  We compare velocity structure in the Polaris Flare molecular cloud at scales
ranging from 0.015 pc to 20 pc to simulations of supersonic hydrodynamic and
MHD turbulence computed with the ZEUS MHD code. We use several different
statistical methods to compare models and observations. The Delta-variance
wavelet transform is most sensitive to characteristic scales and scaling laws,
but is limited by a lack of intensity weighting. The scanning-beam
size-linewidth relation is more robust with respect to noisy data. Obtaining
the global velocity scaling behaviour requires that large-scale trends in the
maps not be removed but treated as part of the turbulent cascade. We compare
the true velocity PDF in our models to velocity centroids and average line
profiles in optically thin lines, and find that the line profiles reflect the
true PDF better unless the map size is comparable to the total line-of-sight
thickness of the cloud. Comparison of line profiles to velocity centroid PDFs
can thus be used to measure the line-of-sight depth of a cloud. The observed
density and velocity structure is consistent with supersonic turbulence with a
driving scale at or above the size of the molecular cloud and dissipative
processes below 0.05 pc. Ambipolar diffusion could explain the dissipation. The
velocity PDFs exclude small-scale driving such as that from stellar outflows as
a dominant process in the observed region. In the models, large-scale driving
is the only process that produces deviations from a Gaussian PDF shape
consistent with observations. Strong magnetic fields impose a clear anisotropy
on the velocity field, reducing the velocity variance in directions
perpendicular to the field. (abridged)
