Markov property of Lagrangian turbulence*

Based on direct numerical simulations with point-like inertial particles, with Stokes numbers St = 0,0.5, 3, and 6, transported by homogeneous and isotropic turbulent flows, we present in this letter for the first time evidence for the existence of Markov property in La- grangian turbulence. We show that the Markov property is valid for a finite step size larger than a Stokes-number–dependent Einstein-Markov coherence time scale. This enables the de- scription of multi-scale statistics of Lagrangian particles by Fokker-Planck equations, which can be embedded in an interdisciplinary approach linking the statistical description of turbulence with fluctuation theorems of non-equilibrium stochastic thermodynamics and local flow structures. The formalism allows estimation of the stochastic thermodynamics entropy exchange associated with the particles Lagrangian trajectories. Entropy-consuming trajectories of the particles are related to specific evolution of velocity increments through scales and may be seen as intermittent struc- tures. Statistical features of Lagrangian paths and entropy values are thus fixed by the fluctuation theorems.