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

The Energy Dissipation Rate of Supersonic, Magnetohydrodynamic Turbulence in Molecular Clouds