Lagrangian irreversibility and energy exchanges in rotating-stratified turbulent flows

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.