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

We develop a mean-field theory of compressibility effects in turbulent magnetohydrodynamics and passive scalar transport using the quasi-linear approximation and the spectral τ-approach. We find that compressibility decreases the α effect and the turbulent magnetic diffusivity both at small and large magnetic Reynolds numbers, R_m. Similarly, compressibility decreases the turbulent diffusivity for passive scalars both at small and large Péclet numbers, P_e. On the other hand, compressibility does not affect the effective pumping velocity of the magnetic field for large R_m, but it decreases it for small R_m. 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.