Turbulence in stratified and rotating turbulent flows is characterized by an interplay between waves and eddies, resulting in continuous exchanges between potential and kinetic energy. Here, we study how these processes affect the turbulent energy cascade from large to small scales, which manifests itself by an irreversible evolution of the relative kinetic energy between two tracer particles. We find that when r_{0}, the separation between particles, is below a characteristic length ℓ_{t}, potential energy is on average transferred to kinetic energy, reducing time irreversibility, and conversely when r_{0}>ℓ_{t}. Our Letter reveals that the scale ℓ_{t} coincides with the buoyancy length scale L_{B} over a broad range of configurations until a transition to a wave-dominated regime is reached.
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