  A few seconds after bounce in a core-collapse supernova, the shock wave
passes the density region corresponding to resonant neutrino oscillations with
the ``atmospheric'' neutrino mass difference. The transient violation of the
adiabaticity condition manifests itself in an observable modulation of the
neutrino signal from a future galactic supernova. In addition to the shock wave
propagation effects that were previously studied, a reverse shock forms when
the supersonically expanding neutrino-driven wind collides with the slower
earlier supernova ejecta. This implies that for some period the neutrinos pass
two subsequent density discontinuities, giving rise to a ``double dip'' feature
in the average neutrino energy as a function of time. We study this effect both
analytically and numerically and find that it allows one to trace the positions
of the forward and reverse shocks. We show that the energy dependent neutrino
conversion probabilities allow one to detect oscillations even if the energy
spectra of different neutrino flavors are the same as long as the fluxes
differ. These features are observable in the \bar\nu_e signal for an inverted
and in the \nu_e signal for a normal neutrino mass hierarchy, provided the
13-mixing angle is ``large'' (sin^2\theta_{13}\gg 10^{-5}).
