A statistical mechanics model of isotropic turbulence well-defined within the context of the $\mathsf{\epsilon}$ expansion

Abstract

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 $\epsilon$.