Anomalous Scaling in Kolmogorov-1941 Turbulence

We show that the Kolmogorov-1941 picture of fully developed hydrodynamic turbulence (with the scaling of the structure functions Sn(R) ∝ Rn/3) necessarily leads to an anomalous scaling for correlation functions which include the rate of energy dissipation e(t,r), these correlation functions being described by an independent index. The mechanism for anomalous scaling, suggested on the basis of the Navier-Stokes equation, is the multi-step interaction of eddies from the inertial interval with eddies at the viscous scale via a set of eddies of intermediate scales.