Square of the frequency as a function of k_x. In this plot R = 10²   km, ρ_p = 100ρ_c, and v_Ap = 100   km   s^-1. Thick lines correspond to the full dispersion relation for the slab (Eq. (22)), while thin lines represent the solutions of the single interface (Eq. (17)). The dashed lines correspond to the C ₊  solution while the solid lines represent the C ₋  solution.The dotted vertical line represents the critical wavenumber calculated using Eq. (32).