We perform numerical simulations of nonlinear MHD waves in a gravitationally stratified molecular cloud that is bounded by a hot and tenuous external medium. We study the relation between the strength of the turbulence and various global properties of a molecular cloud, within a 1.5-dimensional approximation. Under the influence of a driving source of Alfvénic disturbances, the cloud is lifted up by the pressure of MHD waves and reaches a steady state characterized by oscillations about a new time-averaged equilibrium state. The nonlinear effect results in the generation of longitudinal motions and many shock waves; however, the wave kinetic energy remains predominantly in transverse, rather than longitudinal, motions. There is an approximate equipartition of energy between the transverse velocity and fluctuating magnetic field (as predicted by small-amplitude theory) in the region of the stratified cloud that contains most of the mass; however, this relation breaks down in the outer regions, particularly near the cloud surface, where the motions have a standing-wave character. This means that the Chandrasekhar-Fermi formula applied to molecular clouds must be significantly modified in such regions. Models of an ensemble of clouds show that for various strengths of the input energy, the velocity dispersion in the cloud σ ∝ Z0.5, where Z is a characteristic size of the cloud. Furthermore, σ is always comparable to the mean Alfvén velocity of the cloud, consistent with observational results.
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