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Title: Kappa distributions and isotropic turbulence
Authors: Gravanis, Elias 
Akylas, Evangelos 
Panagiotou, Constantinos 
Livadiotis, George 
Major Field of Science: Natural Sciences
Field Category: Mathematics
Keywords: DNS;Isotropic turbulence;Kappa distribution;Kappa index;Karman-Howarth equation;PDF;Structure functions;Superstatistics
Issue Date: 7-Nov-2019
Source: Entropy, 2019, vol. 21, no. 11, articl. no. 1093
Volume: 21
Issue: 11
Project: ERATOSTHENES: Excellence Research Centre for Earth Surveillance and Space-Based Monitoring of the Environment 
Journal: Entropy 
Abstract: In this work, the two-point probability density function (PDF) for the velocity field of isotropic turbulence is modeled using the kappa distribution and the concept of superstatistics. The PDF consists of a symmetric and an anti-symmetric part, whose symmetry properties follow from the reflection symmetry of isotropic turbulence, and the associated non-trivial conditions are established. The symmetric part is modeled by the kappa distribution. The anti-symmetric part, constructed in the context of superstatistics, is a novel function whose simplest form (called "the minimal model") is solely dictated by the symmetry conditions. We obtain that the ensemble of eddies of size up to a given length r has a temperature parameter given by the second order structure function and a kappa-index related to the second and the third order structure functions. The latter relationship depends on the inverse temperature parameter (gamma) distribution of the superstatistics and it is not specific to the minimal model. Comparison with data from direct numerical simulations (DNS) of turbulence shows that our model is applicable within the dissipation subrange of scales. Also, the derived PDF of the velocity gradient shows excellent agreement with the DNS in six orders of magnitude. Future developments, in the context of superstatistics, are also discussed.
ISSN: 1099-4300
DOI: 10.3390/e21111093
Rights: © by the authors.
Type: Article
Affiliation : Cyprus University of Technology 
University of Cyprus 
Southwest Research Institute 
Appears in Collections:Publications under the auspices of the EXCELSIOR H2020 Teaming Project/ERATOSTHENES Centre of Excellence

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