Mode competition in cylindrical flows driven by sidewall oscillations.

The transition from a two-dimensional to three-dimensional flow in systems with spatial O(2) symmetry and spatiotemporal Z(2) symmetry happens in many fluid systems, like wakes or periodically forced flows. In most of these systems, the dynamics after the first bifurcation is very complex and involves cascades of bifurcations in a very narrow parameter range. A numerical study of a flow in an enclosed cylindrical cavity driven by axial oscillations of the sidewall, which allows a detailed study of the secondary bifurcations and the corresponding mode interactions, is presented. The study focuses on a codimension-2 point that acts as the organizing center of the dynamics for moderate values of the forcing frequency. The unraveled dynamics is very rich, including slow-fast dynamics and hysteresis, and may help understand the bifurcation cascades in more complex systems.