Two-Vortex Models for Vortex Breakdown

A simple Hamiltonian dynamical systems model for vortex breakdown of the bubble-type (B-type) is developed and analyzed. This model is constructed using the flow induced by two point vortices moving in a half-plane immersed in an ideal (= inviscid and incompressible) fluid with an ambient uniform horizontal velocity. It is shown — using a combination of modern dynamical systems theory and numerical analysis — that the flows generated by this model capture most of the dynamical features exhibited in B-type vortex breakdown, including the existence of chaotic regimes. Examples are provided to illustrate the variety and complexity of vortex breakdown type flows that can be produced with these models.