  To study how supernova feedback structures the turbulent interstellar medium,
we construct 3D models of vertically stratified gas stirred by discrete
supernova explosions, including vertical gravitational field and parametrized
heating and cooling. The models reproduce many observed characteristics of the
Galaxy such as global circulation of gas (i.e., galactic fountain) and the
existence of cold dense clouds in the galactic disk. Global quantities of the
model such as warm and hot gas filling factors in the midplane, mass fraction
of thermally unstable gas, and the averaged vertical density profile are
compared directly with existing observations, and shown to be broadly
consistent. We find that energy injection occurs over a broad range of scales.
There is no single effective driving scale, unlike the usual assumption for
idealized models of incompressible turbulence. However, >90% of the total
kinetic energy is contained in wavelengths shortward of 200 pc. The shape of
the kinetic energy spectrum differs substantially from that of the velocity
power spectrum, which implies that the velocity structure varies with the gas
density. Velocity structure functions demonstrate that the phenomenological
theory proposed by Boldyrev is applicable to the medium. We show that it can be
misleading to predict physical properties such as the stellar initial mass
function based on numerical simulations that do not include self-gravity of the
gas. Even if all the gas in turbulently Jeans unstable regions in our
simulation is assumed to collapse and form stars in local freefall times, the
resulting total collapse rate is significantly lower than the value consistent
with the input supernova rate. Supernova-driven turbulence inhibits star
formation globally rather than triggering it.
