在真實的變動海面中，起伏的水位是由許多不同來源的波列交互作用而成，其中兩波列交會情形甚為常見，而兩波列交會的現象中又以駐波情況最為重要。此乃因由兩完全相同但反向的前進波列交會或由入射波經全反射而形成的重力駐波，其會存在的一週期中有波壓雙峰的現象，對於船隻航行安全與保護海岸線的護堤有重要的影響，故不得不考慮其形成之原因。
本文根據陳 (1989,1990) 對於重力駐波與兩波交會之研究，經攝動展開法則與chain rule 微分處理方式下展開至第三階解析結果，探討兩完全相同但反向前進的波列交會形成的重力駐波，由其間非線性作用所產生的波壓雙峰現象，並描述其在不同波浪條件下的演化情況。同時對於產生波壓雙峰現象的項次進行檢視，並比對此兩波列的直接合成的波壓後，找出導致雙峰的非線性項，再引入Nagai (1969)與何 (2003) 之重力駐波的波壓試驗驗證，可以得到良好的一致性。至於隨相對水深與波浪尖銳度於不同水深位置處的雙峰相位偏離，其變化趨勢亦被本文所論述。

The real phenomena of sea surface are interacting by much kind of different waves.In these phenomena, the gravity standing wave is most important. The gravity standing wave is formed by two progressive waves that possessing same properties but opposite directions. Gravity standing wave can also form by the interaction of a progressive wave with it’s totally reflection wave. Because of the nonlinear interaction of two waves, there must result a double-crest phenomenon of wave pressure. It is dangerous for the
navigation of ship when the double-crest appears, and it’s certainly to take the phenomenon into consideration when we are going to design a jetty.
In this paper, it bases on the reference of Chen (1989, 1990) who obtained a third-order approximation of two-wave trains interactions in a uniform depth wave field.
Further, in this paper, it checks the result that the double-crest phenomenon is formed by which one of these nonlinear terms. Furthermore, research the influences of wave steepness, wave periods, and water depths these factors will cause the crest diverges is also the purpose.

摘 要 .................................................................................................................................i
Abstract .............................................................................................................................. ii
目錄 .................................................................................................................................. I
圖目錄 .............................................................................................................................. II
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.研究方法 ............................................................................................................ 2
1-4.本文組織架構 .................................................................................................... 3
第二章 波動系統之描述及波動場之解析 .................................................................. 4
2-1 波動流場之控制方程式 ................................................................................... 7
2.1-1 第一階(線性)解： ................................................................................. 8
2.1-2 第二階解： ............................................................................................ 9
2.1-3 第三階解： .......................................................................................... 10
2-2 波動場之檢核 ............................................................................................... 17
第三章 駐波波壓雙峰現象之項次探究 .................................................................... 23
3-1 兩反向波列之線性合成波壓 ......................................................................... 23
3-2 駐波之波壓 ..................................................................................................... 28
3-3 兩來源反向波列線性疊加之波壓與駐波之波壓間的差異 ......................... 31
第四章 駐波波壓雙峰現象於不同波浪條件的變化 ................................................ 33
4-1 理論與實驗之驗證 ....................................................................................... 34
4-2 同相位下線性合成與含非線作用間對所言波壓性差異之比較 ............... 43
4-3 不同波浪條件下駐波雙峰現象之變化 ....................................................... 80
第五章 結論與建議 .................................................................................................... 85

1. 陳陽益，蔡清標 ( 1985 ) “重力駐波之解析”，第八屆海洋工程研討會論文
集，303 頁-325 頁。
2. 陳陽益，張憲國 ( 1988 ) “駐波波壓之五階近似解”，第十屆海洋工程研討
會論文集，233 頁-254 頁。
3. 陳陽益 ( 1988 ) “重力駐波”，港灣技術第三期，71 頁-107 頁。
4. 陳陽益 ( 1989 ) “兩波交會系統化與流場機構”，港灣技術第四期，27 頁-60
頁。
5. 陳陽益，邱永芳，莊文傑 ( 1989 ) “前進重力波與駐波之關聯”，第十一屆
海洋工程研討會論文集，273 頁-298 頁。
6. 陳陽益 ( 1990 ) “等深水中兩規則前進重力波列交會之解析”，港灣技術第
五期，1 頁-45 頁。
7. 陳陽益，邱永芳 ( 1990 ) “短峰波-兩規則前進波列交會之一例”，港灣技術
第五期，125 頁-162 頁。
8. 何俊業 ( 2003 ) “重力駐波流場試驗研究”，國立中山大學碩士論文。
9. Rankine, W.J.M (1865) “Supplement to a paper on stream-lines”, Phil. Mag.
(4), 29, pp.25-25.
10. Rayleigh, L. (1876) “On waves”, Phil. Mag. (5), 1, pp.257-279.
11. Tadjbaksh, I. and Keller, J. B. (1960) “A non-linear random model of gravity
waves”, I.J. Math. And Mech. 8, (5), pp.643-652.
12. Fultz, D. (1962) “An experimental note on finite amplitude standing gravity
waves”, J. Fluid Mech. 13, pp.193-212.
13. Edge, R. D. and Walters, G. (1964) “The period of standing gravity waves of
largest amplitude on water”, J. Geophys. Res. 69, pp.1674-1675.
14. Goda, Y. and Kakizaki, S (1966) “Study on finite amplitude standing waves
and their pressure upon a vertical wall”, Rep. Port Harbor Res. Inst. Japan,
vol.5, No.10.
15. Phillips, O. M. (1960) “On the dynamics of unsteady gravity waves of finite
amplitude”, Part 1, J. Fluid Mech. 9, pp.193-217.
16. Long-Higgins, M. S. (1962) “Resonant interactions between two trains of
gravity waves”, J. Fluid Mech. 12, pp.321-332.
88
17. Benney, D.T. (1962) “Nonlinear gravity wave interaction”, J. F. M. 14,
577-588.
18. Bretherton, F. P. (1964) “Resonant interaction between waves” The case of
discrete oscillations J. Fluid Mech. 20, pp.457-479.
19. Hasselmann, K. (1962), “On the nonlinear energy transfer in a gravity-wave
spectrum” Part 1, General theory, J. F. M. 12, 481-500.
20. Hasselmann, K. (1962), “On the nonlinear energy transfer in a gravity-wave
spectrum” Part 2, Conservation theorems, J. F. M. 15, 273-281.
21. Longuet-Higgins, M.S. and Smith, N.D. (1966) “An experiment on third order
resonant wave interactions” J. Fluid Mech. 25, pp.417-435.
22. McGoldrick, L.F., Phillips, O.M., Huang, N. and Hodgson, T. (1966)
“Measurements on resonant wave interactions” J. Fluid Mech. 25, pp.437-456.
23. Phillips, O.M. (1967) “Theoretical and Experimental Studies of Gravity Wave
Interaction” Proc. Roy. Soc. Lond. A. 299, pp.104-119.
24. Goda, Y. (1967) “The fourth order approximation to the pressure of standing
waves”, Coastal Engineering in Japan. Vol.10, pp.1-11.
25. Nagai, S. (1964) “On several problems of standing waves”, Proc. 11th Conf.
Coastal Eng. In Japan, pp.29-34.