Analysis of Velocity Fluctuation in Turbulence based on Generalized Statistics.pdf

1 Analysis of Velocity Fluctuation in Turbulence based on 0 Generalized Statistics 0 2 T. Arimitsu v o Institute of Physics, University of Tsukuba, Ibaraki 305-8571, Japan N N. Arimitsu 2 Graduate School of EIS, Yokohama Nat’l. University, Kanagawa 240-8501, Japan (10 October 2001) ] h c e The numerical experiments of turbulence conducted by Gotoh et al. m are analyzed precisely with the help of the formulae for the scaling ex- ponents of velocity structure function and for the probability density - t function of velocity fluctuations. These formulae are derived by the a present authors with the multifractal aspect based on the statistics that t s are constructed on the generalized measures of entropy, i.e., the exten- . t sive R´enyi’s or the non-extensive Tsallis’ entropy. It is shown, explicitly, a that there exist two scaling regions, i.e., the upper scaling region with m larger separations which may correspond to the scaling range observed - by Gotoh et al., and the lower scaling region with smaller separations d n which is a new scaling region extracted first by the present systematic o analysis. The