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Crisis bifurcations in plane Poiseuille flow
Stefan Zammert1, Bruno Eckhardt1
1Fachbereich Physik, Philipps-Universität Marburg, D-35032 Marburg, Germany and J.M. Burgerscentrum, Delft University of Technology, 2628 CD Delft, The Netherlands.
Summary
Crisis bifurcations drive transitions in shear flows, moving from attractors to chaotic saddles. These events increase dynamic complexity and state space coverage in transitional plane Poiseuille flow.
Area of Science:
- Fluid dynamics
- Nonlinear dynamics
- Chaos theory
Background:
- Shear flows exhibit routes to turbulence resembling dynamical system bifurcations.
- Crisis bifurcations are key, causing global transitions and expanding state space dynamics.
Purpose of the Study:
- Investigate exterior and interior crisis bifurcations in transitional plane Poiseuille flow.
- Analyze the transition from attractors to chaotic saddles.
- Understand the role of bifurcations in increasing dynamic complexity.
Main Methods:
- Direct numerical simulations of transitional plane Poiseuille flow.
- Focus on a mirror-symmetric subspace.
- Tracing state space dynamics from initial coherent structures.
Main Results:
- Observed the appearance of three-dimensional exact coherent structures.
- Documented the transition to a chaotic saddle via an exterior crisis.
- Identified multiple interior crises with new states and intermittent behavior at intermediate Reynolds numbers.
Conclusions:
- Crisis bifurcations significantly enhance the complexity of shear flow dynamics.
- These bifurcations lead to more comprehensive state space coverage.
- The study elucidates a key mechanism in the transition to turbulence.
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