Kinetic Energy Decay Rates of Supersonic and Super-Alfvénic Turbulence in Star-Forming Clouds

We compute 3D models of supersonic, sub-Alfv\'enic, and super-Alfv\'enic decaying turbulence, with an isothermal equation of state appropriate for star-forming interstellar clouds of molecular gas. We find that in 3D the kinetic energy decays as ${t}^{\ensuremath{-}\ensuremath{\eta}}$, with $0.85<\ensuremath{\eta}<1.2$. In 1D magnetized turbulence actually decays faster than unmagnetized turbulence. We compared different algorithms, and performed resolution studies reaching ${256}^{3}$ zones or ${70}^{3}$ particles. External driving must produce the observed long lifetimes and supersonic motions in molecular clouds, as undriven turbulence decays too fast.