Lagrangian Irreversibility in Stratified Turbulence

Abstract

Stable stratification reorganizes turbulence, suppressing vertical motion and altering the balance between vortical and strain-dominated flow structures. How these changes affect the temporal asymmetry of kinetic-energy exchange along fluid-particle trajectories remains incompletely understood. Using direct numerical simulations of homogeneous Boussinesq turbulence, we investigate Lagrangian power statistics across four local velocity-gradient topology classes and three nonzero stratification strengths, with an unstratified reference case. With increasing stratification, the global power variance decreases while the standardized skewness becomes more negative, indicating enhanced asymmetry despite weaker fluctuations. Conditioning on local topology reveals distinct responses: axial-strain-dominated regions exhibit the most negative total-power skewness at all stratification strengths, whereas biaxial-strain-dominated regions change sign from positive to negative under stratification. Horizontal and vertical component powers also respond differently, revealing directional dependence. Among the dynamical contributions to power, the pressure contribution, nearly symmetric in the unstratified case, becomes more negatively skewed with increasing stratification. Energy-conditioned pressure statistics further indicate altered pressure-mediated energy redistribution. Finally, tracer persistence-time distributions exhibit exponential tails, with time scales that differ across topology classes and respond differently to stratification. Increasing stratification is thus accompanied by three concurrent changes: enhanced asymmetry of Lagrangian power, modified energy redistribution by pressure, and altered temporal sampling of local flow structures by tracers. These co-occurring signatures characterize the response to stratification, though their causal relations remain to be established.