Analyses of turbulence in a wind tunnel by a multifractal theory for probability density functions

TL;DR

This paper applies a multifractal theory to analyze the probability density functions of energy dissipation rates in wind tunnel turbulence, revealing the roles of coherent and incoherent elements and their boundary.

Contribution

It introduces a new multifractal PDF framework that accurately models both the tail and central parts of turbulence PDFs, validated against wind tunnel data.

Findings

Tail PDF fits Tsallis-type distribution with one parameter.

Central PDF modeled by a three-parameter trial function.

Identified the boundary as the instability interface between coherent and incoherent turbulence elements.

Abstract

The probability density functions (PDFs) for energy dissipation rates, created from time-series data of grid turbulence in a wind tunnel, are analyzed in a high precision by the theoretical formulae for PDFs within multifractal PDF theory which is constructed under the assumption that there are two main elements constituting fully developed turbulence, i.e., coherent and incoherent elements. The tail part of PDF, representing intermittent coherent motion, is determined by Tsallis-type PDF for singularity exponents essentially with one parameter with the help of new scaling relation whose validity is checked for the case of the grid turbulence. For the central part PDF representing both contributions from the coherent motion and the fluctuating incoherent motion surrounding the former, we introduced a trial function specified by three adjustable parameters which amazingly represent scaling behaviors in much wider area not restricted to the inertial range. From the investigation of the difference between two difference formulae approximating velocity time-derivative, it is revealed that the connection point between the central and tail parts of PDF extracted by theoretical analyses of PDFs is actually the boundary of the two kinds of instabilities associated respectively with coherent and incoherent elements.