Heteroclinic path to spatially localized chaos in pipe flow

Abstract

In shear flows at transitional Reynolds numbers, localized patches of turbulence, known as puffs, coexist with the laminar flow. Recently, Avila et al., Phys. Rev. Let. 110, 224502 (2013) discovered two spatially localized relative periodic solutions for pipe flow, which appeared in a saddle-node bifurcation at low speeds. Combining slicing methods for continuous symmetry reduction with Poincaré sections for the first time in a shear flow setting, we compute and visualize the unstable manifold of the lower-branch solution and show that it contains a heteroclinic connection to the upper branch solution. Surprisingly this connection even persists far above the bifurcation point and appears to mediate puff generation, providing a dynamical understanding of this phenomenon.

10 pages, 5 figures

References in corpus (8)

• Turbulence transition and the edge of chaos in pipe flow
• Asymmetric, helical and mirror-symmetric travelling waves in pipe flow
• Laminar-turbulent boundary in plane Couette flow
• The Openpipeflow Navier--Stokes Solver
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• Reduction of SO(2) symmetry for spatially extended dynamical systems
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• Turbulent dynamics of pipe flow captured in a reduced model: puff relaminarisation and localised `edge' states

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• Heteroclinic and Homoclinic Connections in a Kolmogorov-Like Flow
• Inferring symbolic dynamics of chaotic flows from persistence
• Geometry of transient chaos in streamwise-localized pipe flow turbulence
• Analysis and modeling of localized invariant solutions in pipe flow
• A traveling wave bifurcation analysis of turbulent pipe flow
• Dynamics-based machine learning of transitions in Couette flow