Markov property of Lagrangian turbulence

TL;DR

This paper provides the first evidence that Lagrangian turbulence exhibits Markov properties, enabling a stochastic thermodynamics approach to analyze particle trajectories and their entropy exchange in turbulent flows.

Contribution

It demonstrates the Markov property in Lagrangian turbulence for the first time and links it to Fokker-Planck equations and fluctuation theorems in non-equilibrium thermodynamics.

Findings

Markov property holds for finite step sizes dependent on the Stokes number.

Lagrangian particle statistics can be described by Fokker-Planck equations.

Entropy exchange along trajectories relates to intermittent flow structures.

Abstract

Based on direct numerical simulations with point-like inertial particles, with Stokes numbers, $\textrm{St}=0, 0.5$, $3$, 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 Lagrangian 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 description 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 structures. Statistical features of Lagrangian paths and entropy values are thus fixed by the fluctuation theorems.