Chantry, M., Willis, A.P. and Kerswell, R.R. (2014) Genesis of Streamwise-Localized Solutions from Globally Periodic Traveling Waves in Pipe Flow. Physical Review Letters , 112 (16). ISSN 0031-9007
Abstract
The aim in the dynamical systems approach to transitional turbulence is to construct a scaffold in phase space for the dynamics using simple invariant sets (exact solutions) and their stable and unstable manifolds. In large (realistic) domains where turbulence can coexist with laminar flow, this requires identifying exact localized solutions. In wall-bounded shear flows, the first of these has recently been found in pipe flow, but questions remain as to how they are connected to the many known streamwise-periodic solutions. Here we demonstrate that the origin of the first localized solution is in a modulational symmetry-breaking Hopf bifurcation from a known global traveling wave that has twofold rotational symmetry about the pipe axis. Similar behavior is found for a global wave of threefold rotational symmetry, this time leading to two localized relative periodic orbits. The clear implication is that many global solutions should be expected to lead to more realistic localized counterparts through such bifurcations, which provides a constructive route for their generation
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2014 American Physical Society. Reproduced in accordance with the publisher's self-archiving policy. |
Dates: |
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Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Science (Sheffield) > School of Mathematics and Statistics (Sheffield) |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 12 May 2015 12:58 |
Last Modified: | 23 Mar 2018 02:35 |
Published Version: | http://dx.doi.org/10.1021/ol501670210.1103/PhysRev... |
Status: | Published |
Publisher: | American Physical Society |
Refereed: | Yes |
Identification Number: | 10.1103/PhysRevLett.112.164501 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:85946 |