The Lagrangian dynamics of steady vortex breakdown bubbles

We study the phase-space bifurcations of a simple dynamical system to elucidate the role of swirl intensity on the complexity of the dynamics of particle paths in steady vortex breakdown bubbles. We show that there is a range of swirl numbers within which very small stationary disturbances superimposed on a steady, axisymmetric, vortex breakdown velocity field could have a profound effect on the Lagrangian dynamics, leading to a rich mixture of regular and chaotic behavior. Sufficiently high swirl intensity, on the other hand, can stabilize the Lagrangian orbits and yield vortex breakdown bubbles with integrable (axisymmetric) dynamics even when the transporting velocity field is not axisymmetric. We support these findings by presenting computational results for the flow in a closed cylinder with a rotating bottom.