Numerical solutions to the eigenproblem Eqs. (11), (12), (13), (14), and (15). From top to bottom: global MTI eigenfunctions for azimuthal order m = 30, 50, 100, respectively. From left to right: global MTI eigenfunctions for mode number n = 3, 12, respectively. From top to bottom in each subfigure: perturbations of density, azimuthal velocity, radial velocity, and temperature as a function of the radius. The potential vector perturbation is not shown because it simply relates to that of radial velocity through Eq. (15). Real parts of the modes are in plain lines, while imaginary parts are in dashed lines. The part whose corresponding line type is absent is zero. The modes oscillate in space up to their respective turning points, r_c, and evanescent beyond.