  The neutrinos detected from the next Galactic core-collapse supernova will
contain valuable information on the internal dynamics of the explosion. One
mechanism leading to a temporal evolution of the neutrino signal is the
variation of the induced neutrino flavor mixing driven by changes in the
density profile. With one and two dimensional hydrodynamical simulations we
identify the behavior and properties of prominent features of the explosion.
Using these results we demonstrate the time variation of the neutrino crossing
probabilities due to changes in the MSW neutrino transformations as the star
explodes by using the S-matrix - Monte Carlo - approach to neutrino
propagation. After adopting spectra for the neutrinos emitted from the
proto-neutron star we calculate for a Galactic supernova the evolution of the
positron spectra within a water Cerenkov detector and the ratio of charged
current to neutral current event rates for a heavy water - SNO like - detector
and find that these detector signals are feasible probes of a number of
explosion features.
