Physics – Condensed Matter
Scientific paper
1995-07-30
Physics
Condensed Matter
13 Pages. Tex file and Postscript figure included in uufiles compressed format. Needs macro uiucmac.tex, available from cond-m
Scientific paper
10.1063/1.868685
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 $(\ln\,\Re)^{-1}$ 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 $D_{LL}(r, \Re)$ for different values of Re is bounded by an envelope. In one generic scenario, close to the envelope, $D_{LL}(r, \Re)$ 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 $(\ln\,\Re)^{-1}$. 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.
Barenblatt Grigory I.
Goldenfeld Nigel
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