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I model the multi-phase interstellar medium (ISM) randomly heated and shockedby supernovae, with gravity, differential rotation and other parameters weunderstand to be typical of the solar neighbourhood. The simulations are 3Dextending horizontally 1 x 1 kpc squared and vertically 2 kpc, symmetric aboutthe galactic mid-plane. They routinely span gas number densities 1/10000 to 100per cubic cm, temperatures 100 to 100 MK, speeds up to 10000 km/s and Machnumber up to 25. Radiative cooling is applied from two widely adoptedparameterizations, and compared directly to assess the sensitivity of theresults to cooling. There is strong evidence to describe the ISM as comprisingwell defined cold, warm and hot regions, which are statistically close tothermal and total pressure equilibrium. This result is not sensitive to thechoice of parameters considered here. The distribution of the gas densitywithin each can be robustly modelled as lognormal. Appropriate distinction isrequired between the properties of the gases in the supernova active mid-planeand the more homogeneous phases outside this region. The connection between thefractional volume of a phase and its various proxies is clarified. An exactrelation is then derived between the fractional volume and the filling factorsdefined in terms of the volume and probabilistic averages. These results arediscussed in both observational and computational contexts. The correlationscale of the random flows is calculated from the velocity autocorrelationfunction; it is of order 100 pc and tends to grow with distance from themid-plane. The origin and structure of the magnetic fields in the ISM is alsoinvestigated in non-ideal MHD simulations. A seed magnetic field, with volumeaverage of roughly 4 nG, grows exponentially to reach a statistically steadystate within 1.6 Gyr.

Supernovae Driven Turbulence In The Interstellar Medium