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

We compute 3D models of supersonic, sub-Alfvénic, and super-Alfvénic 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 $t^{-\eta }$, with $0.85<\mathrm{}\eta <1.2\mathrm{}$. 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.