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Entropy 2019, 21(3), 326; https://doi.org/10.3390/e21030326

About Universality and Thermodynamics of Turbulence

1
SPEC, CEA, CNRS, Université Paris-Saclay, CEA Saclay, 91191 Gif-sur-Yvette, France
2
CNRS, ONERA, Arts et Metiers ParisTech, University of Lille, Centrale Lille, FRE 2017-LMFL-Laboratoire de Mécanique des Fluides de Lille—Kampé de Fériet, F-59000 Lille, France
3
School of Atmospheric Sciences, Sun Yat-sen University, Guangzhou 510275, China
*
Author to whom correspondence should be addressed.
Received: 26 February 2019 / Revised: 18 March 2019 / Accepted: 20 March 2019 / Published: 26 March 2019
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Abstract

This paper investigates the universality of the Eulerian velocity structure functions using velocity fields obtained from the stereoscopic particle image velocimetry (SPIV) technique in experiments and direct numerical simulations (DNS) of the Navier-Stokes equations. It shows that the numerical and experimental velocity structure functions up to order 9 follow a log-universality (Castaing et al. Phys. D Nonlinear Phenom. 1993); this leads to a collapse on a universal curve, when units including a logarithmic dependence on the Reynolds number are used. This paper then investigates the meaning and consequences of such log-universality, and shows that it is connected with the properties of a “multifractal free energy”, based on an analogy between multifractal and thermodynamics. It shows that in such a framework, the existence of a fluctuating dissipation scale is associated with a phase transition describing the relaminarisation of rough velocity fields with different Hölder exponents. Such a phase transition has been already observed using the Lagrangian velocity structure functions, but was so far believed to be out of reach for the Eulerian data. View Full-Text
Keywords: turbulence; intermittency; multifractal; thermodynamics turbulence; intermittency; multifractal; thermodynamics
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Geneste, D.; Faller, H.; Nguyen, F.; Shukla, V.; Laval, J.-P.; Daviaud, F.; Saw, E.-W.; Dubrulle, B. About Universality and Thermodynamics of Turbulence. Entropy 2019, 21, 326.

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