  We study the properties of ISM substructure and turbulence in hydrodynamic
(AMR) galaxy simulations with resolutions up to 0.8 pc and 5x10^3 Msun. We
analyse the power spectrum of the density distribution, and various components
of the velocity field. We show that the disk thickness is about the average
Jeans scale length, and is mainly regulated by gravitational instabilities.
From this scale of energy injection, a turbulence cascade towards small-scale
is observed, with almost isotropic small-scale motions. On scales larger than
the disk thickness, density waves are observed, but there is also a full range
of substructures with chaotic and strongly non-isotropic gas velocity
dispersions. The power spectrum of vorticity in an LMC-sized model suggests
that an inverse cascade of turbulence might be present, although energy input
over a wide range of scales in the coupled gaseous+stellar fluid could also
explain this quasi-2D regime on scales larger than the disk scale height.
Similar regimes of gas turbulence are also found in massive high-redshift disks
with high gas fractions. Disk properties and ISM turbulence appear to be mainly
regulated by gravitational processes, both on large scales and inside dense
clouds. Star formation feedback is however essential to maintain the ISM in a
steady state by balancing a systematic gas dissipation into dense and small
clumps. Our galaxy simulations employ a thermal model based on a barotropic
Equation of State (EoS) aimed at modelling the equilibrium of gas between
various heating and cooling processes. Denser gas is typically colder in this
approach, which is shown to correctly reproduce the density structures of a
star-forming, turbulent, unstable and cloudy ISM down to scales of a few
parsecs.
