# Advection by Compressible Turbulent Flows: Renormalization Group Study of Vector and Tracer Admixture

## TL;DR

This paper uses renormalization group methods to analyze the universal scaling behavior of passive vector and tracer fields advected by compressible turbulent flows near four spatial dimensions.

## Contribution

It extends previous work by applying a double expansion in parameters y and epsilon to study the inertial range behavior of advected fields in compressible turbulence.

## Key findings

- Both advected fields show similar universal scaling at one-loop approximation.
- Critical dimensions of tensor composite operators are calculated in leading order.
- The model demonstrates consistent inertial range asymptotic behavior for passive fields.

## Abstract

Advection-diffusion problems of magnetic field and tracer field are analyzed using the field theoretic perturbative renormalization group. Both advected fields are considered to be passive, i.e., without any influence on the turbulent environment, and advecting velocity field is generated by compressible version of stochastic Navier-Stokes equation. The model is considered in the vicinity of space dimension $d=4$ and is a continuation of previous work [N.V. Antonov et al., Phys. Rev. E 95, 033120 (2017)]. The perturbation theory near the special dimension $d=4$ is constructed within a double expansion scheme in $y$ (which describes scaling behavior of the random force that enters a stochastic equation for the velocity field) and $\epsilon=4-d$. We show that up to one-loop approximation both types of advected fields exhibit similar universal scaling behavior. In particular, we demonstrate this statement on the inertial range asymptotic behavior of the correlation functions of advected fields. The critical dimensions of tensor composite operators are calculated in the leading order of $(y,\epsilon)$ expansion.