Simulation of vortex sheet roll-up: chaos, azimuthal waves, ring merger

This article reviews some recent simulations of vortex sheet roll-up using the vortex blob method. In planar and axisymmetric flow, the roll-up is initially smooth but irregular small-scale features develop later in time due to the onset of chaos. A numerically generated Poincaré section shows that the vortex sheet flow resembles a chaotic Hamiltonian system with resonance bands and a heteroclinic tangle. The chaos is induced by a self-sustained oscillation in the vortex core rather than external forcing. In three-dimensional flow, an adaptive treecode algorithm is applied to reduce the CPU time from O ( N 2 ) to O ( N log N ), where N is the number of particles representing the sheet. Results are presented showing the growth of azimuthal waves on a vortex ring and the merger of two vortex rings. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.