  In this study we investigate the formation and properties of prestellar and
protostellar cores using hydrodynamic, self-gravitating Adaptive Mesh
Refinement simulations, comparing the cases where turbulence is continually
driven and where it is allowed to decay. We model observations of these cores
in the C$^{18}$O$(2\to 1)$, NH$_3(1,1)$, and N$_2$H$^+(1\to 0)$ lines, and from
the simulated observations we measure the linewidths of individual cores, the
linewidths of the surrounding gas, and the motions of the cores relative to one
another. Some of these distributions are significantly different in the driven
and decaying runs, making them potential diagnostics for determining whether
the turbulence in observed star-forming clouds is driven or decaying. Comparing
our simulations with observed cores in the Perseus and $\rho$ Ophiuchus clouds
shows reasonably good agreement between the observed and simulated core-to-core
velocity dispersions for both the driven and decaying cases. However, we find
that the linewidths through protostellar cores in both simulations are too
large compared to the observations. The disagreement is noticably worse for the
decaying simulation, in which cores show highly supersonic infall signatures in
their centers that decrease toward their edges, a pattern not seen in the
observed regions. This result gives some support to the use of driven
turbulence for modeling regions of star formation, but reaching a firm
conclusion on the relative merits of driven or decaying turbulence will require
more complete data on a larger sample of clouds as well as simulations that
include magnetic fields, outflows, and thermal feedback from the protostars.
