2015/02/28 by Stefan Zammert, Bruno Eckhardt · 41 citations
Computer Science · Engineering · Environmental Science · Mathematics · Physics and Astronomy · #Attractor #Bifurcation #Chaotic #Classical mechanics #Computer science #Flow (mathematics) #Fluid Dynamics and Turbulent Flows #Geometry #Hagen–Poiseuille equation #Mathematical analysis #Mathematics #Mechanics #Nonlinear Dynamics and Pattern Formation #Nonlinear system #Physics #Plane (geometry) #Plant Water Relations and Carbon Dynamics #Reynolds number #Saddle #Saddle point #Saddle-node bifurcation #Space (punctuation) #State space #Subspace topology #Turbulence #nlin.CD #physics.flu-dyn
paper · pdf · doi:10.1103/physreve.91.041003
published in Physical Review E 91(4), 041003 (American Physical Society)
openalex publication_date 2015/04/30 · arxiv created 2015/05/11 · arxiv updated 2015/05/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.