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The turbulent and wavy upper ocean: transition from geostrophic flows to internal waves and stimulated generation of near-inertial waves


We study the mesoscale to submesoscale (10-300 km) dynamics of the upper ocean, with particular attention to the partitioning between geostrophic flows and internal waves, and the interaction between these two types of flow. Using 13 years of shipboard ADCP transects in Drake Passage, we show that internal waves account for more than half of the upper-ocean kinetic energy at scales between 10-40 km; a transition from the dominance of geostrophic flow to inertia-gravity waves occurs at 40 km. We further show that a global numerical model with embedded tides reproduces this partitioning between upper-ocean geostrophic flows and inertia-gravity waves. Using the output of this model, we show that in the Kuroshio Extension upper-ocean submesoscale (10-100 km) geostrophic flow and inertia-gravity waves undergo vigorous seasonal cycles that are out of phase: geostrophic flows peak in late winter/early spring, while the projection of inertia-gravity waves at the surface peaks in late summer/early fall.

The observational and modeling evidence of the importance of both geostrophic flows and internal gravity waves at mesoscales to submesoscales hints on the interaction between these two types of flow. To better understand these interactions, we analyze a simple model that couples barotropic quasi-geostrophic flow and near-inertial waves. There are two mechanisms of energy transfer from geostrophic flow to externally forced near-inertial waves: the refractive convergence of the wave action density into anti-cyclones (and divergence from cyclones); and the enhancement of wave-field gradients by geostrophic straining. Unforced inviscid numerical solutions of this reduced model reveal that geostrophic straining accounts for most of stimulated generation, which represents 10-20$\%$ of the decay of the initial balanced energy. Consideration of the dissipative problem reveals that wave dissipation generates both quasi-geostrophic potential vorticity locally and geostrophic kinetic energy. And this wave streaming mechanism is non-negligible in forced-dissipative solutions, which equilibrate even without bottom drag.

In a separate study, we derive a Galerkin approximation for the surface-active quasi-geostrophic system using standard vertical modes. While the Galerkin expansions of streamfunction and potential vorticity do not satisfy the inversion relation exactly, the series converge with no Gibbs oscillations. With enough modes, the Galerkin series provide a good approximation to the streamfunction throughout the domain, which can be used to advect potential vorticity in the interior and buoyancy at the surfaces.

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