  Neutrinos escaping from a core collapse supernova a few seconds after bounce
pass through the shock wave, where they may encounter one or more resonances
corresponding to $\Delta m^2_{\rm atm}$. The neutrino mass eigenstates in
matter may stay coherent between these multiple resonances, giving rise to
oscillations in the survival probabilities of neutrino species. We provide an
analytical approximation to these inevitable phase effects, that relates the
density profile of the shock wave to the oscillation pattern. The phase effects
are present only if the multiple resonances encountered by neutrinos are
semi-adiabatic, which typically happens for $10^{-5} \lsim \sin^2 \theta_{13}
\lsim 10^{-3}$. The observability of these oscillations is severely limited by
the inability of the detectors to reconstruct the neutrino energy faithfully.
For typical shock wave profiles, the detection of these phase effects seems
rather unlikely. However, if the effects are indeed identified in the $\nuebar$
spectra, they would establish inverted hierarchy and a nonzero value of
$\theta_{13}$.
