Near-inertial wave propagation in a curved front

In this work, we study the effect of flow curvature, or angular momentum, on the propagation and trapping characteristics of near-inertial waves (NIWs) in a curved front. The curved front is idealised as a baroclinic vortex in cyclogeostrophic balance. Motivated by ocean observations, we employ a Gaussian base flow, which by construction possesses a shield of oppositely signed vorticity surrounding its core, and we consider both cyclonic and anticyclonic representations of this flow. Following two main assumptions, i.e. that (i) the horizontal wavelength of the NIW is smaller than the length scale of the background flow (the WKBJ approximation), and (ii) the vertical wavelength of the NIW is smaller than the radial distance of interest, we derive the NIW dispersion relation and discuss the group velocity and direction of energy propagation. We show that the curvature can (i) increase the critical depth and horizontal extent of the trapping region, (ii) reduce NIW activity at the centre of the anticyclonic vortex core and enhance it in the cyclonic shield surrounding the core for high curvatures, (iii) lead to NIW trapping in the anticyclonic shield surrounding the cyclonic core, and (iv) increase the available band of NIW frequencies that are trapped. The solutions from the ray-tracing method are supported by numerical solutions of the governing equations linearised about the cyclogeostrophic base state. Finally, these methods are applied to an idealised model of oceanic mesoscale Arctic eddies showing an increase in the critical depth of trapping. Our results – while applied to polar eddies – equally apply at lower latitudes in both oceans and atmospheres, highlighting the potential importance of flow curvature in controlling the propagation of NIW energy.