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Title: Superstatistics and isotropic turbulence
Authors: Gravanis, Elias 
Akylas, Evangelos 
Michailides, Constantine 
Livadiotis, George 
Major Field of Science: Engineering and Technology
Field Category: Civil Engineering
Keywords: Superstatistics;Kappa index;Gamma distribution;Kappa distribution;Isotropic turbulence;Structure functions;PDF;DNS
Issue Date: 1-Apr-2021
Source: Physica A: Statistical Mechanics and its Applications, 2021, vol. 567, aticl. no. 125694
Volume: 567
Journal: Physica A: Statistical Mechanics and its Applications 
Abstract: In this work, we analyze the capacity of the superstatistics construction to provide modeling of the velocity field probability density functions (PDFs) of isotropic turbulence. Generalizing along the lines of the kappa distribution, superstatistics is understood here as a PDF for the statistical temperature that depends on a single dimensionful parameter and a dimensionless parameter , which both depend on the size of the fluid eddies and the Reynolds number, and possibly on auxiliary dimensionless constants that depend only on the Reynolds number. We show that such superstatistics –in some sense, the simplest class of models– cannot provide PDFs for scales outside the dissipation subrange for the currently accessible Reynolds numbers in Direct Numerical Simulations (DNS). The obstruction results from realizability constraints and an associated bound, and is related to the flatness factor of the velocity derivative distribution. Greater values of the flatness extend the applicability of superstatistics to larger scales. We argue that phenomenologically effective superstatistics models will require a value of flatness F25 or larger in order to cover the inertial subrange scales. The argument is assisted by constructing and analyzing a family of models which derive from modifying the gamma distribution in the regime of large statistical temperatures and nearly realize the realizability bound.
ISSN: 0378-4371
DOI: 10.1016/j.physa.2020.125694
Rights: © Elsevier
Attribution-NonCommercial-NoDerivatives 4.0 International
Type: Article
Affiliation : Cyprus University of Technology 
Southwest Research Institute 
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