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Crisis bifurcations in plane Poiseuille flow

Stefan Zammert and Bruno Eckhardt

  • Fachbereich Physik, Philipps-Universität Marburg, D-35032 Marburg, Germany and J.M. Burgerscentrum, Delft University of Technology, 2628 CD Delft, The Netherlands

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Phys. Rev. E 91, 041003(R) – Published 30 April, 2015

DOI: https://doi.org/10.1103/PhysRevE.91.041003

Abstract

Many shear flows follow a route to turbulence that has striking similarities to bifurcation scenarios in low-dimensional dynamical systems. Among the bifurcations that appear, crisis bifurcations are important because they cause global transitions between open and closed attractors, or indicate drastic increases in the range of the state space that is covered by the dynamics. We here study exterior and interior crisis bifurcations in direct numerical simulations of transitional plane Poiseuille flow in a mirror-symmetric subspace. We trace the state space dynamics from the appearance of the first three-dimensional exact coherent structures to the transition from an attractor to a chaotic saddle in an exterior crisis. For intermediate Reynolds numbers, the attractor undergoes several interior crises, in which new states appear and intermittent behavior can be observed. The bifurcations contribute to increasing the complexity of the dynamics and to a more dense coverage of state space.

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Phys. Rev. E 91, 041003(R)– Published 30 April, 2015
  • Received 10 February 2015

©2015 American Physical Society

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