Transmission coefficient (|T|, left panel) and reflection coefficient (|R|, right panel) when the box is at the pole. The coefficients are plotted in the regime R < 1∕4 (a possibly unstable case, see Sect. 3.4.4) as a function of the Rossby number R_o and the inertial frequency ω. The hatched areas do not feature critical points and correspond to regions where ω > k_x R_o in our peculiar geometry (see Appendix D.2 for this particular matter). Vertical and longitudinal wave numbers are fixed: k_x = 0.1 and k_z = 0.1. Moreover, the contours that correspond to coefficients |R| and |T| that are equal to one are indicated by solid black lines. Crosses mark the set of parameters used in Fig. 9for the analysis of the behaviour of the velocity in the three-layer model.