臺灣博碩士論文加值系統

本文主旨在以 Lagrangian描述方式，來解析二度空間中，行進在緩斜坡底床上的規則前進重力波之波動流場；並以一系列的試驗研究，來驗證在Lagrangian描述方式下的解析解之適足性。接著，進一步將本文的解析解，應用至該波動流場的極限情況--碎波，發現此解析解在碎波特性的判斷比一般的經驗式，更為準確。
就細節而言，在Lagrangian方式探究緩斜坡底床上的非線性前進波傳遞問題，本文引入導致水深變化因素的底床坡度α，及保有波浪非線性特性的深海波浪尖銳度ε兩個重要參數，進行系統化之雙攝動展開，以解析此非線性理論至O(ε^3α^0) 階次量。其次，本文以試驗研究的方式來量測(1)．水粒子運動軌跡，(2)．淺化過程中持續變化的波形，(3)．向岸傳遞連續演化至碎波的波速；以此三個波動場之物理特性，來驗證本文解析的真確性。本文理論的極限為恰發生碎波時，應用K.S.P. 指標，即u/Cw=1 來判斷碎波，因此可得本文解析解之碎波波高、碎波水深、波速變化等特性。
本文之解析解滿足自由表面常壓條件與垂直斷面處總質量傳輸量平衡式。本解析解可描述在緩斜坡底床上前進波的波動場，由深水至臨近碎波點的波形、水粒子運動軌跡及波速…等動力特性；在應用本文理論於描述碎波的過程中發現，本文解析解所得之碎波特性與試驗結果比較，兩者相當符合。而且由於本文對底床坡度α攝動展開，故在較陡坡情況較往昔學者的經驗式適用。

The purpose of this thesis is applying Lagrangian approach to analyze shoreward progressive waves over a gently sloping bottom. A series of laboratorial experiments were executed to validate the analytical results. Then, the theory is extended to the prediction of wave breaking and the resulting breaking criteria are shown to be more accurate than regression formula in the literature.
In the analysis, a two-parameter perturbation were used that employs both bottom slope α and wave steepness ε , and the solution is expanded up to the order. Based on this analytical solution, water particle trajectory, waveform and wave velocity in the shoaling process are calculated and their counterparts in the laboratorial experiment are recorded for comparison. Then, the analytical solution is used to derive the wave height, the water depth, and the wave velocity for a breaking wave where the Kinematic Stability Parameter (K.S.P.) u/Cw equaling one is adopted as the breaking criteria.
In deriving the O( ε^3α^0) solution, the following conditions are satisfied at each order: (a) The pressure on the free surface is constant, and (b) the mass flux is conserved at each vertical cross section. This solution can accurately describe the waveform, the water particle trajectory and the wave velocity all the way from the deep water to the breaking point, as is shown by the comparison with the laboratorial experiments. The perturbation with respect to the bottom slope α is included and the flow at the bottom is consistent with the sloping bottom condition. Consequently, the present analytical solution can provide better breaking criteria than previous regression formula, especially in the case of large sloping angles.

目錄
誌謝 I
中文摘要 II
英文摘要 Ⅲ
目錄 Ⅴ
表目錄 Ⅶ
圖目錄 Ⅷ
符號說明 XI
第1章、 緒論 1
1-1 研究動機與目的 1
1-2 文獻回顧 2
1-3 本文組織架構 6
第2章、 波動系統之描述 7
2-1 控制方程式及邊界條件 7
2-2前進波動系統化攝動展開之理論解析 9
第3章、理論解析 21
3-1 ε^m α^n m+n=1 階解 21
3-1-1 ε^1 α^0階解 21
3-2 ε^m α^n m+n=2 階解 24
3-2-1 ε^1 α^1階解 24
3-2-2 ε^2 α^0階解 28
3-3 ε^m α^n m+n=3 階解 34
3-3-1 ε^1 α^2階解 34
3-3-2 ε^3 α^0階解 37
3-4分析與檢核 42
第4章、 試驗驗證 46
4-1試驗設備與儀器 46
4-2試驗配置 51
4-3試驗方法、步驟及條件 54
4-4試驗量測資料之處理 56
4-5 緩斜坡底床上波浪水位的變化 60
4-6沿緩斜坡底床上前進波中質點的運動軌跡量測分析
與理論印證 65
4-7緩斜坡底床上前進波波速(位相速度)量測分析
與理論印證 70
第5章、 結果與討論 76
5-1 緩斜坡底床上波形的演化 76
5-2質點運動軌跡及波速 79
5-3波浪碎波特性 82
第6章、 結論與建議 87
6-1 結論 87
6-2 建議 89
參考文獻 90
附錄A: 緩斜坡底床上Csae 2~9水位變化圖 98
附錄B: 試驗之質點軌跡的時序列資料 122

1.陳陽益、湯麟武(1992)，“平緩坡度底床上前進的表面波”，第十四屆海洋工程研討會論文集，1頁-22頁。
2.陳陽益(1994a)，“等深水中非旋轉性的自由表面前進重力波之Lagrangian方式的攝動解析”，第十六屆海洋工程研討會論文集，A1頁-A29頁。
3.陳陽益(1994b)，“等深水中非旋轉性的自由表面重力駐波之Lagrangian方式的攝動解析”，第十六屆海洋工程研討會論文集，A30頁-A59頁。
4.陳陽益(1995)，“Lagrangian 與 Eulerian 解下前進重力波與重力駐波的動力特性”，第十七屆海洋工程研討會論文集，19頁-36頁。
5.陳陽益(1996)，“非旋轉性前進波的 Eulerian 與 Lagrangian 解間的轉換性”，第十八屆海洋工程研討會論文集，1頁-13頁。
6.陳陽益(1997)，“平緩坡度底床上前進的表面波”，第十九屆海洋工程研討會論文集，112頁-121頁。
7.陳陽益、張富東(1999)，“平緩坡度底床上前進波的試驗研究”，第二十一屆海洋工程研討會論文集，165頁-174頁。
8.陳陽益、黃啟暘(2000)，“Lagrangian方式下平緩底床上之前進波”，第二十二屆海洋工程研討會論文集，79頁-88頁。
9.陳陽益(2003 I)，“非陡坡底床上前進波的非線性解析：I. 系統化攝動展開模式”，第二十五屆海洋工程研討會論文集，39頁-48頁。
10.陳陽益(2003II)，“非陡坡底床上前進波的非線性解析：II. 至 階的解析解及印證”，第二十五屆海洋工程研討會論文集，49頁-58頁。
11.許弘莒 (2005) “斜坡底床上前進波的非線性解析”，國立成功大學論文。
12.陳陽益、許弘莒、李孟學(2007)， “非陡斜坡底床上前進波之非線性Eulerian解與Lagrangian解間的轉換及波浪變形至碎波(1/3)”，第二十九屆海洋工程研討會論文集， 171頁-176頁。
13.李政達(2008) “波流場中質點運動特性之試驗研究”，國立中山大學論文。
14.林楚佑 (2011) “Lagrangian 系統下孤立波特性之解析”，國立中山大學論文。
15.廖奕鈞 (2011) “波浪作用下啟動沙量試驗研究”， 國立中山大學論文。
16.Asu, I., Lale, B. (2002) “Applications of A Numerical Model to Wave Propagation on mild slopes,” China Ocean Engineering, Vol. 16, pp. 569-576.
17.Biesel, F. (1952) “Study of wave propagation in water of gradually varying depth. Gravity Waves,” U.S. National Bureau of Standards, Circular Vol.521, pp. 243-253.
18.Buldakov, E.V., Taylor, P.H., Taylor, R.E. (2006) “New asymptotic description of nonlinear water waves in Lagrangian Coordinates,” Journal of Fluid Mechanics, Vol. 562, pp. 431-444.
19.Chamberlain, P.G., Porter, D. (1995) “The Modified Mild-Slope Equation,” Journal of Fluid Mechanics, Vol. 291, pp. 393-407.
20.Chen, Y.Y., Yang, B.D., Tang, L.W., Ou, S.H., Hsu, J.R.C. (2004) “Transformation of progressive waves propagating obliquely on a gentle slope,” Journal of Waterways, Port, Coastal and Ocean Engineering, Vol.119, pp. 162-169.
21.Chen, Y.Y., Hwung, H.H., Hsu, H.C. (2005) “Theoretical analysis of surface waves propagation on sloping bottoms part 1,” Wave Motion, Vol. 42, pp. 335-351.
22.Chen, Y.Y., Hsu, H.C., Chen, G.Y., Hwung, H.H. (2006) “Theoretical analysis for surface waves propagation on sloping bottoms, Part 2,” Wave Motion, Vol. 43, pp. 339-356.
23.Chen, Y.Y., Hsu, H.C. (2009) “A third-order asymptotic solution of nonlinear standing water waves in Lagrangian coordinates,” Chinese Physics B, Vol. 18, pp. 861-871.
24.Chen, Y.Y., Hsu, H.C., Chen, G.Y., (2010.) “Lagrangian experiment and solution for irrotational finite-amplitude progressive gravity waves at uniform depth,” Fluid Dynamics Research, Vol. 42, pp. 045501.
25.Chen, Y.Y., Hsu, H.C., Chang, H.K. (2012a) “The irrotational progressive gravity waves propagating on uniform currents in Lagrangian analysis and experiments Part1. Theoretical analysis,” Acta Physics Sinica, Vol. 61, pp. 034702.
26.Chen, Y.Y., Lin, C.Y., Li, M.S., Lee, C.T. (2012b) “The irrotational progressive gravity waves propagating on uniform currents in Lagrangian analysis and experiments Part2. Experimental verification,” Acta Physics Sinica, Vol. 61, pp. 034703.
27.Chen, Y.Y., Li, M.S., Hsu, H.C. (2012c) “Theoretical and experimental study of particle trajectories for nonlinear water waves propagating on a sloping bottom,” Philosophical Transactions of the Royal Society A, Vol. 370, pp. 1543-1571.
28.Chu,V.H., Mei, C.C. (1970) “On slowly-varying Stokes waves,” Journal of Fluid Mechanics, Vol. 41, pp. 873–887.
29.Constantin, A. (2001) “Edge waves along a sloping beach,” Journal of Physics A: Mathematical and General, Vol. 34, pp. 9723-9731.
30.Deo, M.C., Jagdale, S.S. (2003) “Prediction of breaking waves with neural networks,” Ocean Engineering, Vol. 30, pp. 1163-1178.
31.Ehrnstr&;ouml;m, M., Wahl&;eacute;n, E. (2008) “On the fluid motion in standing waves,” Journal of Nonlinear Mathematical Physics, Vol. 15, pp. 74-86.
32.Elgar, S., Guza, R.T. (1985) “Shoaling gravity waves： comparisons between field observations. Linear theory and a nonlinear model,” Journal of Fluid Mechanics, Vol. 158, pp. 47-70.
33.Gaillard, D.D. (1904) “Wave action in relation to engineering structure,” U.S. Army, Corps of Engineers, Beach Erosion Board, Technical Report, No. 13.
34.Galvin, C.J. (1968) “Breaker type classification on three laboratory beaches,” Journal of Geophysical Research, Vol. 73, pp. 3651-3659.
35.Gerstner, F.J. (1802) “Theorie de wellen,” Abh. d. K. bohm. Ges. Wiss. reprinted in Ann der Physik, Vol. 32, pp. 412-440.
36.Goda,Y. (1970) “A synthesis of breaker indices,” Transactions of the Japan Society of Civil Engineering, Vol. 2, pp. 227-230.
37.Goda, Y. (1974) “New wave pressure formula for composite breakwater,” Proceedings of 14th International Conference on Coastal Engineering, pp. 1702-1720.
38.Goda, Y. (1975) “Irregular wave deformation in the surf zone,” Coastal Engineering In Japan, Vol. 18, pp. 13-26.
39.Goda, Y. (2004) “A 2-D random wave transformation model with gradational breaker index,” Coastal Engineering Journal, Vol. 46, pp. 1-38.
40.Goda, Y. (2010) Reanalysis of regular and random breaking wave statistics, Coastal Engineering Journal, Vol. 52, pp. 71-106.
41.Gotoh, H., Sakai, T. (1999) “Lagrangian simulation of breaking waves using particle method,” Coastal Engineering Journal, Vol. 41, pp. 303-326.
42.Hamada, T. (1951) “Breakers and beach erosion, Port and Harbor Research Institute,” Ministry of Transportation, Japan, Vol. 165.
43.Hansen, J.B. (1990) “Periodic waves in the surf zone: Analysis of experimental data,” Coastal Engineering, Vol. 14, pp. 19-41.
44.Hu, D.M. (1985) “Analytical solution of linear wave potential function on sloping bottom,” Acta Oceanological Sinica, Vol. 4, pp. 539-533.
45.Hsu, H.C., Chen, Y.Y., Wang, C.F. (2010) “Perturbation analysis of the short-crested waves in Lagrangian coordinates,” Nonlinear Analysis Series B: Real World Applications, Vol. 11, pp.1522-1536.
46.Iversen, H.W. (1952) “Waves and breakers in shoaling water,” Proceedings of 3rd International Conference on Coastal Engineering, pp. 1-12.
47.Iwagaki, Y., Sakai, Tsukioka, T.K., Sawai, N. (1974) “Relationship between vertical Distribution of water particle Velocity and type of breaker on beachs,” Coastal Engineering In Japan, Vol. 17, pp. 51-58.
48.Kennedy, A.B., Chen, Q., Kirby, J.T., Dalrymple, R.A. (1999), “Boussineaq modeling of wave transformation, breaking, and run-up, I, 1D,” Journal of Waterways, Port, Coastal and Ocean Engineering, Vol. 126, pp. 39-47.
49.Lamb, H. (1932) Hydrodynamics. 6th edn. Cambridge University Press.
50.Le M&;eacute;haut&;eacute; B., Koh, R.C.Y. (1967) “On the Breaking of waves arriving at an angle to the shore,” Journal of Hydraulic Research, Vol. 5, pp. 67-88.
51.Li, R., Wang, H. (1999) “Nonlinear Effect of Wave Propagation in Shallow Water,” China Ocean Engineering, Vol. 13, pp. 109-114.
52.Liu, P.L.F., Dingemans, M.W. (1989) “Derivation of the third-order evolution equations for weakly nonlinear water waves propagating over uneven bottoms,” Wave Motion, Vol. 11, pp. 41-64.
53.Longuet-Higgins, M.S. (1953) “Mass transport in water waves.” Philosophical Transactions of the Royal Society A, Vol. 245, pp. 533-581.
54.Longuet-Higgins, M.S., Stewart, R.W. (1964) “Radiation stress in water wave – a physical discussion with applications,” Deep Sea Research, Vol. 11, pp. 3-26.
55.Longuet-Higgins, M.S. (1986) “Eulerian and Lagrangian aspects of surface waves, ” Journal of Fluid Mechanics, Vol. 173, pp. 683-707.
56.Mason, M.A. (1941) “A study of progressive oscillatory waves in water,” U.S. Army, Corps of Engineers, Beach Erosion Board, Technical Report, No. 1.
57.Mei, C.C. (1983), “The Applied Dynamics of Ocean Surface Waves,” pp. 420-426, John Wiely.
58.Miche, A. (1944) “Mouvements ondulatoires de la mer en profondeur constante ou d&;eacute;croissante, ” Annales des ponts et chaussees , pp. 25-78, 131-164, 270-292, 369-406.
59.Naciri, M., Mei, C.C. (1993) “Evolution of short gravity waves on long gravity waves, ” Physics of Fluids A , Vol. 5, pp. 1869-1878.
60.Ng, C.O. (2004a) “Mass transport in a layer of power-law fluid forced by periodic surface pressure,” Wave Motion, Vol. 39, pp. 241-259.
61.Ng, C.O. (2004b) “Mass transport and set-ups due to partial standing surface waves in a two layer viscous system,” Journal of Fluid Mechanics, Vol. 520, pp. 297-325.
62.Ng, C.O. (2004c) “Mass transport in gravity waves revisited,” Journal of Geophysical Research-Oceans, Vol. 109, pp. C04012.
63.Ng, C.O., Zhang, X.Y. (2007) “Mass Transport in water waves over a thin layer of soft Viscoelastic mud,” Journal of Fluid Mechanics, Vol. 573, pp. 105-130.
64.Nwogu, O. (1993) “Alternative form of Bousssinesq equations for nearshore wave propagation,” Journal of Waterways, Port, Coastal and Ocean Engineering, Vol. 119, pp. 618-638.
65.Ogawa, Y., Shuto, N. (1984) “Run-up of periodic waves on beaches of non-uniform slope,” Proceedings of 19th International Conference on Coastal Engineering, pp. 328-334.
66.Pierson, W.J. (1962) “Perturbation analysis of the Navier-Stokes equations in Lagrangian form with selected linear solution,” Journal of Geophysical Research, Vol. 67, pp. 3151-3160.
67.Porter, D., Staziker, D.J. (1995), “Extensions of the Mild-Slope Equation,” Journal of Fluid Mechanics, Vol. 300, pp. 367-382.
68.Rakine, W.J.M. (1863) “On the exact form of waves near the surface of deep water,” Philosophical Transactions of the Royal Society of London, Vol. 153, pp. 127-138.
69.Rattanapitikon, W., Shibayama, T. (2000) “Verification and modification of breaker height formulas,” Coastal Engineering Journal, Vol. 42, pp. 389-406.
70.Rienecker, M.M. and Fenton, J.D. (1981), “A Fourier approximation method for steep water waves,” Journal of Fluid Mechanics, Vol. 140, pp. 119-137.
71.Saeki, H.S. Hanayasu, A.O., Takgi, K. (1971) “The shoaling and run-up height of the solitary wave,” Coastal Engineering in Japan, Vol. 14, pp. 25-42.
72.Sanderson, B. (1985) “A Lagrangian solution for internal waves,” Journal of Fluid Mechanics, Vol. 152, pp. 191-137.
73.Seyama, A., Kimura, A. (1988) “The measured properties of irregular wave breaking and wave height change after breaking on slope,” Proceedings of 21st International Conference on Coastal Engineering, pp. 419-432.
74.Smith, J. M., Kraus, N. C. (1990) “Laboratory study on macro-features of wave breaking over bars and artificial reefs,” Technical Report CERC-90-12, WES, US Army Corps of Engineers.
75.Street, R.L., Camfield F.E. (1966) “Observations and experiments on solitary wave deformation,” Proceedings of 10th International Conference on Coastal Engineering, pp. 284-301.
76.Sunamura, T., Horikawa, K. (1974) “Two-dimensional beach ransformation due to waves,” Proceedings of 14th International Conference on Coastal Engineering, pp. 920-938.
77.Sunamura, T. (1980) “A laboratory study of offshore transport of sediment and a model for eroding beaches,” Proceedings of 17th International Conference on Coastal Engineering, pp. 1051-1070.
78.Sunamura, T. (1983) “Determination of breaker height and depth in the field,” Annual Report of the Institute of Geosciience, Universityof Tsukuba, Vol. 8, pp. 53-54.
79.Suquet, F. (1950) “Experimental study on the breaking of waves,” La Houille Blancha, Vol. May to June, pp. 362.
80.Tang, L. W. (1966) “Coastal Engineering researches on the western coast of Taiwan,” Proceedings of 10th International Conference on Coastal Engineering,, pp. 1274-1290.
81.Tanimoto, K., Nakamura, S., Zhao, Q. (1996) “Evaluation of wave motions and radiation stress on steep slope,” Proceedings. 43th Japan Coastal Engineering Conference, pp. 26-31.
82.Tsai, C.P., Chen, H.B., Hwung, H.H., Hwuang, M.J. (2005) “Examination of empirical formulas for wave shoaling and breaking on steep slopes,” Ocean Engineering, Vol. 32, pp. 469-483.
83.Wei, G., Kirby, J. T., Grilli, S. T., Subramanya, R. (1995), “A fully nonlinear Boussinesq model for surface waves,” Journal of Fluid Mechanics, Vol. 294, pp. 71-92.
84.Yakubovich, E.I., Zenkovich, D.A. (2001) “Matrix approach to Lagrangian fluid dynamics,” Journal of Fluid Mechanics, Vol. 443, pp. 167-196.
85.Zhang, H., Hong, G., Ding, P. and Cao, Z. (2001) “Numerical Simulation of Non-Linear Wave Propagation in Waters of Mildly Varying Topography with Complicated Boundary,” China Ocean Engineering, Vol. 15, pp. 37-52.
86.Zhang, X.Y., Ng, C.O. (2006) “On the oscillatory and mean motions due to waves in thin viscoelastic layer,” Wave Motion, Vol. 43, pp. 397-405.
87.Zhao, Q., Nakamura, S., and Tanimoto, K. (1996) “Distribution of particle velocities due to waves on very deep slope bottom,” 10th Congress of IAHR-APD, pp. 365-372.