Analysis of accelerations in turbulence based on generalizaed statistics

TL;DR

This paper derives an analytical PDF for turbulence accelerations using multifractal analysis with generalized entropy, successfully matching experimental data from high Reynolds number fluid flows.

Contribution

It introduces a new analytical expression for the acceleration PDF in turbulence based on generalized entropy, advancing the theoretical understanding of turbulence statistics.

Findings

The derived PDF fits well with experimental data at high Reynolds number.

Multifractal analysis with Tsallis or Rényi entropy effectively models turbulence accelerations.

The approach provides a unified framework for turbulence acceleration statistics.

Abstract

An analytical expression of probability density function (PDF) of accelerations in turbulence is derived with the help of the multifractal analysis based on generalized entropy, i.e., the Tsallis or the R\'{e}nyi entropy. It is shown that the derived PDF explains quite well the one obtained by Bodenschatz and coworkers in the measurement of fluid particle accelerations in the Lagrangian frame at $R_\lambda = 970$.