Renormalization group analysis of a turbulent compressible fluid near $d = 4$ : Crossover between local and non-local scaling regimes

TL;DR

This paper investigates the scaling behavior of a compressible turbulent fluid near four dimensions using renormalization group analysis, revealing a new fixed point that could influence turbulence scaling regimes.

Contribution

It introduces the possibility of a new scaling regime in compressible turbulence at four dimensions, expanding understanding of turbulence universality classes.

Findings

Existence of an additional fixed point in the RG flow.

Potential crossover between local and non-local scaling regimes.

Implication of a new turbulence scaling behavior near d=4.

Abstract

We study scaling properties of the model of fully developed turbulence for a compressible fluid, based on the stochastic Navier-Stokes equation, by means of the field theoretic renormalization group (RG). The scaling properties in this approach are related to fixed points of the RG equation. Here we study a possible existence of other scaling regimes and an opportunity of a crossover between them. This may take place in some other space dimensions, particularly at $d = 4$. A new regime may there arise and then by continuity moves into $d = 3$. Our calculations have shown that there really exists an additional fixed point, that may govern scaling behaviour.