Anomalous Scaling in Kolmogorov--1941 Turbulence

Abstract

We show that the Kolmogorov-1941 picture of fully developed hydrodynamic turbulence (with the scaling of the structure functions $S_n(R)\propto R^{n/3}$) necessarily leads to an anomalous scaling for correlation functions which include the rate of energy dissipation $\epsilon (t,\mathbf{r})$, 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.

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References in corpus (1)

• The multifractal nature of turbulent energy dissipation

Cited by in corpus (5)

• Exact Resummations in the Theory of Hydrodynamic Turbulence: I The Ball of Locality and Normal Scaling
• Towards a Nonperturbative Theory of Hydrodynamic Turbulence:Fusion Rules, Exact Bridge Relations and Anomalous Viscous Scaling Functions
• Exact Resummations in the Theory of Hydrodynamic Turbulence: II A Ladder to Anomalous Scaling
• Exact Resummations in the Theory of Hydrodynamic Turbulence: III. Scenarios for Anomalous Scaling and Intermittency
• Hydrodynamic Turbulence: a 19th Century Problem with a challenge for the 21st Century