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In shear flows at transitional Reynolds numbers, localized patches ofturbulence, known as puffs, coexist with the laminar flow. Recently, Avila etal., Phys. Rev. Let. 110, 224502 (2013) discovered two spatially localizedrelative periodic solutions for pipe flow, which appeared in a saddle-nodebifurcation at low speeds. Combining slicing methods for continuous symmetryreduction with Poincar\'e sections for the first time in a shear flow setting,we compute and visualize the unstable manifold of the lower-branch solution andshow that it contains a heteroclinic connection to the upper branch solution.Surprisingly this connection even persists far above the bifurcation point andappears to mediate puff generation, providing a dynamical understanding of thisphenomenon.

Heteroclinic path to spatially localized chaos in pipe flow