Multifractal PDF analysis for intermittent systems

TL;DR

This paper introduces a multifractal PDF analysis method for intermittent systems, explaining various PDFs from simulations and experiments, and offers a new way to determine scaling exponents from velocity fluctuation PDFs.

Contribution

It extends the PDF formula to include energy dissipation rates and demonstrates its effectiveness in explaining experimental and simulation data, providing a novel approach to extract scaling exponents.

Findings

The formula explains PDFs from simulations and experiments.

It enables extraction of intermittency and scaling exponents.

Provides a new method for analyzing velocity fluctuation PDFs.

Abstract

The formula for probability density functions (PDFs) has been extended to include PDF for energy dissipation rates in addition to other PDFs such as for velocity fluctuations, velocity derivatives, fluid particle accelerations, energy transfer rates, etc, and it is shown that the formula actually explains various PDFs extracted from direct numerical simulations and experiments performed in a wind tunnel. It is also shown that the formula with appropriate zooming increment corresponding to experimental situation gives a new route to obtain the scaling exponents of velocity structure function, including intermittency exponent, out of PDFs of velocity fluctuations.