Regularized point-vortex simulations are presented for vortex sheet
roll-up in planar and axisymmetric flow. The sheet forms a vortex pair in
the planar case and a vortex ring in the axisymmetric case. Initially the
sheet rolls up into a smooth spiral, but irregular small-scale features
develop later in time which are attributed to the onset of chaos in the
vortex sheet flow. Numerical evidence will be presented to justify this
conclusion, including a Poincare section of the vortex sheet flow which
displays resonance bands and a heteroclinic tangle, the generic features
of a chaotic Hamiltonian system. The chaos seen here is induced by a
self-sustained oscillation in the vortex core rather than external
forcing. The results are clarified by reference to two well-known vortex
models, the oscillating vortex pair studied by Rom-Kedar, Leonard and
Wiggins, and the strained elliptic vortex studied by Kida. (This is joint
work with Monika Nitsche, University of New Mexico).
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