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 baroclinicmesoscale eddy Ž eld characterizedby a continuouswavenumber spectrum. The in uence of the eddy Ž eld on the horizontal dispersion of the differentNIO modes is analyzed using a vertical normal mode expansion. Previous studies have identiŽ ed two dispersion regimes: trapping and strong dispersion. We examine the modes in physical and spectral space to assess which regime prevails. Numerical and analytical results show the prevalence of a trapping regime. For each NIO mode, there exists a critical horizontal wavenumber, kc , that separates large-scale NIO structures, where trapping dominates, from the much less energetic small-scale NIO structures, where strong dispersion dominates. The maximum efŽ ciency of dispersion for scales close to kc concentrates NIO kinetic energy at these scales. The wavenumber kc results from a balance between refraction and dispersion. This balance Ž rst occurs at the highest wavenumber. Thereafter, kc , which has dimensional expression kc 2 5 p/( ftRm 2 ), decreases with time at a rate inversely proportional to the radius of deformation, Rm , 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 Ž laments near sharp vorticity fronts, whereas lower NIO mode energy is concentratedwithin the core of mesoscale anticyclonic vortices. For large times, a saturation mechanism stops the time-evolution of kc at a value close to the peak of the kinetic energy spectrum of the QG  ow Ž eld.