In this work, we study a blinking vortex-uniform stream map. This map
arises as an idealized, but essential, model of time-dependent convect
ion past concentrated vorticity in a number of fluid systems. The map
exhibits a rich variety of phenomena, yet it is simple enough so as to
yield to extensive analytical investigation. The map's dynamics is do
minated by the chaotic scattering of fluid particles near the vortex c
ore, Studying the paths of fluid particles, it is seen that quantities
such as residence time distributions and exit-vs-entry positions scal
e in self-similar fashions. A bifurcation is identified in which a sad
dle fixed point is created upstream at infinity. The homoclinic tangle
formed by the transversely intersecting stable and unstable manifolds
of this saddle is principally responsible for the observed self-simil
arity. Also, since the model is simple enough, various other propertie
s are quantified analytically in terms of the circulation strength, st
ream velocity, and blinking period. These properties include: entire h
ierarchies of fixed points and periodic points, the parameter values a
t which these points undergo conservative period-doubling. bifurcation
s, the structure of the unstable manifolds of the saddle fixed and per
iodic points, and the detailed structure of the resonance zones inside
the vortex core region. A connection is made between a weakly dissipa
tive version of our map and the Ikeda map from nonlinear optics. Final
ly, we discuss the essential ingredients that our model contains for s
tudying how chaotic scattering induced by time-dependent flow past vor
tical Structures produces enhanced diffusivities. (C) 1995 American In
stitute of Physics.