Reynolds number effect on the velocity increment skewness in isotropic turbulence

Abstract

Second and third order longitudinal structure functions and wavenumber spectra of isotropic turbulence are computed using the eddy-damped quasi-normal Markovian model (EDQNM) and compared to results of the multifractal formalism. It is shown that both the multifractal model and EDQNM give power-law corrections to the inertial range scaling of the velocity increment skewness. For the multifractal formalism, this is an intermittency correction that persists at any high Reynolds number. For EDQNM, this correction is a finite Reynolds number effect, and it is shown that very high Reynolds numbers are needed for this correction to become insignificant with respect to intermittency corrections. 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.