  The hydrodynamic state of the interstellar medium (ISM) heated and randomly
stirred by supernovae (SNe) is investigated. We use a three-dimensional
non-ideal hydrodynamic ISM model in a domain extending 0.5 x 0.5 kpc
horizontally and 2 kpc vertically to explore the relative importance of various
physical and numerical effects on the multi-phase, turbulent ISM. We include
both Type I and II SNe, the latter occurring only in dense regions. First we
investigate the role of the thermal instability in the temperature range
300-6100 K, comparing results obtained for two different cooling functions, one
susceptible to the instability, the other stable. The presence of thermal
instability in the system is mainly visible as the tendency of the gas to avoid
the relevant temperature range, as it quickly evolves towards either colder or
warmer phases. Nevertheless, the formation of dense structures for both cooling
functions appears to be dominated by expanding and colliding supernova
remnants, rather than by the thermal instability. As we need to include a
finite thermal conduction coefficient to resolve the thermal instability with
our uniform grid, we also explore the effects of changing Prandtl number on the
system. The purely divergent SN forcing is found to produce significant amounts
of vorticity. The relative vorticity is around 0.6-0.7 for the highest Prandtl
numbers explored, Pr=40, and is observed to diminish almost by a factor of two
for the lowest Prandtl numbers studied, Pr=1. Rotation laws with angular
velocity decreasing or increasing outwards are investigated, enabling us to
separate the contributions to kinetic helicity due to rotation and shear. When
angular velocity decreases outwards, these two contributions partly cancel each
other, resulting in a smaller net helicity.
