Skip to main content
Log in

Numerical simulation of irregular wave overtopping against a smooth sea dike

  • Published:
China Ocean Engineering Aims and scope Submit manuscript

Abstract

Based on the filtered Navier-Stokes equations and Smagorinsky turbulence model, a numerical wave flume is developed to investigate the overtopping process of irregular waves over smooth sea dikes. Simulations of fully nonlinear standing wave and regular wave’s run-up on a sea dike are carried out to validate the implementation of the numerical wave flume with wave generation and absorbing modules. To model stationary ergodic stochastic processes, several cases with different random seeds are computed for each specified irregular wave spectrum. It turns out that the statistical mean overtopping discharge shows good agreement with empirical formulas, other numerical results and experimental data.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Avgeris, T. V. K. and Prinos, P., 2004. Boussinesq modeling of wave interaction with porous submerged breakwaters, Proc. 29th Int. Conf. Coastal Eng., 604–616.

  • Besley, P., 1999. Overtopping of Seawalls: Design and Assessment Manual, Hydraulics Research Wallingford, Report W178.

  • Boo, S.Y., 1994. A numerical wave tank for nonlinear irregular wave by 3D HOBEM, Int. J. Offshore Polar Eng., 4(4): 265–272.

    Google Scholar 

  • Boo, S.Y., 2002. Linear and nonlinear irregular waves and forces in a numerical wave tank, Ocean Eng., 29(5): 475–493.

    Article  Google Scholar 

  • Chen, Y. P., Li, Z. W. and Zhang, C. K., 2004. Development of a fully nonlinear numerical wave tank, China Ocean Eng., 18(4): 501–514.

    Google Scholar 

  • Hieu, P. D. and Tanimoto, K., 2006. Verification of a VOF-based two-phase flow model for wave breaking and wave-structure interactions, Ocean Eng., 33(11–12): 1565–1588.

    Article  Google Scholar 

  • Lara, J. L., Garcia, N. and Losada, I. J., 2006. RANS modeling applied to random wave interaction with submerged permeable structures, Coast. Eng., 53(5–6): 395–417.

    Article  Google Scholar 

  • Li, B., 2008. A 3-D model based on Navier-Stokes equations for regular and irregular water wave propagation, Ocean Eng., 35(17–18): 1842–1853.

    Article  Google Scholar 

  • Li, B. X., Yu, Y. X. and Zhang, N. C., 2004. Development of 2-D numerical random wave tank and its application, Marine Science Bulletin, 23(5): 1–9. (in Chinese)

    MATH  Google Scholar 

  • Li, T. Q., Troch, P. and de Rouck, J., 2004. Wave overtopping over a sea dike, J. Comput. Phys., 198(2): 686–726.

    Article  MathSciNet  MATH  Google Scholar 

  • Liang, X. F., Yang, J. M., Li, J., Xiao, L. F. and Li, X., 2010. Numerical simulation of irregular wave-simulation irregular wave train, Journal of Hydrodynamics, Ser. B., 22(4): 537–545.

    Article  Google Scholar 

  • Liang, X. F., Yang, J. M., Li, J. and Li, X., 2011. A numerical study on local characteristics of predetermined irregular wave trains, Ocean Eng., 38(4): 651–657.

    Article  Google Scholar 

  • Liu, Y. N., Guo, X. Y., Wang, B. L. and Liu, H., 2007. Numerical simulation of wave overtopping over seawalls using the RANS equations, Journal of Hydrodynamics, Ser. A., 22(6): 682–688. (in Chinese)

    Google Scholar 

  • Lu, Y. J., Liu, H., Wu, W. and Zhang, J. S., 2007. Numerical simulation of two-dimensional overtopping against seawalls armored with artificial units in regular waves, Journal of Hydrodynamics, Ser. B., 19(3): 322–329.

    Article  Google Scholar 

  • Mayer, S., Garapon, A. and Sorensen, L. S., 1998. A fractional step method for unsteady free-surface flow with applications to nonlinear wave dynamics, Int. J. Numer. Methods Fluids, 28(2): 293–315.

    Article  MATH  Google Scholar 

  • Mohd-Yusof, J., 1997. Combined Immersed-Boundary/B-Spline Methods for Simulations of Flow in Complex Geometries, Technical Report, Center for Turbulence Research.

  • Ning, D. Z., Teng, B., Zhou, B. Z. and Liu Z., 2008. Application of source generation of waves in 3D fully nonlinear numerical wave tank, Journal of Dalian Maritime University, 34(2): 1–11. (in Chinese)

    Google Scholar 

  • Owen, M. W., 1980. Design of Seawalls Allowing for Wave Overtopping, Hydraulics Research Wallingford, No. EX924. UK.

  • Pilliod, J. E. and Puckett, E. G., 2004. Second-order accurate volume-of-fluid algorithms for tracking material interfaces, J. Comput. Phys., 199(2): 465–502.

    Article  MathSciNet  MATH  Google Scholar 

  • Saad, Y., 1993. A flexible inner-outer preconditioned GMRES algorithm, SIAM Journal on Scientific and Computing, 14(2): 461–469.

    Article  MathSciNet  MATH  Google Scholar 

  • Smagorinsky, J., 1963. General circulation experiments with the primitive equations: I. The basic experiment, Monthly Weather Review, 91(3): 99–164.

    Article  Google Scholar 

  • Soliman, A. S. M., 2003. Numerical Study Of Irregular Wave Overtopping and Overflow, Ph.D. Thesis, University of Nottingham, UK.

    Google Scholar 

  • Sun, M. M., 2010. Study of Overtopping Discharge and Overtopping Flow on Allowing Part of the Overtopping Dike, Master Thesis, Ocean University of China. (in Chinese)

  • Wang, B. L. and Liu, H., 2005. Higher order Boussinesq-type equations for water waves on uneven bottom, Applied Mathematics and Mechanics, 26(6): 774–784. (in Chinese)

    Article  MATH  Google Scholar 

  • Wei, G., Kirby, J. T. and Sinha, A., 1999. Generation of waves in Boussinesq models using a source function method, Coast. Eng., 36(4): 271–299.

    Article  Google Scholar 

  • Zhan, J. M., Li, Y. S. and Wai, O. W. H., 2002. Numerical modeling of multi-directional irregular waves incorporating 2-D numerical wave absorber and subgrid turbulence, Ocean Eng., 30(1): 23–46.

    Article  Google Scholar 

  • Zhou, Q. J., Wang, B. L., Lan, Y. M. and Liu, H., 2005. Numerical simulation of wave overtopping over seawalls, Chinese Quarterly of Mechanics, 26(4): 629–633. (in Chinese)

    Google Scholar 

  • Van Der Meer, J. W. and Janssen, J. P. F. M., 1995. Wave run-up and wave overtopping at dikes, in: Wave Forces on Inclined and Vertical Wall Structure, Ed. N. Kobayashi and Z. Demirbilek, 1–27.

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Hua Liu  (刘 桦).

Additional information

This project was financially supported by the National Natural Science Foundation of China (Grant No. 10972138), the Natural Science Foundation of Shanghai Municipality (Grant No. 11ZR1418200), Key Project of Science and Technology Commission of Shanghai Municipality (Grant No. 09231203402) and Key Doctoral Programme Foundation of Shanghai Municipality (Grant No. B206).

Rights and permissions

Reprints and permissions

About this article

Cite this article

Guo, Xy., Wang, Bl. & Liu, H. Numerical simulation of irregular wave overtopping against a smooth sea dike. China Ocean Eng 26, 153–166 (2012). https://doi.org/10.1007/s13344-012-0011-7

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13344-012-0011-7

Key words

Navigation