  Turbulent motions are essential to the mixing of entrained fluids and are
also capable of amplifying weak initial magnetic fields by small-scale dynamo
action. Here we perform a systematic study of turbulent mixing in magnetized
media, using three-dimensional magnetohydrodynamic simulations that include a
scalar concentration field. We focus on how mixing depends on the magnetic
Prandtl number, Pm, from 1 to 4 and the Mach number, M}, from 0.3 to 2.4. For
all subsonic flows, we find that the velocity power spectrum has a k^-5/3 slope
in the early, kinematic phase, but steepens due to magnetic back reactions as
the field saturates. The scalar power spectrum, on the other hand, flattens
compared to k^-5/3 at late times, consistent with the Obukohov-Corrsin picture
of mixing as a cascade process. At higher Mach numbers, the velocity power
spectrum also steepens due to the presence of shocks, and the scalar power
spectrum again flattens accordingly. Scalar structures are more intermittent
than velocity structures in subsonic turbulence while for supersonic
turbulence, velocity structures appear more intermittent than the scalars only
in the kinematic phase. Independent of the Mach number of the flow, scalar
structures are arranged in sheets in both the kinematic and saturated phases of
the magnetic field evolution. For subsonic turbulence, scalar dissipation is
hindered in the strong magnetic field regions, probably due to Lorentz forces
suppressing the buildup of scalar gradients, while for supersonic turbulence,
scalar dissipation increases monotonically with increasing magnetic field
strength. At all Mach numbers, mixing is significantly slowed by the presence
of dynamically-important small-scale magnetic fields, implying that mixing in
the interstellar medium and in galaxy clusters is less efficient than modeled
in hydrodynamic simulations.
