Density scaling and anisotropy in supersonic magnetohydrodynamic turbulence

We study the statistics of density for supersonic turbulence in a medium with magnetic pressure larger than the gaseous pressure. Our simulations exhibit clumpy density structures, with the contrast increasing with the Mach number. At Mach 10, the densities of some clumps are 3 orders of magnitude higher than the mean density. These clumps give rise to a flat and approximately isotropic density spectrum corresponding to the random distribution of clumps in space. We claim that the clumps originate from our random, isotropic turbulence driving. When the contribution from those clumps is suppressed by studying the logarithm of density, the density statistics exhibit scale-dependent anisotropy consistent with the models in which density structures arise from shearing by Alfven waves. It is noteworthy that originally such models were advocated for the case of low-Mach, nearly incompressible turbulence.