Snakes and ladders: localized solutions of plane Couette flow.

Academic Article


  • 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.
  • Authors

  • Schneider, Tobias M
  • Gibson, John
  • Burke, John
  • Status

    Publication Date

  • March 12, 2010
  • Has Subject Area

    Published In


  • math.DS
  • nlin.PS
  • physics.flu-dyn
  • Digital Object Identifier (doi)

    Pubmed Id

  • 20366430
  • Start Page

  • 104501
  • Volume

  • 104
  • Issue

  • 10