Inertial range and the finite Reynolds number effect of turbulence

Abstract

The Kolmogorov 4 5 law, which is the unique, exact relationship of inertial-range statistics, is applied to investigate the finite Reynolds number effect, in particular to study how the width of the inertial range of finite Reynolds number turbulence changes with the Taylor microscale Reynolds number R . It is found that there is no inertial range when R р2000 and, within tolerance of 1% error, R should be higher than 10 4 in order to have an inertial range wider than one decade. The so-called inertial range found in experiments and simulations is just a scaling range and is not the same as Kolmogorov's inertial range. The finite Reynolds number effect cannot be neglected within such a scaling range and should be considered in comparing experiments ͑or simulations͒ with theories of the inertial-range statistics. ͓S1063-651X͑96͒03112-1͔

Spectral analysis of structure functions and their scaling exponents in forced isotropic turbulence

“…The use of spectral methods to calculate the structure functions is known in the literature through the work by Bos et al [28], Tchoufag et al [27], and Qian [25,26]. We will now briefly explain the reason for doing it this way.…”

“…There is, however, an alternative to the use of generalized structure functions. This is the pseudospectral method.Inusing this for some of the present work, we followed the example of Qian [25,26], Tchoufag, Sagaut, and Cambon [27], and Bos, Chevillard, Scott, and Rubinstein [28], who obtained S 2 and S 3 from the energy and energy transfer spectra, respectively, by means of exact quadratures.…”

“…In Sec. V we describe the theoretical basis for using the pseudospectral method [25][26][27][28], which includes a rigorous derivation of the forcing in the real-space energy balance equation. This is followed by the introduction of a scaling exponent in Sec.…”

Scaling law of resolved-scale isotropic turbulence and its application in large-eddy simulation

“…With the resolved-scale energy spectrum and energy transfer spectrum obtained from EDQNM theory, we can calculate the corresponding resolved-scale structure functions with the transform equations derived by Qian [5,6].…”

“…There are also several researchers who doubted the anomalous scaling law. Qian [5,6] argued that the anomalous scaling law might be a finite Reynolds effect (FRE), while K41 theory should be satisfied at infinite Reynolds number. Barenlatt [7] argued that the relative scaling exponent in ESS theory should not be an anomalous number 0.70 but should remain 2/3.…”