Background density and flow speed as a function of radial distance from loop axis. Two profiles are distinguished: one designated E (left column) and described by Eq. (1), the other designated N (right) and described by Eq. (2). A series of values for the density profile steepness p and flow profile steepness u is examined and given by different colors as denoted. For illustration, we choose a density contrast of ρ₀/ρ_∞ = 25 and a flow magnitude of U₀ = 0.08 v_A∞, where v_A∞ represents the Alfvén speed at large distances.