On the ERG approach in $3 - d$ Well Developed Turbulence

TL;DR

This paper applies the Renormalization Group method to model well-developed isotropic turbulence, successfully reproducing the Kolmogorov energy spectrum and constants consistent with experimental data.

Contribution

It demonstrates the effectiveness of the RG approach in capturing universal turbulence behavior while preserving Galilei invariance.

Findings

Power law energy spectrum $q^{-5/3}$ confirmed

Kolmogorov constant $C_K$ matches experimental values

Universal behavior related to stochastic forcing observed

Abstract

We apply the method of the Renormalization Group (GR), following the Polchinski point of view, to a model of well developed and isotropic fluid turbulence. The Galilei-invariance is preserved and a universal behavior, related to the change of the stochastic stirring force, is evident by the numerical results in the inertial region, where a scale-invariant behavior also appear. The expected power law of the energy spectrum ($q^{-{5\over 3}}$) is obtained and the Kolmogorov constant $C_K$ agrees with experimental data.