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研究生:張家華
研究生(外文):Chia-Hua Chang
論文名稱:非線性造波在時間領域之理論分析
論文名稱(外文):Analytic Solution of Nonlinear Wavemaking in the Time Domain
指導教授:李兆芳李兆芳引用關係
指導教授(外文):Jaw-Fang Lee
學位類別:碩士
校院名稱:國立成功大學
系所名稱:水利及海洋工程學系碩博士班
學門:工程學門
學類:河海工程學類
論文種類:學術論文
論文出版年:2002
畢業學年度:90
語文別:中文
論文頁數:50
中文關鍵詞:攝動法泰勒級數展開
外文關鍵詞:perturbation methodTaylor series expansion
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  本文目的在對非線性直擺式造波問題提出一時間領域之二階理論解。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。Lee, Kuo and Lee(1989)所提出求解一階問題之方法則應用來求解第二階解。在求解方法上,為先對時間作Laplace轉換,再對x函數作Fourier Cosine轉換,然後問題即成為可以求解的y函數之常微分方程式。然而,在第二階解中出現在自由水面和造波板界上非齊性之條件,則需利用到第一階解。在推導上和過去不同的為本文使用實數推導。
  本文二階理論可以描述水槽中由造波板運動所造出非線性波浪之時間變化;即波浪由靜止,發展,以至於完全發展之時間過程。本文所得理論解之收斂特性和波浪尖銳度,以及水槽長度之關係文中也討論到,對於水槽愈長和愈高之波浪尖銳度,理論解中級數解之項數需要更多。本文理論也與穩定週期性之二階理論解比較,比較結果在波形和量的大小,雖然二階自由波的存在讓波形在空間變化上沒有重複性,造成比較上之困難,但比較結果趨勢上仍很一致。由二階解和一階解之比較可知在波峰和波谷附近非線性效應較明顯,在發展中或完全發展之波形都可能有歪斜或不對稱之情形。
  The purpose of this study is to present a second-order analytic solution for the nonlinear flap wavemaker problem in the time domain. The potential wave theory is used to describe the wave motion. Taylor series expansion and the perturbation method are used to express the nonlinear boundary value problem into a first-order and a second-order problem. A solution procedure proposed by Lee, Kuo and Lee (1989) solving the first-order problem is applied to solve for the second-order problem. The second-order problem nonhomogeneous conditions appearing on the free surface and the wavemaker boundary are calculated using the first-order solution. On contrary to previous studies real variables are used in the present derivation.
  The present second-order analytic solution can be used to describe waves generated by the wavemaker motion in the wave channel in the time domain. Convergence characteristics of the present solution are discussed with respect to wave steepness and length of the wave channel. For longer wave channel and higher wave steepness the more number of terms used in Fourier series is required. The present theoretical results are compared with the second-order analytic theory of frequency domain, and comparisons are favorable in over all tendency and magnitudes, although free waves involved in the generated surface elevation make no repeated waveforms. The second-order wave forms in the time-domain compared with the first-order solution indicates that nonlinear effects can be significant at wave peak and trough, typical wave forms can be skewed and unsymmetrical for waves at developing and developed stages.
中文摘要…………………………………………………………………….…… i
英文摘要………..……………………………………………..…..……………. iii
致謝…………….……………………………………………………….. v
目錄………………………………………………………………………….. vii
圖目錄……………………………………………..……………..……..…. ix
表目錄………………………………………...……………………………..xiii
符號表……………………………………………………..……………… xv
第 一 章 緒論…………...….…..……………………………………………….. 1
1.1 前言…………………………………………………………………… 1
1.2 文獻回顧……………………………….………………………...…… 2
1.3 研究方法………………………………………………….……...…… 3
1.4 本文組織…………………….…………………………………...…… 3
第 二 章 理論分析…………….………………………………………………... 5
2.1 問題的描述………………………………...…………………………. 5
2.2 理論解析……………………………………………………………… 6
2.4 直擺式造波第一階解………………………………………………… 9
2.6 直擺式造波第二階解……………………………………………….. 10
第 三 章 計算結果與討論…………………………………………………….. 19
3.1 水槽長度對於收斂性的影響……………...………………………... 19
3.2 波浪尖銳度的影響………………………………………………….. 20
3.3 結果與分析………………………………………………………….. 21
3.3.1 收斂項數對於求解精度之影響……………..………..………….. 21
3.3.2 不同時間的波形變化………….………………………………….22
3.3.3 與劉(2002)理論值作比較……………………………………… 22
第 四 章 結論與建議………………….…………………..…………………... 25
參考文獻..……………….………………………………..…………………... 49
附錄A 第一階理論解析解……..…………………..……..…………………….. A-1
附錄B 二階邊界值問題中一階相乘項之推導……….….……………………..B-1
附錄C 第二階部分推導整理…………………………………..………………..C-1
附錄D 第二階勢能函數表示式………………………………..………………..D-1
附錄E 自由表面水位變化第二階表示式.…………..…………………………. E-1
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2.Finkelstein, A. (1953), “The Initial Boundary Value Problem for Transient Water Wave”, Ph. D. Dissertation, New York University, New York.
3.Kennard,E. H. (1949), “Generation of Surface Waves by a Moving Partition”, Quarterly of Applied Mathematics, Vol. 41, pp. 525-571.
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6.Lee, J.-F, Kuo, J.-R, Lee, C.-P. (1989), “ Transient Wavemaker Theory, Journal of Hydraulic Research”, Vol. 27 , No. 5, pp. 651-663, 1989.
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12.Wu, Y-C.(1987), “Constant wave form generated by a highed wavemaker of finite draft in water of constant depth” ,Proceeding of 9th Ocean Engineering Conference in Taiwan, R.O.C., Tainan,pp.552-569.
13.李兆芳和陳春錦 ,1990 , 邊界元素法模擬非線性造波 ,第十二屆海洋工程研討會議論文集, pp. 55-73。
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17.劉正琪,2002,波浪通過潛堤之二階理論解析,國立成功大學水利及海洋工程研究所,博士論文。
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