On the influence of wavy riblets on the slip behaviour of viscous fluids

  • Matthieu Bonnivard
  • Francisco J. Suárez-Grau
  • Giordano Tierra


In this work, we use the homogenization theory to investigate the capability of wavy riblet patterns to influence the behaviour of a viscous flow near a ribbed boundary. Starting from perfect slip conditions on the wall, we show that periodic oscillations of wavy riblets in the lateral direction may induce a friction effect in the direction of the flow, contrary to what happens with straight riblets. Finally, we illustrate this effect numerically by simulating riblet profiles that are widely used in experimental studies: the V-shape, U-shape, and blade riblets.

Mathematics Subject Classification

35B27 35Q35 74A55 


Viscous fluids Slip condition Rough boundary Straight riblets Wavy riblets Homogenization 


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Copyright information

© Springer International Publishing 2016

Authors and Affiliations

  • Matthieu Bonnivard
    • 1
  • Francisco J. Suárez-Grau
    • 1
    • 2
  • Giordano Tierra
    • 3
  1. 1.Univ. Paris Diderot, Sorbonne Paris Cité, Laboratoire Jacques-Louis Lions, UMR 7598, UPMC, CNRSParisFrance
  2. 2.Dpto. Ecuaciones Diferenciales y Análisis NuméricoUniversidad de SevillaSevilleSpain
  3. 3.Mathematical Institute, Faculty of Mathematics and PhysicsCharles UniversityPrague 8Czech Republic

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