China Ocean Engineering

, Volume 31, Issue 5, pp 539–548 | Cite as

Numerical simulation of the three-dimensional wave-induced currents on unstructured grid

  • Ping Wang
  • Ning-chuan Zhang
  • Shuai Yuan
  • Wei-bin Chen
Article
  • 28 Downloads

Abstract

By coupling the three-dimensional hydrodynamic model with the wave model, numerical simulations of the threedimensional wave-induced current are carried out in this study. The wave model is based on the numerical solution of the modified wave action equation and eikonal equation, which can describe the wave refraction and diffraction. The hydrodynamic model is driven by the wave-induced radiation stresses and affected by the wave turbulence. The numerical implementation of the module has used the finite-volume schemes on unstructured grid, which provides great flexibility for modeling the waves and currents in the complex actual nearshore, and ensures the conservation of energy propagation. The applicability of the proposed model is evaluated in calculating the cases of wave set-up, longshore currents, undertow on a sloping beach, rip currents and meandering longshore currents on a tri-cuspate beach. The results indicate that it is necessary to introduce the depth-dependent radiation stresses into the numerical simulation of wave-induced currents, and comparisons show that the present model makes better prediction on the wave procedure as well as both horizontal and vertical structures in the wave-induced current field.

Keywords

three-dimensional wave-induced current undertow unstructured grid radiation stress numerical simulation 

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References

  1. Berkhoff, J.C.W., 1972. Computation of combined refraction-diffraction, Proceedings of the 13th International Conference Coastal Engineering, ASCE, New York, 471–490.Google Scholar
  2. Boris, J.P. and Book, D.L., 1997. Flux-corrected transport. I. SHASTA, A fluid transport algorithm that works, Journal of Computational Physics, 11(1), 38–69.CrossRefMATHGoogle Scholar
  3. Borthwick, A.G.L. and Foote, Y.L.M., 2002. Wave-induced nearshore currents at a tri-cuspate beach in the UKCRF, Proceedings of the Institution of Civil Engineers-Water and Maritime Engineering, 154(4), 251–263.CrossRefGoogle Scholar
  4. Castelle, B., Bonneton, P., Sénéchal, N., Dupuis, H., Butel, R., and Michel, D., 2006. Dynamics of wave-induced currents over an alongshore non-uniform multiple-barred sandy beach on the Aquitanian Coast, France, Continental Shelf Research, 26(1), 113–131.CrossRefGoogle Scholar
  5. Chen, C.S., Liu, H.D. and Beardsley, R.C., 2003. An unstructured grid, finite-volume, three-dimensional, primitive equations ocean model: Application to coastal ocean and estuaries, Journal of Atmospheric and Oceanic Technology, 20(1), 159–186.CrossRefGoogle Scholar
  6. Chen, Q., Kirby, J.T., Dalrymple, R.A., Kennedy, A.B. and Chawla, A., 2000. Boussinesq modeling of wave transformation, breaking, and runup. II: 2D, Journal of Waterway, Port, Coastal, and Ocean Engineering, 126(1), 48–56.Google Scholar
  7. Choi, J., Lim, C.H., Lee, J.I. and Yoon, S.B., 2009. Evolution of waves and currents over a submerged laboratory shoal, Coastal Engineering, 56(3), 297–312.CrossRefGoogle Scholar
  8. Dong, P. and Anastasiou, K., 1991. A numerical model of the vertical distribution of longshore currents on a plane beach, Coastal Engineering, 15(3), 279–298.CrossRefGoogle Scholar
  9. Hong, G.W., 1996. Mathematical models for combined refraction-diffraction of waves on non-uniform current and depth, China Ocean Engineering, 10(4), 433–454.Google Scholar
  10. Johnson, H.K., Karambas, T.V., Avgeris, I., Zanuttigh, B., Gonzalez-Marco, D. and Caceres, I., 2005. Modelling of waves and currents around submerged breakwaters, Coastal Engineering, 52(10–11), 949–969.CrossRefGoogle Scholar
  11. Larson, M. and Kraus, N.C., 1991. Numerical model of longshore current for bar and trough beaches, Journal of Waterway, Port, Coastal, and Ocean Engineering, 117(4), 326–347.Google Scholar
  12. Li, M., Fernando, P. T., Pan, S. Q., O’Connora, B.A. and Chen, D.Y., 2007. Development of a quasi-3d numerical model for sediment transport prediction in the coastal region, Journal of Hydro-Environment Research, 1(2), 143–156.CrossRefGoogle Scholar
  13. Longuet-Higgins, M.S., 1970. Longshore currents generated by obliquely incident sea waves: 1, Journal of Geophysical Research, 75(33), 6778–6789.CrossRefGoogle Scholar
  14. Longuet-Higgins, M.S. and Stewart, R.W., 1964. Radiation stresses in water waves; a physical discussion, with applications, Deep Sea Research and Oceanographic Abstracts, 11(4), 529–562.CrossRefGoogle Scholar
  15. MacMahan, J.H., Thornton, E.B. and Reniers, A.J.H.M., 2006. Rip current review, Coastal Engineering, 53(2–3), 191–208.CrossRefGoogle Scholar
  16. Mellor, G., 2005. Some consequences of the three-dimensional current and surface wave equations, Journal of Physical Oceanography, 35(11), 2291–2298.MathSciNetCrossRefGoogle Scholar
  17. Mellor, G.L. and Yamada, T., 1982. Development of a turbulence closure model for geophysical fluid problems, Reviews of Geophysics, 20(4), 851–875.CrossRefGoogle Scholar
  18. Nobuoka, H., Roelvink, J.A., Reniers, A.J.H.M. and Mimura, N., 2005. Vertical profile of radiation stresses for 3D nearshore currents model, Coastal Dynamics, 33, 1–14.Google Scholar
  19. Okayasu, A., Shibayama, T. and Horikawa, K., 1988. Vertical variation of undertow in the surf zone, Proceedings of the 21st International Conference on Coastal Engineering, ASCE, Yokohama, 478–491.Google Scholar
  20. Roland, A., Cucco, A., Ferrarin, C., Hsu, T.W., Liau, J.M., Ou, S.H., Umgiesser, G. and Zanke, U., 2009. On the development and verification of a 2-D coupled wave-current model on unstructured meshes, Journal of Marine Systems, 78(S), S244–S254.CrossRefGoogle Scholar
  21. Svendsen, I.A. and Lorenz, R.S., 1989. Velocities in combined undertow and longshore currents, Coastal Engineering, 13(1), 55–79.CrossRefGoogle Scholar
  22. Tajima, Y. and Madsen, O.S., 2006. Modeling near-shore waves. surface rollers, and undertow velocity profiles, Journal of Waterway, Port, Coastal, and Ocean Engineering, 132(6), 429–438.Google Scholar
  23. Tang, J., Shen, Y.M. and Qiu, D.H., 2008. Numerical study of pollutant movement in waves and wave-induced long-shore currents in surf zone, Acta Oceanologica Sinica, 27(1), 122–131.Google Scholar
  24. Tang, J. and Wei, M.F., 2010. Numerical simulation of near-shore wave-induced currents on unstructured grid, Acta Oceanologica Sinica, 32(6), 41–46.Google Scholar
  25. Ting, F.C.K. and Kirby, J.T., 1994. Observation of undertow and turbulence in a laboratory surf zone, Coastal Engineering, 24(1–2), 51–80.CrossRefGoogle Scholar
  26. Tong, F.F., Shen, Y.M., Tang, J. and Cui, L., 2010. Numerical modeling of the hyperbolic mild-slope equation in curvilinear coordinates, China Ocean Engineering, 24(4), 585–596.Google Scholar
  27. Veeramony, J. and Svendsen, I.A., 2000. The flow in surf-zone waves, Coastal Engineering, 39(2–4), 93–122.CrossRefGoogle Scholar
  28. Wang, P. and Zhang, N.C., 2014. A large-scale wave-current coupled module with wave diffraction effect on unstructured meshes, Science China Physics, Mechanics & Astronomy, 57(7), 1331–1342.CrossRefGoogle Scholar
  29. Wang, P. and Zhang, N.C., 2015. Numerical simulation of wave refraction-diffraction over the large-scale region on unstructured meshes, Chinese Journal of Computational Mechanics, 32(1), 14–20, 26. (in Chinese)Google Scholar
  30. Warner, J.C., Sherwood, C.R., Signell, R.P., Harris C.K. and Arango H.G., 2008. Development of a three-dimensional. regional, coupled wave, current, and sediment-transport model, Computers & Geosciences, 34(10), 1284–1306.CrossRefGoogle Scholar
  31. Wei, G., Kirby, J.T. and Grilli, S.T., 1995. A fully nonlinear boussinesq model for surface waves. Part 1. Highly nonlinear unsteady waves, Journal of Fluid Mechanics, 294, 71–92.MathSciNetCrossRefMATHGoogle Scholar
  32. Wu, C.S. and Liu, P.L.F., 1985. Finite element modeling of nonlinear coastal currents, Journal of Waterway, Port, Coastal, and Ocean Engineering, 111(2), 417–432.Google Scholar
  33. Xia, H.Y., Xia, Z.W. and Zhu, L.S., 2004. Vertical variation in radiation stress and wave-induced current, Coastal Engineering, 51(4), 309–321.CrossRefGoogle Scholar
  34. Xie, M.X., 2011. Establishment. validation and discussions of a three dimensional wave-induced current model, Ocean Modelling, 38 (3–4), 230–243.CrossRefGoogle Scholar
  35. Yoon, S.B., Cho, Y.S. and Lee, C., 2004. Effects of breaking-induced currents on refraction-diffraction of irregular waves over submerged shoal, Ocean Engineering, 31(5–6), 633–652.CrossRefGoogle Scholar
  36. Zhang, D., 2004. Numerical Simulation of Large-Scale Wave and Currents, Ph.D. Thesis, National University of Singapore, Singapore.Google Scholar
  37. Zheng, J.H., Mase, H., Demirbilek, Z. and Lin, L.H, 2008. Implementation and evaluation of alternative wave breaking formulas in a coastal spectral wave model, Ocean Engineering, 35(11–12), 1090–1101.CrossRefGoogle Scholar
  38. Zheng, J.H. and Tang, Y., 2009. Numerical simulation of spatial lag between wave breaking point and location of maximum wave-induced current, China Ocean Engineering, 23(1), 59–71.MathSciNetGoogle Scholar
  39. Zheng, J.H., Yan, Y.X. and Peng, S.Y., 2000. Vertical distribution of wave induced excess momentum fluxes, Journal of Hohai University, 28(1), 8–13. (in Chinese)Google Scholar
  40. Zou, Z.L., Wang, S.P., Qiu, D.H., Wang, Y., Wang, F.L and Dong, G.H., 2003. Longshore currents of random waves on different plane beaches, China Ocean Engineering, 17(2), 265–276.Google Scholar

Copyright information

© Chinese Ocean Engineering Society and Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  • Ping Wang
    • 1
  • Ning-chuan Zhang
    • 2
  • Shuai Yuan
    • 1
  • Wei-bin Chen
    • 2
  1. 1.National Marine Environmental Monitoring CenterDalianChina
  2. 2.State Key Laboratory of Coastal and Offshore EngineeringDalian University of TechnologyDalianChina

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