DOES FULLY-DEVELOPED TURBULENCE EXIST - REYNOLDS-NUMBER INDEPENDENCE VERSUS ASYMPTOTIC COVARIANCE

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 (In 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 LL alternative generic scenario, both the Kolmogorov constant CK and corrections to Kolmogorov's linear relation for the third-order structure function D-LLL(r) are proportional to (In 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. (C) 1995 American Institute of Physics.