On the stability of non-columnar swirling flows

Abstract

The linear stability of an inviscid, axisymmetric and non-columnar swirling flow in a finite length pipe is studied. A novel linearized set of equations for the development of infinitesimal axially-symmetric disturbances imposed on a base non-columnar rotating flow is derived. Then, a general mode of an axisymmetric disturbance, that is not limited to the axially-periodic mode, is introduced and an eigenvalue problem is obtained. A neutral mode of disturbance exists at the critical state. The asymptotic behavior of the branches of non-columnar solutions that bifurcate at the critical state is given. Using asymptotic techniques, it is shown that the critical state is a point of exchange of stability for these branches of solutions. This result, together with a previous result of Wang and Rusak [Phys. Fluids 8, 1007 (1996)] on the stability of columnar vortex flows, completes the investigation on the stability of all branches of solutions near the critical state. Results reveal the important relation between stability of vortex flows and the physical mechanism leading to the axisymmetric vortex breakdown phenomenon.