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Generation and stability of inertia-gravity waves. (English) Zbl 1383.76146

Summary: 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.

MSC:

76E09 Stability and instability of nonparallel flows in hydrodynamic stability
76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction
76U05 General theory of rotating fluids
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