  We study two limiting cases of turbulence forcing in numerical experiments:
solenoidal (divergence-free) forcing, and compressive (curl-free) forcing, and
compare our results to observations reported in the literature. We solve the
equations of hydrodynamics on grids with up to 1024^3 cells for purely
solenoidal and purely compressive forcing. Eleven lower-resolution models with
mixtures of both forcings are also analysed. We find velocity dispersion--size
relations consistent with observations and independent numerical simulations,
irrespective of the type of forcing. However, compressive forcing yields
stronger turbulent compression at the same RMS Mach number than solenoidal
forcing, resulting in a three times larger standard deviation of volumetric and
column density probability distributions (PDFs). We conclude that the strong
dependence of the density PDF on the type of forcing must be taken into account
in any theory using the PDF to predict properties of star formation. We supply
a quantitative description of this dependence. We find that different observed
regions show evidence of different mixtures of compressive and solenoidal
forcing, with more compressive forcing occurring primarily in swept-up shells.
