  We model the complex distribution of atomic hydrogen (HI) in the interstellar
medium (ISM) assuming that it is driven entirely by supernovae (SN). We develop
and assess two different models. In the first approach, the simulated volume is
randomly populated with non-overlapping voids of a range of sizes. This may
relate to a snapshot distribution of supernova-remnant voids, although somewhat
artificially constrained by the non-overlap criterion. In the second approach,
a simplified time evolution (considering momentum conservation as the only
governing constraint during interactions) is followed as SN populate the space
with the associated input mass and energy.
  We describe these simulations and present our results in the form of images
of the mass and velocity distributions and the associated power spectra. The
latter are compared with trends indicated by available observations. In both
approaches, we find remarkable correspondence with the observed statistical
description of well-studied components of the ISM, wherein the spatial spectra
have been found to show significant deviations from the Kolmogorov spectrum.
One of the key indications from this study, regardless of whether or not the
SN-induced turbulence is the dominant process in the ISM, is that the apparent
non-Kolmogorov spectral characteristics (of HI and/or electron column density
across thick or thin screens) needed to explain related observations may not at
all be in conflict with the underlying turbulence (i.e. the velocity structure)
being of Kolmogorov nature. We briefly discuss the limitations of our
simulations and the various implications of our results.
