Theoretical Prediction of Turbulent Skin Friction on Geometrically Complex Surfaces

  • Pierre Sagaut
  • Yulia Peet
Part of the ERCOFTAC Series book series (ERCO, volume 14)


This article can be considered as an extension of the paper of Fukagata et al. (Phys. Fluids 14:L73, 2002) who derived an analytical expression for the componential contributions into skin friction in a turbulent channel, pipe and plane boundary layer flows. In this paper, we extend theoretical analysis of Fukagata et al. limited to canonical cases with two-dimensional mean flow to a fully three-dimensional situation allowing complex wall shapes. We start our analysis by considering arbitrarily-shaped surfaces and then formulate a restriction on a surface shape for which the current analysis is valid. Theoretical formula for skin friction coefficient is thus given for streamwise and spanwise homogeneous surfaces of any shape, as well as some more complex configurations, including spanwise-periodic wavy patterns. Current theoretical analysis is validated using the results of Large Eddy Simulations of a turbulent flow over straight and wavy riblets with triangular and knife-blade cross-sections. Decomposition of skin friction into different componential contributions allows to analyze the influence of different dynamical effects on a drag modification by riblet-covered surfaces.


Large Eddy Simulation Skin Friction Drag Reduction Skin Friction Coefficient Turbulent Term 
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.



Dr. Yves Charon (IFP, France) is gratefully acknowledged for many enlightening discussions. This project was supported by ANR as project ANR-PANH-READY.


  1. 1.
    Bechert, D.W., Bartenwerfer, M.: The viscous flow on surfaces with longitudinal ribs. J. Fluid Mech. 206, 105–129 (1989) CrossRefGoogle Scholar
  2. 2.
    Bechert, D.W., Bruse, M., Hage, W., Van Der Hoeven, J.G.T., Hoppe, G.: Experiments on drag-reducing surfaces and their optimization with an adjustable geometry. J. Fluid Mech. 338, 59–87 (1997) CrossRefGoogle Scholar
  3. 3.
    Charron, Y., Lepesan, E., Surface structurée tri dimensionnelle à onde transverse en vue d’une réduction de la traînée aérodynamique. Patent FR 2899 945, 2007 Google Scholar
  4. 4.
    Choi, K.-S.: Near-wall structure of a turbulent boundary layer with riblets. J. Fluid Mech. 208, 417–458 (1989) CrossRefGoogle Scholar
  5. 5.
    Choi, K.-S.: Near-wall structure of turbulent boundary layer with spanwise-wall oscillation. Phys. Fluids 14(7), 2530–2542 (2002) CrossRefGoogle Scholar
  6. 6.
    Choi, H., Moin, P., Kim, J.: Active turbulence control for drag reduction in wall-bounded flows. J. Fluid Mech. 262, 75–110 (1994) zbMATHCrossRefGoogle Scholar
  7. 7.
    Ferrante, A., Elghobashi, S.: On the physical mechanisms of drag reduction in a spatially developing turbulent boundary layer laden with microbubbles. J. Fluid Mech. 503, 345–355 (2004) zbMATHCrossRefGoogle Scholar
  8. 8.
    Fukagata, K., Iwamoto, K., Kasagi, N.: Contribution of Reynolds stress distribution to the skin friction in wall-bounded flows. Phys. Fluids 14, L73 (2002) CrossRefGoogle Scholar
  9. 9.
    Fukagata, K., Kasagi, N., Koumoutsakos, P.: A theoretical prediction of friction drag reduction in turbulent flow by superhydrophobic surfaces. Phys. Fluids 18, 051703 (2006) CrossRefGoogle Scholar
  10. 10.
    Gad-El-Hak, M.: Flow Control. Cambridge University Press, Cambridge (2000) zbMATHCrossRefGoogle Scholar
  11. 11.
    Iwamoto, K., Fukagata, K., Kasagi, N., Suzuki, Y.: Friction drag reduction achievable by near-wall turbulence manipulation at high Reynolds numbers. Phys. Fluids 17, 011702 (2005) CrossRefGoogle Scholar
  12. 12.
    Laadhari, F., Skandaji, L., Morel, R.: Turbulence reduction in a boundary layer by a local spanwise oscillating surface. Phys. Fluids A6(10), 3218–3220 (1994) CrossRefGoogle Scholar
  13. 13.
    Lumley, J., Blossey, P.: Control of turbulence. Annu. Rev. Fluid Mech. 30, 311–327 (1998) MathSciNetCrossRefGoogle Scholar
  14. 14.
    Peet, Y., Sagaut, P., Charron, Y.: Turbulent drag reduction using sinusoidal riblets with triangular cross-section. In: 38th AIAA Fluid Dynamics Conference and Exhibit. AIAA Paper 2008-3745 (2008) Google Scholar
  15. 15.
    Rebeck, H., Choi, K.-S.: A wind-tunnel experiment on real-time opposition control of turbulence. Phys. Fluids 18, 035103 (2006) CrossRefGoogle Scholar
  16. 16.
    Robinson, S.K.: Coherent motions in the turbulent boundary layer. Annu. Rev. Fluid Mech. 23, 601 (1991) CrossRefGoogle Scholar
  17. 17.
    Walsh, M.J.: Riblets, In: Bushnell, D.M., Heffner, J.N. (eds.) Viscous Drag Reduction in Boundary Layers, pp. 203–261. AIAA, Washington (1990) Google Scholar

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© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.Institut Jean Le Rond d’AlembertUniversité Pierre et Marie CurieParis cedex 5France

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