Analysis of velocity derivatives in turbulence based on generalized statistics

N. Arimitsu; T. Arimitsu

doi:10.1209/epl/i2002-00318-5

All issues

Volume 60 / No 1 (October 2002)

Europhys. Lett., 60 1 (2002) 60-65

Abstract

Issue		Europhys. Lett. Volume 60, Number 1, October 2002


Page(s)		60 - 65
Section		Atomic and molecular physics
DOI		https://doi.org/10.1209/epl/i2002-00318-5
Published online		01 September 2002

Europhys. Lett., 60 (1), pp. 60-65 (2002)

Analysis of velocity derivatives in turbulence based on generalized statistics

N. Arimitsu¹ and T. Arimitsu²

¹ Graduate School of EIS, Yokohama Nat'l. University - Kanagawa 240-8501, Japan
² Institute of Physics, University of Tsukuba - Ibaraki 305-8571, Japan

Received: 8 January 2002
Accepted: 12 July 2002

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 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.

PACS: 47.27.-i – Turbulent flows, convection, and heat transfer / 47.53.+n – Fractals / 47.52.+j – Chaos

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