A simple model of chaotic advection and scattering

Chaos
Gustavo StolovitzkyLawrence Sirovich

Abstract

In this work, we study a blinking vortex-uniform stream map. This map arises as an idealized, but essential, model of time-dependent convection 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 dominated by the chaotic scattering of fluid particles near the vortex core. Studying the paths of fluid particles, it is seen that quantities such as residence time distributions and exit-vs-entry positions scale in self-similar fashions. A bifurcation is identified in which a saddle 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-similarity. Also, since the model is simple enough, various other properties are quantified analytically in terms of the circulation strength, stream velocity, and blinking period. These properties include: entire hierarchies of fixed points and periodic points, the parameter values at which these points undergo conservative period-doubling bifurcations, the structure of the unstable manifolds of the saddle f...Continue Reading

References

Jan 15, 1990·Physical Review. a·F J RomeirasE Ott
Dec 10, 1990·Physical Review Letters·L YuQ Chen
Jul 1, 1991·Chaos·George M. Zaslavsky
Jan 1, 1993·Chaos·G. A. CecchiA. J. Santillan
Oct 1, 1993·Chaos·Edward Ott, Tamas Tel
Oct 1, 1993·Chaos·James B. Kadtke, Evgeny A. Novikov

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Citations

Jul 11, 2006·Chaos·Jesús M SeoaneYing-Cheng Lai
Jun 5, 2003·Chaos·Gyorgy KarolyiTamas Czaran
Jun 5, 2003·Chaos·Tamas TelJames Kadtke
Dec 18, 2012·Reports on Progress in Physics·Jesús M Seoane, Miguel A F Sanjuán
Dec 16, 1996·Physical Review Letters·J C SommererH E Gilreath
Aug 7, 2007·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Jesús M SeoaneYing-Cheng Lai
Jan 22, 2002·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Adilson E Motter, Ying-Cheng Lai

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