Vortex breakdown as a catastrophe

By studying swirling viscous jets, we develop a new explanation of vortex breakdown, show how solution non-uniqueness appears through cusp and fold catastrophes as the Reynolds number Re increases, and obtain analytical solutions for Re --> infinity. Although inviscid theories also involve fold catastrophe, they have a strong limitation: the dependence of the head H and circulation Gamma(d) on stream function Psi is undetermined inside a recirculatory zone. Analytical continuation and stagnation zone models used to resolve this indeterminacy appear inadequate for swirling jets: H(Psi) and Gamma(d)(Psi), which we obtain here by the inviscid limit, differ from those based on the inviscid theories. We therefore suggest a new model consistent with the limiting transition. Also, we analyze turbulent vortex breakdown with a conical wake which has been recently observed at large Re.