中 文 摘 要

本文針對在均勻靜穩大氣下，於均勻等深的真實流體中由兩性質相同，方向相反的前進波交會形成之重力駐波流場加以解析。異於前人之常以邊界層問題處理黏性流場，本文承續陳和楊(1996)以完整的Navior-Stokes 方程式. 加以解析整個流場。導述邊界條件時首先，對自由表面處，考量自由表面處的壓力、剪力及表面張力等因素，依動力平衡原則，導述波動之自由表面動力邊界條件。接著，對底床情況，先考慮底床為完全滑動之情形，續推及底床為完全黏著之情形，最後推至底床為非完全黏著之情形。在建立了邊界條件、控制方程式後，利用攝動展開法找出二階的控制方程式及邊界條件後，便可得到前進波與駐波流場二階之通解；而使得所有之底床情況甚至理想流體流場之情形皆可被含括。從解析的結果，除了可得知底床的邊界效應會受相對水深 及底床黏著程度的影響，此外由二階的解析解得知不論是在前進波或者是駐波流場中，都可得到超射高度變化、水平流速分量隨位相變化圖不對稱、二階剪力與一階剪力的位相差與數值隨相對水深、相對尖銳度及黏著程度變化；而在駐波流場中又可發現交互作用項的存在不僅會影響邊界層中的物理量，相對水深越小對於邊界層外的物理量亦會有越大的影響。

ABSTRACT

Under stationary atmosphere and on uniform depth, this paper treats the standing waves in real fluids formed by two progressive waves possessing same properties but in opposite direction. Being different from the preceding scholars who usually treated the waves in real fluids with boundary layer theory, the author uses complete Navior-Stokes Equ. to analyze the entire flow field. When dealing with the free surface dynamical boundary condition, under the equilibrium of forces, the author takes account of atmosphere pressure, shear stress and surface tension. As for the bottom condition, at first consider the perfect smooth, then no-sliding and sliding condition. After constructing the boundary conditions and the governing equation, perturbation method is used to get those of second order, and the second order solution can be derived. In addition to relative depth , the bottom-adherence affects the bottom boundary effect. No matter in progressive or standing wave fields, we can see the variation of over-shot height, the asymmetric diagrams of fluid particle’s horizontal velocity with phases, the phase difference between the second and first order bottom shear. Besides, in standing wave field, the existence of second-order interaction term not only affects the flow field in the boundary layer but also the field outside it.

目錄
中文摘要 III
英文摘要 IV
圖表目錄 V
符號說明 VIII
第一章緒論 1
1.1 研究目的 1
1.2 文獻回顧與本文處理方式 2
1.3 本文組織 5
第二章真實流體之行為與控制方程式
2.1 駐波波動流場的基本描述 6
2.2 駐波波動流場之基本控制方程式 7
2.3 波動流場之邊界條件 7
2.4 邊界條件的展開 11
第三章真實流體中之流場機構與展開處理 14
3.1 流場機構的描述 14
3.2 流場結構解析 15
3.2.1 完全滑動的底床情況 15
3.2.2 完全黏著的底床情況 26
3.2.3 非完全滑動亦非完全黏著的底床情況 52
第四章驗證比較及特性的描述 79
4.1 理論的印證 79
4.2 流場的剪力與水平流速分布 91
4.3 解析結果的分析 91
第五章結論與建議 118
5.1 結論 118
5.2 建議 119
參考文獻 120
附錄A 124
附錄B 126
附錄C 134
附錄D 142
附錄E 149
附錄F 152
附錄G 158
誌謝 166

參 考 文 獻
1.Aoki , H. 1980 “Higher order calculation of finite periodic standing gravity waves by means of the computer.” J. Phys. Soc. Japan Vol.49 ,No.4, pp.1958-1606.
2.Concus , P. 1962 “Standing capillary-gravity waves of finite amplitude.” J. Fluid mesh .14,pp.568-576.
3.Edge, R.D. & Walters, G. 1964 “ The period of standing gravity waves of largest amplitude on water.” J. Geophys Res.69, pp. 1647-1675.
4.Fultz, D.1962 ”An experimental note on finite amplitude standing gravity waves .” J. Fluid Mesh. 13, pp. 193-212.
5.Goda, Y.1967 “The fourth order approximation to the pressure of standing wave.” Coastal Eng. in Japan, Vol.10, pp. 1-11.
6.Grant , M.A. 1973 “Standing stokes waves of maximum height.” J. Fluid mesh. 60,pp. 593-604.
7.Harrison , W.J.1908 “The influence of viscosity and capillarity on waves of finite amplitude .” Proc. Lond. Math. Soc. Ser2 , pp.107 -121.
8.Hocking , L.M.1987 ”The damping of capillary-gravity waves at rigid boundary “ J. Fluid Mesh. pp. 253-266.
9.Horikawa, K. & Wadanabe, A 1968 “Laboratory study on oscillatory boundary layer flow.
10.Hough ,S.S. 1896 ” On the influence of viscosity on waves and currents.” Proc. Lond. Math. Soc. Ser .128, pp264-288.
11.Jonsson, I.G. 1966 “ wave boundary layer and friction factors ”Coastal Eng. pp.127-147.
12.Kajiura, K 1968 “ A model of the bottom boundary layer in water waves.” Bull. Earthquake Res. Inst. University of Tokyo, Vol. 46.
13.Keulegan, G.H.1959. “Energy dissipation in standing waves in rectangular basins.” J. fluid Mech ,pp.33-50.
14.Lamb, Sir H. 1932 ” Hydrodynamics” Cambridge Press 6th edition,section327.
15.Longuet-Higgins, M.A.1953 ”Mass transport in water waves. ”Phil. Tran. Roy. Soc. A.245, pp. 535-581.
16.Longuet-Higgins, M.A.1957 “The mechanics of the boundary layer near the bottom in a progressive wave.” Proc. 6th Conf .on Coastal Eng . pp .184-193.
17.Longuet-Higgins, M.A. 1960 “Mass transport in the boundary layer at a free oscillation surface.” J. Fluid Mech. 8,pp. 293-306.
18.Longuet-Higgins , M.A. 1969 “Action of a variable stress at the surface of water waves.” Phys. Fluids 12,pp. 737-740.
19.Longuet-Higgins, M.A.1973 “On the form of the highest progressive and standing waves in deep water.” Proc. R. Soc. Lond. A.311,pp 445-456.
20.Mei ,C.C.＆Liu, L.F.1973 ”The damping of surface gravity waves in a bounded liquid .” J. Fluid Mech. 59 , pp 239-256.
21.Miche, M. 1944 ”Mouvements ondulatoires des mers en profondeur constante ou decroissante. ”Annales des Ponts et Chaussees , pp. 25-78.
22.Masaru Mizugu “Second-Order Solution Of Laminar Boundary Layer Flow Under Waves.” Coastal Eng. in Japan Vol. 30, No. 1,1987.
23.Noda, H.1968 “A study on mass transport in boundary layers in standing waves.” Coastal Eng. Vol.1 , pp. 227-247.
24.Okamura, M. 1986”Maximum wave steepness and instabilities of finite amplitude standing gravity waves.’’ Fluid Dynamics Res.(North-Holland), 1,pp.201-214.
25.Penny,W.G.＆Price,A.T.1952 ”Finite periodic stationary gravity waves in a perfect liquid.” Phil. Trans. R .Soc .Lond.A.244, pp. 254-284.
26.Phillps, O.M.1977 “The dynamics of the upper ocean.” Cambridge University Press, London 2th edition.
27. Rayleigh, J.W.S. 1915 “Deep water waves, progressive or standing, to the third order of approximation.” Proc. R. Soc. Lond. A.91,pp 345-353.
28. Riedel, P.H.＆Kamphuis, J.W.＆ Brebner,A.1972 “Measurement of bed shear under waves.” Coastal Eng.pp.587-603.
29. Rottman, J.W.1982 “Steep standing waves at a fluid interface.” J. Fluid mech. 124, pp283-306.
30.Schwartz, L.W.＆Whitney, A.k.1981 “A semi-analytic solution for nonlinear standing waves in deep water.”J. Fluid .Mech. 107,pp.141-171.
31.Stokes,G.G. 1845 ”On the theories of the internal friction of fluid in motion, and of the equilibrium and motion of elastic solids .”Trans .Camb. Phil. Soc.8, pp. 287-305.
32.Stokes,G.G. 1847 “On the theory of oscillatory waves.” Trans. Camb. Phil. Soc.8, pp. 441-455.
33.stewart, R.W. 1967 “Mechanics of the air-sea interface.” Phys. Fluids suppl.10, pp. 47-54.
34.Tadjbakhsh, I.＆Keller, J.B.1960 “Standing surface waves of finite amplitude.” J. Fluid Mech. 8, pp. 442-451.
35.Talor,Sir G. 1953 “An experimental study of standing waves.” Proc. R. Soc. Lond. A. 218 , pp. 44-59.
36.盧家驥1977 ”淺海波在海底產生剪力之理論及實驗研究”國立成功大學水利及海洋工程研究所碩士論文.
37.王壵臹1982 ”有限振幅重複波作用下底床剪力之研究”國立成功大學水利及海洋工程研究所碩士論文.
38.陳陽益1989 “直立堤面上重複波的解析” 港灣技術研究所78-研(9).
39.陳陽益1990 “波動流體之一些真實性”第三屆基礎港灣數值(數學)模式研習會論文集，pp.1-41.
40.陳陽益1996 “真實流體中之前進波”港灣技術第十一卷第一期pp.57-88.
41.陳陽益、楊炳達 1996 ”真實流體中之重力駐波” 國立中山大學海洋環境學系研究所碩士論文.
42.許泰文1990 ”波浪作用下底部紊流邊界層之研究”國立成功大學水利及海洋研究所博士論文.
43.鄭中南1996 ”波動底部邊界層特性之實驗探討”國立中興大學土木工程研究所碩士論文.