Profile of a supersonic equilibrium flow (solid) corresponding to a rapidly expanding flux tube with decreasing magnetic field (dashed). Smooth profiles of the Alfvén speed for c_A(0) = 2 and c_A(0) = 6 are plotted with dotted lines. The lower two panels display the continuous variation of c_A(0) from to 2 to 6 and the corresponding real and imaginary frequencies of the eigenmodes. The solid and dashed lines correspond to unstable modes. Strongly damped modes are not shown.