Global instabilities of internal gravity waves

Internal gravity waves are particularly important in the ocean where they are generated by different mechanisms, interaction of currents or tides with topography, or coupling with waves at the thermocline. By their breaking they are thought to influence the deep ocean mixing and so contribute to the thermohaline circulation. We reconsider the experiment and theory of Bourget et al who considered stationary quasi-monochromatic beam to include the influence of a uniform background horizontal flow. Specifically we consider two limit cases: the non translating wave maker in which the waves are stationary and the wave maker translation at the horizontal phase velocity which to the classical lee wave problem of a sinusoidal mountain. We show that the global stability properties of these different flows differ strongly whereas locally they involve the same unstable gravity wave solution. This change in global stability is then linked to the absolute or convective nature of the local instability which are for the first time determined for a periodic base flow and for 2D wave packets.