The excitation of spiral density waves through turbulent fluctuations in accretion discs II: Numerical Simulations with MRI driven turbulence

摘要

We present fully three-dimensional local MRI simulations with the object ofstudying the excitation of non-axisymmetric spiral density waves that areobserved to always be present in such simulations. They are potentiallyimportant for affecting protoplanetary migration through the action ofassociated stochastic gravitational forces and producing residual transport inMHD inactive regions. The simulations we perform are with zero net flux andproduce mean activity levels of alpha ~ 0.005. We reveal the nature of themechanism responsible for the excitation of these waves by determining the timedependent evolution of the Fourier transforms of the participating statevariables. The dominant waves are found to have no vertical structure and to beexcited during periodically repeating swings in which they change from leadingto trailing. The initial phase of the evolution of such a swing is found to bein excellent agreement with that expected from the WKBJ theory developed in apreceding paper by Heinemann & Papaloizou. We demonstrate that the important source terms causing excitation of thewaves are related to a quantity that reduces to the potential vorticity forsmall perturbations from the background state with no vertical dependence. Wefind that the root mean square density fluctuations associated with the wavesare positively correlated with both this quantity and the general level ofhydromagnetic turbulence. The mean angular momentum transport associated withspiral density waves generated in our simulations is estimated to be asignificant fraction of that associated with the turbulent Reynolds stress.