Upper panels: numerical solutions of Eq. (11) for two different values of ϵ and corresponding normalized frequency λ = ω/2Ω₀. μ = cosθ, where θ is co-latitude, hence μ = 0 corresponds to the equator and μ = 1 corresponds to the northern pole. We take s = 1 and during the simulations. Lower panels: corresponding analytical solutions plotted from Eq. (34); left panel shows the solution with n = 1 and the right panel shows the solution with n = 3.