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Numerical study of the run-up of a solitary wave after propagation over a saw-tooth-shaped submerged breakwater

  • Sun, Jiawen (National Marine Environmental Monitoring Center) ;
  • Ma, Zhe (State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology) ;
  • Wang, Dongxu (College of Engineering, Ocean University of China) ;
  • Dong, Sheng (College of Engineering, Ocean University of China) ;
  • Zhou, Ting (State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology)
  • Received : 2019.06.06
  • Accepted : 2019.11.18
  • Published : 2020.12.31

Abstract

A numerical model is established to investigate the run-up of a solitary wave after propagating over a triangular saw-tooth-shaped submerged breakwater. A rectangular-shaped submerged breakwater is simulated for comparison. Several factors, including the submerged depth, the lagoon length and the beach slope, are selected as independent variables. The free surface motions and velocity fields of the solitary wave interacting with the submerged breakwater are discussed. The results show that the submerged depth and lagoon length play significant roles in reducing the run-up. The influence of the beach slope is not significant. At the same submerged depth, the triangular saw-tooth-shaped submerged breakwater has only a slightly better effect than the rectangular-shaped submerged breakwater on the run-up reduction. However, a calmer reflected wave profile could be obtained with the rougher surface of the saw-tooth-shaped submerged breakwater. The study conclusions are expected to be useful for the conceptual design of saw-tooth-shaped submerged breakwaters.

Keywords

Acknowledgement

The study was supported by the Natural Science Foundation of China-Shandong Joint Fund Project (U1706226) and the Natural Science Foundation of China (51779236, 51809053, 51709140).

References

  1. Carevic, D., Loncar, G., Prsic, M., 2013. Wave parameters after smooth submerged breakwater. Coast. Eng. 79, 32-41. https://doi.org/10.1016/j.coastaleng.2013.04.004
  2. Chan, I., Liu, P.L.F., 2012. On the runup of long waves on a plane beach. J. Geophys. Res.: Oceans 117 (C8).
  3. Chang, K., Hsu, T., Liu, P.L.F., 2001. Vortex generation and evolution in water waves propagating over a submerged rectangular obstacle: Part I. solitary waves. Coast. Eng. 44 (1), 13-36. https://doi.org/10.1016/S0378-3839(01)00019-9
  4. Chen, L., Ning, D., Teng, B., Zhao, M., 2017. Numerical and experimental investigation of nonlinear wave-current propagation over a submerged breakwater. J. Eng. Mech. 143 (9), 04017061. https://doi.org/10.1061/(ASCE)EM.1943-7889.0001271
  5. Christou, M., Swan, C., Gudmestad, O.T., 2008. The interaction of surface water waves with submerged breakwaters. Coast. Eng. 55 (12), 945-958. https://doi.org/10.1016/j.coastaleng.2008.02.014
  6. Feng, X., Yin, B., Gao, S., Wang, P., Bai, T., Yang, D., 2017. Assessment of tsunami hazard for coastal areas of Shandong Province, China. Appl. Ocean Res. 62, 37-48. https://doi.org/10.1016/j.apor.2016.12.001
  7. Goseberg, N., Wurpts, A., Schlurmann, T., 2013. Laboratory-scale generation of tsunami and long waves. Coast. Eng. 79, 57-74. https://doi.org/10.1016/j.coastaleng.2013.04.006
  8. Hirt, C.W., Nichols, B.D., 1981. Volume of fluid (VOF) method for the dynamics of free boundaries. J. Comput. Phys. 39 (1), 201-225. https://doi.org/10.1016/0021-9991(81)90145-5
  9. Hsiao, S., Lin, T., 2010. Tsunami-like solitary waves impinging and overtopping an impermeable seawall: experiment and RANS modeling. Coast. Eng. 57 (1), 1-18. https://doi.org/10.1016/j.coastaleng.2009.08.004
  10. Irtem, E., Seyfioglu, E., Kabdasli, S., 2011. Experimental investigation on the effects of submerged breakwaters on tsunami run-up height. J. Coast. Res. 64 (s), 516-520.
  11. Ji, Q., Dong, S., Luo, X., Guedes Soares, C., 2017. Wave transformation over submerged breakwaters by the constrained interpolation profile method. Ocean Eng. 136, 294-303. https://doi.org/10.1016/j.oceaneng.2017.03.037
  12. Jiang, X., Zou, Q., Zhang, N., 2017. Wave load on submerged quarter-circular and semicircular breakwaters under irregular waves. Coast. Eng. 121, 265-277. https://doi.org/10.1016/j.coastaleng.2016.11.006
  13. Kasem, T.H.M.A., Sasaki, J., 2010. Multiphase modeling of wave propagation over submerged obstacles using Weno and level set methods. Coast Eng. J. 52 (3), 235-259. https://doi.org/10.1142/S0578563410002166
  14. Li, M., Zhao, X., Ye, Z., Lin, W., Chen, Y., 2018. Generation of regular and focused waves by using an internal wave maker in a CIP-based model. Ocean Eng. 167, 334-347. https://doi.org/10.1016/j.oceaneng.2018.08.048
  15. Madsen, P.A., Fuhrman, D.R., Schaffer, H.A., 2008. On the solitary wave paradigm for tsunamis. J. Geophys. Res.: Oceans 113 (C12).
  16. Menter, F.R., 1994. Two-equation Eddy-viscosity turbulence models for engineering applications. AIAA J. 32 (8), 1598-1605. https://doi.org/10.2514/3.12149
  17. Qu, K., Ren, X.Y., Kraatz, S., 2017. Numerical investigation of tsunami-like wave hydrodynamic characteristics and its comparison with solitary wave. Appl. Ocean Res. 63, 36-48. https://doi.org/10.1016/j.apor.2017.01.003
  18. Qu, K., Tang, H.S., Agrawal, A., Cai, Y., Jiang, C.B., 2018. Numerical investigation of hydrodynamic load on bridge deck under joint action of solitary wave and current. Appl. Ocean Res. 75, 100-116. https://doi.org/10.1016/j.apor.2018.02.020
  19. Rambabu, A.C., Mani, J.S., 2005. Numerical prediction of performance of submerged breakwaters. Ocean Eng. 32 (10), 1235-1246. https://doi.org/10.1016/j.oceaneng.2004.10.023
  20. Schimmels, S., Sriram, V., Didenkulova, I., 2016. Tsunami generation in a large scale experimental facility. Coast. Eng. 110, 32-41. https://doi.org/10.1016/j.coastaleng.2015.12.005
  21. Shing, T.K.C., 2014. Experimental Study on the Effect of Submerged Breakwater Configuration on Long Wave Run-Up Reduction. The University of Hawaii, Hawaii.
  22. Silva, R., Losada, I.J., Losada, M.A., 2000. Reflection and transmission of tsunami waves by coastal structures. Appl. Ocean Res. 22, 215-223. https://doi.org/10.1016/S0141-1187(00)00012-2
  23. Sriram, V., Didenkulova, I., Sergeeva, A., Schimmels, S., 2016. Tsunami evolution and run-up in a large scale experimental facility. Coast. Eng. 111, 1-12. https://doi.org/10.1016/j.coastaleng.2015.11.006
  24. Synolakis, C.E., 1987. The runup of solitary waves. J. Fluid Mech. 185, 523-545. https://doi.org/10.1017/S002211208700329X
  25. Wang, D., Dong, S., Sun, J., 2019a. Numerical modeling of the interactions between waves and a Jarlan-type caisson breakwater using OpenFOAM. Ocean Eng. 188, 106230. https://doi.org/10.1016/j.oceaneng.2019.106230
  26. Wang, D., Sun, J., Gui, J., et al., 2019b. A numerical piston-type wave-maker toolbox for the open-source library OpenFOAM. J. Hydrodyn. 31, 800. https://doi.org/10.1007/s42241-018-0116-4
  27. Wang, J., He, G., You, R., Liu, P., 2018b. Numerical study on interaction of a solitary wave with the submerged obstacle. Ocean Eng. 158, 1-14. https://doi.org/10.1016/j.oceaneng.2018.03.064
  28. Wang, D., Sun, J., Gui, J., Ma, Z., Fang, K., 2018. Numerical simulation of solitary wave transformation over reef profile based on InterDyMFoam. The Ocean Eng. 36 (2), 47-55.
  29. Williams, I.A., Fuhrman, D.R., 2016. Numerical simulation of tsunami-scale wave boundary layers. Coast. Eng. 110, 17-31. https://doi.org/10.1016/j.coastaleng.2015.12.002
  30. Wu, Y.T., Hsiao, S.C., Huang, Z.C., Hwang, K.S., 2012. Propagation of solitary waves over a bottom-mounted barrier. Coast. Eng. 62, 31-47. https://doi.org/10.1016/j.coastaleng.2012.01.002
  31. Yao, Y., Tang, Z., Jiang, C., He, W., Liu, Z., 2018. Boussinesq modeling of solitary wave run-up reduction by emergent vegetation on a sloping beach. J. Hydro-Environ. Res. 19, 78-87. https://doi.org/10.1016/j.jher.2018.03.001
  32. Young, D.M., Testik, F.Y., 2011. Wave reflection by submerged vertical and semicircular breakwaters. Ocean Eng. 38 (10), 1269-1276. https://doi.org/10.1016/j.oceaneng.2011.05.003
  33. Zhang, N., Zhang, Q., Zou, G., Jiang, X., 2016. Estimation of the transmission coefficients of wave height and period after smooth submerged breakwater using a non-hydrostatic wave model. Ocean Eng. 122, 202-214. https://doi.org/10.1016/j.oceaneng.2016.06.037
  34. Zhuang, F., Lee, J., 1996. A viscous rotational model for wave overtopping over marine structure. In: Proceedings of the 25th International Conference on Coastal Engineering. ASCE, Orlando, Florida.

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