  I discuss the role of self-gravity and radiative heating and cooling in
shaping the nature of the turbulence in the interstellar medium (ISM) of our
galaxy. The heating and cooling cause it to be highly compressible, and, in
some regimes of density and temperature, to become thermally unstable, tending
to spontaneously segregate into warm/diffuse and cold/dense phases. On the
other hand, turbulence is an inherently mixing process, tending to replenish
the density and temperature ranges that would be forbidden under thermal
processes alone. The turbulence in the ionized ISM appears to be transonic
(i.e, with Mach numbers $\Ms \sim 1$), and thus to behave essentially
incompressibly. However, in the neutral medium, thermal instability causes the
sound speed of the gas to fluctuate by up to factors of $\sim 30$, and thus the
flow can be highly supersonic with respect to the dense/cold gas, although
numerical simulations suggest that this behavior corresponds more to the
ensemble of cold clumps than to the clumps' internal velocity dispersion.
Finally, coherent large-scale compressions in the warm neutral medium (induced
by, say, the passage of spiral arms or by supernova shock waves) can produce
large, dense molecular clouds that are subject to their own self-gravity, and
begin to contract gravitationally. Because they are populated by nonlinear
density fluctuations, whose local free-fall times are significantly smaller
than that of the whole cloud, the fluctuations terminate their collapse
earlier, giving rise to a regime of hierarchical gravitational fragmentation,
with small-scale collapses occurring within larger-scale ones. Thus, the
"turbulence" in molecular clouds may be dominated by a gravitationally
contracting component at all scales.
