2017/03/30 by Nazmi Burak Budanur, Björn Hof
Engineering · Environmental Science · Mathematics · Physics and Astronomy · #Bifurcation #Classical mechanics #Combustion and flame dynamics #Flow (mathematics) #Fluid Dynamics and Turbulent Flows #Geometry #Laminar flow #Mathematics #Mechanics #Physics #Plant Water Relations and Carbon Dynamics #Reynolds number #Saddle #Saddle point #Turbulence #nlin.CD #nlin.PS #physics.flu-dyn
paper · pdf · doi:10.1017/jfm.2017.516
published as Journal of Fluid Mechanics, 827, 2017 · 10 pages, 5 figures
arxiv created 2017/03/30 · openalex publication_date 2017/08/18 · arxiv updated 2017/09/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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. Lett. , vol. 110, 2013, 224502) discovered two spatially localized relative periodic solutions for pipe flow, which appeared in a saddle-node bifurcation at low Reynolds number. 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 extends towards the neighbourhood of the upper-branch solution. Surprisingly, this connection even persists far above the bifurcation point and appears to mediate the first stage of the puff generation: amplification of streamwise localized fluctuations. When the state-space trajectories on the unstable manifold reach the vicinity of the upper branch, corresponding fluctuations expand in space and eventually take the usual shape of a puff.