On the linear stability of inviscid incompressible swirling flows

Recently, Barston has studied the linear stability of plane, parallel flows of an inviscid, incompressible homogeneous fluid to two dimensional disturbances which are more general than normal mode disturbances. In this paper, we use the method of Barston to study the linear stability of swirling flows of an inviscid, incompressible, homogeneous fluid confined between two concentric cylinders. We show that the flow is stable if the gradient of the vorticity either vanishes nowhere in the flow domain or vanishes throughout the flow domain. Also, we obtain sufficient conditions for the stability of flows whose vorticity gradients have a simple zero or two distinct simple zeros. Lastly, we show that any swirling flow whose vorticity, gradient has a simple zero or two distinct simple zeros can be made stable by the addition of a background swirl to it.