Axial phase speed v_ph as a function of longitudinal wavenumber k for a loop with profile N. The black and red curves correspond to the static case (U₀ = 0) and a case with flow (U₀ = 0.08 v_A∞ and u = 100), respectively. Here for the density parameters, a contrast of 25 and a steepness p = 100 are chosen. The horizontal dotted line corresponds to v_ph = 0. The curves in the first (fourth) quadrant are labeled (). The rest of the symbols represent the wavenumber cutoffs (please see text for details).