本研究應用二維非線性數值水槽模擬不規則波通過系列潛堤所造成的布拉格共振現象。數值模式基於勢能理論，採用線性元素(linear element method)求解邊界積分公式(Boundary Integral Equation, BIE)，非線性自由液面邊界條件採用Mixed Eulerian and Lagrangian method (MEL)搭配四階Runge-Kutta method (RK4)處理。不規則波造波方式是採用線性波理論搭配JONSWAP波譜，在時間領域下給定造波邊界上的速度分佈，同時在水槽兩端設置數值消波區，以消除結構物造成的反射波以及透過波。
數值計算結果顯示，規則波與系列潛堤交互作用的布拉格反射現象，與實驗及其他數值模式研究呈現良好的吻合性；而在不規則波其的結果與規則波案例的趨勢亦相當類似。雖不規則波之布拉格反射率小於規則波案例，但其布拉格共振的頻率範圍則較規則波者為寬，對實際海域有較大的適用性。再者針對波浪通過系列潛堤之影響參數進行有系統的探討，布拉格反射強度隨相對堤高比、潛堤堤頂寬、潛堤列數及堤腳坡度等的增加而遞增，但在相對堤高較大情況，反射率尖峰值會有向低頻偏移的現象。

A 2-D fully nonlinear numerical wave tank (NWT) is developed to investigate the Bragg resonance scattered by submerged multi-array breakwaters for random waves. This model is based on a boundary integral equation method with linear element scheme. The fully nonlinear free surface boundary condition is treated using the Mixed Eulerian-Lagrangian method and the 4th-order Runge-Kutta method. The incident random waves are generated by JONSWAP spectrum at one end of the wave tank. Two damping zones are deployed at both ends of the NWT to absorb the energy of the reflected and transmitted waves.
In the regular wave cases, the results of Bragg reflection calculated are in good agreement with that of other experiments and numerical models. In addition, the simulated spectrum of random waves is also verified by the original input spectrum. The results of the random waves have the same trend as those of the Regular waves. The reflection coefficient for random waves at the first peak of resonance is about 70 percent of that of the regular wave, but the frequency of band width of Bragg effect has become wider and this advantage may compensate the peak reduction. Finally, we may conclude that the present model is adequate to use as a tool for coastal protection. Systematic studies for random waves propagating over series submerged breakwaters are conducted. The Bragg reflection will be enhanced with the increase of relative height, the length of bars, the number of breakwaters, and the toe angle of submerged breakwaters. In this study, it also reveals that the frequency of peak reflection for higher breakwaters has down shift phenomenon.

中文摘要 Ⅰ
英文摘要 Ⅱ
誌謝 Ⅲ
目錄 Ⅳ
圖目錄 Ⅶ
表目錄 Ⅹ
一、 諸論
1.1研究動機與目的 1
1.2文獻回顧 3
1.2.1非線性數值造波水槽 3
1.2.2波浪與系列潛堤的非線性交互作用 4
1.3本文組織 6
二、理論基礎
2.1控制方程式及邊界積分公式 7
2.1.1控制方程式(Governing equation) 7
2.1.2邊界積分公式 8
2.2規則波數值水槽 8
2.2.1造波邊界(Inflow boundary condition, IBC) 8
2.2.2底床邊界(Bottom boundary condition, BBC) 9
2.2.3直立壁邊界(Wall boundary condition, WBC) 9
2.2.4自由液面邊界(Free surface boundary condition, FSBC) 10
2.2.4.1 Eulerian座標系統 10
2.2.4.1 Lagrangian座標系統 10
2.2.4.3數值消波區 11
2.3不規則波造波水槽 12
2.3.1造波函數 12
2.3.2數值消波區 13
2.3.3造波流程 14
2.4邊界元素法(Boundary Element Method) 15
2.5數值方法 17
2.5.1曲線座標系統 17
2.5.2自由液面與固體交界面速度修正 18
2.5.3 4th-order Runge-Kutta method 19
2-5-4網格重置(node-regirdding procedure) 19
2-5-5平滑化(smoothing scheme) 20
2-6程式流程圖 21
三、數值驗證
3.1造波函數檢驗 22
3.1.1規則波案例驗證 22
3.1.2不規則波案例驗證 26
3.2數值水槽反射率檢驗 29
3.2.1不規則波反射率計算 29
3.2.2結構物不存在時之反射率 30
3.3波與系列潛堤交互作用 33
3.3.1規則波與系列潛堤驗證 33
3.3.2不規則波與系列潛堤驗證 35
四、結果與討論
4.1系列潛堤 36
4.1.1規則波及不規則波影響 36
4.1.2潛堤列數影響 38
4.1.3相對堤高比影響 41
4.1.4堤腳坡度影響 43
4.1.5相對堤頂寬影響 45
4.1.6相對堤間距影響 46
4.2綜合比較 48
4.2.1潛堤數量及相對提高比影響 48
4.2.2堤腳坡度及潛堤形式影響 50
4.2.3現場施工之最佳配置建議 51
五、結論與建議
5.1結論 52
5.2建議 54
參考文獻 55
附錄A 海岸保護工法 58

1.陳陽益、湯麟武(1990)「波床底床上規則前進重力波之解析」，第12屆海洋工程研討會論文集，台灣台北，第 270-305 頁。
2.張憲國 (1994) 「人工沙洲形狀對表面重力波反射率之影響」，第16屆海洋工程研討會論文集，第A-108-A-121頁。
3.李兆芳、黃玄 (1996) 「波浪與潛式透水結構物互相作用分析」，第18屆海洋工程研討會論文集，第273-281頁。
4.黃材成、林怡成 (1997) 「透水潛堤波浪特性之實驗研究」，第19屆海洋工程研討會論文集，第220-227頁。
5.岳景雲、曹登皓、陳丙奇 (1997) 「波浪通過系列潛堤反射率之研究」，第八屆全國海岸工程學術討論會暨1997年海峽兩岸港口及海岸開發研討會論文集(下)，第683-690頁。
6.岳景雲、曹登皓、翁文凱(2000)，「波浪通過不透水雙列潛堤之研究」，兩岸港口及海岸開發研討會論集，台灣新竹，第 112-118 頁。
7.郭金棟(2004)，「海岸保護-海岸環境創造序論」。台北：財團法人中興工程科技研究發展基金會。
8.經濟部水利署(2004) ，「海灘侵蝕防治新科技研發(1/4~4/4)總摘要報告」。2-2頁。
9.許榮中、蔡清標(2007)，「海岸開發與保育」。台北：科技圖書股份有限公司。21-38頁。
10.陳韋銘、唐宏結、黃材成(2007)「應用非線性數值水槽研究不規則波與固定浮體之交互作用」，第29屆海洋工程研討會論文集，第643-648頁。
11.Bouws, E., Gunther, H., Rosenthal, W., and Vincent, C.L.,1987. Similarity of the wind wave spectrum in finite depth water. Part 2：statistical relations between shape and growth stage. Dt. Hydrogr. Z. 40.
12.Cho, Y.S., Yoo, S.B. Lee, J.I., Yoon, T.H., 2001. A concept of beach protection with submerged breakwaters. Jounral of Coastal Research 34 (special issue), 671-678.
13.Cho, Y.-S., Lee, J., 2004. Experimental study of strong reflection of regular water waves over submerged breakwaters in tandem. Ocean Engineering 31, 1325–1335.
14.Cointe, R., 1990. Numerical simulation of a wave channel. Engineering Analysis with Boundary Elements 7(4), 167-177.
15.Davies, A.G., Heathershaw, A.D., 1984. Surface propagation over sinusoidally varying topography. Journal of Fluid Mechanics 144, 419-443.
16.Goda, Y., 1999. A comparative review on the functional forms of directional wave spectrum. Coastal Engineering Journal 41(1), 1-20.
17.Goda, Y., Suzuki, Y., 1976. Estimation of incident and reflected waves in random wave experiments. Proceedings of the 15th International Conference Coastal Engineering, pp. 628-650.
18.Grilli, S.T., Svendsen, I.A., 1990. Corner problems and global accuracy in the boundary element solution of nonlinear wave flows. Engineering Analysis with Boundary Elements 7(4), 178-195.
19.Hsu, T.W., Hsiao, S.C., Ou, S.H., Wang, S.K., Yang, B.D., Chou, S.E., 2007. An application of Boussinesq equations to Bragg reflection of irregular waves. Ocean Engineering 34, 870-883.
20.Huang, C.C., Tang, H.J., Wang, C.T., 2007. A fully nonlinear wave-current numerical wave tank based on BEM. : Proceedings of 17th International Offshore and Polar Engineering Conference, pp. 2100-2106.
21.Kim, M.H., Celebi, M.S., Kim, D.J., 1998. Fully nonlinear interactions of waves with a three-dimensional body in uniform currents. Applied Ocean Research 20, 309-321.
22.Kim, C.H., Clément, A.H., Tanizawa, K., 1999. Recent research and development of numerical wave tank - A review. Int. J. Offshore and Polar Eng., 9(4), 241-256.
23.Koo, W.C., Kim, M.H., 2004. Freely floating-body simulation by a 2D fully nonlinear numerical wave tank. Ocean Engineering 31, 2011-2046.
24.Longuet-Higgins, M.S., Cokelet, E., 1976. The deformation of steep surface waves on water I. A numerical method of computation. Proc. Royal Society, London, Series A350, 1-26.
25.Massel, S.R., 1993. Extended refraction-diffraction equation for surface waves. Coastal Engineering 19, 97-126 .
26.Miles, J., 1981. Oblique surface-wave diffraction by a cylindrical obstacle. Dynamics of Atmospheres and Oceans 6, 121-123.
27.Ohyama, T., Nadaoka, K., 1991. Development of a numerical wave tank for analysis of nonlinear and irregular wave field. Fluid Dynamics Research 8, 231-251.
28.Sen, D., Pawlowski, J.S., Lever, J., Hinchey, M.J., 1990. Two-dimensional numerical modeling of large motions of floating bodies in waves. Proc. 5th Int. Conf. on Num. Hydro., pp. 351-373.
29.Tanizawa, K., 1996. Long time fully nonlinear simulation of floating body motions with artificial damping zone. Journal of the Society of Naval Architects of Japan 180, 311-319.
30.Tanizawa, K., 2000. The state of the art on numerical wave tank. Proceedings of 4th Osaka Colloquium on Seakeeping Performance of Ships , pp.95-114.