Small scale structures of turbulence in terms of entropy and fluctuation theorems

André Fuchs, Sílvio M. Duarte Queirós, Pedro G. Lind, Alain Girard, Freddy Bouchet, Matthias Wächter, and Joachim Peinke
Phys. Rev. Fluids 5, 034602 – Published 11 March 2020

Abstract

We present experimental evidence that, together with the integral fluctuation theorem, which is fulfilled with high accuracy, a detailed-like fluctuation theorem holds for large entropy values in cascade processes in turbulent flows. Based on experimental data, we estimate the stochastic equations describing the scale-dependent cascade process in a turbulent flow by means of Fokker-Planck equations, and from the corresponding individual cascade trajectories an entropy term can be determined. Since the statistical fluctuation theorems set the occurrence of positive and negative entropy events in strict relation, we are able to verify how cascade trajectories, defined by entropy consumption or entropy production, are linked to turbulent structures: Trajectories with entropy production start from large velocity increments at large scale and converge to zero velocity increments at small scales; trajectories with entropy consumption end at small scale velocity increments with finite size and show a lower bound for small scale increments. A linear increase with the magnitude of the negative entropy value is found. This indicates a tendency to local discontinuities in the velocity field. Our findings show no lower bound of negative entropy values and thus for the corresponding piling up velocity differences of the small scale structures.

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  • Received 5 April 2019
  • Accepted 29 January 2020

DOI:https://doi.org/10.1103/PhysRevFluids.5.034602

©2020 American Physical Society

Physics Subject Headings (PhySH)

Fluid DynamicsStatistical Physics & Thermodynamics

Authors & Affiliations

André Fuchs1,*, Sílvio M. Duarte Queirós2, Pedro G. Lind3,4, Alain Girard5, Freddy Bouchet6, Matthias Wächter1, and Joachim Peinke1

  • 1Institute of Physics and ForWind, University of Oldenburg, Küpkersweg 70, D-26129 Oldenburg, Germany
  • 2Centro Brasileiro de Pesquisas Físicas and National Institute of Science and Technology for Complex Systems, Rua Dr. Xavier Sigaud 150, 2290-180 Urca, Rio de Janeiro–RJ, Brazil
  • 3Department of Computer Science, OsloMet–Oslo Metropolitan University, 4 St. Olavs plass, N-0130 Oslo, Norway
  • 4Instituto Universitário de Lisboa (ISCTE-IUL), ISTAR-IUL, Avenida Forças Armadas, P-1649-026 Lisboa, Portugal
  • 5INAC-SBT, UMR CEA-Grenoble University, CEA Grenoble, 17 rue des Martyrs, F-38054 Grenoble, France
  • 6Univ Lyon, Ens de Lyon, Univ Claude Bernard, CNRS, Laboratoire de Physique, F-69364 Lyon, France

  • *andre.fuchs@uni-oldenburg.de

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Vol. 5, Iss. 3 — March 2020

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