  We examine the stability of standing, spherical accretion shocks. Accretion
shocks arise in core collapse supernovae (the focus of this paper), star
formation, and accreting white dwarfs and neutron stars. We present a simple
analytic model and use time-dependent hydrodynamics simulations to show that
this solution is stable to radial perturbations. In two dimensions we show that
small perturbations to a spherical shock front can lead to rapid growth of
turbulence behind the shock, driven by the injection of vorticity from the now
non-spherical shock. We discuss the ramifications this instability may have for
the supernova mechanism.
