Core Dynamics in Vortex Pairs and Rings

Abstract

The roll-up of an initially flat planar and axisymmetric vortex sheet is computed numerically, using the inviscid vortex blob method. The sheets roll up into a vortex pair and a vortex ring respectively. This paper documents the onset of chaotic particle motion near the vortex core. The observed behaviour is generic for perturbed Hamiltonian dynamical systems. In the present case, the perturbation arises from self-sustained oscillations, similar to the oscillations in Kida’s solutions for an elliptic vortex patch evolving in a strain field. Furthermore, the paper shows that such oscillations are also present in a viscous flow. This suggests that the core dynamics observed in the vortex sheet flow will also arise in a real viscous flow.