Equilibrium flow profiles (solid) for a moderately expanding tube with u₀(L) = 1 and u₀(L) = 4. The corresponding magnetic field is plotted in arbitrary units with dashed lines and the profiles of the normalised Alfvén speed are shown with dotted lines. The lower two panels display the continuous variation of u₀(L) from to 1 to 4 and the corresponding real and imaginary frequencies of the eigenmodes. An unstable mode (solid) is shown. The remaining modes are heavily damped. The real and imaginary parts of one such mode are plotted with a dotted lines.