Thermal and Magnetorotational Instability in the Interstellar Medium

We have performed three sets of numerical experiments designed to study turbulence in the interstellar medium (ISM) driven by the magnetorotational instability. Our models are local, account for galactic rotation and shear, include magnetic fields, and a cooling function which permits two stable phases of gas in pressure equilibrium. The first set of simulations was performed in two dimensions, in the radial-vertical plane. These simulations laid the groundwork for the future 3D models to come. The numerical method for including the cooling function, as well as conduction, was developed and implemented. These simulations gave us a glimpse into the workings of the MRI in the presence of a two-phase medium. In our second set of simulations we extend our models to three dimensions. This allowed us to study the saturated state of the MRI in the presence of a two-phase medium. The scaling of velocity dispersion with density was found to be steeper than that of single phase models, so that at low densities larger turbulent amplitudes were found. The interaction between MRI driven turbulence and the phase structure of the gas was examined in detail. We concluded that turbulence can drive gas into a thermally unstable state, but a two phase model of the ISM was still a fairly good approximation. Finally, we added vertical gravity to our third set of models. Now, rather than specify the mean density, the vertical distribution of gas in the simulation domain is determined self-consistently. In these models cold dense clouds form due to TI and sink to the mid-plane. Turbulence driven by the MRI thickens the disk compared to non-turbulent models by as much as 100%. Turbulent amplitudes in the cold medium are relatively low, however, as the increased concentration of cold clouds near the mid-plane keep them relatively isolated from the more turbulent warm medium. Whether or not the MRI is a significant source of turbulence in the ISM is still a question without a definitive answer, but this thesis has made significant progress in furthering our understanding of the behavior of the MRI in a two-phase medium