臺灣博碩士論文加值系統

本論文透過攝動法展開有旋性流場在無黏性、不可壓縮的二維流體運動之控制方程式及邊界條件，推導出雙主頻波在線性剪力流中之三階解析解，其包含流函數、波浪運動之勢函數及水面位移函數。為處理有旋性流時自由液面動力邊界條件中無法消去的勢函數對時間偏微分項，引用Tsao (1959) 及 Kishida and Sobey (1988) 提出之概念，即在剪力流之渦旋量為一定值時，波浪運動可獨立以非旋性流處理。而透過第三階解中對兩波之角頻率作攝動法展開，在有流與渦度作用的情形下之振幅離散效應也可由解析解觀察出來。
本文所推導之三階解析解也退化到單主頻波或均勻流的情況，分別與陳與莊(1990)、Madsen and Fuhrman (2006) 及Kishida and Sobey (1988)之解作驗證。其退化後之數學表示式及水面位移函數與水平速度剖面的作圖皆顯示結果互相吻合。
另外，本文也透過推導出的解析解直接探討剪力流的流速與渦旋量對於波長、最大粒子運動速度等物理特性之影響。而非線性雙主頻波產生之束縛長波受流速與渦度的影響在本文中也有進一步的討論。

A third-order analytical solution for bichromatic waves on currents with constant vorticity is derived by using perturbation method. Unlike the derivation of monochromatic waves, moving-frame method cannot be used in the case of bichromatic waves because there are multiple waves with different celerities and the flow can in no way be steady-state. Also, for shear currents which is rotational flow, velocity potential cannot be defined. However, with the consideration of the wave part of the fluid motion remaining irrotational (Tsao, 1959 and Kishida and Sobey, 1988), some of the terms in the expanded boundary conditions can be ignored, thus the derivations can be further processed. As a result, the third-order explicit expressions of the stream function, the velocity potential and the surface elevation are obtained. The nonlinear dispersion relation is also derived to account for the interacting wave components with different frequencies and amplitudes.
The obtained solutions including the nonlinear dispersion relation are verified by reducing to those of previous results in the case of monochromatic waves and uniform currents of Chen and Juang (1990), Madsen and Fuhrman (2006) and Kishida and Sobey (1988). The comparisons between the solutions are shown to be in good agreements.
The influence of current velocity and vorticity on the wave characteristics such as wavelength and maximum particle velocity is illustrated. Comparisons between different wave and current conditions are also made. Finally, the influence of shear currents on the intensities of bound long wave components induced by the nonlinear wave-wave interaction of bichromatic waves are also discussed.

Abstract I
中文摘要 III
Acknowledgements IV
Contents V
List of Tables VIII
List of Figures IX
List of Symbols XVII
Chapter 1 Introduction 1
1-1 Motivation 1
1-2 Scope of Present Study 3
Chapter 2 Literature Review 5
2-1 Review of Theory for Monochromatic Waves on Uniform Currents 5
2-2 Review of Theory for Bichromatic Waves on Uniform Currents 10
2-3 Review of Theory for Monochromatic Waves on Linear Shear Currents 20
Chapter 3 Bichromatic Waves on Linearly Varying Currents 25
3-1 Assumptions 25
3-2 Mathematical Formulation 27
3-2-1 Governing Differential Equations 28
3-2-2 Bottom Boundary Condition (BBC) 32
3-2-3 Kinematic Free Surface Boundary Condition (KFSBC) 32
3-2-4 Dynamic Free Surface Boundary Condition (DFSBC) 32
3-2-5 Combined Free Surface Boundary Condition (CFSBC) 36
3-2-6 Summary 37
3-3 Taylor Expansion of the Free Surface Boundary Conditions 39
3-4 Perturbation Approach 40
3-4-1 Zeroth-Order Problem 41
3-4-2 First-Order Problem 42
3-4-3 Second-Order Problem 46
3-4-4 Third-Order Problem 50
3-4-5 Summary 60
3-5 Wave Amplitude Modification 63
3-6 Bichromatic Wave Example 66
Chapter 4 Solutions Verification 69
4-1 Verification with Monochromatic Waves on Uniform Currents 69
4-2 Verification with Bichromatic Waves on Uniform Currents 75
4-3 Verification with Monochromatic Waves on Linear Shear Currents 92
Chapter 5 Results and Discussions 97
5-1 Difference between First- and Third-Order Solutions 97
5-2 Influence of Shear Currents on Wavelength 107
5-3 Influence of Shear Currents on Maximum Horizontal Velocity 114
5-4 Influence of Shear Currents on Bound Long Waves 118
Chapter 6 Conclusions and Future Works 138
6-1 Concluding Remarks 138
6-2 Future Works 141
Reference 142
Appendix 147
A-1 Procedure of Derivation 147
A-1-1 First-Order Solutions 147
A-1-2 Second-Order Solutions 149
A-1-3 Second-Order Correction to the Angular Frequency 156
A-1-4 Third-Order Solutions 164
A-2 Procedure of Verification 172
A-2-1 Verification with Monochromatic Waves on Uniform Currents 172
A-2-2 Verification with Bichromatic Waves on Uniform Currents 183
A-2-3 Verification with Monochromatic Waves on Linear Shear Currents 192
碩士論文審查委員意見回覆表 202
Vita 205

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