Turbulence Generation by Shock-Acoustic-Wave Interaction in Core-Collapse Supernovae

Convective instabilities in the advanced stages of nuclear shell burning can play an important role in neutrino-driven supernova explosions. In our previous work, we studied the interaction of vorticity and entropy waves with the supernova shock using a linear perturbations theory. In this paper, we extend our work by studying the effect of acoustic waves. As the acoustic waves cross the shock, the perturbed shock induces a field of entropy and vorticity waves in the post-shock flow. We find that, even when the upstream flow is assumed to be dominated by sonic perturbations, the shock-generated vorticity waves contain most of the turbulent kinetic energy in the post-shock region, while the entropy waves produced behind the shock are responsible for most of the density perturbations. The entropy perturbations are expected to become buoyant as a response to the gravity force and then generate additional turbulence in the post-shock region. This leads to a modest reduction of the critical neutrino luminosity necessary for producing an explosion, which we estimate to be less than $ \sim 5 \% $.