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Effects of the wave directionality on wave transformation

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Abstract

A numerical model is proposed based on the time domain solution of the Boussinesq equations using the finite element method in this paper. The typical wave diffraction through a breakwater gap is simulated to validate the numerical model. Good agreements are obtained between the numerical and experimental results. Further, the effects of the wave directionality on the wave diffraction through a breakwater gap and the wave transformation on a planar bathymetry are numerically investigated. The results show that the wave directional spreading has a significant effect on the wave diffraction and refraction. However, when the directional spreading parameter s is larger than around 40, the effects of the wave directional spreading on the wave transformation can be neglected in engineering applications.

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References

  1. FEDDERSEN F. Effect of wave directional spread on the radiation stress: Comparing theory and observations[J]. Coastal Engineering, 2004, 51(5–6): 473–481.

    Article  Google Scholar 

  2. ILLC S., CHADWICK A. J. and FLEMING C. Detached breakwater: An experimental investigation and implication for design Part1 hydrodynamics[J]. Proceedings of the Institution of Civil Engineerings-Maritime Engineering, 2005, 158(3): 91–102.

    Article  Google Scholar 

  3. PUJIANIKI N., KIOKA W. Nonlinear evolution of wave groups in directional sea[C]. Proceedings of 7th International Conference on Asian and Pacific Coasts. Bali, Indonesia, 2013.

    Google Scholar 

  4. NASERIZADEH R., BINGHAM H. B. and NOORZAD A. A coupled boundary element-finite difference solution of the elliptic modified mild slope equation[J]. Engineering Analysis with Boundary Elements, 2011, 35(1): 25–33.

    Article  MathSciNet  Google Scholar 

  5. HAMIDI M. E., HASHEMI M. R. and TALEBBEYDOKHTI N. et al. Numerical modelling of the mild slope equation using localized differential quadrature method[J]. Ocean Engineering, 2012, 47: 88–103.

    Google Scholar 

  6. RUSU E., GONCALVES M. and SOARES C. G. Evaluation of the wave transformation in an open bay with two spectral models[J]. Ocean engineering, 2011, 38(16): 1763–1781.

    Article  Google Scholar 

  7. ILIC S, Van Der WESTHUYSEN A. J. and ROELVINK J. A. et al. Multidirectional wave transformation around detached breakwaters[J]. Coastal Engineering, 2007, 54(10): 775–789.

    Article  Google Scholar 

  8. FUHRMAN D. R., BINGHAM H. B. and MADSEN P. A. Nonlinear wave-structure interactions with a high-order Boussinesq model[J]. Coastal Engineering, 2005, 52(8): 655–672.

    Article  Google Scholar 

  9. MADSEN P. A., FUHRMAN D. R. High-order Boussinesq-type modeling of nonlinear wave phenomena in deep and shallow water. Advances in numerical simulation of nonlinear water waves[M]. Singapore: World Scientific, 2010, 245–285.

    MATH  Google Scholar 

  10. KAZOLEA M., DELIS A. L. and NIKOLOS I. K. et al. An unstructured finite volume numerical scheme for extended 2D Boussineq-type equations[J]. Coastal Engineering, 2012, 69: 42–66.

    Article  Google Scholar 

  11. STEINMOELLER D. T., STASTNA M. and LAMB K. G. Fourier pseudospectral methods for 2D Boussinesq-type equation[J]. Ocean Modelling, 2012, 52–53: 76–89.

    Article  Google Scholar 

  12. FANG Ke-zhao, ZHANG Zhe and ZOU Zhi-li et al. Modelling of 2-D extended Boussinesq equations using a hybrid numerical scheme[J]. Journal of Hydrodynamics, 2014, 26(2): 187–198.

    Article  Google Scholar 

  13. DARIPA P. Higher order Boussinesq equation for two way propagation of shallow water waves[J]. European Journal of Mechanics B/Fluids, 2006, 25(6): 1008–1021.

    Article  MathSciNet  Google Scholar 

  14. LI Y., LIU S. and YU Y. et al. Numerical modelling of multi-directional irregular waves through breakwaters[J]. Applied Mathematical Modelling, 2000, 24(8–9): 551–574.

    Article  Google Scholar 

  15. LIU S., SUN Z. and LI J. An unstructured FEM model based on Boussinesq equations and its application to the calculation of multidirectional wave run-up in a cylinder group[J]. Applied Mathematical Modelling, 2012, 36(9): 4146–4164.

    Article  MathSciNet  Google Scholar 

  16. SUN Zhong-bin, LIU Shu-xue and LI Jin-xuan, Numerical study of multidirectional focusing wave runup on a vertical surface-piercing cylinder[J]. Journal of Hydrodynamics, 2012, 24(1): 86–96.

    Article  Google Scholar 

  17. BEJI S., NADAOKA K. A formal derivation and numerical modelling of the improved Boussinesq equations for varying depth[J]. Ocean Engineering, 1996, 23(8): 691–704.

    Article  Google Scholar 

  18. YU Y., LIU S. and LI Y. et al. Refraction and diffraction of random waves through breakwater[J]. Ocean Engineering, 2000, 27(5): 489–509.

    Article  Google Scholar 

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Authors and Affiliations

  1. State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology, Dalian, 116024, China

    Shu-xue Liu  (柳淑学) & Jin-xuan Li  (柳淑学)

  2. River and Harbor Engineering Department, Nanjing Hydraulic Research Institute, Nanjing, 210029, China

    Zhong-bin Sun  (孙忠滨)

Authors
  1. Shu-xue Liu  (柳淑学)
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  2. Jin-xuan Li  (柳淑学)
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  3. Zhong-bin Sun  (孙忠滨)
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Corresponding author

Correspondence to Jin-xuan Li  (柳淑学).

Additional information

Project supported by the National Natural Science Foundation of China (Grant Nos. 51079023, 51221961 and 51309050), the National Basic Research Development Program of China (973 Program, Grant Nos. 2013CB036101, 2011CB013703).

Biography: LIU Shu-xue (1965-), Male, Ph. D., Professor

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Liu, Sx., Li, Jx. & Sun, Zb. Effects of the wave directionality on wave transformation. J Hydrodyn 27, 708–719 (2015). https://doi.org/10.1016/S1001-6058(15)60533-9

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  • DOI: https://doi.org/10.1016/S1001-6058(15)60533-9

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