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Snakes and Ladders: Localized Solutions of Plane Couette Flow

Tobias M. Schneider, John F. Gibson, and John Burke
Phys. Rev. Lett. 104, 104501 – Published 8 March 2010
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Abstract

We demonstrate the existence of a large number of exact solutions of plane Couette flow, which share the topology of known periodic solutions but are localized in one spatial dimension. Solutions of different size are organized in a snakes-and-ladders structure strikingly similar to that observed for simpler pattern-forming partial differential equations. These new solutions are a step towards extending the dynamical systems view of transitional turbulence to spatially extended flows.

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  • Received 14 December 2009

DOI:https://doi.org/10.1103/PhysRevLett.104.104501

©2010 American Physical Society

Synopsis

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Snakes and ladders

Published 22 March 2010

The ability to predict structurally localized patches in a fluid provides a step toward describing the evolution from laminar to turbulent flow.

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Authors & Affiliations

Tobias M. Schneider1, John F. Gibson2, and John Burke3

  • 1School of Engineering and Applied Sciences, Harvard University, 29 Oxford Street, Cambridge, Massachusetts 02138, USA
  • 2School of Physics, Georgia Institute of Technology, 837 State Street, Atlanta, Georgia 30332, USA
  • 3Department of Mathematics and Statistics, Boston University, Boston, Massachusetts 02215, USA

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Issue

Vol. 104, Iss. 10 — 12 March 2010

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