Spatial Instability of a Swirling Flow

The instability of a swirling flow of an inviscid and incompressible fluid is studied on the assumption that the wave number k=k_r+ik_i of the disturbance is complex while its frequency w is real, This implies that the disturbance increases 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 ω=ω_r+iω_i is complex, The results show that spatial instability analysis is a useful tool for the comprehensive understanding of the instability behaviours of a swirling flow.