Extended elliptic mild slope equation incorporating the nonlinear shoaling effect

• Autorzy: Xiao Q. L. , Li Ch. H. , Fu X. Y. , Wang M. J.
• Języki publikacji: EN

Abstrakty

EN

The transformation during wave propagation is significantly important for the calculations of hydraulic and coastal engineering, as well as the sediment transport. The exact wave height deformation calculation on the coasts is essential to near-shore hydrodynamics research and the structure design of coastal engineering. According to the wave shoaling results gained from the elliptical cosine wave theory, the nonlinear wave dispersion relation is adopted to develop the expression of the corresponding nonlinear wave shoaling coefficient. Based on the extended elliptic mild slope equation, an efficient wave numerical model is presented in this paper for predicting wave deformation across the complex topography and the surf zone, incorporating the nonlinear wave dispersion relation, the nonlinear wave shoaling coefficient and other energy dissipation factors. Especially, the phenomenon of wave recovery and second breaking could be shown by the present model. The classical Berkhoff single elliptic topography wave tests, the sinusoidal varying topography experiment, and complex composite slopes wave flume experiments are applied to verify the accuracy of the calculation of wave heights. Compared with experimental data, good agreements are found upon single elliptical topography and one-dimensional beach profiles, including uniform slope and step-type profiles. The results indicate that the newly-developed nonlinear wave shoaling coefficient improves the calculated accuracy of wave transformation in the surf zone efficiently, and the wave breaking is the key factor affecting the wave characteristics and need to be considered in the nearshore wave simulations.

Słowa kluczowe

EN

nonlinear dispersion relation; nonlinear shoaling coefficient; extended elliptic mild slope equation; surf zone; wave transformation

• Wydawca: Gdańsk University of Technology, Faculty of Ocean Engineering & Ship Technology
• Czasopismo: Polish Maritime Research
• Rocznik: 2016
• Tom: S 1
• Strony: 44--51
• Opis fizyczny: Bibliogr. 23 poz., rys.

Twórcy

autor

Xiao Q. L.

• Key Laboratory of Coastal Disaster and Defence, Ministry of Education, Hohai University, Nanjing, China
• College of Harbour, Coastal and Offshore Engineering, Hohai University, Nanjing, China

autor

Li Ch. H.

• Key Laboratory of Coastal Disaster and Defence, Ministry of Education, Hohai University, Nanjing, China

autor

Fu X. Y.

• Key Laboratory of Coastal Disaster and Defence, Ministry of Education, Hohai University, Nanjing, China

autor

Wang M. J.

• Key Laboratory of Coastal Disaster and Defence, Ministry of Education, Hohai University, Nanjing, China

Bibliografia

• 1. Akbarpour Jannat, M. R., & Asano, T. (2007). External forces of sediment transport in surf and swash zones induced by wave groups and their associated long waves. Coastal Engineering Journal, 49(02), 205-227.
• 2. Berkhoff, J. C. W., Booy, N., & Radder, A. C. (1982). Verification of numerical wave propagation models for simple harmonic linear water waves. Coastal Engineering, 6(3), 255-279.
• 3. Cerrato, A., González, J. A., & Rodríguez-Tembleque, L. (2016). Boundary element formulation of the Mild-Slope equation for harmonic water waves propagating over unidirectional variable bathymetries. Engineering Analysis with Boundary Elements, 62, 22-34.
• 4. Chang, G., Ruehl, K., Jones, C. A., Roberts, J., & Chartrand, C. (2016). Numerical modeling of the effects of wave energy converter characteristics on nearshore wave conditions. Renewable Energy, 89, 636-648.
• 5. Chella, M. A., Bihs, H., Myrhaug, D., & Muskulus, M. (2015). Hydrodynamic characteristics and geometric properties of plunging and spilling breakers over impermeable slopes. Ocean Modelling.
• 6. Hamidi, M. E., Hashemi, M. R., Talebbeydokhti, N., & Neill, S. P. (2012). Numerical modelling of the mild slope equation using localised differential quadrature method. Ocean Engineering, 47, 88-103.
• 7. Korotkevich, A. O., Dyachenko, A. I., & Zakharov, V. E. (2016). Numerical simulation of surface waves instability on a homogeneous grid. Physica D: Nonlinear Phenomena, 321, 51-66.
• 8. Lin, X., & Yu, X. (2015). A finite difference method for effective treatment of mild-slope wave equation subject to non-reflecting boundary conditions. Applied Ocean Research, 53, 179-189.
• 9. Li, R. J., Zhang, Y., & Gao, H. S. (2004). A wave nonlinear dispersion relation and its application. Ocean Eng./Haiyang Gongcheng, 22(3), 20-24.
• 10. Lupieri, G., & Contento, G. (2015). Numerical simulations of 2-D steady and unsteady breaking waves. Ocean Engineering, 106, 298-316.
• 11. Maa, J. Y., Hsu, T. W., & Lee, D. Y. (2002). The RIDE model: an enhanced computer program for wave transformation. Ocean Engineering, 29(11), 1441-1458.
• 12. Nagayama, S. (1983). Study on the change of wave height and energy in the surf zone. Bachelor thesis, Yokohama National University, Japan (in Japanese).
• 13. Rincon, M. A., & Quintino, N. P. (2016). Numerical analysis and simulation for a nonlinear wave equation. Journal of Computational and Applied Mathematics, 296, 247-264.
• 14. Salmon, J. E., & Holthuijsen, L. H. (2015). Modeling depthinduced wave breaking over complex coastal bathymetries. Coastal Engineering, 105, 21-35.
• 15. Salmon, J. E., Holthuijsen, L. H., Zijlema, M., van Vledder, G. P., & Pietrzak, J. D. (2015). Scaling depth-induced wavebreaking in two-dimensional spectral wave models. Ocean Modelling, 87, 30-47.
• 16. Sharma, A., Panchang, V. G., & Kaihatu, J. M. (2014). Modeling nonlinear wave–wave interactions with the elliptic mild slope equation. Applied Ocean Research, 48, 114-125.
• 17. Stockdon, H. F., Holman, R. A., Howd, P. A., & Sallenger, A. H. (2006). Empirical parameterization of setup, swash, and runup. Coastal engineering, 53(7), 573-588.
• 18. Thompson, D. A., Karunarathna, H., & Reeve, D. (2016). Comparison between wave generation methods for numerical simulation of bimodal seas. Water Science and Engineering, 9(1), 3-13.
• 19. Tsai, C. P., Chen, H. B., Hwung, H. H., & Huang, M. J. (2005). Examination of empirical formulas for wave shoaling and breaking on steep slopes. Ocean Engineering, 32(3), 469-483.
• 20. Yu, J., & Zheng, G. (2012). Exact solutions for wave propagation over a patch of large bottom corrugations. Journal of Fluid Mechanics, 713, 362-375.
• 21. Zhao, L., Panchang, V., Chen, W., Demirbilek, Z., & Chhabbra, N. (2001). Simulation of wave breaking effects in two-dimensional elliptic harbor wave models. Coastal Engineering, 42(4), 359-373.
• 22. Yoon, BI; Woo, SB. (2013). Tidal asymmetry and flood/ ebb dominance around the Yeomha channel in the Han River Estuary, South Korea. Journal of coastal research, 65, 1242-1246.
• 23. Chen, M; Han, DF. (2015). Multi-grid model for crowd’s evacuation in ships based on cellular automata. Polish maritime research, 22(1), 75-81.