  Molecular clouds are observed to be turbulent, but the origin of this
turbulence is not well understood. As a result, there are two different
approaches to simulating molecular clouds, one in which the turbulence is
allowed to decay after it is initialized, and one in which it is driven. We use
the adaptive mesh refinement (AMR) code, Orion, to perform high-resolution
simulations of molecular cloud cores and protostars in environments with both
driven and decaying turbulence. We include self-gravity, use a barotropic
equation of state, and represent regions exceeding the maximum grid resolution
with sink particles. We analyze the properties of bound cores such as size,
shape, linewidth, and rotational energy, and we find reasonable agreement with
observation. At high resolution, the different rates of core accretion in the
two cases have a significant effect on protostellar system development. Clumps
forming in a decaying turbulence environment produce high-multiplicity
protostellar systems with Toomre-Q unstable disks that exhibit characteristics
of the competitive accretion model for star formation. In contrast, cores
forming in the context of continuously driven turbulence and virial equilibrium
form smaller protostellar systems with fewer low-mass members. Our simulations
of driven and decaying turbulence show some statistically significant
differences, particularly in the production of brown dwarfs and core rotation,
but the uncertainties are large enough that we are not able to conclude whether
observations favor one or the other.
