Explosive instability due to flow over a rippled bottom

In this paper, we study Bragg resonance, i.e., the triad interaction between surface and/or interfacial waves with a bottom ripple, in the presence of background velocity. We show that when one of the constituent waves of the triad has negative energy, the amplitudes of all the waves grow exponentially. This is very different from classic Bragg resonance in which one wave decays to cause the growth of the other. The instabilities we observe are "explosive" and are different from normal mode shear instabilities since our velocity profiles are linearly stable. Our work may explain the existence of large-Amplitude internal waves over periodic bottom ripples in the presence of tidal flow observed in oceans and estuaries.