Stochastic Navier-Stokes equation for a compressible fluid: two-loop approximation

TL;DR

This paper models turbulence in compressible fluids using a stochastic Navier-Stokes equation, applying field theory and renormalization group techniques to identify fixed points and analyze scaling behavior.

Contribution

It introduces a two-loop perturbative analysis of the stochastic Navier-Stokes equation for compressible fluids, advancing understanding of turbulence modeling.

Findings

Two fixed points of the RG equations identified.

Perturbation theory constructed up to two-loop order.

Scaling behavior of random force fluctuations analyzed.

Abstract

A model of fully developed turbulence of a compressible fluid is briefly reviewed. It is assumed that fluid dynamics is governed by a stochastic version of Navier-Stokes equation. We show how corresponding field theoretic-model can be obtained and further analyzed by means of the perturbative renormalization group. Two fixed points of the RG equations are found. The perturbation theory is constructed within formal expansion scheme in parameter $y$, which describes scaling behavior of random force fluctuations. Actual calculations for fixed points' coordinates are performed to two-loop order.