Horizontal dispersion of near-inertial oscillations in a turbulent mesoscale eddy field

We study the dispersion of wind-induced near-inertial oscillations (NIOs) in a fully turbulent baroclinic mesoscale eddy field characterized by a continuous wavenumber spectrum. The influence of the eddy field on the horizontal dispersion of the different NIO modes is analyzed using a vertical normal mode expansion. Previous studies have identified two dispersion regimes: trapping and strong dispersion. We examine the modes in physical and spectral spaces to investigate which regime prevails.

Numerical and analytical results show that the trapping regime prevails.For each NIO mode, there exists a critical horizontal wavenumber that separates large-scale NIO structures, where trapping dominates, from the much less energetic small-scale NIO structures, where strong dispersion dominates. The maximum efficiency of dispersion for scales close to the critical wavenumber concentrates NIO kinetic energy at these scales.

The critical wavenumber results from a balance between refraction and dispersion. This balance first occurs at the highest wavenumber. Thereafter the critical wavenumber decreases with time, at a rate inversely proportional to the radius of deformation of the baroclinic NIO mode considered. As a consequence, at any given time, higher NIO baroclinic mode energy can mostly be found in small-scale negative vorticity structures, such as filaments near sharp vorticity fronts, whereas lower NIO mode energy is concentrated within the core of mesoscale anticyclonic vortices. For large times, a saturation mechanism stops the time-evolution of the critical wavenumber at a value close to the peak of the kinetic energy spectrum of the QG flow field.