Axisymmetric absolute instability of swirling jets

The spatio-temporal stability of axisymmetric inviscid disturbances to swirling jets is investigated. There is a known difficulty associated with the pinch-point controlling absolute instability. Previous authors have noted that for axisymmetric waves the pinch-point moves into the left half of the complex wavenumber plane as the swirl increases. This behaviour appears unphysical because such waves diverge exponentially in the radial direction. However, our recent understanding of this phenomenon in the context of the rotating disk boundary layer tells us that it implies that confining the flow by placing it inside a cylinder concentric with the jet axis, will be destabilizing for absolute instabilities, even when this cylinder has very large radius. This prediction is confirmed, and it is shown for the first time that swirling jets can become absolutely unstable to axisymmetric waves. The possible connection with vortex breakdown is discussed.