本論文為利用二維數值模式在造波水槽中模擬均勻流與剪力流條件下規則波通過拋物線型結構物之物理現象及其兩者間的差異。本論文所使用的數值模式為求解雷諾平均方程式(RANS)，並結合 閉合紊流模式進行模擬，再利用流體體積法(VOF)描述自由液面的變化。而為避免波-流同時由入射邊界產生時造成不必要的衝擊與下游邊界反射的問題，本文分別使用緩衝函數(ramp function)與輻射邊界條件(RBC)解決此問題。
為了測試本模式的模擬能力，本論文以Chen等人(2012)的理論與實驗及Tsao(1959)所推導的理論作驗證，其驗證內容包括質點運動軌跡、波形與速度剖面。從模式模擬的結果可知，本模式具有良好的模擬能力。
本論文主要探討主題為規則波通過拋物線型結構物時，在均勻流與剪力流條件下的現象進行比較，討論的主題包括渦度場、速度場、質點運動軌跡、壓力分佈及波形。

This study aims to simulate the regular wave propagating over a submerged parabolic obstacle in the uniform current and shear current using the two-dimensional numerical model named COBRAS. The present numerical model solves the Reynolds Averaged Navier-Stokes (RANS) equations combined with turbulence closure model, and the free surface deformation are tracked by using volume of fluid method (VOF). To avoid the unwanted fluctuation and reflection with the coexistence of wave and current, a ramp function is used and the outflow phase velocity of the radiation boundary condition is also modified.
The present numerical model simulation capability is validated by the theoretical solution and laboratory experiment of Chen et al. (2012), and analytical solution of Tsao (1959). Comparisons among the experimental data, analytical solution and present numerical results are in good agreements.
Then, the regular wave propagating over a submerged parabolic obstacle in the uniform current and shear current is investigated. Detailed discussions including the vorticity field, velocity field, particle trajectories, pressure distribution, and spatial surface profile are given.

1. Brevik, I., (1980). Flume experiment on waves and currents. II. Coast. Eng., 4, 89-110.
2. Brink-Kjaer, O., (1976). Gravity waves on a current: the influence of vorticity, a sloping bed and dissipation. Series paper 12. Inst. Of Hydrodyn.. & Hydraulic Engig., Tech. University of Denmark.
3. Chen, Y.-Y., Hsu, H.-C., Hwung, H.-H. (2012). Particle trajectories beneath wave-current interaction in a two-dimensional field. Nonlin. Processes Geophys., 19, 185-197
4. Chorin, A.J., (1968). Numerical solution of Navier-Stokes equations. Math. Comp., 22, 745-762.
5. Chorin, A.J., (1969). On the convergence of discrete approximations of the Navier-Stokes equations. Math. Comp., 23, 341-353.
6. 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.
7. Jonsson, I.G., (1990). Wave-current interaction. In: From the Sea: Ocean Engineering Science, vol. 9. Wiley, New York, p. 71.
8. Kirby, J. T., Chen, T. M., (1989). Surface waves on vertically sheared flows: Approximate dispersion relations. J. Geophys. Res., 94, 1013-1027.
9. Kishida, N., Sobey, R.J., (1988). Stokes theory for waves on a linear shear current. J. Eng. Mech., 114, 1317-1334.
10. Kothe, D.b., Mjolsness, R.C., Torrey, M.D.,(1991). RIPPLE: a new model for incompressible flows with free surface. Rep. LA-12007-MS, Los Alamos National Laboratory.
11. Lin, P.,(1998). Numerical modeling of breaking wave. Ph.D dissertation, Cornell University, Ithaca, USA.
12. Lin, P., Liu., P.L.-F., (1988a). A numerical study of breaking waves in the surf zone. J. Fluid Mech., 359, 239-264
13. Lin, P., Liu., P.L.-F., (1988b). Turbulence transport, vorticity dynamics, and solute mixing under plunging breaking waves in surf zone. J. Geophys. Res., 103(C8), 15677-15694
14. Liu., P.L.-F., Lin, P., Chang, K.-A., (1999). Numerical modeling of wave interaction with porous structure. J. Waterw. Port Coast. Ocean Eng., ASCE,125(6), 322-330.
15. Marin, F., (1999). Velocity and turbulence distributions in combined wave-current flows over a rippled bed. Journal of Hydraulic Research, 37(4): 501-16.
16. Peregrine, D. H., (1976). Interaction of water waves and currents. Adv. Appl. Mech., 16, 9-117.
17. Rodi, W.,(1980). Turbulence Model and Their Application in Hydraulics: a State of the Art Review. International Association for Hydraulic Research, Delft, The Netherlands. 9021270021
18. Shih, T.-H., Zhu, J., Lumley, J.L.J (1996). Calculation of wall-bounded complex flows and free shear flows. Int. J. Numer. Mech. Fluids, 23 (11), 1133-1144 Dec.
19. Simmen, J. A., Saffman, P. G., (1985). Steady deep water waves on a linear shear current. Stud. Appl. Maths, 73, 35-57.
20. Soulsby, R.L., Hamm, L., Klopman, G., Myrhaug, D., Simons, R.R., Thomas, G.P., (1993). Wave-current interaction within and outside the bottom boundary layer. Coast. Eng., 21, 41-69.
21. Teles Da Silva, A. F., Peregrine, D. H., (1988). Steep, steady surface waves on water of finite depth with constant vorticity. J. Fluid Mech., 195, 281-302.
22. Thomas, G.P., (1981). Wave-current interactions: an experimental and numerical study. Part 1. Linear waves. J. Fluid Mech., 110, 457-474.
23. Thomas, G.P., (1990). Wave-current interactions: an experimental and numerical study. Part 2. Nonlinear waves. J. Fluid Mech., 216, 505-536.
24. Thomas, G.P., Klopman, G., (1997). Wave-current interactions in the near-shore region. In: Hunt JN, editor. Gravity waves in water of finite depth, Advances in fluid mechanics. Computational Mechanics Publications, 66-84.
25. Tsao, S., (1959). Behaviour of surface waves on a linearly varying flow. Tr. Mosk. Fiz.-Tekh. Inst. Issled. Mekh. Prikl. Mat. 3, 66-84.
26. Zaman, M.H., Togashi, H., Yu, X., (1994). Modeling wave-current interaction over an uneven sea bottom. Proceedings of the Civil Engineering in the Ocean, JSCE, 25-30.
27. Zaman, M.H., Hiraishi, T., (1999). Nonlinear model for wave fields with current. Report of the Port and Harbor Research Institute, Japan 38 (3), 1-27.
28. Zaman, M.H., Togashi, H., (1996). Experimental study on interaction among waves, currents and bottom topography. Proceedings of the Civil Engineering in the Ocean, JSCE, 49-54.
29. Zaman, M.H., Togashi, H., (1997). Modeling horizontally two dimensional wave-current coexistence field over uneven topography. Proceedings of the 7th International Offshore and Polar Engineering Conference, ISOPE-97, vol. III, HI, USA, pp. 838-845.
30. Zaman, M.H., Togashi, H.Baddour, R.E., (2008). Deformation of monochromatic water wave trains propagating over a submerged obstacle in the presence of uniform currents. Ocean Eng., 35, 823-833.
31. 洪靖博，2011，「Numerical Study of Linear Waves Propagating over a Submerged Parabolic Obstacle in the Presence of a Steady Uniform Current」，國立成功大學水利及海洋工程研究所碩士論文。