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Large eddy simulation of boundary layer flow under cnoidal waves

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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.

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References

  1. Sawamoto, M., Yamashita, T.: Sediment transport rate due to wave action. J. Hydrosci. Hydr. Eng. 4, 1–15 (1986)

    Google Scholar 

  2. Fredsøe, J., Deigaard, R.: Mechanics of Coastal Sediment Transport. World Scientific, Singapore (1992)

    Google Scholar 

  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. 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)

    Article  Google Scholar 

  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)

    Article  MATH  Google Scholar 

  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)

    Article  MATH  Google Scholar 

  7. Vittori, G., Verzicco, R.: Direct simulation of transition in an oscillatory boundary layer. J. Fluid Mech. 371, 207–232 (1998)

    Article  MATH  Google Scholar 

  8. Jensen, B.L., Sumer, B.M., Fredsøe, J.: Turbulent oscillatory boundary layers at high Reynolds numbers. J. Fluid Mech. 206, 265–297 (1989)

    Article  Google Scholar 

  9. Sarpkaya, T.: Coherent structures in oscillatory boundary layers. J. Fluid Mech. 253, 105–140 (1993)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  MATH  Google Scholar 

  12. Costamagna, P., Vittori, G., Blondeaux, P.: Coherent structures in oscillatory boundary layers. J. Fluid Mech. 474, 1–33 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  13. Lin, P., Zhang, W.: Numerical simulation of wave-induced laminar boundary layers. Coast. Eng. 55, 400–408 (2008)

    Article  Google Scholar 

  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. 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)

    Article  MATH  Google Scholar 

  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)

    Article  Google Scholar 

  17. Kondo, J.: Operational Method. Baifukan, Tokyo (1956)

    Google Scholar 

  18. Nadaoka, K., Yagi, H., Nihei, Y., et al.: Characteristics of turbulent structure in asymmetrical oscillatory flow. Proc. Coast. Eng. 41, 141–145 (1994)

    Article  Google Scholar 

  19. Nadaoka, K., Yagi, H., Nihei, Y., et al.: Turbulent structure of asymmetrical oscillatory flow. Proc. Coast. Eng. 43, 441–445 (1996)

    Article  Google Scholar 

  20. Ribberink, J.S., Al-Salem, A.A.: Sheet flow and suspension of sand in oscillatory boundary layers. Coast. Eng. 25, 205–225 (1995)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  22. Schlatter, P., Örlü, R.: Assessment of direct numerical simulation data of turbulent boundary layers. J. Fluid Mech. 659, 116–126 (2010)

  23. Spalart, P.R.: Direct simulation of a turbulent boundary layer up to \({\rm R}_{\theta }=1410\). J. Fluid Mech. 187, 61–98 (1988)

    Article  MATH  Google Scholar 

  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)

    Article  Google Scholar 

  25. Wilcox, D.C.: Reassessment of the scale-determining equation for advanced turbulent models. AIAA J. 26, 1299–1310 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  26. Menter, F.R.: Two-equation eddy-viscosity turbulence models for engineering applications. AIAA J. 32, 1598–1605 (1994)

    Article  Google Scholar 

  27. Suntoyo: Study on turbulent bottom boundary layer under non-linear waves and its application to sediment transport. [Ph.D. Thesis], Tohoku University (2006)

  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)

    Article  MATH  Google Scholar 

  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. 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)

  31. Piomelli, U., Balaras, E.: Wall-layer models for large-eddy simulations. Annu. Rev. Fluid Mech. 34, 349–374 (2002)

    Article  MathSciNet  Google Scholar 

  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)

  33. Qiang, Z.: Turbulent statistics and bursting characteristics of typical wall flows. [Ph.D. Thesis], Graduate School of Chinese Academy of Sciences Doctoral (2005)

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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).

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Authors and Affiliations

  1. Key Laboratory for Mechanics in Fluid Solid Coupling Systems, Institute of Mechanics, Chinese Academy of Sciences, Beijing, 100190, China

    Yin-Jun Li, Jiang-Bo Chen & Ji-Fu Zhou

  2. School of Aerospace Engineering, Beijing Institute of Technology, Beijing, 100081, China

    Qiang Zhang

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  1. Yin-Jun Li
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  2. Jiang-Bo Chen
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  3. Ji-Fu Zhou
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  4. Qiang Zhang
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Correspondence to Ji-Fu Zhou.

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Li, YJ., Chen, JB., Zhou, JF. et al. Large eddy simulation of boundary layer flow under cnoidal waves. Acta Mech. Sin. 32, 22–37 (2016). https://doi.org/10.1007/s10409-015-0486-6

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  • DOI: https://doi.org/10.1007/s10409-015-0486-6

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