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A Numerical Investigation of the Reduction of Solitary Wave Runup by A Row of Vertical Slotted Piles

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To improve the current understanding of the reduction of tsunami-like solitary wave runup by the pile breakwater on a sloping beach, we developed a 3D numerical wave tank based on the CFD tool OpenFOAM® in this study. The Navier-Stokes equations were applied to solve the two-phase incompressible flow, combined with an LES model to solve the turbulence and a VOF method to capture the free surface. The adopted model was firstly validated with existing empirical formulas for solitary wave runup on the slope without the pile structure. It is then validated using our new laboratory observations of the free surface elevation, the velocity and the pressure around a row of vertical slotted piles subjected to solitary waves, as well as the wave runup on the slope behind the piles. Subsequently, a set of numerical simulations were implemented to analyze the wave reflection, the wave transmission, and the shoreline runup with various offshore wave heights, offshore water depths, adjacent pile spaces and beach slopes. Finally, an improved empirical equation accounting for the maximum wave runup on the slope was proposed by taking the presence of the pile breakwater into consideration.

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  1. Cao, H.J. and Wan, D.C., 2015. RANS-VOF solver for solitary wave run-up on a circular cylinder, China Ocean Engineering, 29(2), 183–196.

  2. Chaplin, J.R., Flintham, T., Greated, C. and Skyner, D., 1992. Breaking Wave Forces on A Vertical Cylinder, Health and Safety Executive, London.

  3. Chella, M.A., Bihs, H., Myrhaug, D. and Muskulus, M., 2017. Breaking solitary waves and breaking wave forces on a vertically mounted slender cylinder over an impermeable sloping seabed, Journal of Ocean Engineering and Marine Energy, 3(1), 1–19.

  4. Dean, R.G. and Dalrymple, R.A., 1991. Water Wave Mechanics for Engineers and Scientists, World Scientific, Singapore.

  5. Fan, X., Zhang, J.X., and Liu, H., 2019. Numerical investigation of run-ups on cylinder in steep regular wave, China Ocean Engineering, 33(5), 601–607.

  6. Grilli, S.T., Svendsen, I.A. and Subramanya, R., 1997. Breaking criterion and characteristics for solitary waves on slopes, Journal of Waterway, Port, Coastal, and Ocean Engineering, 123(3), 102–112.

  7. Higuera, P., Lara, J.L. and Losada, I.J., 2013a. Realistic wave generation and active wave absorption for Navier-Stokes models: Application to OpenFOAM®, Coastal Engineering, 71. 102–118.

  8. Higuera, P., Lara, J.L. and Losada, I.J., 2013b. Simulating coastal engineering processes with OpenFOAM®, Coastal Engineering, 71. 119–134.

  9. Hirt, C.W. and Nichols, B.D., 1981. Volume of fluid (VOF) method for the dynamics of free boundaries, Journal of Computational Physics, 39(1), 201–225.

  10. Hsiao, S.C., Hsu, T.W., Lin, T.C. and Chang, Y.H., 2008. On the evolution and run-up of breaking solitary waves on a mild sloping beach, Coastal Engineering, 55(12), 975–988.

  11. Huang, Z.H. and Yuan, Z.D., 2010. Transmission of solitary waves through slotted barriers: a laboratory study with analysis by a long wave approximation, Journal of Hydro-Environment Research, 3(4), 179–185.

  12. Irtem, E., Gedik, N., Kabdasli, M.S. and Yasa, N.E., 2009. Coastal forest effects on tsunami run-up heights, Ocean Engineering, 36(3–4), 313–320.

  13. Jacobsen, N.G., Fuhrman, D.R. and Fredsøe, J., 2012. A wave generation toolbox for the open-source CFD library: OpenFOAM®, International Journal for Numerical Methods in Fluids, 70(9), 1073–1088.

  14. Jiang, C.B., Liu, X.J., Yao, Y. and Deng, B., 2019. Numerical investigation of solitary wave interaction with a row of vertical slotted piles on a sloping beach, International Journal of Naval Architecture and Ocean Engineering, 11(1), 530–541.

  15. Jiang, C.B, Yao, Y., Deng, Y. and Deng, B., 2015. Numerical investigation of solitary wave interaction with a row of vertical slotted piles, Journal of Coastal Research, 31(6), 1502–1511.

  16. Kamath, A., Chella, M.A., Bihs, H. and Arntsen, Ø.A., 2016. Breaking wave interaction with a vertical cylinder and the effect of breaker location, Ocean Engineering, 128. 105–115.

  17. Lee, J.J., Skjelbreia, J. E. and Raichlen, F., 1982. Measurement of velocities in solitary waves, Journal of the Waterway, Port, Coastal and Ocean Division, 108. 200–218.

  18. Leonard, A., 1975. Energy cascade in largeeddy simulations of turbulent fluid flows, Advances in Geophysics, 18. 237–248.

  19. Lin, P.Z., 2004. A numerical study of solitary wave interaction with rectangular obstacles, Coastal Engineering, 51(1), 35–51.

  20. Liu, H.W., Ghidaoui, M.S., Huang, Z.H., Yuan, Z.D. and Wang, J., 2011. Numerical investigation of the interactions between solitary waves and pile breakwaters using BGK-based methods, Computers & Mathematics with Applications, 61(12), 3668–3677.

  21. Menon, S., Yeung, P.K. and Kim, W.W., 1996. Effect of subgrid models on the computed interscale energy transfer in isotropic turbulence, Computers & Fluids, 25(2), 165–180.

  22. Mo, W.H. and Liu, P.L.F., 2009. Three dimensional numerical simulations for non-breaking solitary wave interacting with a group of slender vertical cylinders, International Journal of Naval Architecture and Ocean Engineering, 1(1), 20–28.

  23. Mo, W.H., Irschik, K., Oumeraci, H. and Liu, P.L.F., 2007. A 3D numerical model for computing non-breaking wave forces on slender piles, Journal of Engineering Mathematics, 58(1-4), 19–30.

  24. Mo, W.H., Jensen, A. and Liu, P.L.F., 2013. Plunging solitary wave and its interaction with a slender cylinder on a sloping beach, Ocean Engineering, 74. 48–60.

  25. Nistor, I. and Palermo, D., 2015. Post-tsunami engineering forensics: Tsunami impact on infrastructure-lessons from 2004 Indian Ocean, 201. Chile, and 2011 Tohoku Japan Tsunami Field Surveys, in: Esteban, M., Takagi, H. and Shibayama, T. (eds.), Handbook of Coastal Disaster Mitigation for Engineers and Planners, Butter-worth-Heinemann, Oxford, pp. 417–435.

  26. OpenFOAM Foundation, 2016. OpenFOAM® User Guide.[2016-11-25].

  27. Pope, S.B., 2000. Turbulent Flows, Cambridge University Press, Cambridge, UK.

  28. Raby, A., Macabuag, J., Pomonis, A., Wilkinson, S. and Rossetto, T., 2015. Implications of the 2011 Great East Japan Tsunami on sea defence design, International Journal of Disaster Risk Reduction, 14. 332–346.

  29. Saelevik, G., Jensen, A. and Pedersen, G., 2013. Runup of solitary waves on a straight and a composite beach, Coastal Engineering, 77. 40–48.

  30. Synolakis, C.E., 1987. The runup of solitary waves, Journal of Fluid Mechanics, 185. 523–545.

  31. Tai, B., Ma, Y.X., Niu, X.Y., Dong, G.H. and Perlin, M., 2019. Experimental investigation of impact forces induced by plunging breakers on a vertical cylinder, Ocean Engineering, 189. 106362.

  32. Xiao, H. and Huang, W.R., 2015. Three-dimensional numerical modeling of solitary wave breaking and force on a cylinder pile in a coastal surf zone, Journal of Engineering Mechanics, 141(8), A4014001.

  33. Yao, Y., Du, R.C., Jiang, C.B., Tang, Z.J. and Yuan, W.C., 2015. Experimental study of reduction of solitary wave run-up by emergent rigid vegetation on a beach, Journal of Earthquake and Tsunami, 9(5), 1540003.

  34. Yao, Y., He, F., Tang, Z.J. and Liu Z.S., 2018b. A study of tsunamilike solitary wave transformation and run-up over fringing reefs, Ocean Engineering, 149. 142–155.

  35. Yao, Y., Tang, Z.J., He, F. and Yuan, W.C, 2018c. Numerical investigation of solitary wave interaction with double row of vertical slotted piles, Journal of Engineering Mechanics, 144(1), 04017147.

  36. Yao, Y., Tang, Z.J., Jiang, C.B., He, W.R. and Liu, Z.S., 2018a. Boussinesq modeling of solitary wave run-up reduction by emergent vegetation on a sloping beach, Journal of Hydro-environment Research, 19. 78–87.

  37. Yoshizawa, A. and Horiuti, K., 1985. A statistically-derived subgrid-scale kinetic energy model for the large-eddy simulation of turbulent flows, Journal of the Physical Society of Japan, 54(8), 2834–2839.

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Author information

Correspondence to Zheng-zhi Deng.

Additional information

Foundation item: This work was financially supported by the National Natural Science Foundation of China (Grant Nos. 51679014 and 51839002), the Hunan Science and Technology Plan Program (Grant No. 2017RS3035) and the Open Foundation of Key Laboratory of Key Technology on Hydropower Development of Hunan Province (Grant No. PKLHD201706).

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Yao, Y., Jia, M., Mao, D. et al. A Numerical Investigation of the Reduction of Solitary Wave Runup by A Row of Vertical Slotted Piles. China Ocean Eng 34, 10–20 (2020).

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Key words

  • Wave runup
  • solitary wave
  • slotted piles
  • Navier-Stokes equations