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 $3 \times 10^{-5} < \sin^{2}{\theta_{13}} < 10^{-2}$.