Supersonic random motions are observed in dark clouds and are traditionally interpreted as Alfv{e}n 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: beta ~1 and beta << 1, where beta is the ratio of gas pressure and magnetic pressure: beta=P_g/P_m. Our results, combined with observational tests, show that the model with beta ~ 1 is consistent with the observed properties of molecular clouds, while the model with beta << 1 has several properties that are in conflict with the observations. We also 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. Magnetically dominated cores form early in the evolution, while later on the intermittency in the density field wins out.
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