Volume 137, Number 5, March 2022
|Number of page(s)||6|
|Section||Fluid and nonlinear dynamics|
|Published online||04 May 2022|
Markov property of Lagrangian turbulence
1 Institute of Physics and ForWind, University of Oldenburg - Küpkersweg 70, D-26129 Oldenburg, Germany
2 Univ. Grenoble Alpes, CNRS, Grenoble INP*, LEGI - F-38000 Grenoble, France
3 Laboratoire de Physique de l'École Normale Supérieure de Lyon, CNRS & Université de Lyon 46 allée dItalie, F-69364 Lyon Cedex 07, France
4 Univ. Grenoble Alpes, CNRS, Grenoble INP, Institut Néel - F-38000 Grenoble, France
5 Universidad de Buenos Aires, Facultad de Ciencias Exactas y Naturales, Departamento de Física, & IFIBA, CONICET - Ciudad Universitaria, Buenos Aires 1428, Argentina
Received: 30 November 2021
Accepted: 16 February 2022
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 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.
© 2022 The author(s)
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