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 \(S(r) \cong cr^{\alpha_0}[\ln(r/\eta)]^{\alpha_1}\), where η 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 α 0=0 can describe turbulence statistics in the near-dissipation range r > η, 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.
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PACS: 47.27.-i, 47.27.Gs.
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Bershadskii, A. Beyond Scaling and Locality in Turbulence. J Stat Phys 128, 721–739 (2007). https://doi.org/10.1007/s10955-007-9322-0
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DOI: https://doi.org/10.1007/s10955-007-9322-0