Does intermittency affect the inertial transfer rate in stationary isotropic turbulence?

TL;DR

This study uses direct numerical simulations to examine how intermittency influences inertial transfer in stationary isotropic turbulence, finding that intermittency averages out and does not alter the Kolmogorov-Obukhov energy transfer picture.

Contribution

It provides evidence that internal intermittency does not affect the ensemble-averaged inertial transfer rate in stationary isotropic turbulence.

Findings

Inertial flux becomes scale-invariant at higher Reynolds numbers.

Energy spectra follow the -5/3 power law in the inertial range.

Intermittency effects diminish with ensemble averaging.

Abstract

Direct numerical simulations of the forced Navier-Stokes equations were performed, in which each shell-averaged quantity evolved from a value appropriate to an initial Gaussian state, to fluctuate about a mean value. Once the transient had passed, mean values (and their associated statistics) were obtained by sampling the evolved time-series at intervals of the order of an eddy-turnover time. This was repeated for a range of Taylor-Reynolds numbers from 10.6 to 335.2. With increasing Reynolds number, our results for energy spectra, transfer spectra and inertial flux supported the Kolmogorov-Obukhov picture of turbulent energy transfer. In particular, we observed the onset of scale-invariance of the inertial flux, accompanied by the onset of the -5/3 power law in the energy spectrum for the corresponding inertial range of wavenumbers. Detailed comparisons showed that our results were in agreement with those found in many other investigations. Flow visualization methods were used to study the internal intermittency. This phenomenon is seen in single realisations but was found to average out with increasing number of realisations under ensemble-averaging. Following a critical review of the literature relating to the controversy about intermittency effects versus finite-Reynolds number corrections, it was concluded that, for the case of stationary isotropic turbulence, internal intermittency cannot affect the Kolmogorov-Obukhov picture, as this is constructed entirely in terms of ensemble-averaged mean quantities.