Exact Coherent Structures in Turbulent Shear Flows

  • Fabian Waleffe
Part of the Notes on Numerical Fluid Mechanics and Multidisciplinary Design book series (NNFM, volume 105)


Exact coherent structures are three-dimensional, nonlinear traveling wave solutions of the Navier-Stokes equations. These solutions are typically unstable from onset, yet they capture the basic statistical and structural features of low Reynolds number turbulent shear flows remarkably well. These exact coherent structures have now been found in all canonical shear flows: plane Couette, Poiseuille and pipe flow. They are generic for shear flows and exist for both no-slip and stress boundary conditions. Their discovery opens up new avenues for turbulence research and forces a fundamental rethinking of the true nature of turbulence.


Travel Wave Solution Unstable Manifold Stable Manifold Lower Branch Branch Solution 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Fabian Waleffe
    • 1
  1. 1.Departments of Mathematics and Engineering PhysicsUniversity of WisconsinMadisonUSA

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