Coupled Evolution of Near-inertial Waves and Quasigeostrophic Flow

A fundamental concern of ocean circulation theory are the pathways by which kinetic energy cascades from the large scales of wind forcing, tides, and eddying mesoscale flows to the small scales of internal wave breaking. Near-inertial waves with local Coriolis frequency f₀ are likely a key participant, since they comprise half of the total kinetic energy in oceanic internal waves, have small vertical scales, and are exposed to energetic interaction with non-wave mesoscale and submesoscale flows by their low frequencies and slow propagation. Here, we present an asymptotic model which isolates the nonlinear and coupled co-evolution of near-inertial waves and quasigeostrophic flow from the Boussinesq equations. A principal result of the “NIW-QG” model implied by its two conservation laws is that near-inertial waves — which may be externally forced by winds, tides, or flow-topography interaction — can extract energy from mesoscale or submesoscale quasigeostrophic flows. A second and separate implication of the model is that this wave-flow interaction catalyzes a loss of near-inertial energy to freely propagating near-inertial second harmonic waves with frequency 2f₀. The newly-produced 2f₀ waves both propagate rapidly to depth and transfer energy back to the near-inertial wavefield at very small vertical scales. The upshot of this 2f₀ generation is a two-step mechanism whereby quasigeostrophic flow catalyzes a nonlinear cascade of near-inertial energy to the small scales of wave breaking and mixing.