GASDYNAMICAL STABILITY OF SHEAR-FLOW IN SPIRAL ARMS OF DISK GALAXIES

Using a linear, finite difference hydrodynamic code, we investigate th e dynamical stability of gas how within the spiral arms of disk galaxi es by considering an initial value problem. Assuming a shock to be pre sent, we test the postshock stability of the flow in the presence of r apidly varying shear, which is characteristic of the region adjacent t o shocks in spiral arms. Our method involves carrying out a linearized perturbation analysis on the postshock flow. The perturbations have a simple plane wave form in the azimuthal direction. We include radial as well as azimuthal velocities in the background flow. The region und er investigation extends from the shock front to the location at which the radial velocity becomes supersonic. This is a semiglobal calculat ion in the sense that its extent is small on a galactic scale but enco mpasses postshock how structure. We do not consider self-gravity here. Despite the existence of several potentially destabilizing elements, the hows examined were found to be linearly stable, in general agreeme nt with millimeter-wave observations of laminar how structure in M51. In particular, the shock is Kelvin-Helmholtz stable, and the inner har dwall boundary conditions do not lead to global Papaloizou-Pringle ins tabilities. The key stabilizing feature of the flow appears to be the presence of radial velocity. We suggest that radial flow stabilizes ga lactic shocks by altering the nature of the dynamics at the corotation radius of the semiglobal mode. Since fluid elements of the unperturbe d system cannot comove with the modal pattern speed, energy exchange i s profoundly affected. This may also at least partly account for why i t is that accretion markedly stabilizes disks that are linearly unstab le to Papaloizou-Pringle modes.