On the Evolution of a Wind-Generated Inertial Wave in a Vortex Dipole

Olivier Asselin, Scripps Institution of Oceanography, UC San Diego, United States, Leif N Thomas, Stanford University, Stanford, CA, United States, William R Young, University of California, La Jolla, CA, United States and Luc Rainville, University of Washington, Seattle, WA, United States
The Near-Inertial Shear and Kinetic Energy in the North Atlantic experiment (NISKINe) provided the first direct evidence of wind-generated near-inertial wave refraction by geostrophic vorticity. As reported in a companion observational study, vorticity in the flow caused local shifts in the wave frequency. A few inertial periods following the generating storm, a wave beam is observed at depth, consistent with propagation of wave energy downwards and towards the negative vorticity region. To rationalize these observations, we employ the model of Young & Ben Jelloul (1997) and describe the evolution of an inertial oscillation initially confined to the mixed layer in a fixed barotropic geostrophic flow. We first consider an idealized dipole flow with constant stratification. Wave energy in the mixed layer is rapidly focused into negative vortices, which then act as near-inertial waveguides that drain wave energy downwards into the deeper ocean. Wave beams are seen most clearly in regions of large vorticity gradient. Along the axis joining the vortex cores, one may derive a leading-order analytical solution describing a monochromatic near-inertial wave propagation downwards and towards the anticyclone. It is found that both its horizontal and vertical wavenumbers grow linearly with time, such that the slope of the wave beam does not vary in time. The horizontal wavenumber grows proportionally to the local vorticity gradient, whereas the vertical wavenumber additionally depends on depth and stratification. In this simple model, the characteristics of the wave beam can thus be predicted with knowledge of the local vorticity gradient, stratification and depth alone. These relations provide useful guidance to analyze simulations with the more realistic flow and stratification profiles mimicking the NISKINe observations. Both the frequency shift and the wave beams are reproduced qualitatively in the model. Quantitative discrepancies and their potential sources are discussed.