Radiative damping of near-inertial oscillations in the mixed layer

An idealized model of the transmission of near-inertial waves from the mixe d layer into the deeper ocean is studied in order to assess the combined ef fects of background geostrophic vorticity and the planetary vorticity gradi ent. The model geostrophic flow is steady and barotropic with a streamfunct ion psi = -Psi cos(2 alpha gamma); the planetary vorticity gradient is mode led using the beta-effect. After projection onto vertical modes, each modal amplitude satisfies a Schrodinger-like wave equation (in gamma and t) in w hich beta gamma + (psi(gamma gamma)/2) plays the role of a potential. With realistic parameter values, this potential function has a periodically spac ed set of minima inclined by the beta-effect. The initial near-inertial excitation is horizontally uniform, but strong sp atial modulations rapidly develop: at 20 days the near-inertial energy leve l is largest near the minima of the beta gamma + (psi(gamma gamma)/2) poten tial. Near the maxima of the beta gamma + (psi(gamma gamma)/2) potential, t he mixed-layer near-inertial energy rapidly decreases, but, at these same h orizontal locations, energy maxima appear immediately below the base of the mixed layer. The beta-effect and the geostrophic vorticity act in concert to produce a r apid vertical transmission of near-inertial energy and shear. Because of th is radiation damping, the energy density of the spatially averaged, near-in ertial oscillations in the mixed layer falls to about 10% of the initial le vel after 15 days. However, at the minima of the beta gamma + (psi(gamma ga mma)/2) potential, concentrations of near-inertial energy persist in the mi xed layer for at least forty days.