A general vector field coupled to a strongly compressible turbulent flow

TL;DR

This paper models a transverse vector field passively advected by a strongly compressible turbulent flow, establishing its large-scale scaling behavior through a renormalizable field theoretic approach.

Contribution

It introduces a general ${\

Findings

Establishes the scaling behavior of a passively advected vector field in compressible turbulence.

Shows the model is equivalent to a renormalizable field theory with an infrared fixed point.

Highlights the limitation of the one-loop approximation in determining the fixed-point value of parameter ${\

Abstract

We consider the model of a transverse vector (e.g. magnetic) field with the most general form of the nonlinearity, known as the ${\cal A}$ model, passively advected by a strongly compressible turbulent flow, governed by the randomly stirred Navier-Stokes equation. The full stochastic problem is equivalent to a certain renormalizable field theoretic model with an infrared attractive fixed point. Thus, the scaling behaviour for the large-scale, long-distance behaviour is established. However, the question whether the parameter ${\cal A}$ tends to a certain fixed-point value of the renormalization group equations or remains arbitrary, cannot be answered within the one-loop approximation of our study.