本文目的在對平面水池非線性方向造波問題提出二階理論解。波浪場是利用勢能波浪理論描述，所求解非線性問題則利用泰勒級數展開，配合攝動法將問題表示成第一階和第二階問題。延伸劉(2002)所提出求解斷面水槽造波理論之方法直接求解平面水池非線性方向造波理論，並且利用複數推導理論。在第二階解過程中，由於自由水面及造波板運動均為非齊性之邊界條件，因此第二階解必須分離成第二階Stokes波以及第二階自由波。
　　本文所提出之理論解可以降階成斷面水槽造波問題之表示式。由本文之理論指出隨著方向角度增加則振幅會隨著增大，亦表示可以更有效的造波。對於動量傳輸之問題，在 方向上之動量傳輸分量其值為零，然而在 方向上應存有一反向淨值之動量傳輸分量，可以在平面水池中產生環流之問題。當方向角度及造波衝程較小，本文理論與試驗比較可以得到很好的模擬結果。另一方面，當方向角度及衝程較大，由於實際造波機為有限寬度之造波板連續運動，因此理論解與試驗結果有明顯的差異。

　　In this thesis, a nonlinear directional wavemaking problem in the plane wave basin is solved analytically up to the second-order. The potential wave theory is used to describe the wave motion. Under the assumption of steady and periodic motion, the corresponding boundary-value problem is written into the first-order and the second-order problems, using the Taylor series expansion and the perturbation method on the free surface and the wavemaker boundaries. A solution method developed by Liu (2002) for the two-dimensional wavemaker problem is applied directly for the present problem, in which complex variables are used in the derivations. In the second-order solution, because of the nonhomogeneous conditions imposed on the free surface and the wavemaker, the solution has to be divided into a Stokes wave solution and a free wave solution.
　　The present analytic solution can be reduced into exactly the same expression for the two-dimensional wavemaker problem. The present theory indicates that with the increased directional angle the generated wave amplitudes can be increased, which means the wavemaking can be more effective. The momentum transport in the direction perpendicular to the wavemaker is null, however, in the parallel direction there is a net mass transport moves away from the wave field, which can cause circulation problem in the wave basin. The present theory compared very well with the experimental results for cases of small wave angles and wavemaker amplitudes. On the other hand, for large wavemaker motions the discrete and finite paddle sizes of the wavemaker are not negligible, large discrepancies are observed between experiments and present analytic solution.

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