Wave-like domains and colatitude θ₀ (degrees) for waves with ellipsoidal turning surface ℰ satisfying sub-harmonic resonance condition (13). Left panel: ℰ₁ wave: Ω₀ = 3.4, N₀/Ω_s = 2. Right panel: ℰ₂ wave: Ω₀ = 4, N₀/Ω_s = 10. Dashed grey ellipsoidal curve is given by Eq. (14). Vertical dashed grey line is the asymptotic curve given by , where s is the cylindrical radius from the spin axis. Waves satisfying the sub-harmonic resonance condition disappear along the polar axis when z ≤ |1 − Ω₀|/(N₀/Ω_s).