Gravity Waves Affecting Geostrophic Balanced Motions in a Rotating Shallow Water

Theoretical and numerical examination of various possible interactions between fast inertia-gravity waves and slow balanced quasi-geostrophic motions is carried out in a rotating shallow water. Using asymptotic analysis, a set of evolution equations will be presented for the potential vorticity. These equations capture the slow dynamics of the rotating shallow water to a higher degree of accuracy than the lowest order approximate model - the quasi-geostrophic equation. These new asymptotic reduced models, whose validity is confirmed by numerical experiments, point out that fast waves can energetically interact with slow balanced motions. The results from asymptotic models will be complemented by a series of high resolution numerical simulations of the rotating shallow water equations in regimes not directly accessible by asymptotic analysis, such as characterizing turbulent wave-vortex interactions. The main findings of these simulations is that the presence of strong waves can significantly impact the balanced motion. For instance, it is observed that wave activity can prevent vortex mergers and inverse cascades, these being well known features of balanced models such as the quasi-geostrophic equation.