A wind-driven model of the ocean surface layer with wave radiation physics

Surface windstress transfers energy to the surface mixed layer of the ocean, and this energy partly radiates as internal gravity waves with near-inertial frequencies into the stratified ocean below the mixed layer where it is available for mixing. Numerical and analytical models provide estimates of the energy transfer into the mixed layer and the fraction radiated into the interior, but with large uncertainties, which we aim to reduce in the present study. An analytical slab model of the mixed layer used before in several studies is extended by consistent physics of wave radiation into the interior. Rayleigh damping, controlling the physics of the original slab model, is absent in the extended model and the wave-induced pressure gradient is resolved. The extended model predicts the energy transfer rates, both in physical and wavenumber-frequency space, associated with the wind forcing, dissipation in the mixed layer, and wave radiation at the base as function of a few parameters: mixed layer depth, Coriolis frequency and Brunt-Vaisala frequency below the mixed layer, and parameters of the applied windstress spectrum. The results of the model are satisfactorily validated with a realistic numerical model of the North Atlantic Ocean.