A SIMPLE-MODEL OF CHAOTIC ADVECTION AND SCATTERING

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.