Unified Multifractal Description of Velocity Increments Statistics in Turbulence: Intermittency and Skewness

TL;DR

This paper develops a unified multifractal framework to describe the complete probability density functions of velocity increments in turbulence, capturing intermittency and skewness across all scales and Reynolds numbers.

Contribution

It introduces a universal multifractal model using a single parameter function D(h) and a constant R* to comprehensively describe velocity increment statistics in turbulence.

Findings

Unified description of symmetric and asymmetric PDFs of velocity increments.

Prediction of skewness of velocity derivatives across scales.

Applicable to various Reynolds numbers and experimental conditions.

Abstract

The phenomenology of velocity statistics in turbulent flows, up to now, relates to different models dealing with either signed or unsigned longitudinal velocity increments, with either inertial or dissipative fluctuations. In this paper, we are concerned with the complete probability density function (PDF) of signed longitudinal increments at all scales. First, we focus on the symmetric part of the PDFs, taking into account the observed departure from scale invariance induced by dissipation effects. The analysis is then extended to the asymmetric part of the PDFs, with the specific goal to predict the skewness of the velocity derivatives. It opens the route to the complete description of all measurable quantities, for any Reynolds number, and various experimental conditions. This description is based on a single universal parameter function D(h) and a universal constant R*.