Travelling Wave Solutions in Square Duct Flow

  • Shinya OkinoEmail author
  • Masato Nagata
  • Håkan Wedin
  • Alessandro Bottaro
Part of the Springer Proceedings in Physics book series (SPPHY, volume 141)


Three nonlinear travelling wave solutions for square duct flow are discovered. One of them, the asymmetric solution, which is predicted by the stability analysis, bifurcates from the mirror-symmetric solution found by Okino et al., J. Fluid Mech. 657, 413 (2010). The solution is characterized by asymmetric crosssectional flow patterns with streamwise vortices attached to one of the side walls. The other two solutions, which have rotational symmetry by π and π /2, respectively, are found by a homotopy approach using artificially arranged body forces. Each of the new solutions shows striking similarity to that of pipe flow.


Skin Friction Travel Wave Solution Rotational Symmetry Neutral Point Streamwise Vortex 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Shinya Okino
    • 1
    Email author
  • Masato Nagata
    • 1
  • Håkan Wedin
    • 2
  • Alessandro Bottaro
    • 2
  1. 1.Department of Aeronautics and Astronautics, Graduate School of EngineeringKyoto UniversityKyotoJapan
  2. 2.Dipartmento di Ingegneria, delle Costruzioni, dell’Ambiente e del TerritorioUniversity of GenovaGenoaItaly

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