Harmonious Representation of PDF's reflecting Large Deviations

TL;DR

This paper introduces a novel multifractal analysis framework using two Tsallis distributions to accurately model turbulence PDFs, outperforming traditional models like log-normal and p-models.

Contribution

It presents a harmonious representation of multifractal analysis with dual Tsallis distributions, improving the accuracy of turbulence PDF modeling.

Findings

Harmonious MFA accurately models turbulence PDFs.

Outperforms traditional models like log-normal and p-model.

Provides a unified framework for multifractal analysis.

Abstract

The framework of multifractal analysis (MFA) is distilled to the most sophisticated one. Within this transparent framework, it is shown that the harmonious representation of MFA utilizing two distinct Tsallis distribution functions, one for the tail part of probability density function (PDF) and the other for its center part, explains the recently observed PDF's of turbulence in the highest accuracy superior to the analyses based on other models such as the log-normal model and the $p$ model.