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Generation and stability of inertia–gravity waves

Published online by Cambridge University Press:  04 November 2016

P. Maurer ,
S. Joubaud  and
P. Odier
P. Maurer*
Affiliation:
Univ Lyon, Ens de Lyon, Univ Claude Bernard Lyon 1, CNRS, Laboratoire de Physique, F-69342 Lyon, France
S. Joubaud*
Affiliation:
Univ Lyon, Ens de Lyon, Univ Claude Bernard Lyon 1, CNRS, Laboratoire de Physique, F-69342 Lyon, France
P. Odier*
Affiliation:
Univ Lyon, Ens de Lyon, Univ Claude Bernard Lyon 1, CNRS, Laboratoire de Physique, F-69342 Lyon, France
*
†Email addresses for correspondence: paco.maurer@ens-lyon.fr, sylvain.joubaud@ens-lyon.fr, philippe.odier@ens-lyon.fr
†Email addresses for correspondence: paco.maurer@ens-lyon.fr, sylvain.joubaud@ens-lyon.fr, philippe.odier@ens-lyon.fr
†Email addresses for correspondence: paco.maurer@ens-lyon.fr, sylvain.joubaud@ens-lyon.fr, philippe.odier@ens-lyon.fr
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Abstract

In the ocean, stratification and rotation allow for the existence of inertia–gravity waves. Instabilities of these waves, such as triadic resonant instability (TRI), may play a key role in the mixing process of the deep ocean. In an experimental set-up, we generate inertia–gravity waves which may become unstable depending on the background rotation and wave frequency. The instability produces secondary waves that match the spatial and temporal resonance conditions of TRI. The effect of rotation is introduced in a pre-existing theory and results in a prediction of the growth rate of TRI in the case of an infinite plane wave. The issue of finite size of the beam is then addressed using a simple model in which we show that the instability is enhanced in a given range of Coriolis parameter. Finally, we compare the experimental threshold of the instability with the model, and find good agreement except at higher rotation rate. At constant primary wave frequency, we analyse the evolution of the secondary wave characteristics with rotation. The appearance of unexpected sub-inertial secondary waves may be related to the discrepancy observed between predicted and experimental thresholds at higher rotation.

JFM classification

Instability: Instability Geophysical and Geological Flows: Internal waves Geophysical and Geological Flows: Waves in rotating fluids
Type
Papers
Information
Journal of Fluid Mechanics , Volume 808 , 10 December 2016 , pp. 539 - 561
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Copyright
© 2016 Cambridge University Press 

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