Verification of the scaling relation within MPDFT by analyzing PDFs for energy dissipation rates out of 40963 DNS

The PDFs for energy dissipation rates, extracted by Kaneda and Ishihara from their 40963 DNS for fully developed turbulence, are analyzed within the framework of multifractal probability density function theory (MPDFT) to a high accuracy. MPDFT is a statistical mechanical ensemble theory for analyzing intermittent phenomena providing fat-tail probability density functions (PDFs). Recently, MPDFT has been improved by introducing a new scaling relation so as to be able to analyze intermittency through any series of PDFs with arbitrary magnification δδ (>1). It was fixed to a unique value δ=2δ=2. Since the value of δδ can be determined freely by observers, the choice of δδ should not affect observables. The validity of the generalized MPDFT is verified successfully through the precise analyses of several series of PDFs with different values of δδ. In the course of 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. This may benefit the wavelet analysis of turbulence.