Radiation of mixed layer near-inertial oscillations into the ocean interior

The radiation from the mixed layer into the interior of the ocean of near-inertial oscillations in the presence of the beta effect is reconsidered as an initial-value problem. Making use of the fact that the mixed layer depth is much smaller than the total depth of the ocean, the solution is obtained in the limit of an ocean that is effectively infinitely deep. For a uniform initial condition, analytical results for the velocity, horizontal kinetic energy density, and fluxes are obtained. This is the canonical solution for the radiation of near-inertial oscillations in the vertical, which captures the basic mechanisms due to the beta effect, and leads to the formation of small scales in the vertical. By superposing events, an average vertical wavenumber spectrum is constructed. The predicted decay of near-inertial mixed layer energy in the presence of the beta effect occurs on a timescale similar to that observed.