  Velocity statistics is a direct probe of the dynamics of interstellar
turbulence. Its observational measurements are very challenging due to the
convolution between density and velocity and projection effects. We introduce
the projected velocity structure function, which can be generally applied to
statistical studies of both sub- and super-sonic turbulence in different
interstellar phases. It recovers the turbulent velocity spectrum from the
projected velocity field in different regimes, and when the thickness of a
cloud is less than the driving scale of turbulence, it can also be used to
determine the cloud thickness and the turbulence driving scale. By applying it
to the existing core velocity dispersion measurements of the Taurus cloud, we
find a transition from the Kolmogorov to the Burgers scaling of turbulent
velocities with decreasing length scales, corresponding to the large-scale
solenoidal motions and small-scale compressive motions, respectively. The
latter occupy a small fraction of the volume and can be selectively sampled by
clusters of cores with the typical cluster size indicated by the transition
scale.

Astrophysics of Galaxies;Instrumentation and Methods for Astrophysics