Profiles of the equilibrium quantities with c_A(0) = 0.5, u₀(0) = 0.45 and u₀(L) = 0.2 for a horizontal flux tube are shown with different linestyles in the upper panel. All quantities are constant when s > L. Speed and distance are normalised with respect to the constant sound speed c_s and the length of the nonuniform layer L, respectively (see text for an extended discussion). The middle and lower panels show the corresponding real and imaginary parts of the eigenmode frequencies plotted against u₀(L). The solid, dotted, dashed and dot-dashed lines represent the first, second, third and fourth modes.