  The work investigates the coupling between ion-acoustic waves and neutrino
flavor oscillations in a non-relativistic electron-ion plasma under the
influence of a mixed neutrino beam. Neutrino oscillations are mediated by the
flavor polarization vector dynamics in a material medium. The linear dispersion
relation around homogeneous static equilibria is developed. When resonant with
the ion-acoustic mode, the neutrino flavor oscillations can transfer energy to
the plasma exciting a new fast unstable mode in extreme astrophysical
scenarios. The growth rate and the unstable wavelengths are determined in
typical type II supernovae parameters. The predictions can be useful for a new
indirect probe on neutrino oscillations in nature.
