Scaling relations of compressible MHD turbulence

We study scaling relations of compressible and strongly magnetized turbulence using isothermal numerical simulations with resolution 512(3). We find a good correspondence of our results with the Fleck model of compressible hydrodynamic turbulence. In particular, we find that the density-weighted velocity, i.e., rho(1/3)u, proposed by Kritsuk and coworkers obeys the Kolmogorov scaling, i. e.,epsilon(v) (k) similar to k(-5/3), for the high Mach number turbulence. Similarly, we find that the exponents of the third-order structure functions for stay equal to unity v for all Mach numbers studied. The higher order correlations obey the She-Leveque scalings corresponding to the two- dimensional dissipative structures, and this result does not change with the Mach number either. In contrast to velocity u, which exhibits different scaling parallel and perpendicular to the local magnetic field, the scaling of v is similar in both directions. In addition, we find that the peaks of density create a hierarchy in which both v physical and column densities decrease with the scale in accordance to the Fleck predictions. This hierarchy can be related to ubiquitous small ionized and neutral structures (SINS) in the interstellar gas. We believe that studies of statistics of the column density peaks can provide both a consistency check for the turbulence velocity studies and insight into supersonic turbulence, when the velocity information is not available.