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Nonlinear Processes in Geophysics An interactive open-access journal of the European Geosciences Union
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Volume 26, issue 3
Nonlin. Processes Geophys., 26, 283–290, 2019
https://doi.org/10.5194/npg-26-283-2019
© Author(s) 2019. This work is distributed under
the Creative Commons Attribution 4.0 License.
Nonlin. Processes Geophys., 26, 283–290, 2019
https://doi.org/10.5194/npg-26-283-2019
© Author(s) 2019. This work is distributed under
the Creative Commons Attribution 4.0 License.

Research article 21 Aug 2019

Research article | 21 Aug 2019

Explosive instability due to flow over a rippled bottom

Anirban Guha1,2,* and Raunak Raj1,* Anirban Guha and Raunak Raj
  • 1Environmental and Geophysical Fluids Group, Department of Mechanical Engineering, Indian Institute of Technology, Kanpur, U.P. 208016, India
  • 2Institute of Coastal Research, Helmholtz-Zentrum Geesthacht, Geesthacht 21502, Germany
  • *These authors contributed equally to this work.

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.

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Short summary
Waves observed on the ocean surface often nonlinearly interact among themselves and undergo algebraic growth – a mechanism known as resonant triad interaction. Bragg resonance is a special resonant triad in which one of the constituent waves is the ocean's undulating bottom boundary. Here we show that, in the presence of an ocean current, two surface waves or a surface wave and an interfacial wave (wave existing at the ocean pycnocline) can undergo exponential growth.
Waves observed on the ocean surface often nonlinearly interact among themselves and undergo...
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