Equilibrium flow profiles (solid) for a rapidly expanding tube with u₀(0) = 0.5 and u₀(0) = 1.5. The corresponding decreasing magnetic field is plotted with dashed lines and the profiles of the Alfvén speed are shown with dotted lines. For values of u₀(0) higher than 1.5 the magnetic field is no longer a decreasing function of height. The lower two panels display the continuous variation of u₀(0) from 0.5 to 1.5 and the corresponding real and imaginary frequencies of the eigenmodes. Unstable modes appear with increasing flow speed (solid and dashed lines).