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Journal of fluid mechanics, 2002-03, Vol.454, p.47-69
Ort / Verlag
Cambridge, UK: Cambridge University Press
Erscheinungsjahr
2002
Quelle
Alma/SFX Local Collection
Beschreibungen/Notizen
Regularized point-vortex simulations are presented for vortex sheet motion 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: gaps and folds appear in the spiral
core and a thin wake is shed behind the vortex ring. These features are due to the
onset of chaos in the vortex sheet flow. Numerical evidence and qualitative theoretical
arguments are presented to support this conclusion. Past the initial transient the flow
enters a quasi-steady state in which the vortex core undergoes a small-amplitude
oscillation about a steady mean. The oscillation is a time-dependent variation in
the elliptic deformation of the core vorticity contours; it is nearly time-periodic, but
over long times it exhibits period-doubling and transitions between rotation and
nutation. A spectral analysis is performed to determine the fundamental oscillation
frequency and this is used to construct a Poincaré section of the vortex sheet flow.
The resulting section displays the generic features of a chaotic Hamiltonian system,
resonance bands and a heteroclinic tangle, and these features are well-correlated with
the irregular features in the shape of the vortex sheet. The Poincaré section also
has KAM curves bounding regions of integrable dynamics in which the sheet rolls
up smoothly. The chaos seen here is induced by a self-sustained oscillation in the
vortex core rather than external forcing. Several well-known vortex models are cited
to justify and interpret the results.