  The compressibility of molecular cloud (MC) turbulence plays a crucial role
in star formation models, because it controls the amplitude and distribution of
density fluctuations. The relation between the compressive ratio (the ratio of
powers in compressive and solenoidal motions) and the statistics of turbulence
has been previously studied systematically only in idealized simulations with
random external forces. In this work, we analyze a simulation of large-scale
turbulence (250 pc) driven by supernova (SN) explosions that has been shown to
yield realistic MC properties. We demonstrate that SN driving results in MC
turbulence with a broad lognormal distribution of the compressive ratio, with a
mean value $\approx 0.3$, lower than the equilibrium value of $\approx 0.5$
found in the inertial range of isothermal simulations with random solenoidal
driving. We also find that the compressibility of the turbulence is not
noticeably affected by gravity, nor are the mean cloud radial (expansion or
contraction) and solid-body rotation velocities. Furthermore, the clouds follow
a general relation between the rms density and the rms Mach number similar to
that of supersonic isothermal turbulence, though with a large scatter, and
their average gas density PDF is described well by a lognormal distribution,
with the addition of a high-density power-law tail when self-gravity is
included.
