Eur. Phys. J. B 18, 95-101 (2000)
https://doi.org/10.1007/s100510070082

Local multifractal thermodynamics of 3D turbulence

¹ Department of Physics, Chuo University, Tokyo 112 8551, Japan
² Machanaim Center, PO Box 31155, Jerusalem 91000, Israel
³ Department of Systems Engineering, Nagoya Institute of Technology, Nagoya 466 8555, Japan

Received: 21 July 2000
Published online: 15 November 2000

Abstract

Using results of a direct numerical simulation (DNS) of 3D turbulence we show that the observed generalized scaling (i.e. scaling moments versus moments of different orders) is consistent with a lognormal-like distribution of turbulent energy dissipation fluctuations with moderate amplitudes for all space scales available in this DNS (beginning from the molecular viscosity scale up to largest ones). Local multifractal thermodynamics has been developed to interpret the data obtained using the generalized scaling, and a new interval of space scales with inverse cascade of generalized energy has been found between dissipative and inertial intervals of scales for sufficiently large values of the Reynolds number.