Non-ideal MHD turbulent decay in molecular clouds
  It is well known that non-ideal magnetohydrodynamic effects are important in
the dynamics of molecular clouds: both ambipolar diffusion and possibly the
Hall effect have been identified as significant. We present the results of a
suite of simulations with a resolution of 512-cubed of turbulent decay in
molecular clouds incorporating a simplified form of both ambipolar diffusion
and the Hall effect simultaneously. The initial velocity field in the
turbulence is varied from being super-Alfv\'enic and hypersonic, through to
trans-Alfv\'enic but still supersonic.
  We find that ambipolar diffusion increases the rate of decay of the
turbulence increasing the decay from $t^{-1.25}$ to $t^{-1.4}$. The Hall effect
has virtually no impact in this regard. The power spectra of density, velocity
and the magnetic field are all affected by the non-ideal terms, being steepened
significantly when compared with ideal MHD turbulence with exponents. The
density power spectra components change from about 1.4 to about 2.1 for the
ideal and non-ideal simulations respectively, and power spectra of the other
variables all show similar modifications when non-ideal effects are considered.
Again, the dominant source of these changes is ambipolar diffusion rather than
the Hall effect. There is also a decoupling between the velocity field and the
magnetic field at short length scales. The Hall effect leads to enhanced
magnetic reconnection, and hence less power, at short length scales. The
dependence of the velocity dispersion on the characteristic length scale is
studied and found not to be power-law in nature.
