  We study how the influence of the shock wave appears in neutrino oscillations
and the neutrino spectrum using density profile of adiabatic explosion model of
a core-collapse supernova which is calculated in an implicit Lagrangian code
for general relativistic spherical hydrodynamics. We calculate expected event
rates of neutrino detection at SK and SNO for various theta_{13} values and
both normal and inverted hierarchies. The predicted event rates of bar{nu}_e
and nu_e depend on the mixing angle theta_{13} for the inverted and normal
hierarchies, respectively, and the influence of the shock appears for about 2 -
8 s when sin^2 2 theta_{13} is larger than 10^{-3}. These neutrino signals for
the shock propagation is decreased by < 30 % for bar{nu}_e in inverted (SK) or
by < 15 % for nu_e in normal hierarchy (SNO) compared with the case without
shock. The obtained ratio of the total event for high-energy neutrinos (20 MeV
< E_{nu} < 60 MeV) to low-energy neutrinos (5 MeV < E_{nu} < 20 MeV) is
consistent with the previous studies in schematic semi-analytic or other
hydrodynamic models of the shock propagation. The time dependence of the
calculated ratio of the event rates of high-energy to low-energy neutrinos is a
very useful observable which is sensitive to theta_{13} and hierarchies.
Namely, time-dependent ratio shows clearer signal of the shock propagation that
exhibits remarkable decrease by at most factor \sim 2 for bar{nu}_e in inverted
(SK), whereas it exhibits smaller change by \sim 10 % for nu_e in normal
hierarchy (SNO). Observing time-dependent high-energy to low-energy ratio of
the neutrino events thus would provide a piece of very useful information to
constrain theta_{13} and mass hierarchy, and eventually help understanding the
propagation how the shock wave propagates inside the star.
