsible for transient effects, whereas resonant triads control the long-term dynamics. We compare the development of triple vorticity correlations by pure linear theory, statistical EDQNM theory, experiments and DNS. The dominance of cyclonic vertical vorticity is explained without instabilities arguments. For stable stratification, strong nonlinearity only affects the pure toroidal mode, whereas any interaction involving the poloidal mode deals with weak gravity-wave turbulence. We then explore the toroidal cascade. We show its consistency with a spherical shell-to-shell direct cascade. It can explain the angular energy drain from quasi-2D modes to quasi-1D VSHF modes, which quantifies the horizontal layering of the flow, again without advocating instability mechanisms
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