Edge of Chaos in a Parallel Shear Flow

Joseph D. Skufca, James A. Yorke, and Bruno Eckhardt
Phys. Rev. Lett. 96, 174101 – Published 5 May 2006

Abstract

We study the transition between laminar and turbulent states in a Galerkin representation of a parallel shear flow, where a stable laminar flow and a transient turbulent flow state coexist. The regions of initial conditions where the lifetimes show strong fluctuations and a sensitive dependence on initial conditions are separated from the ones with a smooth variation of lifetimes by an object in phase space which we call the “edge of chaos.” We describe techniques to identify and follow the edge, and our results indicate that the edge is a surface. For low Reynolds numbers we find that the surface coincides with the stable manifold of a periodic orbit, whereas at higher Reynolds numbers it is the stable set of a higher-dimensional chaotic object.

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  • Received 9 May 2005

DOI:https://doi.org/10.1103/PhysRevLett.96.174101

©2006 American Physical Society

Authors & Affiliations

Joseph D. Skufca1,*, James A. Yorke2,†, and Bruno Eckhardt3,4,‡

  • 1Department of Mathematics, University of Maryland, College Park, Maryland, USA
  • 2University of Maryland, College Park, Maryland, USA
  • 3Burgers Program, IREAP and IPST, University of Maryland, College Park, Maryland, USA
  • 4Fachbereich Physik, Philipps-Universität Marburg, 35032 Marburg, Germany

  • *Electronic address: jskufca@clarkson.edu
  • Electronic address: yorke2@ipst.umd.edu
  • Electronic address: bruno.eckhardt@physik.uni-marburg.de

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Issue

Vol. 96, Iss. 17 — 5 May 2006

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