“Intermittency” in Hydrodynamic Turbulence as Intermediate Asymptotics to Kolmogorov Scaling

Abstract

A physical interpretation of a recent Navier-Stokes based theory for scaling in developed hydrodynamic turbulence is presented. It is proposed that corrections to the normal Kolmogorov scaling behavior of the $n$th order velocity structure functions are finite Reynolds number 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.