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

Abstract

A synopsis of an analytical theory of scaling in developed turbulence is proposed on the basis of the Navier-Stokes equations. It is shown that corrections to the normal Kolmogorov 1941 scaling behavior of the $n$-th order velocity structure functions are finite Re effects which disappear when the inertial interval exceeds 5-6 decades. These corrections originate from the correlation between the velocity differences and energy dissipation which are characterized by an anomalous (subcritical) exponent. The values of the experimentally observed scaling indices for the $n$-th order structure functions for $n$ between 4 and 14 are in agreement with our findings.