Heteroclinic path to spatially localized chaos in pipe flow Journal Article

Author(s): Budanur, Nazmi B; Hof, Björn
Article Title: Heteroclinic path to spatially localized chaos in pipe flow
Affiliation IST Austria
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. 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.
Keywords: Transition to turbulence; Nonlinear dynamical systems; chaos
Journal Title: Journal of Fluid Mechanics
Volume: 827
ISSN: 1469-7645
Publisher: Cambridge University Press  
Date Published: 2017-08-18
Start Page: Article number: 827
DOI: 10.1017/jfm.2017.516
Notes: We are indebted to A. P. Willis for making his DNS code and invariant solutions available on openpipeflow.org, to P. Cvitanovic, M. Avila and G. Kawahara for fruitful discussions, and to Y. Duguet for his critical reading of an early version of the manuscript. This research was supported in part by the National Science Foundation under grant no. NSF PHY11-25915.
Open access: yes (repository)
IST Austria Authors
  1. Björn Hof
    46 Hof