The effect of swirl on jets and wakes: Linear instability of the Rankine vortex with axial flow

The effect of swirl on jets and wakes is investigated by analyzing the inviscid spatiotemporal instability of the Rankine vortex with superimposed plug flow axial velocity profile. The linear dispersion relation is derived analytically as a function of two nondimensional control parameters: the swirl ratio S and the external axial flow parameter a ( a>−0.5 for jets, a−0.5) become absolutely unstable (AI) to the axisymmetric mode m=0 only for a sufficiently large external axial counterflow a1.61, AI occurs, even for coflowing jets (a>0). As S is gradually increased, the transitional mode to AI successively becomes m=0, −1, −2, −3, etc. In the absence of swirl, wakes (a0.091. For S>0.47, AI occurs even for coflowing wakes (a