Crisis bifurcations in plane Poiseuille flow

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.

References in corpus (13)

• The Significance of Simple Invariant Solutions in Turbulent Flows
• Recurrent motions within plane Couette turbulence
• Streamwise-localized solutions at the onset of turbulence in pipe flow
• Periodic orbits near onset of chaos in plane Couette flow
• Laminar-turbulent boundary in plane Couette flow
• On the transient nature of localized pipe flow turbulence
• Turbulent-laminar patterns in plane Poiseuille flow
• Spatially localized solutions of shear flows
• Streamwise and doubly-localised periodic orbits in plane Poiseuille flow
• Experimental scaling law for the sub-critical transition to turbulence in plane Poiseuille flow
• From travelling waves to mild chaos: a supercritical bifurcation cascade in pipe flow
• Increasing lifetimes and the growing saddles of shear flow turbulence
• Long wavelength instability of coherent structures in plane Couette flow

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• Emergence of spatio-temporal dynamics from exact coherent solutions in pipe flow
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• Direct path from turbulence to time-periodic solutions
• Linear feedback control of invariant solutions in channel flow
• Streamwise decay of localized states in channel flow
• Harbingers and latecomers - The order of appearance of exact coherent structures in plane Poiseuille flow
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• Analysis and modeling of localized invariant solutions in pipe flow
• A probabilistic protocol for the assessment of transition and control
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• Optimizing the control of transition to turbulence using a Bayesian method
• Symmetry groups and invariant solutions of plane Poiseuille flow