本文擬應用二維數值波浪模式，探討規則波在斜坡底床上溯升的波流特性。為模擬黏性流體的運動行為，模式求解二維時變的雷諾平均方程式 (Reynolds Averaged Navier-Stokes equations, RANS) 及低雷諾數紊流傳輸模式 ( model)。並結合等位函數法 (Level Set Method) 及質點等位函數法 (Particle Level Set Method) 追蹤複雜的自由液面變化。為模擬流體與固體邊界之間的互制行為，本模式擬採用質量守恆邊界法 (Mass-Conserved Boundary Method)。此法可於卡式座標下，滿足不規則固體邊界條件，模擬波浪水體於斜坡底床附近的流場演變情形。為瞭解規則波於斜坡底床上溯升的波流場特性，本文擬改變不同波浪條件，入射至不同坡度的斜坡底床，觀察其自由液面演變情形，並探討在不同相位下的瞬時流場及堤面波壓分佈情形。由自由液面與水下流速的演變，可看出有部分駐波的現象發生。邊界層流場存在回流 (reverse flow) 現象，為自由液面高程差所影響。由堤面波壓可知，波壓正負向與其對應的自由液面高程變化有關。此外，為定性研究週期波浪長時間作用於斜坡底床的波流場特性，本文亦探討各條件下的週期平均流場及堤前底床最大剪應力。結果顯示在斜坡坡面上存在類似穩環流胞 (steady recirculating cell) 的現象。

In present study, a 2-D numerical viscous wave flume was applied to represent the characteristic of wave and flow field as regular waves run-up on a sloping bed. The unsteady, two-dimensional Reynolds Averaged Navier-Stokes (RANS) equations and the turbulence model ( model) were solved for simulating the behavior of real fluid. The level set method and the particle level set method were adopted to capture the complex free surface evolution. The Mass-Conserved Boundary Method (MCBM) was applied to represent the fluid-solid interaction in the vicinity of irregular solid boundary under the Cartesian grid system. This study is proposing to investigate the wave run-ups with different incident regular waves and bed slopes. The free-surface evolutions, the flow fields and the wave pressures on the sloping bed are discussed. Partial standing waves and the reverse flows within boundary layer are reproduced in this study. The evolutions of wave pressure on the sloping bed are related to the instantaneous wave elevations. Furthermore, steady recirculating cell are detected from the mean velocity field upon the sloping bed.

1. Carrier, G. and H. Greenspan "Water waves of finite amplitude on a sloping beach." J. Fluid Mech 4(1): 97-109. (1958).
2. Chen, C. J. and H. C. Chen "Finite analytic numerical method for unsteady two-dimensional Navier-Stokes equations." Journal of computational physics 53(2): 209-226. (1984).
3. De Waal, J. and J. Van der Meer "Wave runup and overtopping on coastal structures", ASCE AMERICAN SOCIETY OF CIVIL ENGINEERS. (1992).
4. Enright, D., R. Fedkiw, et al. "A hybrid particle level set method for improved interface capturing." Journal of computational physics 183(1): 83-116. (2002).
5. Granthem, K. N. "A model study of wave run-up on sloping structures", University of California, Department of Engineering. (1953).
6. Hall and Watts "Laboratory investigation of the vertical rise of solitary waves on impermeable slopes." Tech. Memo 33(US Army Corps of Engineer): 14. (1953).
7. Hara, T. and C. C. Mei "Oscillating flows over periodic ripples." J. Fluid Mech 211(1832): 209. (1990).
8. Hashimoto, K. and M. S. Pritzker "Electron microscopic study of reticulohistiocytoma: an unusual case of congenital, self-healing reticulohistiocytosis." Archives of dermatology 107(2): 263. (1973).
9. Hsiao, S. C., T. W. Hsu, et al. "On the evolution and run-up of breaking solitary waves on a mild sloping beach." Coastal Engineering 55(12): 975-988. (2008).
10. Hughes, S. A. "Estimation of wave run-up on smooth, impermeable slopes using the wave momentum flux parameter." Coastal Engineering 51(11): 1085-1104. (2004).
11. Hunt, I. A. "Design of seawalls and breakwaters." Journal of Waterways and Harbours Division 85: 123-152. (1959).
12. Kennedy, A. B., Q. Chen, et al. "Boussinesq modeling of wave transformation, breaking, and runup. I: 1 D." Journal of Waterway, Port, Coastal and Ocean Engineering 126(1): 39-47. (2000).
13. Lange, M. A. and T. J. Ahrens Fragmentation of ice by low velocity impact. (1982).
14. Launder, B. and D. Spalding "The numerical computation of turbulent flows." Computer methods in applied mechanics and engineering 3(2): 269-289. (1974).
15. Li, Y. and F. Raichlen "Non-breaking and breaking solitary wave run-up." Journal of Fluid Mechanics 456: 295-318. (2002).
16. Lin, P., Chang "Runup and rundown of solitary waves on sloping beaches." Journal of Waterway, Port, Coastal, and Ocean Engineering 125(5): 247-255. (1999).
17. Madsen, P. A., O. Sørensen, et al. "Surf zone dynamics simulated by a Boussinesq type model. Part I. Model description and cross-shore motion of regular waves." Coastal Engineering 32(4): 255-287. (1997).
18. Nadaoka, K., M. Hino, et al. "Structure of the turbulent flow field under breaking waves in the surf zone." Journal of Fluid Mechanics 204(1): 359-387. (1989).
19. Noarayanan, L., K. Murali, et al. "Role of Vegetation on Beach Run-up due to Regular and Cnoidal Waves." Journal of Coastal Research 28(1A): 123-130. (2012).
20. Osher, S. and J. A. Sethian "Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations." Journal of computational physics 79(1): 12-49. (1988).
21. Peng, D., B. Merriman, et al. "A PDE-based fast local level set method." Journal of computational physics 155(2): 410-438. (1999).
22. Raichlen, F. and J. Hammack Jr "Run-up due to Breaking and Non-breaking Waves." Coastal Engineering: 1937-1955. (1974).
23. Sainflou "Essai sur les diques maritimes verticales." Annales des Ponts et Chaussees 98(1): 5-48. (1928).
24. Sakakiyama, T. and P. L. F. Liu "Laboratory experiments for wave motions and turbulence flows in front of a breakwater." Coastal Engineering 44(2): 117-139. (2001).
25. Saville "Wave run-up on shore structures." Journal of the Waterways and Harbors Division, ASCE 82(925). (1956).
26. Shtencel, V. PRESSURE UPON VERTICAL WALL PROM STANDING WAVES. (1972).
27. Sumer, B. M. and J. Fredsøe "Experimental study of 2D scour and its protection at a rubble-mound breakwater." Coastal Engineering 40(1): 59-87. (2000).
28. Synolakis, C. E. "The runup of solitary waves." Journal of Fluid Mechanics 185(1): 523-545. (1987).
29. Ting, F. C. K. and J. T. Kirby "Observation of undertow and turbulence in a laboratory surf zone." Coastal Engineering 24(1): 51-80. (1994).
30. Wang, C. Y. "On high-frequency oscillatory viscous flows." J. Fluid Mech 32(Part 1). (1968).
31. Wassing, F. "Model investigation on wave run-up carried out in the Netherlands during the past twenty years. " (1957).
32. Wood, D. J., G. K. Pedersen, et al. "Modelling of run up of steep non-breaking waves." Ocean engineering 30(5): 625-644. (2003).
33. Zelt, J. "The run-up of nonbreaking and breaking solitary waves." Coastal Engineering 15(3): 205-246. (1991).
34. Lin, C.Y.,” Simulation of Breaking Waves Using Particle Level Set Method.”， 國立成功大學水利及海洋工程研究所博士論文. (2007)
35. 陳志欣，”應用質量守恆邊界法模擬波浪於不規則近岸結構物上之溯升與越波”， 國立成功大學水利及海洋工程研究所博士論文. (2011)