Cross-sectional cuts of the density at the tube center, z = 0, for the modes with m = 2 (top left), m = 3 (top right), m = 4 (bottom left), and m = 5 (bottom right). An initially abrupt boundary with l/R = 0, a density contrast of ρ_i/ρ_e = 5, and a velocity amplitude of v₀/v_A, i = 0.05 is considered in all cases. Only a subregion of the complete numerical domain in the vicinity of the flux tube is shown. A snapshot of the evolution at t/P_k = 1.84 is displayed in the still image. The complete temporal evolution is available in the accompanying movie.