Acta Mechanica Sinica

, Volume 32, Issue 1, pp 22–37 | Cite as

Large eddy simulation of boundary layer flow under cnoidal waves

  • Yin-Jun Li
  • Jiang-Bo Chen
  • Ji-Fu Zhou
  • Qiang Zhang
Research Paper
  • 91 Downloads

Abstract

Water waves in coastal areas are generally nonlinear, exhibiting asymmetric velocity profiles with different amplitudes of crest and trough. The behaviors of the boundary layer under asymmetric waves are of great significance for sediment transport in natural circumstances. While previous studies have mainly focused on linear or symmetric waves, asymmetric wave-induced flows remain unclear, particularly in the flow regime with high Reynolds numbers. Taking cnoidal wave as a typical example of asymmetric waves, we propose to use an infinite immersed plate oscillating cnoidally in its own plane in quiescent water to simulate asymmetric wave boundary layer. A large eddy simulation approach with Smagorinsky subgrid model is adopted to investigate the flow characteristics of the boundary layer. It is verified that the model well reproduces experimental and theoretical results. Then a series of numerical experiments are carried out to study the boundary layer beneath cnoidal waves from laminar to fully developed turbulent regimes at high Reynolds numbers, larger than ever studied before. Results of velocity profile, wall shear stress, friction coefficient, phase lead between velocity and wall shear stress, and the boundary layer thickness are obtained. The dependencies of these boundary layer properties on the asymmetric degree and Reynolds number are discussed in detail.

Graphical abstract

Keywords

Boundary layer structure Turbulence Large eddy simulation Cnoidal wave 

Notes

Acknowledgments

We very much appreciate the financial support to this work from the National Natural Science Foundation of China (Grants 11172307 and11232012) and 973 Program (2014CB046200).

References

  1. 1.
    Sawamoto, M., Yamashita, T.: Sediment transport rate due to wave action. J. Hydrosci. Hydr. Eng. 4, 1–15 (1986)Google Scholar
  2. 2.
    Fredsøe, J., Deigaard, R.: Mechanics of Coastal Sediment Transport. World Scientific, Singapore (1992)Google Scholar
  3. 3.
    Tanaka, H., Sana, A., Yamaji, H., et al.: Experimental and numerical investigation on asymmetric oscillatory boundary layers. J. Hydrosci. Hydr. Eng. 16, 117–126 (1998)Google Scholar
  4. 4.
    Tanaka, H., Sumer, B.M., Lodahl, C.: Theoretical and experimental investigation on laminar boundary layers under cnoidal wave motion. Coast. Eng. J. 40, 81–98 (1998)CrossRefGoogle Scholar
  5. 5.
    Carstensen, S., Sumer, B.M., Fredsøe, J.: Coherent structures in wave boundary layers. Part 1. Oscillatory motion. J. Fluid Mech. 646, 169–206 (2010)CrossRefMATHGoogle Scholar
  6. 6.
    Gonzalez-Rodriguez, D., Madsen, O.S.: Boundary-layer hydrodynamics and bedload sediment transport in oscillating water tunnels. J. Fluid Mech. 667, 48–84 (2011)CrossRefMATHGoogle Scholar
  7. 7.
    Vittori, G., Verzicco, R.: Direct simulation of transition in an oscillatory boundary layer. J. Fluid Mech. 371, 207–232 (1998)CrossRefMATHGoogle Scholar
  8. 8.
    Jensen, B.L., Sumer, B.M., Fredsøe, J.: Turbulent oscillatory boundary layers at high Reynolds numbers. J. Fluid Mech. 206, 265–297 (1989)CrossRefGoogle Scholar
  9. 9.
    Sarpkaya, T.: Coherent structures in oscillatory boundary layers. J. Fluid Mech. 253, 105–140 (1993)CrossRefGoogle Scholar
  10. 10.
    Hino, M., Kashiwayanagi, M., Nakayama, A., et al.: Experiments on the turbulence statistics and the structure of a reciprocating oscillatory flow. J. Fluid Mech. 131, 363–400 (1983)CrossRefGoogle Scholar
  11. 11.
    Salon, S., Armenio, V., Crise, A.: A numerical investigation of the Stokes boundary layer in the turbulent regime. J. Fluid Mech. 570, 253–296 (2007)CrossRefMATHGoogle Scholar
  12. 12.
    Costamagna, P., Vittori, G., Blondeaux, P.: Coherent structures in oscillatory boundary layers. J. Fluid Mech. 474, 1–33 (2003)CrossRefMathSciNetMATHGoogle Scholar
  13. 13.
    Lin, P., Zhang, W.: Numerical simulation of wave-induced laminar boundary layers. Coast. Eng. 55, 400–408 (2008)CrossRefGoogle Scholar
  14. 14.
    Lambkin, D.O., Collins, M.B., Paphitis, D.: Wave period and flow asymmetry effects on transition to turbulence in relation to sediment dynamics. J. Geophys. Res. 109, 1–10 (2004)Google Scholar
  15. 15.
    Lin, P., Li, C.W.: A \(\sigma \)-coordinate three-dimensional numerical model for surface wave propagation. Int. J. Numer. Meth. Fluids 38, 1045–1068 (2002)CrossRefMATHGoogle Scholar
  16. 16.
    Lee, S.K., Cheung, K.F.: Laminar and turbulent bottom boundary layer induced by nonlinear water waves. J. Hydraul. Eng. 126, 631–644 (1999)CrossRefGoogle Scholar
  17. 17.
    Kondo, J.: Operational Method. Baifukan, Tokyo (1956)Google Scholar
  18. 18.
    Nadaoka, K., Yagi, H., Nihei, Y., et al.: Characteristics of turbulent structure in asymmetrical oscillatory flow. Proc. Coast. Eng. 41, 141–145 (1994)CrossRefGoogle Scholar
  19. 19.
    Nadaoka, K., Yagi, H., Nihei, Y., et al.: Turbulent structure of asymmetrical oscillatory flow. Proc. Coast. Eng. 43, 441–445 (1996)CrossRefGoogle Scholar
  20. 20.
    Ribberink, J.S., Al-Salem, A.A.: Sheet flow and suspension of sand in oscillatory boundary layers. Coast. Eng. 25, 205–225 (1995)CrossRefGoogle Scholar
  21. 21.
    Tanaka, H., Yamaji, H., Sana, A., et al.: A generation method of asymmetric oscillatory motion simulating cnoidal waves. Coast. Eng. J. 40, 291–306 (1998)CrossRefGoogle Scholar
  22. 22.
    Schlatter, P., Örlü, R.: Assessment of direct numerical simulation data of turbulent boundary layers. J. Fluid Mech. 659, 116–126 (2010)Google Scholar
  23. 23.
    Spalart, P.R.: Direct simulation of a turbulent boundary layer up to \({\rm R}_{\theta }=1410\). J. Fluid Mech. 187, 61–98 (1988)CrossRefMATHGoogle Scholar
  24. 24.
    Sana, A., Tanaka, H., Yamaji, H., et al.: Hydrodynamic behavior of asymmetric oscillatory boundary layers at low Reynolds numbers. J. Hydraul. Res. 132, 1086–1096 (2006)CrossRefGoogle Scholar
  25. 25.
    Wilcox, D.C.: Reassessment of the scale-determining equation for advanced turbulent models. AIAA J. 26, 1299–1310 (1988)CrossRefMathSciNetMATHGoogle Scholar
  26. 26.
    Menter, F.R.: Two-equation eddy-viscosity turbulence models for engineering applications. AIAA J. 32, 1598–1605 (1994)CrossRefGoogle Scholar
  27. 27.
    Suntoyo: Study on turbulent bottom boundary layer under non-linear waves and its application to sediment transport. [Ph.D. Thesis], Tohoku University (2006)Google Scholar
  28. 28.
    Gayen, B., Sarkar, S., Taylor, J.R.: Large eddy simulation of a stratified boundary layer under an oscillatory current. J. Fluid Mech. 643, 233–266 (2010)CrossRefMATHGoogle Scholar
  29. 29.
    Radhakrishnan, S., Piomelli, U.: Large-eddy simulation of oscillating boundary layers: model comparison and validation. J. Geophys. Res. 113, 1–14 (2008)Google Scholar
  30. 30.
    Lohmann, I.P., Fredsøe, J., Sumer, B.M., et al.: Large eddy simulation of the ventilated wave boundary layer. J. Geophys. Res. 111, 1–21 (2006)Google Scholar
  31. 31.
    Piomelli, U., Balaras, E.: Wall-layer models for large-eddy simulations. Annu. Rev. Fluid Mech. 34, 349–374 (2002)CrossRefMathSciNetGoogle Scholar
  32. 32.
    Piomelli, U.: Large-eddy and direct simulation of turbulent flows. Short course delivered at CFD2001-9e conference annuelle de la Societe canadienne de CFD, 19–20. Kitchener (2001)Google Scholar
  33. 33.
    Qiang, Z.: Turbulent statistics and bursting characteristics of typical wall flows. [Ph.D. Thesis], Graduate School of Chinese Academy of Sciences Doctoral (2005)Google Scholar

Copyright information

© The Chinese Society of Theoretical and Applied Mechanics; Institute of Mechanics, Chinese Academy of Sciences and Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Yin-Jun Li
    • 1
  • Jiang-Bo Chen
    • 1
  • Ji-Fu Zhou
    • 1
  • Qiang Zhang
    • 2
  1. 1.Key Laboratory for Mechanics in Fluid Solid Coupling Systems, Institute of MechanicsChinese Academy of SciencesBeijingChina
  2. 2.School of Aerospace EngineeringBeijing Institute of TechnologyBeijingChina

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