  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 Alfvenic
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 (aspredicted by small-amplitude theory) in the
region of the stratified cloud which 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
$\sigma \propto Z^{0.5}$, where $Z$ is a characteristic size of the
cloud.Furthermore, $\sigma$ is always comparable to the mean Alfven velocity of
the cloud, consistent with observational results.
