PDF of Velocity Fluctuation in Turbulence by a Statistics based on Generalized Entropy
Statistical Mechanics
2015-06-24 v3
Abstract
An analytical formula for the probability density function (PDF) of the velocity fluctuation in fully-developed turbulence is derived, non-perturbatively, by assuming that its underlying statistics is the one based on the generalized measures of entropy, the R\'{e}nyi entropy or the Tsallis-Havrda-Charvat (THC) entropy. The parameters appeared in the PDF, including the index which appears in the measures of the R\'{e}nyi entropy or of the THC entropy are determined self-consistently with the help of the observed value of the intermittency exponent. The derived PDF explains quite well the experimentally observed density functions.
Cite
@article{arxiv.cond-mat/0109007,
title = {PDF of Velocity Fluctuation in Turbulence by a Statistics based on Generalized Entropy},
author = {Toshihico Arimitsu and Naoko Arimitsu},
journal= {arXiv preprint arXiv:cond-mat/0109007},
year = {2015}
}
Comments
10 pages, 2 figures