Multifractal analysis of fluid particle accelerations in turbulence

TL;DR

This paper derives an analytical probability density function for fluid particle accelerations in turbulence using multifractal analysis with generalized entropy, successfully matching experimental and DNS data at high Reynolds numbers.

Contribution

It introduces a novel analytical PDF based on multifractal analysis with Tsallis or Rényi entropy, explaining experimental and DNS acceleration data in turbulence.

Findings

Derived PDF matches experimental data at Rλ=690

Derived PDF matches DNS data at Rλ=380

Validates multifractal analysis with generalized entropy for turbulence

Abstract

The probability density function (PDF) of accelerations in turbulence is derived analytically 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 et al. in the measurement of fluid particle accelerations in the Lagrangian frame at $R_\lambda = 690$, and the one by Gotoh et al. in the DNS with the mesh size 1024$^3$ at $R_\lambda = 380$.