We simulate the reactive-hydrodynamic flow for a variety of convective shell burning epochs in supernova progenitor models. The neutrino-cooled stages of carbon, neon, oxygen, and silicon burning are simulated in two and three dimensions. Even in the absence of rotation significant symmetry breaking occurs (10% in rms variation in thermodynamic variables such as temperature and density). These distortions are caused by turbulent convection interacting with stably stratified boundaries. Strong interactions of multiple active shells is seen; it is mediated by waves generated by convection. Some implications for supernova progenitors are presented.