  Observed molecular clouds often appear to have very low star formation
efficiencies and lifetimes an order of magnitude longer than their free-fall
times. Their support is attributed to the random supersonic motions observed in
them. We study the support of molecular clouds against gravitational collapse
by supersonic, gas dynamical turbulence using direct numerical simulation.
Computations with two different algorithms are compared: a particle-based,
Lagrangian method (SPH), and a grid-based, Eulerian, second-order method
(ZEUS). The effects of both algorithm and resolution can be studied with this
method. We find that, under typical molecular cloud conditions, global collapse
can indeed be prevented, but density enhancements caused by strong shocks
nevertheless become gravitationally unstable and collapse into dense cores and,
presumably, stars. The occurance and efficiency of local collapse decreases as
the driving wave length decreases and the driving strength increases. It
appears that local collapse can only be prevented entirely with unrealistically
short wave length driving, but observed core formation rates can be reproduced
with more realistic driving. At high collapse rates, cores are formed on short
time scales in coherent structures with high efficiency, while at low collapse
rates they are scattered randomly throughout the region and exhibit
considerable age spread. We suggest that this naturally explains the observed
distinction between isolated and clustered star formation.
