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Experimental study of parametric subharmonic instability for internal plane waves

Published online by Cambridge University Press:  16 April 2013

Baptiste Bourget ,
Thierry Dauxois ,
Sylvain Joubaud  and
Philippe Odier
Baptiste Bourget
Affiliation:
Laboratoire de Physique de l’École Normale Supérieure de Lyon, Université de Lyon, CNRS, 46 Allée d’Italie, F-69364 Lyon CEDEX 07, France
Thierry Dauxois*
Affiliation:
Laboratoire de Physique de l’École Normale Supérieure de Lyon, Université de Lyon, CNRS, 46 Allée d’Italie, F-69364 Lyon CEDEX 07, France
Sylvain Joubaud
Affiliation:
Laboratoire de Physique de l’École Normale Supérieure de Lyon, Université de Lyon, CNRS, 46 Allée d’Italie, F-69364 Lyon CEDEX 07, France
Philippe Odier
Affiliation:
Laboratoire de Physique de l’École Normale Supérieure de Lyon, Université de Lyon, CNRS, 46 Allée d’Italie, F-69364 Lyon CEDEX 07, France
*
†Email address for correspondence: Thierry.dauxois@ens-lyon.fr
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Abstract

Internal waves are believed to be of primary importance as they affect ocean mixing and energy transport. Several processes can lead to the breaking of internal waves and they usually involve nonlinear interactions between waves. In this work, we study experimentally the parametric subharmonic instability (PSI), which provides an efficient mechanism to transfer energy from large to smaller scales. It corresponds to the destabilization of a primary plane wave and the spontaneous emission of two secondary waves, of lower frequencies and different wave vectors. Using a time-frequency analysis, we observe the time evolution of the secondary waves, thus measuring the growth rate of the instability. In addition, a Hilbert transform method allows the measurement of the different wave vectors. We compare these measurements with theoretical predictions, and study the dependence of the instability with primary wave frequency and amplitude, revealing a possible effect of the confinement due to the finite size of the beam, on the selection of the unstable mode.

JFM classification

Geophysical and Geological Flows: Geophysical and Geological Flows Geophysical and Geological Flows: Internal waves
Type
Papers
Information
Journal of Fluid Mechanics , Volume 723 , 25 May 2013 , pp. 1 - 20
Copyright
©2013 Cambridge University Press 

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Bourget et al. supplementary movie

Movie presenting the horizontal (left panel) and vertical (right panel) density gradients for $0< t <193 T_0$ where $T_0 = 2\pi/\omega_0$ is the primary wave period. The wave is propagating from left to the right. Note that the color scale is the same in both panels. The Brunt-V\"ais\"al\"a frequency is $N = 0.91$ rad/s, the primary wave frequency is $\omega_0/N = 0.74$ and the motion amplitude of the plates of the generator is 0.5 cm.

Download Bourget et al. supplementary movie(Video)
Video 8.7 MB