Case I: . The eigenfunction, φ, normalised radial and axial velocities, ur and uy and polarisation fraction, f, against the wavenumber kr, for the ratios and , kr0 = 0.2, and m = 1, for ka = 0 (left column). This is analogous to the two-shell case. The middle column and right column are for the cases and , with kr0 = 0.2, and m = 1, for ka = 0.1 and ka = 0.5, respectively. The curves are normalised with respect to the eigenfunctions, for comparison.
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