open access

https://doi.org/10.14943/83820

https://hdl.handle.net/2115/69474

Efficient topological chaos embedded in the blinking vortex system

英語

braids

2004

Department of Mathematics, Hokkaido University

Hokkaido University Preprint Series in Mathematics

669

1-18

Periodic orbits forhomeomorphisms on the plane give mathematical braids, which are topologically classified into three types by Thurston-Nielsen (T-N) theory; (1) periodic, (2) reducible, and (3) pseudo-Anosov (pA). If the braid is pA, then the homeomorphism must have an infinitely many number of pe-riodic orbits of distinct periods. This kind of complexity induced by the pA braid is called “topological chaos”, which was introduced by Boyland et. al [4] recently. We investigate numerically the topological chaos embedded in the particle mixing by the blinking vortex system introduced by Aref [1]. It has already been known that the system generates the chaotic advection due to the homoclinic chaos, but the chaotic mixing region is restricted locally in the vicinity of the vortex points. In the present study, we propose an in-genious operation of the blinking vortex system that defines a mathematical braid of pA type. The operation not onlygenerates the chaotic mixing region due to the topological chaos, but also ensures global particle mixing in the whole plane. We give a mathematical explanation for the phenomenon by the T-N theory and some numerical evidences to support the explanation. More-over, we makemention of the relation between the topological chaos and the homoclinic chaos in the blinking vortex system.

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