Explosive instability due to flow over a rippled bottom

TL;DR

This paper investigates how background flow over rippled bottoms can cause explosive wave instabilities through Bragg resonance, explaining large internal waves in oceans and estuaries.

Contribution

It reveals that negative energy waves can lead to exponential growth of wave amplitudes, introducing a new type of explosive instability in stable shear flows.

Findings

Explosive wave growth occurs when negative energy waves are involved.

The instability mechanism differs from classic shear instabilities.

Results may explain large internal waves over rippled bottoms in natural water bodies.

Abstract

In this paper, we study Bragg resonance, i.e. the triad interaction between surface and/or interfacial waves with bottom ripple, in 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 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 presence of tidal flow observed in oceans and estuaries.