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 for wakes). For each azimuthal wave number m, there exists a single unstable Kelvin–Helmholtz mode and an infinite number of neutrally stable inertial waveguide modes. Swirl decreases the temporal growth rate of the axisymmetric Kelvin–Helmholtz mode (m=0), which nonetheless remains unstable for all axial wave numbers. For helical modes (m≠0), small amounts of swirl lead to the widespread occurrence of direct resonances between the unstable Kelvin–Helmholtz mode and the inertial waveguide modes. Such interactions generate, in the low wave number range, neutrally stable wave number bands separated by bubbles of instability. As S increases...