Geometry of transient chaos in streamwise-localized pipe flow turbulence

Abstract

In pipes and channels, the onset of turbulence is initially dominated by localized transients, which lead to sustained turbulence through their collective dynamics. In the present work, we study the localized turbulence in pipe flow numerically and elucidate a state space structure that gives rise to transient chaos. Starting from the basin boundary separating laminar and turbulent flow, we identify transverse homoclinic orbits, the presence of which necessitates a homoclinic tangle and chaos. A direct consequence of the homoclinic tangle is the fractal nature of the laminar-turbulent boundary, which was conjectured in various earlier studies. By mapping the transverse intersections between the stable and unstable manifold of a periodic orbit, we identify the 'gateways' that promote an escape from turbulence.

Accepted for publication in Physical Review Fluids as a Rapid Communication

References in corpus (5)

• Universal continuous transition to turbulence in a planar shear flow
• The Openpipeflow Navier--Stokes Solver
• Reduction of SO(2) symmetry for spatially extended dynamical systems
• The critical point of the transition to turbulence in pipe flow
• Heteroclinic path to spatially localized chaos in pipe flow

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• Symmetry-reduced Dynamic Mode Decomposition of Near-wall Turbulence
• Exact coherent structures and phase space geometry of pre-turbulent 2D active nematic channel flow
• High dimensional tori and chaotic and intermittent transients in magnetohydrodynamic Couette flows
• Aging and memory of transitional turbulence
• Optimizing the control of transition to turbulence using a Bayesian method