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研究生:周世恩
研究生(外文):Shih-En Chou
論文名稱:Boussinesq方程式應用於波浪通過人工沙漣之研究
論文名稱(外文):Boussinesq Equations for Waves PropagatingOver Artificial Sand Bars
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:2003
畢業學年度:91
語文別:中文
論文頁數:90
中文關鍵詞:布拉格反射人工沙漣
外文關鍵詞:Bragg resonanceBoussinesq
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本文以 Wei 等人 (1995) 所提議之二階全非線性 Boussinesq 方程式建立數值模式,並經過一系列的模式測試與驗證以確保其適用性與穩定性,之後再以本文模式探討規則波和不規則波通過 Davies 和 Heathershaw (1984) 及 Kirby 和 Anton (1990) 之人工沙漣底床所產生的布拉格反射效應,並與 Miles (1981) 的反射率理論及 Hsu 等人 (2003) 之演進型態緩坡方程式計算之結果作一比較。結果顯示,在規則波條件時,本文模式可較良好描述發生布拉格共振之尖峰反射率與次諧波共振反射率,顯見本文模式在計算波浪通過人工沙漣底床之適用性應可有所信賴﹔而在不規則波條件時,計算結果顯示其反射率分佈型態與規則波情況有所不同,於主共振區之反射率雖不如規則波為大,但反射率帶寬則較規則波為寬,且由於在非共振區之平均反射率提高,增加可防禦的波浪條件。本文同時探討布拉格反射之影響因數,這些因數包括沙漣個數、沙漣高度及沙漣間距等,計算結果顯示,佈置人工沙漣時適當地增加沙漣個數和加大沙漣高度,可使主共振與次諧波共振反射率變大,而拉大沙漣間距雖可使次諧波共振反射變大,但主共振反射則會減小。
The one part of this paper is to develop the numerical model based on the 2nd — order fully nonlinear Boussinesq equations of Wei et al. (1995), and the Boussinesq model has been applied to compute wave fields for several cases of wave propagation for the rationality of the model. The another part of this paper is to apply the Boussinesq model to the simulation of the Bragg reflection of monochromatic and random waves due to artificial sand bars, for which experimental data have been presented by Davies and Heathershaw (1984) and Kirby and Anton (1990). The numerical results are compared with the theoretical solutions of Miles (1981) and the corresponding results using the evolution equation for mild slope equation of Hsu et al. (2003). For the monochromatic wave, the Boussinesq model can predict the reflection coefficients of the primary and second-harmonic resonance well. For the random waves, the reflection coefficients of the primary resonance are smaller and the reflection bandwidth is wider than the monochromatic wave, so the Bragg reflection of random waves is different from that of the monochromatic wave.
In addition, the Boussinesq model is applied to study the affecting factors of the Bragg reflection, including the number, the height and the spacing of artificial sand bars. The results are that increasing the number and the height of the sand bars, the reflection coefficients of the primary and second-harmonic resonance raise and increasing the spacing of sand bars, the reflection coefficients of the second-harmonic resonance increase, but that of the primary resonance decrease.
誌謝I
摘要III
ABSTRACT III
目錄IV
圖目錄 VI
表目錄 IX
符號說明 X
第一章 緒論 1
1-1 研究動機與目的1
1-2 前人研究 4
1-2-1 BOUSSINESQ 方程式4
1-2-2 布拉格反射7
1-3 本文組織10
第二章 理論基礎11
2-1 二階全非線性 BOUSSINESQ 方程式11
2-2 反射率公式12
2-2-1 規則波計算12
2-2-2 不規則波計算14
2-3 沙漣底床前反射率之理論解析17
第三章 數值模式21
3-1 控制方程式之離散化21
3-1-1 時間項之離散22
3-1-2 空間項之離散24
3-2 邊界條件25
3-2-1 完全反射邊界條件25
3-2-2 消波邊界條件26
3-2-3 入射波邊界條件27
第四章 模式驗證30
4-1 模式基本測試30
4-1-1 消波邊界測試30
4-1-2 造波函數測試32
4-2 波浪通過潛堤之測試36
4-2-1 規則波試驗36
4-2-2 不規則波試驗40
第五章 布拉格反射計算42
5-1 兩倍沙漣間距與波長比值對反射率之影響44
5-2 沙漣個數對反射率之影響57
5-3 沙漣高度對反射率之影響60
5-4 沙漣間距對反射率之影響63
第六章 結論與建議65
6-1 結論65
6-2 建議66
參考文獻67
附錄A. 各型態 BOUSSINESQ 方程式之推導與比較69
A-1二階全非線性 BOUSSINESQ 方程式之推導69
A-1-1控制方程式及邊界條件69
A-1-2在任意水深位置 處之流速勢函數 70
A-1-3水深積分72
A-2 各型態 BOUSSINESQ 方程式之分散性及非線性的適用範圍73
A-2-1 各型態 BOUSSINESQ 方程式74
A-2-2 分散性比較78
A-2-3 非線性比較81
附錄B. 碩士論文審查委員意見回覆表87
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