Reynolds number effect on the velocity increment skewness in isotropic turbulence

TL;DR

This paper compares EDQNM and multifractal models in predicting the Reynolds number dependence of velocity increment skewness in isotropic turbulence, highlighting their similarities, differences, and effects at high Reynolds numbers.

Contribution

It provides a detailed comparison of EDQNM and multifractal models for turbulence, clarifying their predictions of skewness and Reynolds number effects.

Findings

Both models show power-law corrections at high Reynolds numbers.

EDQNM attributes corrections to finite Reynolds effects.

Multifractal formalism attributes corrections to intermittency.

Abstract

Second and third order longitudinal structure functions and wavenumber spectra of isotropic turbulence are computed using the EDQNM model and compared to results of the multifractal formalism. At the highest Reynolds number available in windtunnel experiments, $R_\lambda=2500$, both the multifractal model and EDQNM give power-law corrections to the inertial range scaling of the velocity increment skewness. For EDQNM, this correction is a finite Reynolds number effect, whereas for the multifractal formalism it is an intermittency correction that persists at any high Reynolds number. Furthermore, the two approaches yield realistic behavior of second and third order statistics of the velocity fluctuations in the dissipative and near-dissipative ranges. Similarities and differences are highlighted, in particular the Reynolds number dependence.