Analysis of Velocity Derivatives in Turbulence based on Generalized Statistics
N. Arimitsu, T. Arimitsu
Abstract
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 Renyi entropy or the non-extensive Tsallis entropy, and is used, successfully, to analyze the PDF's observed in the direct numerical simulation (DNS) conducted by Gotoh et al.. The minimum length scale rd/eta in the longitudinal (transverse) inertial range of the DNS is estimated to be rdL/eta = 1.716 (rdT/eta = 2.180) in the unit of the Kolmogorov scale eta.
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