本研究為時間領域造波的理論解析，研究問題為一有限等深水槽，左側為造波板做直推式運動，右側為ㄧ不透水直立壁，將直角座標軸原點設置於靜水面與造波板靜止處之交點，初始水位為水平靜水面，造波板開始運動後，尚未達到完全發展的水位波形，稱之為發展中的波，此即為本理論解析之求解重點。採用複數型態求解問題，先將相關邊界條件作泰勒展開，搭配微小振幅波理論線性化問題。做法上將波浪勢函數以傅立葉級數表示，分別代入邊界條件與起始條件，使用參數變異法(method of variation of parameters)，求得時間領域線性造波之理論解析。
本理論解得水位函數具收斂特性，且與李(1991)同樣問題之解實數部分相同，時間領域波形在傳遞足夠長時間後，偏造波板一側形成完全發展波形，此部分的波形與Dean and Dalrymple(1984)頻率領域的波形相符，亦驗證本理論的正確性。理論解析方法的優勢在於可獲得水槽波形的全貌，本研究著重於發展中的波形，並考量不同相對水深下的特性變化。研究成果顯示，造波板開始啟動造出的第一個波，即最初波，隨時間的增加，波高有漸減，波長漸增的趨勢，且最初波峰傳遞的速度約為定值。第二波則在初期約等於穩定週期波的波高與波長，隨時間變化的性質則與最初波一致，但長波相較於短波在一倍穩定週期波高與波長的週期時間為長。波浪在形成完全發展波之前，會伴隨一個最大波峰，最大波峰並不穩定存在於某序列波之中，最大波隨時間的移動雖有其趨勢，但偶而會往回傳，因此其波速並非定值。

In this research, an analytic solution is derived to study the generation and propagation of waves which is made by a piston-type wavemaker in an experimental channel. The wavemaker has different setting to generate and propagate water waves along the water surface. Our analytic solution to the problem is innovated from inspections of previous solutions, and is applied to study the time evolution of waves. The Fourier cosine transform is applied to deal with the horizontal coordinate which incorporates boundary conditions at two ends of the wave channel. The function of the vertical coordinate is obtained by solving nonhomogeneous differential equations. Our analytic solution has the same form as Lee (1991) in real part. The formula for water elevation is a series where convergence is associated with the length of the channel. The longer the channel, the more terms required for convergence. The analytic solution obtained in this research is then used to study the unsteady formation of water waves. The results indicate that the first generated wave becomes longer as time increases, while the wave heights regularly decrease. After the generation of 3 to 4 waves, steady fully developed waves are generated. The fully developed waves are compared with the wave theory derived by Dean(1984) in the frequency domain, and the result shows high levels of consistency. Our analytic solution is more efficient than other methods comparisons with other studies help to affirm its accuracy.

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