The supernova-driven interstellar medium in star-forming galaxies has Reynolds numbers of the order of $10^{6}$ or even larger. We study, by means of adaptive mesh refinement hydro- and magnetohydrodynamical simulations that cover the full available range (from 10 kpc to sub-parsec) scales, the statistical properties of the turbulent interstellar gas and the dimension of the most dissipative structures. The scalings of the structure functions are consistent with a log-Poisson statistics of supersonic turbulence where energy is dissipated mainly through shocks.
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