Spatial instability of a swirling flow (Q1058909)

The instability of a swirling flow of an inviscid and incompressible fluid is studied on the assumption that the wavenumber \(k=k_ r+ik_ i\) of the disturbance is complex while its frequency \(\omega\) is real. This implies that the disturbance grows with distance along the axis of the swirling flow, but it does not grow with time. The occurrence of such disturbance is called spatial instability, in contrast to the temporal instability, in which k is a real number and \(\omega =\omega_ r+i\omega_ i\) is a complex one. The results show that spatial instability analysis is a useful tool for the comprehensive understanding of the instability behaviours of a swirling flow.