Abstract: The stability of inviscid incompressible swirling flow with slowly divergence is investigated A multiple scale expansion is used to develop a linear stability study of slowly divergent swirling flow with non-axisymmetric disturbances The differental equations of zero-order and first-order disturbance module and governing equation of amplitude variation due to slowly divergent flow are derved The plaschko s equation for slowly divergent swirl-free jet has been extended to slowly divergent flow with swirlin the present study.

Key words: stabilty, swirling flow, vortex flow