Illustrative numerical global MTI eigenmode with m = 50 and n = 20. Top: varying radial wavenumber, $k_r=\sqrt{E-V_{\mathrm{ftd}}}$, as a function of the radius, r. Bottom: a high-order global MTI mode. The turning point, r_c, of the mode is indicated by black dashed vertical lines. It can be found as the single solution to the equation k_r(r) = 0, indicated by the grey dashed horizontal line on the top panel.