  We develop a new semi-dynamical method to study shock revival by neutrino
heating in core- collapse supernovae. Our new approach is an extension of the
previous studies that employ spherically symmetric, steady, shocked accretion
flows together with the light bulb approximation. The latter has been widely
used in the supernova community for the phenomenological investigation of the
criteria for successful supernova explosions. In the present approach, on the
other hand, we get rid of the steady-state condition and take into account
shock wave motions instead. We have in mind the scenario that not the critical
luminosity but the critical fluctuation generated by hydrodynamical
instabilities such as SASI and neutrino-driven convection in the post-shock
region determines the onset of shock revival. After confirming that the new
approach indeed captures the dynamics of revived shock wave qualitatively, we
then apply the method to various initial conditions and find that there is a
critical fluctuation for shock revival, which can be well fit by the following
formula: f_crit ~ 0.8 * (M_in/1.4M_sun) * {1- (rsh/10^8cm)}, in which fcrit
denotes the critical pressure fluctuation normalized by the unperturbed
post-shock value. Min and rsh stand for the mass of the central compact object
and the shock radius, respectively. The critical fluctuation decreases with the
shock radius, whereas it increases with the mass of the central object. We
discuss the possible implications of our results for 3D effects on shock
revival, which is currently controversial in the supernova community.
