Trapping of near-inertial waves and critical layer formation in baroclinic currents

The behaviour of near-inertial waves (NIWs) in baroclinic currents is investigated, with a focus on wave trapping and critical layer dynamics. We present theoretical analysis, supported by numerical simulations, of the Sawyer–Eliassen equation, which describes waves in the plane perpendicular to an arbitrary balanced background flow. Gradients of the background velocity and buoyancy field modulate the wave properties, in particular defining the range of frequencies for which the Sawyer–Eliassen equation is hyperbolic, i.e. wave-like. Variations in the lower limit of this range, the local minimum frequency, lead to the trapping of low-frequency, typically sub-inertial, waves through either total internal reflection or the formation of critical layers. Both mechanisms are studied. We introduce a local coordinate rotation that not only elucidates these dynamics by simplifying the governing equation, but also allows us, through direct analogy, to draw upon theory and intuition developed for barotropic problems. In the majority of physically relevant cases, the transformed coordinates are aligned with and perpendicular to isopycnals, and are thus easily utilised. Employing the coordinate transformation, we consider along-isopycnal modes, and study the behaviour of waves approaching a critical level without the need for a full ray-tracing approximation. Finally, we find qualitative differences in the critical layers that form in strongly and weakly baroclinic flows, most notably in their location. In the weakly baroclinic case, NIW energy accumulates about the minimum in the relative vorticity of the background flow, whereas in the strongly baroclinic case, we find slantwise critical layers concentrated in fronts.