The excitation of spiral density waves through turbulent fluctuations in   accretion discs II: Numerical Simulations with MRI driven turbulence
  We present fully three-dimensional local MRI simulations with the object of studying the excitation of non-axisymmetric spiral density waves that are observed to always be present in such simulations. They are potentially important for affecting protoplanetary migration through the action of associated stochastic gravitational forces and producing residual transport in MHD inactive regions. The simulations we perform are with zero net flux and produce mean activity levels of alpha ~ 0.005. We reveal the nature of the mechanism responsible for the excitation of these waves by determining the time dependent evolution of the Fourier transforms of the participating state variables. The dominant waves are found to have no vertical structure and to be excited during periodically repeating swings in which they change from leading to trailing. The initial phase of the evolution of such a swing is found to be in excellent agreement with that expected from the WKBJ theory developed in a preceding paper by Heinemann & Papaloizou.   We demonstrate that the important source terms causing excitation of the waves are related to a quantity that reduces to the potential vorticity for small perturbations from the background state with no vertical dependence. We find that the root mean square density fluctuations associated with the waves are positively correlated with both this quantity and the general level of hydromagnetic turbulence. The mean angular momentum transport associated with spiral density waves generated in our simulations is estimated to be a significant fraction of that associated with the turbulent Reynolds stress. 
T. Heinemann (University of Cambridge), J. C. B. Papaloizou   (University of Cambridge)