  In this study, we conduct three-dimensional hydrodynamic simulations
systematically to investigate the flow patterns behind the accretion shock
waves that are commonly formed in the post-bounce phase of core-collapse
supernovae. Adding small perturbations to spherically symmetric, steady,
shocked accretion flows, we compute the subsequent evolutions to find what flow
pattern emerges as a consequence of hydrodynamical instabilities such as
convection and standing accretion shock instability (SASI) for different
neutrino luminosities and mass accretion rates. Depending on these two
controlling parameters, various flow patterns are indeed realized. We classify
them into three basic patterns and two intermediate ones; the former includes
sloshing 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 the
pattern realization. The sloshing and spiral motions tend to be dominant for
high accretion rates and low neutrino luminosities, and multiple buoyant
bubbles prevail for low accretion rates and high neutrino luminosities. It is
interesting that the dominant pattern is not always identical between the
semi-nonlinear and nonlinear phases near the critical luminosity; the
intermediate cases are realized in the latter case. Running several simulations
with different random perturbations, we confirm that the realization of flow
pattern is robust in most cases.
