Propagation properties of inertia-gravity waves through a barotropic shear layer and application to the Antarctic polar vortex

The propagation of inertia-gravity waves (IGWs) through a dynamical transport barrier, such as the Antarctic polar vortex edge is investigated using a linear wave model. The model is based on the linearized, inviscid hydrostatic equations on an f -plane. Typical values for the parameters that are appropriate to the Antarctic polar vortex are given. The background flow U is assumed to be barotropic and its horizontal shear is represented by a hyperbolic tangent background wind profile. The wave equation that describes the latitudinal structure of a monochromatic disturbance contains two singularities. The first corresponds to the occurrence of a critical level where the intrinsic wave frequency Ω = ω - kU becomes zero. ω is the absolute wave frequency and k its longitudinal wave number in the direction of U. The second is an apparent singularity and does not give rise to singular wave behaviour. It becomes zero whenever the square of the intrinsic wave frequency Ω² = f (f - U_y , f being the Coriolis frequency and U_y, the horizontal shear of the flow. The wave equation is solved numerically for different values of the angles of incidence of the wave upon the background flow, of the wave frequency, of the horizontal wave number and of the Rossby number. Reflection (|R|) and transmission (|T|) coefficients are determined as a function of these parameters. The results depend on whether the flow is i inertially stable or not. They also depend on the presence and location of the turning levels, where the wave becomes evanescent, with respect to the location of the Ω-critical levels. For inertially stable flows, the wave totally reflects at the turning level and never reaches the critical level. If the background flow is inertially unstable, turning levels can disappear and the wave can now reach the critical level. Then over-reflection, over-transmission and absorption can occur.