Multifractal analysis of the fat-tail PDFs observed in fully developed turbulence

Abstract

The fundamentals of the multifractal analysis (MFA) is given, which is a unified statistical mechanical theory that treats the systems containing intermittent phenomena and representing fat-tail probability density functions (PDFs) for appropriate observables. MFA utilizes two distinct Tsallis-type MaxEnt distribution functions, one for the tail part of PDF and the other for its center part. It is shown that A&A model within MFA can explain the recently observed PDFs of turbulence in the highest accuracy superior to the analyses based on other multifractal models such as the log-normal model and the p model.