Spatial instability of a swirling flow

The instability of a swirling flow of an inviscidand incompressible fluid is studied on the assumption that the wavenumberk=k,+ik _i , of the disturbance is complex while its frequency 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 whichk is a real number and =_r+i_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.This paper was finished in 1981 when the author was a visiting fellow at Cornell University, U.S.A.. The auther is grateful to Prof. S. Leibovich for his guidance and assistance.