於三度空間下，對於等水深中兩自由表面規則前進重力波交會所構成的波動系統，本文於攝動法與chain rule的應用之下，已求得至第三階的整體流場結構解，包含非共振之一般情形與共振之奇特情形。
而當共振之奇特情形發生時，共振波動隨時間與其傳遞移行距離的空間成長的情形，於能通量傳遞轉移下，已可被數學化及圖形化地清楚呈現。
檢核本文所得之解析結果的正確，本文至第三階的流場解可成功退化成單一自由表面規則前進重力波與重力駐波兩特例，且與Longuet-Higgins & Smith (1966)、McGoldrick et al.(1966)兩試驗結果比較後均有很好的吻合結果。

For a wave system of three dimension, produced by the interactions betw een two progressive gravity wave trains on the free water surface in uniform water depth, a perturbation expansion method with chain rule has been applied to obtain the third order solution, including the resonant and non-resonant cases
In the resonant case, the growth of the induced resonant wave motion with time and its propagating time distance is displayed in the form of mathematics and figure clearly, by applying the transmission of the energy flux.
As for verifying the accuracy of this paper, the third order solution is valid when the wave system is degenerated into a progressive gravity wave train on the free water surface and the standing waves respectively. Furthermore, the experimental results of Longuet-Higgins & Smith (1966) and McGoldrick et al.(1966) are cited to compare, presenting the analytical results in this paper are great agreements.

中文摘要 III
英文摘要 IV
圖目錄 V
表目錄 VIII
符號說明 IX
第一章 緒論 1
1.1 研究目的 1
1.2 文獻回顧 1
1.3 本文研究方法 4
1.4 本文組織 4
第二章 理論解析 6
2.1 波動系統之描述 6
2.2 控制方程式 7
2.3 攝動解析解 9
2.3.1 第一階解 9
2.3.2 第二階解 11
2.3.3 第三階解 15
2.4 解析解之印證 31
2.4.1 退化成單一自由表面規則前進重力波情況 33
2.4.2 退化成重力駐波情況 35
第三章 共振現象之探討 38
3.1 共振條件與共振圈 38
3.2 共振波之探討 39
3.2.1 共振時波動流場之解析解 40
3.2.2 共振波動隨時空之成長 43
3.2.3 共振波成長特性之探討 47
第四章 試驗比對 58
4.1 試驗介紹 58
4.2 配合試驗之陳述 63
4.3 結果比對 65
第五章 結論與建議 72
5.1 結論 72
5.2 建議 73
參考文獻 74
附錄A 79

1. 陳陽益，”波浪通用模式與最大波之解析” 國立成功大學博士論文 (1983)
2. 陳陽益•邱永芳•莊文傑，”前進重力波與駐波之關聯” 第11屆海洋工程研討會論文集，第273-298頁 (1986)
3. 林西川，”非線性重力波之數值解析” 國立成功大學博士論文 (1988)
4. 陳陽益，”重力駐波” 港灣技術第三期，第71-107頁 (1988)
5. 陳陽益•許榮中，”檢視兩前進重力波列之交會” 第10屆海洋工程研討會論文集，第79-113頁 (1988)
6. 陳陽益•邱永芳•莊文傑，”前進重力波與駐波之關聯” 第11屆海洋工程研討會論文集，第273-298頁 (1989)
7. 蔡清標•鄭東生，”深海重力駐波之數值解析” 港灣技術第四期，第11-25頁(1989)
8. 蔡清標•鄭東生，”非線性短峰波最高極限之探討” 國科會專題研究報告NSC-77-0209-M005-01(1989)
9. 陳陽益•邱永芳，”短峰波—兩規則前進波列交會之一例” 港灣技術第五期，第125-162頁 (1990)
10. 陳陽益，”等水深中兩規則前進重力波列交會之解析” 港灣技術第五期，第1-45頁 (1990)
11. 張憲國，”有限水深下三重力波列交會波場之非線性交互作用” 國立成功大學博士論文 (1991)
12. 陳陽益，”兩波交會作用之研究” 港灣技術研究所80-研(十三)研究報告 (1991)
13. 陳陽益，”規則前進重力波傳遞於波形底床上” 港灣技術第七期，第17-47頁 (1992)
14. 郭少谷，”單振幅雙向波形底床尚前進波列之傳遞” 國立中山大學碩士論文 (2000)
15. 程嘉彥，”規則前進波列傳遞於三維波形底床上之研究” 國立中山大學博士論文 (2007)
16. Benney, D.T., “Non-linear gravity wave interactions” J. Fluid Mech. 14, pp.577-584 (1962)
17. Bretherton, F.P., “Resonant interaction between waves” The case of discre te oscillations J. Fluid Mech. 20, pp.457-479 (1964)
18. Cokelet, F.D., “Steep gravity waves in water of arbitrary uniform depth” Phil. Trans. Roy. Soc. A. 286, pp.183-230 (1977)
19. Fenton, J.D., “A fifth-order Stokes theory for standing waves” Journal of Waterway, Port, Coastal and Ocean Engineering, A.S.C.E., Vol.3 No.2, pp.216-234 (1985)
20. Fultz, D., “An Experimental Note on Finite-amplitude Standing Gravity Waves” J. Fluid Mech. 13, pp.193-212 (1962)
21. Goda, Y. and Kakizaki, S., “Study on finite amplitude standing waves and their pressure on a vertical wall(in japanese)” Rep. Port Harbour Res. Inst. Japan Vol.5 No.10 (1966)
22. Hammack, J.L. and Henderson, D.M., “Resonant interactions among surface water waves” Annu. Rev. Fluid Mech 25, pp.55-97 (1993)
23. Hasselmann, K., “On the nonlinear energy transfer in a gravity-wave spec trum” Part 1.General theory J. Fluid Mech. 12, pp.481-500 (1962)
24. Hasselmann, K., “On the nonlinear energy transfer in a gravity-wave spec trum” Part 2.Conservation theorems; wave particle analogy; irreversibility J. Fluid Mech. 15, pp.273-281 (1963)
25. Hasselmann, K., “On the nonlinear energy transfer in a gravity-wave spec trum” Part 3.Evaluation of energy flux and swell sea interaction for a Neumann spectrum J. Fluid Mech. 15, pp.385-398 (1963)
26. Hasselmann, K., “Nonlinear interactions treated by the methods of theoret ical physics (with application to the generation of waves by wind)” Proc. Roy. Soc. Lond. A. 299, pp.77-100 (1967)
27. Hsu, J.R.C., Tsuchiya, Y. and Silvester, R., “Third-order Approximation to Short-crested Waves” J. Fluid Mech. 90, pp.179-196 (1979)
28. Hsu, J. R. C., Silveter, R. and Tsuchiya, Y., “Boundary-layer velocities and mass transport in short-crested waves” J. Fluid Mech. 99, pp.321-342 (1980)
29. Hwung, H.H., Tsai, C.P. and Hong, C.H., “Third-order Approximation and Resonant Characteristis of Two Wave Trains Crossing in Intermediate Dep th” Proc. Of Symp. On Ocean Structure Dynamics, Oregon State Univ. U.S.A., pp.168-180 (1984)
30. Longuet-Higgins, M.S., “Resonant interactions between two trains of gra vity waves” J. Fluid Mech. 12, pp.321-332 (1962)
31. Longuet-Higgins, M.S. and Smith, N.D., “An experiment on third order resonant wave interactions” J. Fluid Mech. 25, pp.417-435 (1966)
32. McGoldrick, L.F., “Resonant Interactions Among Capillary-Gravity Waves “ J. Fluid Mech. 21, pp.305-331 (1965)
33. McGoldrick, L.F., Phillips, O.M., Huang, N. and Hodgson, T., “Measure ments on resonant wave interacions” J. Fluid Mech. 25, pp.437-456 (1966)
34. Okamura, M., “Maximum Wave Steepness and Instabilities of Finite – Amplitude Standing Gravity Waves” Fluid Dynamics Res. 1, pp.201-214 (1986)
35. Phillips, O.M., “On the dynamics of unsteady gravity waves of finite amp litude” Part 1.The elementary interactions J. Fluid Mech. 9, pp.193-217 (1960)
36. Phillips, O.M., “Theoretical and Experimental Studies of Gravity Wave Interaction” Proc. Roy. Soc. Lond. A. 299, pp.104-119 (1967)
37. Phillips, O.M., “Wave interaction — the evolution of an idea” J. Fluid Mech. 106, pp.215-227 (1981)
38. Rienecker, M.M. and Fenton, D.J., “A Fourier approximation method for steep water waves” J. Fluid Mech. 104, pp.119-137 (1981)
39. Roberts, A.J., “Highly Nonlinear Short-crested Water Waves” J. Fluid Mech. 135, pp.301-321 (1983)
40. Roberts, A.J. and Schwartz, L.W., “The Calculation of Nonlinear Short- crested Gravity Waves” Phys. Fluids 26, pp.2388-2392 (1983)
41. Schwartz, L.W. and Whitney, A.K., “A Semi-analytical Solution for Non- linear Standing Waves in Deep Water” J. Fluid Mech. 107, pp.147-171 (1981)
42. Simmons, W.F., “A variational method for weak resonant wave interacti ons” Proc. Roy. Soc. Lond. A. 309, pp.551-575 (1969)
43. Stokes, G.G., “On the theory of oscillatory waves” Trans. Camb. Phil. Soc. 8, pp.441-455 (1847)
44. Tadjbakhsh, I. and Keller, J.B., “Standing Surface Waves of Finite Amplit tude” J. Fluid Mech. 8, pp.442-451 (1960)
45. Taylor, G., “An experimental study of standing waves” Proc. Roy. Soc. Lond. A. 211, pp.44-59 (1953)
46. Tomita, H., “Theoretical and Experimental Investigations of Interaction among Deep water Gravity Waves” Ship Res. Inst. Vol.26 No.5, pp.250 -350 (1989)