Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2001-10-17
Physics
Condensed Matter
Statistical Mechanics
10 Pages, 5 figures
Scientific paper
10.1088/0953-8984/14/9/312
The numerical experiments of turbulence conducted by Gotoh et al. are analyzed precisely with the help of the formulae for the scaling exponents of velocity structure function and for the probability density function (PDF) of velocity fluctuations. These formulae are derived by the present authors with the multifractal aspect based on the statistics that are constructed on the generalized measures of entropy, i.e., the extensive R\'{e}nyi's or the non-extensive Tsallis' entropy. It is revealed that there exist two scaling regions separated by a crossover length, i.e., a definite length approximately of the order of the Taylor microscale. It indicates that the multifractal distribution of singularities in velocity gradient in turbulent flow is robust enough to produce scaling behaviors even for the phenomena out side the inertial range.
Arimitsu Naoko
Arimitsu Toshihico
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