Shock propagation and neutrino oscillation in supernova

The effect of the shock propagation on neutrino oscillation in supernova is studied paying attention to evolution of average energy of ${\nu }_e$ and ${\bar{\nu }}_e$. We show that the effect appears as a decrease in average ${\nu }_e$ (in case of inverted mass hierarchy, ${\bar{\nu }}_e$) energy at stellar surface as the shock propagates. It is found that the effect is significant 2 seconds after bounce if $3 \times 10^{-5} < \sin^{2}{\theta_{13}} < 10^{-2}$.