  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 $\ell_t$, potential energy is on average transferred to
kinetic energy, reducing time irreversibility, and conversely when $r_0 >
\ell_t$. Our study reveals that the scale $\ell_t$ coincides with the buoyancy
length scale $L_B$ over a broad range of configurations until a transitional
wave-dominated regime is reached.
