Fast Gravity Waves and Slow Manifolds

High-frequency internal gravity waves are ubiquitous features in rotating stratified flows, and interact nonlinearly with balanced vortices as well as other waves, resulting in energy transfers across multiple scales. Understanding these multiscale exchanges rests on a precise disentangling of internal waves from the balanced flow in a fully nonlinear flow system. This is the focus of this work, which facilitates the understanding of complex nonlinear mechanisms of internal gravity wave generation, such as spontaneous loss of balance, associated with the notion of the 'slow manifold'.

Here I discuss the generation of internal waves by nonlinear processes: spontaneous emission, symmetric instability, and stimulated emission; through different nonlinear flow decomposition methods: nonlinear normal-mode initialization and nonlinear decomposition at higher orders with asymptotic expansion in Rossby number. Wave generation diagnosed with a different approach, namely optimal balance with and without time-averaging is also compared and discussed. An important result is that wave generation by spontaneous emission is generally weak to negligible, becoming significant only at higher orders and high Rossby numbers. Symmetric instability is more effective in wave generation, also at moderate Rossby numbers. Stimulated emission represents a more realistic scenario of wave emission that might be at play in the real ocean conditions, and is expected to be effective even at low Rossby numbers. The results present a new perspective on internal wave energetics in geophysical flows, and call for reevaluation of the energy transfers in and out of the internal gravity wave compartment.