Journal of Mathematical Fluid Mechanics

, Volume 13, Issue 3, pp 429–447 | Cite as

Optimal Microstructures Drag Reducing Mechanism of Riblets

  • Elfriede FriedmannEmail author
  • Thomas Richter


We consider an optimal shape design problem of periodically distributed three-dimensional microstructures on surfaces of swimming bodies in order to reduce their drag. Our model is restricted to the flow in the viscous sublayer of the boundary layer of a turbulent flow. The costs for the optimization problem are very high because the three-dimensional flow equations have to be solved several times. We avoid this problem by approximations: the microscopic optimization problem is reduced applying homogenization. Considering a special geometry (riblets) the resulting so-called macroscopic optimization problem can be additionally reduced to a two-dimensional problem. We analyze the drag reducing mechanism of riblets which are believed to be optimal structures. Therefore we perform direct simulations on the total rough channel for different shapes of microstructures: riblets and fully three-dimensional structures.

Mathematics Subject Classification (2010)

Primary 35B27 Secondary 49Q10 


Shape optimization drag minimization Navier–Stokes equations homogenization couette flow boundary layer 


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Copyright information

© Springer Basel AG 2010

Authors and Affiliations

  1. 1.Interdisciplinary Center for Scientific ComputingUniversity of HeidelbergHeidelbergGermany
  2. 2.Department for Aeronautics and AstronauticsMassachusetts Institute of TechnologyCambridgeUSA

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