In this study, we conduct three-dimensional hydrodynamic simulationssystematically to investigate the flow patterns behind the accretion shockwaves that are commonly formed in the post-bounce phase of core-collapsesupernovae. Adding small perturbations to spherically symmetric, steady,shocked accretion flows, we compute the subsequent evolutions to find what flowpattern emerges as a consequence of hydrodynamical instabilities such asconvection and standing accretion shock instability (SASI) for differentneutrino luminosities and mass accretion rates. Depending on these twocontrolling parameters, various flow patterns are indeed realized. We classifythem into three basic patterns and two intermediate ones; the former includessloshing motion (SL), spiral motion (SP) and multiple buoyant bubble formation(BB); the latter consists of spiral motion with buoyant-bubble formation (SPB)and spiral motion with pulsationally changing rotational velocities (SPP).Although the post-shock flow is highly chaotic, there is a clear trend in thepattern realization. The sloshing and spiral motions tend to be dominant forhigh accretion rates and low neutrino luminosities, and multiple buoyantbubbles prevail for low accretion rates and high neutrino luminosities. It isinteresting that the dominant pattern is not always identical between thesemi-nonlinear and nonlinear phases near the critical luminosity; theintermediate cases are realized in the latter case. Running several simulationswith different random perturbations, we confirm that the realization of flowpattern is robust in most cases.
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