On the generation and propagation of near-inertial waves in strongly baroclinic geostrophic ocean currents

The time-dependent Eliassen-Sawyer equation is used to derive the dispersion and polarization relations for near-inertial waves (NIWs) propagating in strongly baroclinic geostrophic ocean currents with order one Rossby and Richardson numbers typical of submesoscale flows. The dispersion relation is used to trace the characteristics of NIWs with frequencies slightly below the Coriolis frequency, f, in regions of anti-cyclonic relative vorticity in geostrophic jets. This ray-tracing method is applied to both idealized jets and observational data obtained from cross-sections of the Gulf-Stream. These calculations confirm that these waves can be trapped in regions of anti-cyclonic vorticity, but also suggest that NIWs can get trapped in cyclical orbits with non-zero group velocity. Hence, these waves are not necessarily dissipated at critical layers, where the group velocity approaches zero and amplitudes are amplified causing wave breaking. Nevertheless, if NIWs are being resonantly forced, significant wave energy could get trapped in a small region causing higher shear, instability and turbulent dissipation. The polarization relation between the two components of the horizontal velocity vector of the waves is used to derive the wind stress required to resonantly force the NIWs. Owing to the baroclinicity and vorticity of the background flow, the horizontal velocity of the near-inertial waves can differ significantly from being circularly polarized. This, together with the lower frequency, implies that conditions for resonant wind forcing are different within versus outside of strongly baroclinic currents. Further analysis elucidates some of the interesting properties of these waves. First, both baroclinicity and relative vorticity, ζ, modify the minimum frequency which these waves can attain and hence modify the locations of reflections. Even if there were no vertical relative vorticity in the flow, baroclinicity would lower the minimum frequency below the Coriolis frequency. The baroclinicity allows the wave of frequency ω to propagate past the point where the group velocity is horizontal, i.e. where ( f ( f + ζ ) )^1/2 - ω = 0 , as illustrated in Figure 1. The point of minimum frequency, and hence reflection, occurs when the group velocity is parallel to isopycnals, i.e. when ω=(q²/N²)^1/2, where q is the potential vorticity and N² is the buoyancy frequency at which point the waves reflect. Hence, it is the baroclinicity which causes the waves to become trapped in orbits rather than propagate to critical layers. The results from this study are used to interpret observations of trapped NIWs in the anticyclonic warm core of the Gulf Stream. The measurements were made during the winter of 2007 as part of the CLIMODE experiment. The observed stratification in the upper ocean was weak making the Richardson number low implying that both the baroclinicity and vorticity of the current significantly influenced the dynamics of the waves.