Internal gravity waves in the ocean: Global and local stability analysis and computation of transient growth

Internal gravity waves that exists in a linearly stratified fluid are particularly important in the deep ocean. Generated at the bottom of oceans, they transport energy over large distances. It is believed that their destabilization enhances turbulent mixing, a necessary ingredient to maintain the meridional oceanic circulation and the deep oceanic stratification. Through fully non-linear and linear direct numerical simulations, we show that the stability of a gravity wave beam, and its transient growth intensity, strongly depend on the generation mechanism. This mechanism can be described by a single control parameter : the horizontal mean flow. For small mean flows, small scale instabilities dominate, as for internal tides excited beams. For strong mean flows, large scale instabilities dominate as for Lee waves; however, small scales can dominate the short-times growth. By computing the linear impulse response of a monochromatic progressive internal wave, we propose an interpretation based on an absolute and convective theory applied to a 2D periodic flow. We show that most of the unstable modes are well described by the classical triadic instability theory, despite being far from the ideal conditions of its application.