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 Lagrangian turbulence. We show...

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Bibliographic Details
Published in:Europhysics letters 2022-03, Vol.137 (5), p.53001
Main Authors: Fuchs, A., Obligado, M., Bourgoin, M., Gibert, M., Mininni, P. D., Peinke, J.
Format: Article
Language:English
Subjects:
Chaotic Dynamics
Direct numerical simulation
Entropy
Fluid Dynamics
Fluid mechanics
Fokker-Planck equation
Local flow
Mechanics
Nonlinear Sciences
Physics
Theorems
Thermodynamics
Time dependence
Turbulence
Turbulent flow
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Summary: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.
ISSN:0295-5075
1286-4854
DOI:10.1209/0295-5075/ac55f1