Abstract
Abstract. 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.
Highlights
The energy exchange between two counter-propagating surface gravity waves mediated by a bottom ripple, otherwise known as the “Bragg resonance”, is a widely known phenomenon in oceanography and coastal engineering (Davies, 1982; Mei, 1985; Kirby, 1986)
Bragg resonance has been traditionally understood in the absence of any background velocity field, and in such scenarios, the amplitude of one wave decays to cause a growth in the amplitude of the other wave
In the presence of a velocity field, we show that it is possible to have an exponential growth in the amplitudes of the waves
Summary
The energy exchange between two counter-propagating surface gravity waves mediated by a bottom ripple, otherwise known as the “Bragg resonance”, is a widely known phenomenon in oceanography and coastal engineering (Davies, 1982; Mei, 1985; Kirby, 1986). Guha: Explosive instability due to flow over a rippled bottom in the context of Bragg resonance would imply that both of its constituent waves have simultaneous growth while keeping the energy of the system conserved (note that the third “wave” constituting the Bragg triad is the bottom ripple). We find that contrary to typical Bragg resonances, in explosive Bragg resonance the amplitude of the waves is not limited by energy considerations This may explain the presence of large-amplitude internal waves over periodic bottom ripples such as those in the Rotterdam waterway (Pietrzak et al, 1990). Such a large-amplitude response was primarily seen during the strong flood tides and the presence of a velocity field was deemed essential for the same. We expect explosive Bragg resonance to be a general phenomenon that can be realized in a variety of systems
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