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Heteroclinic path to spatially localized chaos in pipe flow

Published online by Cambridge University Press:  18 August 2017

N. B. Budanur Open the ORCID record for N. B. Budanur [Opens in a new window]  and
B. Hof Open the ORCID record for B. Hof [Opens in a new window]
N. B. Budanur*
Affiliation:
IST Austria, Am Campus 1, 3400 Klosterneuburg, Austria Kavli Institute for Theoretical Physics, UC Santa Barbara, Santa Barbara, CA 93106, USA
B. Hof
Affiliation:
IST Austria, Am Campus 1, 3400 Klosterneuburg, Austria
*
†Email address for correspondence: burak.budanur@ist.ac.at
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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.

JFM classification

Nonlinear Dynamical Systems: Chaos Nonlinear Dynamical Systems: Nonlinear Dynamical Systems Instability: Transition to turbulence

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Type
Rapids
Information
Journal of Fluid Mechanics , Volume 827 , 25 September 2017 , R1
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Copyright
© 2017 Cambridge University Press 

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