A Statistical Theory of Isotropic Turbulence Well-Defined within the Context of the $ε$ Expansion

Details A Statistical Theory of Isotropic Turbulence Well-Defined within the Context of the $ε$ Expansion A Statistical Theory of Isotropic Turbulence Well-Defined within the Context of the $ε$ Expansion

2002-02-25

arxiv.org/abs/cond-mat/0202456v2

Physics

Condensed Matter

Statistical Mechanics

16 pages, 2 figures, 4 tables

Scientific paper

10.1140/epjb/e2003-00201-9

A new statistical field-theory model of isotropic turbulence is introduced. The model renormalizes the effects of turbulent stresses into a velocity-gradient-dependent random force. The model is well-defined within the context of the renormalization group $\epsilon$ expansion, as the effective expansion parameter is $O(\epsilon)$. The Kolmogorov constant and $N$ parameter of turbulence are of order unity, in accord with experimental results. Nontrivial intermittency corrections to the single-time structure functions are calculated as a controlled expansion in $\epsilon$.

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