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 $\unicode[STIX]{x1D70F}$-approach. We find that compressibility decreases the $\unicode[STIX]{x1D6FC}$ 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 Péclet 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 Péclet numbers. It can be interpreted as compressible turbophoresis of non-inertial 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.
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