ENHANCED DISPERSION OF NEAR-INERTIAL WAVES IN AN IDEALIZED GEOSTROPHIC FLOW

This paper presents a simplified model of the process through which a geostrophic flow enhances the vertical propagation of near-inertial ac tivity from the mixed layer into the deeper ocean. The geostrophic flo w is idealized as steady and barotropic with a sinusoidal dependence o n the north-south coordinate; the corresponding streamfunction takes t he form psi = -Psi cos(2 alpha y). Near-inertial oscillations are cons idered in linear theory and disturbances are decomposed into horizonta l and vertical normal modes. For this particular flow, the horizontal modes are given in terms of Mathieu functions. The initial-value probl em can then be solved by projecting onto this set of normal modes. A d etailed solution is presented for the case in which the mixed layer is set into motion as a slab. There is no initial horizontal structure i n the model mixed layer; rather, horizontal structure, such as enhance d near-inertial energy in regions of negative vorticity, is impressed on the near-inertial fields by the pre-existing geostrophic flow. Many details of the solution, such as the rate at which near-inertial acti vity in the mixed layer decays, are controlled by the nondimensional n umber, Upsilon = 4 Psi f(0)/(HmixNmix2)-N-2, where f(0) is the inertia l frequency, H-mix is the mixed layer depth, and N-mix is the buoyancy frequency immediately below the base of the mixed layer. When Upsilon is large, near-inertial activity in the mixed layer decays on a time- scale HmixNmix/alpha(2) Psi(3/2)f(0)(1/2). When Upsilon is small, near -inertial activity in the mixed layer decays on a time-scale proportio nal to (NmixHmix2)-H-2/alpha(2) Psi(2)f(0).