Does Fully-Developed Turbulence Exist? Reynolds Number Independence versus Asymptotic Covariance

G. I. Barenblatt; Nigel Goldenfeld

doi:10.1063/1.868685

paper

Does Fully-Developed Turbulence Exist? Reynolds Number Independence versus Asymptotic Covariance

arXiv:cond-mat/9507132 · doi:10.1063/1.868685

Abstract

By analogy with recent arguments concerning the mean velocity profile of wall-bounded turbulent shear flows, we suggest that there may exist corrections to the 2/3 law of Kolmogorov, which are proportional to $(ln ℜ)^{- 1}$ at large Re. Such corrections to K41 are the only ones permitted if one insists that the functional form of statistical averages at large Re be invariant under a natural redefinition of Re. The family of curves of the observed longitudinal structure function $D_{LL} (r, ℜ)$ for different values of Re is bounded by an envelope. In one generic scenario, close to the envelope, $D_{LL} (r, ℜ)$ is of the form assumed by Kolmogorov, with corrections of $O((\lnRe)^{-2})$. In an alternative generic scenario, both the Kolmogorov constant $C_{K}$ and corrections to Kolmogorov's linear relation for the third order structure function $D_{LLL} (r)$ are proportional to $(ln ℜ)^{- 1}$ . Recent experimental data of Praskovsky and Oncley appear to show a definite dependence of $C_{K}$ on Re, which if confirmed, would be consistent with the arguments given here.

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"Intermittency" in Hydrodynamic Turbulence as Intermediate Asymptotic to Kolmogorov41 Scaling

Does Fully-Developed Turbulence Exist? Reynolds Number Independence versus Asymptotic Covariance

Abstract

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