Compressibility in turbulent MHD and passive scalar transport: mean-field theory

TL;DR

This paper develops a mean-field theory to analyze how compressibility influences turbulent magnetohydrodynamics and passive scalar transport, revealing that compressibility generally reduces turbulent effects and introduces new scalar pumping mechanisms.

Contribution

It introduces a novel mean-field theoretical framework for understanding compressibility effects in turbulent MHD and passive scalar transport, including new insights into scalar pumping phenomena.

Findings

Compressibility decreases the alpha effect and turbulent magnetic diffusivity.

Compressibility reduces turbulent diffusivity for passive scalars at all Reynolds and Péclet numbers.

A new passive scalar pumping effect from low to high turbulent intensity regions is identified.

Abstract

We develop a mean-field theory of compressibility effects in turbulent magnetohydrodynamics and passive scalar transport using the quasi-linear approximation and the spectral $\tau$-approach. We find that compressibility decreases the $\alpha$ effect and the turbulent magnetic diffusivity both at small and large magnetic Reynolds numbers, Rm. Similarly, compressibility decreases the turbulent diffusivity for passive scalars both at small and large P\'eclet numbers, Pe. On the other hand, compressibility does not affect the effective pumping velocity of the magnetic field for large Rm, but it decreases it for small Rm. Density stratification causes turbulent pumping of passive scalars, but it is found to become weaker with increasing compressibility. No such pumping effect exists for magnetic fields. However, compressibility results in a new passive scalar pumping effect from regions of low to high turbulent intensity both for small and large P\'eclet numbers. It can be interpreted as compressible turbophoresis of noninertial particles and gaseous admixtures, while the classical turbophoresis effect exists only for inertial particles and causes them to be pumped to regions with lower turbulent intensity.