We study, by means of adaptive mesh refinement hydro- and magnetohydrodynamical simulations that cover a wide range of scales (from kpc to sub-parsec), the dimension of the most dissipative structures and the injection scale of the turbulent interstellar gas, which we find to be about 75 pc, in agreement with observations. This is however smaller than the average size of superbubbles, but consistent with significant density and pressure changes in the ISM, which leads to the break-up of bubbles locally and hence to injection of turbulence. The scalings of the structure functions are consistent with log-Poisson statistics of supersonic turbulence where energy is dissipated mainly through shocks. Our simulations are different from previous ones by other authors as (i) we do not assume an isothermal gas, but have temperature variations of several orders of magnitude and (ii) we have no artificial forcing of the fluid with some ad hoc Fourier spectrum, but drive turbulence by stellar explosions at the Galactic rate, self-regulated by density and temperature thresholds imposed on the ISM gas.
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