  Supersonic random motions are observed in dark clouds and are traditionally
interpreted as Alfven waves, but the possibility that these motions are
super-Alfvenic has not been ruled out. In this work we report the results of
numerical experiments in two opposite regimes; M_a ~ 1 and M_a >> 1, where M_a
is the initial Alfvenic Mach number --the ratio of the rms velocity to the
Alfven speed. Our results show that models with M_a >> 1 are consistent with
the observed properties of molecular clouds that we have tested --statistics of
extinction measurements, Zeeman splitting measurements of magnetic field
strength, line width versus integrated antenna temperature of molecular
emission line spectra, statistical B-n relation, and scatter in that relation--
while models with M_a ~ 1 have properties that are in conflict with the
observations. We find that both the density and the magnetic field in molecular
clouds may be very intermittent. The statistical distributions of magnetic
field and gas density are related by a power law, with an index that decreases
with time in experiments with decaying turbulence. After about one dynamical
time it stabilizes at B ~ n^{0.4}. Magnetically dominated cores form early in
the evolution, while later on the intermittency in the density field wins out,
and also cores with weak field can be generated, by mass accretion along
magnetic field lines.
