Dissipation and Heating in Supersonic Hydrodynamic and MHD Turbulence

We study energy dissipation and heating by supersonic MHD turbulence in molecular clouds using Athena, a new higher-order Godunov code. We analyze the dependence of the saturation amplitude, energy dissipation characteristics, power spectra, sonic scaling, and indicators of intermittency in the turbulence on factors such as the magnetic field strength, driving scale, energy injection rate, and numerical resolution. While convergence in the energies is reached at moderate resolutions, we find that the power spectra require much higher resolutions that are difficult to obtain. In a 1024^3 hydro run, we find a power law relationship between the velocity dispersion and the spatial scale on which it is measured, while for an MHD run at the same resolution we find no such power law. The time-variability and temperature intermittency in the turbulence both show a dependence on the driving scale, indicating that numerically driving turbulence by an arbitrary mechanism may not allow a realistic representation of these properties. We also note similar features in the power spectrum of the compressive component of velocity for supersonic MHD turbulence as in the velocity spectrum of an initially-spherical MHD blast wave, implying that the power law form does not rule out shocks, rather than a turbulent cascade, playing a significant role in the regulation of energy transfer between spatial scales.