Does fully developed turbulence exist? Reynolds number independence versus asymptotic covariance
Abstract
By analogy with recent arguments concerning the mean velocity profile of wallbounded 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[(ln Re)^{2}]. In an alternative generic scenario, both the Kolmogorov constant C_{K} and corrections to Kolmogorov's linear relation for the thirdorder 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.
 Publication:

Physics of Fluids
 Pub Date:
 December 1995
 DOI:
 10.1063/1.868685
 arXiv:
 arXiv:condmat/9507132
 Bibcode:
 1995PhFl....7.3078B
 Keywords:

 Condensed Matter;
 High Energy Physics  Theory;
 Nonlinear Sciences  Chaotic Dynamics
 EPrint:
 13 Pages. Tex file and Postscript figure included in uufiles compressed format. Needs macro uiucmac.tex, available from condmat archive or from ftp://gijoe.mrl.uiuc.edu/pub