Advertisement

China Ocean Engineering

, Volume 33, Issue 4, pp 424–435 | Cite as

A Comparative Study of Numerical Models for Wave Propagation and Setup on Steep Coral Reefs

  • Shan-ju Zhang
  • Liang-sheng ZhuEmail author
  • Kai Zou
Article
  • 27 Downloads

Abstract

Complex factors including steep slopes, intense wave breaking, large bottom friction and remarkable wave setup should be considered while studying wave propagation over coral reefs, and how to simulate wave propagation and setup on coral reefs efficiently has become a primary focus. Several wave models can be used on coral reefs as have been published, but further testing and comparison of the reliability and applicability of these models are needed. A comparative study of four numerical wave models (i.e., FUNWAVE-TVD, Coulwave, NHWAVE and ZZL18) is carried out in this paper. These models’ governing equations and numerical methods are compared and analyzed firstly to obtain their differences and connections; then the simulation effects of the four wave models are tested in four representative laboratory experiments. The results show that all four models can reasonably predict the spectrum transformation. Coulwave, NHWAVE and ZZL18 can predict the wave height variation more accurately; Coulwave and FUNWAVE-TVD tend to underestimate wave setup on the reef top induced by spilling breaker, while NHWAVE and ZZL18 can predict wave setup relatively accurately for all types of breakers; NHWAVE and ZZL18 can predict wave reflection by steep reef slope more accurately. This study can provide evidence for choosing suitable models for practical engineering or establishing new models.

Key words

coral reefs steep slope Boussinesq equations wave propagation and setup wave breaking numerical simulation comparative study 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Notes

Acknowledgments

The authors sincerely thank the reviewers for their constructive comments and suggestions on the first draft of the paper. We also thank professor YAO Yu and WEN Hongjie for providing laboratory data.

References

  1. Buckley, M., Lowe, R. and Hansen, J., 2014. Evaluation of nearshore wave models in steep reef environments, Ocean Dynamics, 64(6), 847–862.CrossRefGoogle Scholar
  2. Buckley, M.L., Lowe, R.J., Hansen, J.E. and Van Dongeren, AR., 2015. Dynamics of wave setup over a steeply sloping fringing reef, Journal of Physical Oceanography, 45(12), 3005–3023.CrossRefGoogle Scholar
  3. Demirbilek, Z., Nwogu, O.G. and Ward, D.L., 2007. Laboratory Study of Wind Effect on Runup Over Fringing reefs, Report 1, Data Rep, US Amry Corps of Engineering, UAA.Google Scholar
  4. Fang, K.Z., Liu, Z.B. and Zou, Z.L., 2016. Fully nonlinear modeling wave transformation over fringing reefs using shock-capturing boussinesq model, Journal of Coastal Research, 32(1), 164–171.CrossRefGoogle Scholar
  5. Gallagher, E.L., Elgar, S. and Guza, R. T., 1998. Observations of sand bar evolution on a natural beach, Journal of Geophysical Research: Oceans, 103(C2), 3203–3215.CrossRefGoogle Scholar
  6. Gourlay, M.R., 1996. Wave set-up on coral reefs. 1. Set-up and wave-generated flow on an idealised two dimensional horizontal reef, Coastal Engineering, 27(3–4), 161–193.CrossRefGoogle Scholar
  7. Kazolea, M., Filippini, A.G., Ricchiuto, M., Abadie, S., Medina, M.M., Morichon, D., Journeau, C., Marcer, R., Pons, K., Le Roy, S., Pedreros, R. and Rousseau, M., 2016. Wave Propagation Breaking, and Overtoping on A 2D Reef: A Comparative Evaluation of Numerical Codes for Tsunami Modelling, Research Report RR-9005, Inria.Google Scholar
  8. Kazolea, M. and Ricchiuto, M., 2018. On wave breaking for Boussinesq-type models, Ocean Modelling, 123, 16–39.CrossRefGoogle Scholar
  9. Kennedy, A.B., Chen, Q., Kirby, J.T. and Dalrymple, R.A., 2000. Boussinesq modeling of wave transformation, breaking, and runup. I: 1D, Journal of Waterway, Port, Coastal, and Ocean Engineering, 126(1), 39–47.CrossRefGoogle Scholar
  10. Kennedy, A.B., Kirby, J.T., Chen, Q. and Dalrymple, R.A., 2001. Boussinesq-type equations with improved nonlinear performance, Wave Motion, 33(3), 225–243.CrossRefzbMATHGoogle Scholar
  11. Kim, G., Lee, C. and Suh, K.D., 2009. Extended Boussinesq equations for rapidly varying topography, Ocean Engineering, 36(11), 842–851.CrossRefGoogle Scholar
  12. Lynett, P.J., Liu, P.L.F., Sitanggang, K.I. and Kim, D.H., 2008. Modeling Wave Generation, Evolution, and Interaction with Depth-Integrated, Dispersive Wave Equations COULWAVE Code Manual, Cornell University Long and Intermediate Wave Modeling Package v.2.0, USA.Google Scholar
  13. Ma, G.F., Shi, F.Y. and Kirby, J.T., 2012. Shock-capturing non-hydrostatic model for fully dispersive surface wave processes, Ocean Modelling, 43–44, 22–35.CrossRefGoogle Scholar
  14. Ma, G.F., Su, S.F., Liu, S. G. and Chu, J.C., 2014. Numerical simulation of infragravity waves in fringing reefs using a shock-capturing non-hydrostatic model, Ocean Engineering, 85, 54–64.CrossRefGoogle Scholar
  15. Metallinos, A.S., Repousis, E.G. and Memos, C.D., 2016. Wave propagation over a submerged porous breakwater with steep slopes, Ocean Engineering, 111, 424–438.CrossRefGoogle Scholar
  16. Roeber, V. and Cheung, K.F., 2012. Boussinesq-type model for energetic breaking waves in fringing reef environments, Coastal Engineering, 70, 1–20.CrossRefGoogle Scholar
  17. Sheremet, A., Kaihatu, J.M., Su, S.F., Smith, E.R. and Smith, J.M., 2011. Modeling of nonlinear wave propagation over fringing reefs, Coastal Engineering, 58(12), 1125–1137.CrossRefGoogle Scholar
  18. Shi, F.Y., Kirby, J.T., Harris, J.C., Geiman, J.D. and Grilli, S.T., 2012a. A high-order adaptive time-stepping TVD solver for Boussinesq modeling of breaking waves and coastal inundation, Ocean Modelling, 43–44, 36–51.CrossRefGoogle Scholar
  19. Shi, F.Y., Kirby, J.T., Tehranirad, B., Harris, J.C. and Grilli, S., 2012b. FUNWAVE-TVD Fully Nonlinear Boussinesq Wave Model with TVD Solver Documentation and User’ s Manual (Version 2.0), University of Delaware, Center for Applied Coastal Research, Newark Delaware.Google Scholar
  20. Skotner, C. and Apelt, C.J., 1999. Application of a Boussinesq model for the computation of breaking waves: Part 2: Wave-induced setdown and setup on a submerged coral reef, Ocean Engineering, 26(10), 927–947.CrossRefGoogle Scholar
  21. Smith, E.R., Hesser, T. and Smith, J.M., 2012. Two- and Three-Dimensional Laboratory Studies of Wave Breaking, Setup, and Runup on Reefs, Dissipation, US Amry Corps of Engineering, UAA.CrossRefGoogle Scholar
  22. Su, S.F., Ma, G.F. and Hsu, T.W., 2015. Boussinesq modeling of spatial variability of infragravity waves on fringing reefs, Ocean Engineering, 101, 78–92.CrossRefGoogle Scholar
  23. Wei, G., Kirby, J.T., Grilli, S.T. and Subramanya, R., 1995. A fully nonlinear Boussinesq model for surface waves. Part I. Highly nonlinear unsteady waves, Journal of Fluid Mechanics, 294, 71–92.MathSciNetCrossRefzbMATHGoogle Scholar
  24. Wen, H.J., Ren, B., Zhang, X. and Yu, X.P., 2019. SPH modeling of wave transformation over a coral reef with seawall, Journal of Waterway, Port, Coastal, and Ocean Engineering, 145(1), 04018026.CrossRefGoogle Scholar
  25. Yao, Y., Huang, Z.H., Monismith, S.G. and Lo, E.Y.M., 2012. 1DH Boussinesq modeling of wave transformation over fringing reefs, Ocean Engineering, 47, 30–42.CrossRefGoogle Scholar
  26. Zhang, S.J., Zhu, L.S. and Li, J.H., 2018. Numerical simulation of wave propagation, breaking, and setup on steep fringing reefs, Water, 10(9), 1147.CrossRefGoogle Scholar
  27. Zhu, L.S. and Hong, G.W., 2001. Numerical calculation for nonlinear waves in water of arbitrarily varying depth with boussinesq equations, China Ocean Engineering, 15(3), 355–369.Google Scholar
  28. Zhu, L.S., Li, M.Q., Zhang, H.S. and Sui, S.F., 2004. Wave attenuation and friction coefficient on the coral-reef flat, China Ocean Engineering, 18(1), 129–136.Google Scholar
  29. Zijlema, M., 2012. Modelling wave transformation across a fringing reef using swash, Proceedings of the 33rd Conference on Coastal Engineering, Coastal Engineering Research Council, Singapore, Spain.Google Scholar
  30. Zou, Z.L. and Fang, K.Z., 2008. Alternative forms of the higher-order Boussinesq equations: Derivations and validations, Coastal Engineering, 55(6), 506–521.CrossRefGoogle Scholar

Copyright information

© Chinese Ocean Engineering Society and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of Civil Engineering and TransportationSouth China University of TechnologyGuangzhouChina

Personalised recommendations