Efficient topological chaos embedded in the blinking vortex system

• Kin Eiko

• Sakajo Takashi

Abstract

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.

Journal

• Hokkaido University Preprint Series in Mathematics

  Hokkaido University Preprint Series in Mathematics 669 1-18, 2004

  Department of Mathematics, Hokkaido University

Keywords

• Topological chaos
• blinking vortex
• chaotic advection
• Thurston-Nielsen theory
• braids

Details

• CRID: 1390853649725431552
• NII Article ID: 120006459380
• DOI: 10.14943/83820
• HANDLE: 2115/69474
• Text Lang: en
• Data Source:
  • JaLC
  • IRDB
  • CiNii Articles
• Abstract License Flag: Allowed