Contradictions in the Large-Wavelength Approximation of Turbulent Flow Past a Wavy Bottom

  • Paolo LuchiniEmail author
Conference paper
Part of the Springer Proceedings in Physics book series (SPPHY, volume 165)


What’s just barely more complicated than a parallel channel flow? A lightly (and slowly) perturbed parallel channel flow. Yet the properties of turbulence, as extracted from a direct numerical simulation, can be very different. One practical example arises in a widespread geophysical application: the formation of ripples in sand. Common wisdom is to use an eddy-viscosity turbulence model to describe it. Our own work on this problem, started in the same vein years ago, was contradicted by simulations using a volume force to represent the streaming effect of the bottom shape modulation. Now, new simulations using an immersed boundary to represent the actual shape of the wall unfold the contradiction: the scales of length involved are much larger than anticipated.


Direct Numerical Simulation Eddy Viscosity Wavy Wall Bottom Shear Stress Sand Ripple 
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  1. 1.
    Benjamin, T.B.: Wave formation in laminar flow down an inclined plane. J. Fluid Mech. 2, 554–574 (1957)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Benjamin, T.B.: Shearing flow over a wavy boundary. J. Fluid Mech. 6, 161–205 (1959)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Charru, F., Andreotti, B., Claudin, P.: Sand Ripples and Dunes. Annu. Rev. Fluid Mech. 45, 469–93 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Jackson, P.S., Hunt, J.C.R.: Turbulent wind flow over a low hill. Q. J. R. Meteorol. Soc. 101, 929–955 (1975)CrossRefGoogle Scholar
  5. 5.
    Luchini, P.: Linearized no-slip boundary conditions at a rough surface. J. Fluid Mech. 737, 349–367 (2013)CrossRefzbMATHGoogle Scholar
  6. 6.
    Luchini, P., Charru, F.: Consistent section-averaged equations of quasi-one-dimensional laminar flow. J. Fluid Mech. 656, 337–341 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Luchini, P., Charru, F.: The phase lead of shear stress in shallow-water flow over a perturbed bottom. J. Fluid Mech. 665, 516–539 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Luchini, P., Russo, S.: A comparison between eddy-viscosity models and direct numerical simulation: the response of turbulent flow to a volume force. 64th Annual Meeting of the APS Division of Fluid Dynamics, Baltimore, MD 20–22, Bull. Am. Phys. Soc. 56–18 (2011)Google Scholar
  9. 9.
    Luchini, P., Russo, S.: A comparison between eddy-viscosity models and direct numerical simulation: the response of turbulent flow to volume forcing. Proceedings of XX Congresso AIMETA di Meccanica Teorica e Applicata, pp. 1–9. Bologna 12–15 Sep 2011Google Scholar
  10. 10.
    Shkadov, V.Ya.: Wave modes in the gravity flow of a thin layer of a viscous fluid. Izv. Akad. Nauk. SSSR, Mekh. Zhidk. Gaza 3: 43–51 (1967)Google Scholar
  11. 11.
    Yih, C.S.: Stability of liquid flow down an inclined plane. Phys. Fluids 6, 321–334 (1963)CrossRefzbMATHGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.DIINUniversità di SalernoFiscianoItaly

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