Numerical solutions of Eq. (11) for three different values of the normalized frequency λ = ω/2Ω₀ (solid lines). μ = cosθ, where θ is the co-latitude, hence μ = 0 corresponds to the equator and μ = 1 corresponds to the northern pole. Left, middle and right panels correspond to the harmonics with ν = 2 (λ = 0.72012), ν = 1 (λ = 0.57518) and ν = 0 (λ = 0.36686), respectively. Dashed lines represent corresponding analytical solutions from Eq. (20). All solutions are concentrated at low latitudes. We take s = 1, ϵ = 100 and α = 0.1 during the simulations.