Dependence on the longitudinal wavenumber k of the phase speed v_ph for a cold cylinder with flow where the transverse distributions of both the equilibrium density and field-aligned flow adopt a step-function form. The asterisks represent the results obtained with BVPSUITE by numerically solving the eigen-value problem, while the dashed lines represent the solution to the analytically derived dispersion relation (Eq. (A.8)). The horizontal dash-dotted lines correspond to the internal and external Alfvén speeds. Here three different values of the internal flow speed U₀ are examined for a density ratio ρ₀/ρ_∞ being 25.