Refraction and Straining of Near-Inertial Waves by Barotropic Eddies

Abstract

Fast-moving synoptic-scale atmospheric disturbances produce large-scale near-inertial waves in the ocean mixed layer. In this paper, we analyze the distortion of such waves by smaller-scale barotropic eddies, with a focus on the evolution of the horizontal wavevector k under the effects of straining and refraction. The model is initialized with a horizontally-uniform (k = 0) surface-confined near-inertial wave, which then evolves according to the phase-averaged model of Young and Ben Jelloul. A steady barotropic vortex dipole is first considered. Shear bands appear in the jet region as wave energy propagate downwards and towards anticyclone. When measured at a fixed location, both horizontal and vertical wavenumbers grow linearly with the time t elapsed since generation such that their ratio, the slope of wave bands, is time-independent. Analogy with passive scalar dynamics suggests that straining should result in the exponential growth of |k|. Here instead, straining is ineffective, not only at the jet center, but also in its confluent and diffluent regions. Low modes rapidly escape below the anticyclonic core such that weakly-dispersive high modes dominate in the surface layer. In the weakly-dispersive limit, k=−t∇ζ(x,y,z)/2 provided that (i) the eddy vertical vorticity ζ evolves according to the barotropic quasi-geostrophic equation; and (ii) k = 0 initially. In steady flows, straining is ineffective because k is always perpendicular to the flow. In unsteady flows, straining modifies the vorticity gradient and hence k, and may account for significant wave-eddy energy transfers.