Dependence of angular frequency ω on axial wavenumber k for both a) a static loop and b) a loop with flow. The numerical results found in Fig. 2 are adopted. The ω–k curve in the first (second) quadrant derives from the curve in the first (fourth) quadrant of Fig. 2. In panel b), the blue curves correspond to the case with a different flow profile steepness, u = 1.1.