本研究目的在於對直推式造波問題提出一個時間領域之二階解析解。求解方法為使用勢能波浪理論，先利用攝動法得到問題的第一階和第二階問題表示式。再利用第一階解進行第二階解的推導。第二階解的推導基本上與第一階解類似，但是水面以及造波邊界條件需要先進行推導歸納整理。在求解上，在波浪前進方向使用Fourier Cosine轉換，在水深方向則配合邊界條件求解，最後再利用起始條件求解。求得解後，使用電腦計算並繪出水位結果，為此需要將級數和進行收斂項測試，條件選定以前項最大差值作為分母，若計算結果不超過0.1%視為收斂，收斂結果水位看不出高頻振動，結果甚好，且收斂值經由測試發現與經過時間沒有太大關連，而與波長及水槽長之比值呈現正相關。確認收斂條件與變數關係後，利用本研究得到的解析解計算與實驗數據進行比較，結果顯示非線性解析解與實驗結果相當一致。由研究顯示非線性解析解比線性解更接近真實波浪，本研究提出之時間領域造波解析解足以用來描述造波問題。

In this study, an analytic solution for the nonlinear problem of wave generation in a wave tank is presented. The solution is based on the Stokes wave theory. Use the perturbation method to divide the problem into linear part and second-order part. The linear solution proposed by Lee and Lin (2017) is used, and the second-order solution is developed following the solution methodology used in the linear solution. After obtaining the solution, use the computer to calculate and plot the result. Then the terms of convergence are tested. If the difference between the next term and the sum of previous terms does not exceed 0.1%, it is regarded as convergence, and the result is very good. The terms of convergence is not closely related to the time but is positively relate to the ratio of the wavelength and the length of the tank through this test. After the test, the analytical solution obtained by this study is compared with the experimental data. The results show that the nonlinear analytical solution is quite consistent with the experimental data. It is shown by the research that the nonlinear analytical solution is closer to the real wave than the linear solution. The time-domain analytical wave solution proposed in this study is sufficient to describe the wave-maker problem.

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