On the onset of unsteadiness in confined vortex flows

Abstract

In the experiment of Escudier [1984 Exp. Fluids, 2, 189–196], the manifestation of vortex breakdown in a cylindrical container has been accompanied by the onset of axisymmetric oscillations when the Reynolds number was increased. In this work, examination of linear stability of the independently considered different parts of the flow domain was performed along with other numerical experiments in the container and an annular geometry to study the physical nature of the oscillatory instability. It is demonstrated that the axisymmetric oscillations observed in these confined flows are not brought about by the vortex breakdown. The results also clarify the basic role in the instability mechanism played by the region of the negative Rayleigh discriminant near the cylindrical wall; this mechanism is associated with traveling Taylor–Görtler vortices. Consistency of the results with the hypothesis of nonaxisymmetric instability in the vortex breakdown is also discussed.