Slow decay of the finite Reynolds number effect of turbulence

Abstract

The third-order structure function is used to study the finite Reynolds number (FRN) effect of turbulence, which refers to the deviation of turbulence statistics observed at finite Reynolds numbers from predictions of the Kolmogorov theories. It is found that the FRN effect decreases as CR(-mu)(lambda), when R(lambda) is high, and mu < or = 6/5. Here R(lambda) is the Taylor-microscale Reynolds number and C is a constant independent of R(lambda). From the exact spectral equations, the decay exponent mu and the constant C are determined for typical fully developed turbulent flows (freely decaying isotropic turbulence and shear flow turbulence), so that the quantitative prediction of the FRN effect is feasible.

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.…”

Measurements of the Kolmogorov constant from laboratory and geophysical wind data

“…Also concerning the validity of the four-fifths law, Refs. [20][21][22][23][24] point out that the four-fifths law becomes valid for (Taylor-based) Reynolds number R λ values significantly higher than the values usually found in the literature. These questions are addressed in Section 5.…”

“…Qian [21] made a theoretical study of finite Reynolds number effects and found that −S 3 (r)/( r) approaches 4/5 with R −α λ , with 2/3 ≤ α ≤ 1 in homogeneous shear flow turbulence [23] and α = 2/3 for free-decaying isotropic turbulence in agreement with Lindborg's theoretical results [19]. Moisy et al [22] investigated the role of the forcing mechanism in a well-controlled low-temperature helium gas experiment.…”