Heteroclinic path to spatially localized chaos in pipe flow

N.B. Budanur, B. Hof, Journal of Fluid Mechanics 827 (2017).


Journal Article | Published | English
Department
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.
Publishing Year
Date Published
2017-08-18
Journal Title
Journal of Fluid Mechanics
Volume
827
Article Number
R1
ISSN
IST-REx-ID

Cite this

Budanur NB, Hof B. Heteroclinic path to spatially localized chaos in pipe flow. Journal of Fluid Mechanics. 2017;827. doi:10.1017/jfm.2017.516
Budanur, N. B., & Hof, B. (2017). Heteroclinic path to spatially localized chaos in pipe flow. Journal of Fluid Mechanics, 827. https://doi.org/10.1017/jfm.2017.516
Budanur, Nazmi B, and Björn Hof. “Heteroclinic Path to Spatially Localized Chaos in Pipe Flow.” Journal of Fluid Mechanics 827 (2017). https://doi.org/10.1017/jfm.2017.516.
N. B. Budanur and B. Hof, “Heteroclinic path to spatially localized chaos in pipe flow,” Journal of Fluid Mechanics, vol. 827, 2017.
Budanur NB, Hof B. 2017. Heteroclinic path to spatially localized chaos in pipe flow. Journal of Fluid Mechanics. 827, R1.
Budanur, Nazmi B., and Björn Hof. “Heteroclinic Path to Spatially Localized Chaos in Pipe Flow.” Journal of Fluid Mechanics, vol. 827, R1, Cambridge University Press, 2017, doi:10.1017/jfm.2017.516.

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