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Inherently unstable internal gravity waves due to resonant harmonic generation

Published online by Cambridge University Press:  13 December 2016

Yong Liang ,
Ahmad Zareei  and
Mohammad-Reza Alam
Yong Liang
Affiliation:
Applied Science and Technology, University of California, Berkeley, CA 94720, USA
Ahmad Zareei
Affiliation:
Department of Mechanical Engineering, University of California, Berkeley, CA 94720, USA
Mohammad-Reza Alam*
Affiliation:
Applied Science and Technology, University of California, Berkeley, CA 94720, USA Department of Mechanical Engineering, University of California, Berkeley, CA 94720, USA
*
†Email address for correspondence: reza.alam@berkeley.edu
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Abstract

Here we show that there exist internal gravity waves that are inherently unstable, that is, they cannot exist in nature for a long time. The instability mechanism is a one-way (irreversible) harmonic-generation resonance that permanently transfers the energy of an internal wave to its higher harmonics. We show that, in fact, there are a countably infinite number of such unstable waves. For the harmonic-generation resonance to take place, the nonlinear terms in the free surface boundary condition play a pivotal role, and the instability does not occur in a linearly stratified fluid if a simplified boundary condition, such as a rigid lid or a linearized boundary condition, is employed. Harmonic-generation resonance presented here provides a mechanism for the transfer of internal wave energy to the higher-frequency part of the spectrum hence affecting, potentially significantly, the evolution of the internal waves spectrum.

JFM classification

Geophysical and Geological Flows: Internal waves Instability: Nonlinear instability
Type
Papers
Information
Journal of Fluid Mechanics , Volume 811 , 25 January 2017 , pp. 400 - 420
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Copyright
© 2016 Cambridge University Press 

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