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 perm itted if one insists that the functional form of statistical averages at large Re be invariant under a natural redefinition of Re. The famil y 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 ge neric scenario, both the Kolmogorov constant CK and corrections to Kol mogorov's linear relation for the third-order structure function D-LLL (r) are proportional to (In Re)(-1). Recent experimental data of Prask ovsky and Oncley appear to show a definite dependence of C-K on Re, wh ich, if confirmed, would be consistent with the arguments given here. (C) 1995 American Institute of Physics.