  Molecular clouds have broad linewidths suggesting turbulent supersonic
motions in the clouds. These motions are usually invoked to explain why
molecular clouds take much longer than a free-fall time to form stars. It has
classically been thought that supersonic hydrodynamical turbulence would
dissipate its energy quickly, but that the introduction of strong magnetic
fields could maintain these motions. In a previous paper it has been shown,
however, that isothermal, compressible, MHD and hydrodynamical turbulence decay
at virtually the same rate, requiring that constant driving occur to maintain
the observed turbulence. In this paper direct numerical computations of
uniformly driven turbulence with the ZEUS astrophysical MHD code are used to
derive the absolute value of energy dissipation as a function of the driving
wavelength and amplitude. The ratio of the formal decay time of turbulence
E_{kin}/\dot{E}_{kin} to the free-fall time of the gas can then be derived as a
function of the ratio of driving wavelength to Jeans wavelength and rms Mach
number, and shown to be most likely far less than unity, again showing that
turbulence in molecular clouds must be constantly and strongly driven.
(abridged)
