本文應用曲線座標數值求解一般化（generalized）Boussinesq方程組，以模擬孤立波通過河川彎道之波流場變化。文內探討渠道寬度、彎曲角度及渠流流速對孤立波與渠流通過彎曲渠道之影響，並以Yen（1965）研究之彎道定量流試驗作為本模式之驗證。數值模式以二階精度之時空中央差分與二時階平均法離散控制方程式，以代數法生成計算網格，並應用逐線矩陣疊代完全滿足非線性方程組與相關邊界條件之關係，因而獲得數值之時間精確解。本文使用上風法（upwind method）處理非線性對流項，以增加計算流況時模式的安定性。本模式先測試孤立波於平直渠道中傳遞之數值結果，由精確度與計算效率之最佳化得到最佳計算格網尺寸後，再據以模擬彎道上波流場之流況。
數值結果顯示：孤立波沿著彎曲渠道傳遞時，其內外側兩壁面波形遲滯現象深受渠道寬度之影響。當波在90度及180度窄渠道（寬度為3倍水深）中傳遞時，彎道內孤立波波峰呈現楔狀分佈特性，通過彎道後孤立波上下游波高變化小於1％，且彎道橫斷面上縱向速度分佈與局部半徑成線性減小。當波在寬渠道（寬度為6倍與9倍水深）中傳遞時，因渠寬增加使孤立波沿外岸岸壁溯升高度增高，且內外岸壁波形之遲滯現象也更顯著，而波通過彎道後需花更長的時間才能恢復原先孤立波平面波形。由於波在彎道內傳遞過程中，因外岸壁側向反射使主波分離出數個小波尾隨其後往下游運動，因此孤立波最終波形不再與入射前波形保持一致，最終主波波高隨渠道寬度的增加而減小。而波流在直線渠道中傳遞的結果顯示，當波流同向時，波高隨渠流流速減小，波長、波速則增加；而當波流反向傳遞時，結果恰好相反。由孤立波同向通過一含流彎道之計算結果可發現，渠道外壁最大溯升高度隨渠流流速而略有增高，而通過彎道後最終孤立波高則隨流速降低。

This thesis investigated the propagation of a solitary wave in river bends by solving the generalized Boussinesq equations (Wu, 1981) in the curvilinear coordinates. The objective is to study effects of the channel width, the bending directions and the flow speed on the transmitted long waves with channel flow over the bend. The experimental data by Yen (1965) is used to validate the numerical model. The numerical methods in use is of the second-order accuracy of central differences and time-averaged scheme with the upwind treatment in convection terms, algebraic grid generation and iterative LSOR technique for seeking time accuracy solutions. In order to obtain the optimal grid size the author considered the evolution of a solitary wave propagating into a straight water channel of uniform depth in later application, by means of the accuracy and efficiency of a numerical solution. The suggest grid size is then applied for the present study of the wave-flow interaction in a channel bend.
The numerical results show that, during a solitary wave traveling through the narrower channels, the transmitted wave crest turns radially straight and inclines higher outward against the outside wall with the wave amplitude changed smaller than 1%, and the longitudinal fluid velocity decreases almost inversely with local radius in the transverse section of the bends. During a solitary wave passing through the wider bend channels, the phase delay and super elevation on the waveform between the internal and external walls is more significant than those of the narrower channels. The transmitted wave takes more time to evolve into a final plane solitary wave. Furthermore, the initial wave disintegrated into several smaller waves because of the lateral reflection form the outside wall in the bends, so that the transmitted wave no longer holds the original shape（wave amplitude becomes smaller when the channel width is extending）.

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