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

Abstract

SUMMARYThe 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 ow U is assumed to be barotropic and its horizontal shear is represented by a hyperbolic tangent background wind pro le. The wave equation that describes the latitudinal structure of a monochromatic disturbance contains two singularities. The rst corresponds to the occurrence of a critical level where the intrinsic wave frequency Ä D ! ¡ kU becomes zero. ! 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 Ä 2 D f .f ¡ U y /, f being the Coriolis frequency and U y the horizontal shear of the ow. The wave equation is solved numerically for different values of the angles of incidence of the wave upon the background ow, of the wave frequency, of the horizontal wave number and of the Rossby number. Re ection (jRj) and transmission (jT j) coef cients are determined as a function of these parameters. The results depend on whether the ow is 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 Ä-critical levels. For inertially stable ows, the wave totally re ects at the turning level and never reaches the critical level. If the background ow is inertially unstable, turning levels can disappear and the wave can now reach the critical level. Then over-re ection, over-transmission and absorption can occur.

On resonant over-reflection of waves by jets

“…Notably, resonant over-reflection was not found by Ollers et al in [69] even though their scattering problem is similar to the one we study in Chapter 4 (and we observe the phenomenon there). We attribute this to the fact that Ollers et al …”

“…• For the model 3, Ollers et al [69] also tried to relate the results of the scattering problem with the condition for a zonal shear flow on the f -plane to be inertially unstable: f (U y − f ) > 0 is fulfilled somewhere in the flow (see Holton [34]). They found that when this condition is satisfied at the critical layer of the incident wave, then over-reflection is favoured although absorption is possible too.…”

“…al. in [69] probably missed out hyper-reflected wave solutions within their model. This conjecture can be easily checked which would be another test for the ideas of resonance over-reflection elaborated in this thesis.…”