Analysis of velocity derivatives in turbulence based on generalized statistics

A theoretical formula for the probability density function (PDF) of velocity derivatives in a fully developed turbulent flow is derived with the multifractal aspect based on the generalized measures of entropy, i.e., the extensive Rényi entropy or the non-extensive Tsallis entropy, and is used, succ...

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Bibliographic Details
Published in:Europhysics letters 2002-10, Vol.60 (1), p.60-65
Main Authors: Arimitsu, N, Arimitsu, T
Format: Article
Language:English
Subjects:
47.27.-i
47.52.+j
47.53.+n
Chaos
Exact sciences and technology
Fluid dynamics
Fractals
Fundamental areas of phenomenology (including applications)
Fundamentals
Physics
Turbulent flows, convection, and heat transfer
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Summary:A theoretical formula for the probability density function (PDF) of velocity derivatives in a fully developed turbulent flow is derived with the multifractal aspect based on the generalized measures of entropy, i.e., the extensive Rényi entropy or the non-extensive Tsallis entropy, and is used, successfully, to analyze the PDFs observed in the direct numerical simulation (DNS) conducted by Gotoh et al. The minimum length scale $r_{{\rm d}}/\eta$ in the longitudinal (transverse) inertial range of the DNS is estimated to be $r_{{\rm d}}^{\rm L}/\eta = 1.716$ ($r_{{\rm d}}^{\rm T}/\eta = 2.180$) in the unit of the Kolmogorov scale η.
ISSN:0295-5075
1286-4854
DOI:10.1209/epl/i2002-00318-5