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Depatrment of Mathematics and Statistics
University of New Mexico
Abstract
I will present simulations of vortex sheet roll-up into
vortex pairs and rings. The roll-up is initially smooth, but
irregular features appear unexpectedly at later times, both in the vortex
core and the rear of the ring. The irregular features are
caused by the onset of chaos in the vortex sheet flow.
I will present qualitative theoretical arguments as well as
numerical evidence to support this conclusion.
In particular, I will show that past the initial transient,
the flow behaves like a periodically perturbed Hamiltonian system,
and displays characteristic features of such systems, namely
resonance bands and a heteroclinic tangle.
In the present case, the perturbation consists of a
self-induced oscillation in the core vorticity rather than being caused by
external forcing. I will give evidence that such oscillations
are also present in Navier-Stokes flows.
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