Lagrangian irreversibility in rotating-stratified turbulent flows

In homogeneous and isotropic turbulence (HIT), two tracer particles separate faster backward than forward in time, a manifestation of the irreversibility induced by the energy flux from large to small scales. We establish that this property extends to flows of geophysical relevance, with broken isotropy. Specifically, we study turbulence in the presence of both solid body rotation (ROT, Coriolis parameter f) and stable stratification (STRAT, Brunt-Väisälä frequency N). At the fixed relative strength of ROT and STRAT N/f = 5, we perform a series of direct numerical simulations (DNS) with increasing strength of both ROT and STRAT from flows that are close to HIT to wave-dominated flows. 

We revisit the energy budget in such flows to account for the potential energy induced by stratification and extend the Karman-Howarth-Monin relations for ROTSTRAT turbulence in the Lagrangian framework. When the flow is forced mechanically, we observe a net flux from kinetic to potential energy at large scales, and surprisingly, from potential to kinetic energy at smaller scales. Finally, we discuss the implications of the flow anisotropy for the relative separation of two particles.