  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.
