Longitudinal cuts at r = R of v_r (top panels), v_ϕ (mid panels), and b_z (bottom panels) corresponding to the fundamental mode (left panels) and the first overtone (right panels). The various lines are for the Lorentzian profile (black solid line), the Gaussian profile (red dotted line), and the parabolic profile (blue dashed line). We used L/R = 100, χ = 50, and ζ = 100 in all cases. Arbitrary units are used.