Analysis of PDFs for energy transfer rates from 4096³DNS – verification of the scaling relation within MPDFT

The probability density functions (PDFs) for energy transfer rates, extracted by Kaneda and Ishihara from their 40963 direct numerical simulation for fully developed turbulence, are analyzed in high accuracy by means of the multifractal probability density function theory (MPDFT), in which a new scaling relation has been proposed. MPDFT is a statistical mechanical ensemble theory for the intermittent phenomena providing fat-tail PDFs. With the proposed scaling relation, MPDFT has been improved to deal with intermittency through any series of PDFs with arbitrary magnification δ (>1). As the value of δ can be determined freely by observers, the choice of δ should not affect observables. The validity of the generalized MPDFT is successfully verified through the precise analyses of several series of PDFs with different values of δ. In addition to the verification, it is revealed that the system of fully developed turbulence has much wider area representing scaling behaviors than the inertial range. With the help of MPDFT, it has become possible to separate the coherent turbulent motion from fluctuations, which may benefit the wavelet analysis of turbulence.