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We have numerically studied the instability of the spherically symmetricstanding accretion shock wave against non-spherical perturbations. We have inmind the application to the collapse-driven supernovae in the post bouncephase, where the prompt shock wave generated by core bounce is commonlystalled. We take an experimental stand point in this paper. Using sphericallysymmetric, completely steady, shocked accretion flows as unperturbed states, wehave clearly observed both the linear growth and the subsequent nonlinearsaturation of the instability. In so doing, we have employed a realisticequation of state together with heating and cooling via neutrino reactions withnucleons. We have done a mode analysis based on the spherical harmonicsdecomposition and found that the modes with l=1, 2 are dominant not only in thelinear regime, but also after the nonlinear couplings generate various modesand the saturation occurs. Varying the neutrino luminosity, we have constructedthe unperturbed states both with and without a negative entropy-gradient. Wehave found that in both cases the growth of the instability is similar,suggesting the convection does not play a dominant role, which also appears tobe supported by the recent linear analysis of the convection in accretion flowsby Foglizzo et al. The real part of the eigen frequency seems to be mainlydetermined by the advection time rather than by the sound-crossing time.Whatever the cause may be, the instability is favorable for the shock revival.Comment: 28 pages, 9 figures, submitted to Ap

Numerical Analysis of Standing Accretion Shock Instability with Neutrino Heating in Supernova Cores