An idealized model of the transmission of near-inertial waves from the mixed layer into the deeper ocean is studied in order to assess the combined effects of background geostrophic vorticity and the planetary vorticity gradient. The model geostrophic flow is steady and barotropic with a streamfunction ψ =-Ψ cos (2αy); the planetary vorticity gradient is modeled using the β-effect. After projection onto vertical modes, each modal amplitude satisfies a Schrödinger-like wave equation (in y and t) in which βy + (ψyy/2) plays the role of a potential. With realistic parameter values, this potential function has a periodically spaced set of minima inclined by the β-effect. The initial near-inertial excitation is horizontally uniform, but strong spatial modulations rapidly develop: at 20 days the near-inertial energy level is largest near the minima of the βy + (ψyy/2) potential. Near the maxima of the βy + (ψyy/2) potential, the mixed-layer near-inertial energy rapidly decreases, but, at these same horizontal locations, energy maxima appear immediately below the base of the mixed layer. The β-effect and the geostrophic vorticity act in concert to produce a rapid vertical transmission of near-inertial energy and shear. Because of this radiation damping, the energy density of the spatially averaged, near-inertial oscillations in the mixed layer falls to about 10% of the initial level after 15 days. However, at the minima of the βy + (ψyy/2) potential, concentrations of near-inertial energy persist in the mixed layer for at least forty days.
Blamforth, N. J., and W. R. Young. 1999. "Radiative damping of near-inertial oscillations in the mixed layer." Journal of Marine Research 57, (4). https://elischolar.library.yale.edu/journal_of_marine_research/2328