Beyond scaling and locality in turbulence

Abstract

An analytic perturbation theory is suggested in order to find finite-size corrections to the scaling power laws. In the frame of this theory it is shown that the first order finite-size correction to the scaling power laws has following form $S(r)\cong c{r}^{{\alpha }_0}[\ln (r/\eta ){]}^{{\alpha }_1}$, where $\eta$ is a finite-size scale (in particular for turbulence, it can be the Kolmogorov dissipation scale). Using data of laboratory experiments and numerical simulations it is shown shown that a degenerate case with ${\alpha }_0=0$ can describe turbulence statistics in the near-dissipation range $r>\eta$, where the ordinary (power-law) scaling does not apply. For moderate Reynolds numbers the degenerate scaling range covers almost the entire range of scales of velocity structure functions (the log-corrections apply to finite Reynolds number). Interplay between local and non-local regimes has been considered as a possible hydrodynamic mechanism providing the basis for the degenerate scaling of structure functions and extended self-similarity. These results have been also expanded on passive scalar mixing in turbulence. Overlapping phenomenon between local and non-local regimes and a relation between position of maximum of the generalized energy input rate and the actual crossover scale between these regimes are briefly discussed.

extended version

References in corpus (5)

• Non-locality and Intermittency in 3D Turbulence
• Probability Densities in Strong Turbulence
• Intermittency and the passive nature of the magnitude of the magnetic field
• Logarithmic scaling in the near-dissipation range of turbulence
• Hidden Scaling in the Quantum Hall Metal-Insulator Transition

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• Nonlocal interactions versus viscosity in turbulence