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研究生:蕭冠宇
研究生(外文):Kuan-yu Hsiao
論文名稱:非線性演進型緩坡方程式在斜坡上的應用
論文名稱(外文):An Application of Nonlinear Evolution Equation for Mild-Slope Equation on Sloping Beach
指導教授:許泰文許泰文引用關係
指導教授(外文):Tai-wen Hsu
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:2008
畢業學年度:96
語文別:中文
論文頁數:61
中文關鍵詞:緩坡方程非線性
外文關鍵詞:Mild-Slope EquationNonlinear
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本文以演進型緩坡方程式 (evolution equation for mild-slope equation,EEMSE ) 之數值模式,將底床坡度展開至α2階,結合輻射邊界條件,推導出非線性演進型緩坡方程 (nonlinear evolution equation of mild-slope equation),用以模擬波浪在斜坡上的波動效應與變形,其效應包括淺化、折射、繞射、反射、碎波與能量消散等。模式計算結果與 Guza和Bowen (1976) 以及楊等人 (2004) 的理論結果進行比較,用以驗證本文模式的正確性與適用性。
底床坡度為1/10、1/5及1/3之情況,本文計算結果與楊等人 (2004)之理論結果有相同的趨勢,唯有在底床坡度為1/5與1/3時,深水和淺水海域兩者之波形相符,而中間性水深漸有差異,此差異隨著底床坡度變陡而變大。與 Guza 和Bowen (1976) 底床坡度為1/40以及1/10之波形比較發現,模式在α1階級數之數值計算結果與理論值相符合。
The evolution equation for mild-slope equation model is expended to second order in bottom slope to derive a nonlinear evolution equation of mild-slope equation. The nonlinear evolution equation of mild-slope equation model is used to simulate wave transformations such as shoaling, refraction, diffraction, reflection, wave breaking and energy dissipation.
In the condition of bottom slope on 1/10, 1/5 and 1/3, the proposed model can modify wave transformations under the sloping bottom by examining Yang’s (2004) theory and calculate the accurate results. The bottom slope on 1/40 and 1/10,
proposed model calculate the accurate results for wave phase with Guza and Bowen’s (1976) theory.
中文摘要 I
英文摘要 II
誌謝 III
目錄 IV
表目錄 VI
圖目錄 VII
符號說明 IX
第一章 緒論 1
1-1 研究動機及目的 1
1-2 前人研究 3
1-3 本文組織 6
第二章 理論分析 7
2-1控制方程式 7
2-2 水深積分方程式 11
2-3 至 階之緩坡方程式 13
2-3-1 階之緩坡方程式 13
2-3-2 階之緩坡方程式 14
2-3-3 階之緩坡方程式 17
2-4 降階之緩坡方程式 20
2-4-1 降階之緩坡方程式 21
2-4-2 降階之緩坡方程式 21
2-4-3 降階之緩坡方程式 22
第三章 數值模式 24
3-1數值方法 24
3-2 邊界條件 26
3-3 起始猜測值 30
第四章 各階量係數項特性分佈 32
4-1 項各參數和相對水深之關係圖 32
4-2 項各參數和相對水深之關係圖 34
第五章 模式驗證 37
5-1模式在 Booij’s ramp 之測試 37
5-2 楊 (2004) 之理論比較 41
5-3 Guza與Bowen (1976) 之理論比較 46
第六章 結論與建議 48
6-1 結論 48
6-2 建議 49
參考文獻 50
附錄 A 54
附錄 B 56
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