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.
- Received 14 December 2009
DOI:https://doi.org/10.1103/PhysRevLett.104.104501
©2010 American Physical Society
Synopsis
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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