於三度空間中，對自由表面規則前進重力波列傳遞於三度空間前後左右皆凹凸起伏之波形底床上所形成之波動流場，本文於攝動法之應用下，引入三個微小的攝動參數，展開解析至第三階次量，包含非共振之一般情況及發生共振之奇特情況，解析結果為函數表示式，於應用上極為方便。
對於規則前進波列傳遞於此底床地形所導引出的底床效應，隨不同水深及凹凸起伏程度、任意選定之入射角度、不同之來源入射波浪尖銳度之變化，皆可為本文理論解析所得之流場結構解所描述之。在非共振情況下，波動流場因底床效應所導引出的特性，隨相對水深之增加而

For gravity wave trains propagating over an arbitrary wavy bottom, a perturbation expansion is developed to the third-order by employing three small perturbation parameters. Both the resonant and non-resonant cases are treated and the singular behavior at resonance is treated separately. All the theoretical results are presented in explicit forms and easy to apply.
The bottom effects of different mean water depths and different degrees of undulation, as well as the steepness of incident waves, are clearly described by the theoretical results. In general non-resonant cases, the surface fluctuations deduced from undulated bottom topography decrease as the relative water depth increases and vice versa. The theory can be applied to the cases for wave trains propagating over wavy bottom topography with any arbitrary incident angles which are closer to natural phenomenon in coastal zone. Not only the well-known Bragg resonance but also the higher-order Bragg resonances are included in resonant cases. Unlike previous studies that analyze specific bottom topographies based on prescribed resonant conditions, both Bragg and higher-order Bragg resonances are revealed through the perturbation procedure step by step. For the resonant wave field, the amplification with propagating distance and time is revealed with the aid of the growth of energy flux.
This theory is successfully verified by reducing to simpler situations. Also, the analytical results for the special case of two-dimensional wavy bottom are compared with experimental data for validation.

中文摘要 Ⅰ
英文摘要 Ⅱ
目錄 Ⅲ
表目錄 Ⅴ
圖目錄 Ⅵ
符號說明 XI
第一章 緒論 1
1.1 研究動機與目的 1
1.2 文獻回顧 4
1.3 本文組織 6
第二章 波動系統之描述 8
2.1 波動流場之基本控制方程式 8
2.2 波動流場之邊界條件 9
2.3 波動流場各階次量之位相 11
第三章 理論解析 13
3.1 第一階解 17
3.2 第二階解 19
3.2.1 非共振之一般情況 20
3.2.2 發生共振之特殊情況 24
3.3 第三階解 29
3.3.1 非共振之一般情況 32
3.3.2 發生共振之特殊情況 42
第四章 波動特性及其共振時空成長 47
4.1非共振一般情況時水位脈動的特性 47
4.2 發生共振之特殊情況時波動之時空成長 48
4.2.1 第二階共振波動之前進成長 48
4.2.2 第三階共振波動之前進成長 53
第五章 理論檢核與試驗印證 69
5.1 理論檢核 69
5.1.1 真實物理實況之檢核 69
5.1.1.1 當底床為水平時 69
5.1.1.2 在深水情況 70
5.1.1.3 沿著任意入射波列方向於起伏底床處流線的滿足 70
5.1.1.3.1 非共振之一般情況 78
5.1.1.3.2 所示的共振之奇特情況 81
5.1.2 簡化成二維之波形底床 83
5.1.2.1 非共振之一般情況 84
5.1.2.2 共振之奇特情況 88
5.2 流場發生反射波之反射率 93
5.2.1 波動流場會產生反射波之機制及反射率 93
5.2.2 至第二階次量者 95
5.2.2.1 單型正弦波波形底床情況 95
5.2.2.2 雙型正弦波波形底床情況 97
5.2.3 於第三階次量才會出現的情況 100
5.2.3.1 單型正弦波波形底床情況 101
5.2.3.2 雙型正弦波波形底床情況 104
5.3 試驗印證 114
5.3.1 單型正弦波波形底床情況 114
5.3.1.1 與Davies＆Heathershaw(1984)之試驗結果比較 114
5.3.2 雙型正弦波波形底床情況 116
5.3.2.1 與Guazzelli et al(1992)之試驗結果比較 117
第六章 結論與建議 155
6.1 結論 155
6.2 建議 157
參考文獻 158
附錄A. 163
附錄B. 167
附錄C. 171
附錄D. 173
附錄E. 178
個人簡歷 181

1. 陳陽益、邱永芳、莊文傑(1989a)，"前進重力波與駐波之關連"，第十一屆海洋工程研討會論文集，273頁-298頁。
2. 陳陽益(1989b)，"兩波交會之系統化與流場機構"，港技術第四期，27頁-60頁。
3. 陳陽益(1990)， "等深水中兩規則前進重力波列交會之解析"，港技術第五期，1頁-45頁。
4. 陳陽益、湯麟武(1990)，"波形底床上規則前進重力波之解析"，第十二屆海洋工程研討會論文集，205頁-220頁。
5. 陳陽益(1991a)，"自由表面規則前進重力波傳遞於波形底床上之共振現象"，中華民國第十五屆全國力學會議論文集，289頁-296頁。
6. 陳陽益(1991b)，"波形底床上規則前進重力波之解析(Ⅱ)"，港灣技術第六期， 55頁-83 頁
7. 陳陽益、何良勝、湯麟武(1991c)，"波形底床上規則前進重力波之解析(Ⅲ)，有限長度之波形底床上波場共振情況"，第十三屆海洋工程研討會論文集，270頁-295頁。
8. 陳陽益(1992)，"規則前進重力波傳遞於波形底床上"，港灣技術第七期，17頁-47頁。
9. 張憲國、許泰文、李逸信(1997)，"波浪通過人工沙洲之試驗研究，第十九屆海洋工程研討會論文集"，242頁-249頁。
10. 郭金棟、陳文俊、陳國書(1999)，"雙列潛堤對海灘防治效益之研究"，第二十一屆海洋工程研討會論文集"，307頁-313頁。
11. 陳陽益、郭少谷(2000)，"三維波形底床上前進波列之傳遞Ⅰ."，第二十二屆海洋工程研討會論文集，9頁-18頁。
12. 郭少谷(2000)，"單振幅雙向波形底床上前進波列之傳遞"，碩士論文，國立中山大學海洋環境及工程學系。
13. Berkhoff, J.C.W. (1972), “Computation of Combined Refraction-Diffraction,” Proceedings of the 13th International Conference on Coastal Engineering, ASCE, Vancouver, Canada, Vol. 1, pp. 471-490.
14. Charberlain, P. G. and Porter, D. (1995), “Decomposition methods for wave scattering by topography with application to ripple beds,” Wave Motion, 22, pp. 201-214.
15. Cheng, C. Y., Chen, Y. Y. and Chen, G. Y. (2007), “A three-dimensional wave field over a bidirectionally periodic ripple bottom,” Ocean Engineering, 34, pp. 303-319.
16. Cho, Y. S. and Lee, C. (2000), “Resonant reflection of waves over sinusoidally varying topographies,” Journal of Coastal Research, 16(3), pp. 870-876.
17. Cokelet, E. D. (1977), “Steep gravity waves in water of arbitrary uniform depth,” Phil. Trans. R. Soc. Land., A. 286, pp. 183-230.
18. Davies, A. G. (1980), “Some interactions between surface water waves and ripples and dunes on the seabed,” Inst. Oceanogr. Sci. Rep. 108.
19. Davies, A. G. (1982a), “On the interaction between surface waves and undulations on the seabed,” J. Marine Research., 40, 2, pp. 331-368.
20. Davies, A. G. (1982b), “The reflection of wave energy by undulations on the seabed,” Dynamics of Atmospheres and Oceans, 6, pp. 207-232.
21. Davies, A. G. and Heathershaw, A. D. (1983), “Surface wave propagation over sinusoidally varying topography: theory and observation,” Inst. Oceanogr. Sci. Report. 159.
22. Davies, A. G. and Heathershaw, A. D. (1984), “Surface wave propagation over sinusoidally varying topography,” J. Fluid Mech., 144, pp. 419-443.
23. Dolan, J. T. (1983), “Wave mechanisms for the formation of multiple longshore bars with emphasis on the Chesapeake Bay,” Master Thesis, Dept. of CE, Univ. of Florida
24. Fenton, J. D. (1985), “A fifth-order Stokes theory for steady waves,” J. Waterway, Port, Coastal and Ocean Engineering, 3, 2, pp. 216-234.
25. Guazzelli, E., Rey, V. and Belzons, M. (1992), “Higher-order Bragg reflection of gravity surface waves by periodic beds,” J. Fluid Mech., 245, pp. 301-317.
26. Hara, T. and Mei, C. C. (1987), “Bragg scattering of surface waves by periodic bars: theory and experiment,” J. Fluid Mech., 178, pp. 221-241.
27. Heathershaw, A. D. (1982), “Seabed-wave resonance and sand bar growth,” Nature, 296, pp. 343-345.
28. Heathershaw, A. D. and Davies, A. G. (1985), “Resonant wave reflection by transverse bedforms and its relation to beaches and offshore bars,” Marine Geology, 62, pp. 321-338.
29. Hsu, T. W., Chang, H. K., Tsai, L. H. (2002), “Bragg reflection of waves by different shapes of artificial bars,” China Ocean Engineering, 16(3), pp. 343–358.
30. Hsu, T. W., Tsai, L. H., Huang, Y. T. (2003), “Bragg scattering of water waves by doubly composite artificial bars,” Coastal Engineering Journal, 45(2), pp. 235–253.
31. Jeffreys, H. (1944), “Motion of waves in shallow water,” Note on the offshore bar problem and reflexion from a bar, Ministry of Supply Wave Rep., 3(London).
32. Kirby, J. T. (1986a) “On the gradual reflection of weakly nonlinear Stokes waves in regions with varying topography,” J. Fluid Mech., 162, pp. 187-209.
33. Kirby, J. T. (1986b), “A general wave equation for waves over rippled beds,” J. Fluid Mech., 162, pp. 171-186.
34. Kirby, J. T. (1989), “Propagation of surface waves over an undulating bed,” Physics of Fluids A, Vol.1, No.11, pp. 1898-1899.
35. Kirby, J. T. and Anton, J. P. (1990), “Bragg Reflection of Waves by Artificial Bars,” Proceedings of the 22nd International Conference on Coastal Engineering, ASCE, Delft, Netherlands, pp. 757-768.
36. Lau, J. and Travis, B. (1973), “Slowly varying Stokes waves and submarine longshore bars,” J. Geophysical Research, Vol. 78, pp. 4489-4497.
37. Lin, S. C., Chen, Y. Y. and Chang, S. G. (1987), “Numerical verification on a 90 interior crest angle in limiting gravity waves, ” J.C.I.E., Vol. 10, NO. 5, pp. 539-542.
38. Liu, Y. and Yue, D. K. P. (1998), “On generalized Bragg scattering of surface waves by bottom ripples,” J. Fluid Mech., 356, 297-326.
39. Longuet-Higgins, M S. (1962), “Resonant interactions between two trains of gravity waves,” J. Fluid Mech., 12, 321-332.
40. Mei, C. C. (1985), “Resonant reflection of surface water waves by periodic sand bars,” J. Fluid Mech., 152, 315-335.
41. Mei, C. C., Hara, T. and Naciri, M. (1988), “Note on Bragg scattering of water waves by parallel bars on the seabed,” J. Fluid Mech., 186, 147-162.
42. Mei, C. C., Hara, T., Yu, J. (2001) “Longshore Bars and Bragg Resonance,” In: Lecture Notes in Physics: Geomorphological Fluid Mechanics, N.J. Balmforth, A. Provenzale (Eds.), Springer-Verlag, Berlin Heidelberg, Vol. 582, pp. 500-527.
43. Miles, J.W. (1981), “Oblique Surface-wave Diffraction by a Cylindrical Obstacle,” Dynamics of Atmospheres and Oceans, Vol. 6, pp. 121-123.
44. Mitra, A. and Greenberg M. D. (1984), “Slow interactions of gravity waves and a corrugated sea bed,” Trans. ASME E: J. Appl. Mech., 51, 251-255.
45. Nielsen, P. (1979), “Some basic concepts of wave sediment transport,” Institute of Hydrodynamic and Hydraulic Engineering Serial Paper 20, Technical University of Denmark.
46. Phillips, O. M. (1960), “On the dynamics of unsteady gravity waves of finite amplitude. Part 1,” J. Fluid Mech., 9, 193-217.
47. Phillips, O. M. (1977), Dynamics of the upper ocean, 2nd ed., Cambridge University Press, London.
48. Porter, R. and Porter, D. (2001), “Interaction of water waves with three- dimensional periodic topography,” J. Fluid Mech., 434, 301-335.
49. Rey, V., Guazzelli, E. and Mei, C. C. (1996), “Resonant reflection of surface gravity waves by one-dimensional doubly sinusoidal beds,” Phy. of Fluids, 8(6), 1525-1530.
50. Rienecker, M. M. and Fenton, J. D. (1981), “A Fourier approximation method for step water waves,” J. Fluid Mech., 140, pp. 119-137.
51. Saylor, J.H. and Hands E.B. (1970), “Properties of longshore bars in the Great Lakes,” Proceedings of the 12th International Conference on Coastal Engineering, ASCE, Vol. 22, 839-853
52. Schwartz, L. W. (1974), “Computer extension and analytic continuation of Stokes expansion for gravity waves,” J. Fluid Mech., 62, pp. 553-578.
53. Short, A. D. (1975), “Multiple Offshore Bars and Standing Waves,” J. Geophysical Research, Vol. 80, No. 27, pp. 3838-3840.
54. Skielbreia, L. and Hendrickson, J. A. (1961), “Fifth order gravity wave theory,” Porc. 7th Conf. Coastal Eng., pp.184-196.
55. Stokes, G. G. (1847), “On the theory of oscillatory waves,” Trans. Camb. Phil. Soc., 8, pp. 441-473.
56. Ursell, F. (1947), “The reflection of waves from a submerged low reef,” Admiralty Res. Lab., Teddington, Middx, Rep., ARL/R5/103.41/W.
57. Wang, S. K., Hsu, T. W., Tsai, L. H., and Chen S. H. (2006), “An application of Miles’ theory to Bragg scattering of water waves by doubly composite artificial bars,” Ocean Engineering, 33, pp. 331-349.
58. Williams, J. M. (1981), “Limiting gravity waves in water of finite depth,” Phil. Trans. Roy. Soc. Lond., A. 302, pp. 139-188.
59. Yu, J. and Mei, C. C. (2003), “Do Longshore Bars Shelter the Shore?” J. Fluid Mech., 404, 251-268.
60. Zhang, L., Kim, M.H. and Edge, B. L. (1999), “Hybrid model for Bragg scattering of water waves by steep multiply-sinusoidal bars,” J. Coastal Research, 15(2), 486-495.