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研究生:童正安
研究生(外文):Cheng-An Tung
論文名稱:孤立波通過直角彎道波場分析
論文名稱(外文):Analysis on Solitary Waves Propagating Through Right-angled Bend in a Channel
指導教授:唐啟釗
指導教授(外文):Chii-Jau Tang
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:77
中文關鍵詞:孤立波彎曲渠道直角彎道
外文關鍵詞:curved channelsolitary wave
相關次數:
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迄今孤立波在平直渠道運行的特性均已被廣泛的研究並獲得許多顯著成果,包含推廣至不同斷面形狀或緩變底床坡度的情形。相對地,孤立波通過彎曲渠道的研究較少探討。為了發展可解析任意角度入射的二維長波模式,本文以數值求解一般化(generalized) Boussinesq (簡稱gB)方程組,並評估適當的邊界條件。應用此模式模擬孤立波通過一直角彎曲渠道時發現:由於傳遞方向與彎曲段斷面的改變,以及尖銳轉角處之繞射現象,波傳與反透射的影響可被適當解析。在反射、透射過程中,比較波形、波高、體積與能量的演變,可發覺彎道上下游的寬度影響內外側壁面波形遲滯時間。當波形通過尖銳內側轉角點,流況產生劇烈變化,加上反射波的互制作用,因此在內側轉角點附近會有波形震盪的情形。數值分析的誤差也因頻散而加劇,將數值模擬結果因不同內側轉角點條件而產生不同程度之差異。本文亦據此分別討論與評估各種條件之適切性。
計算結果可知,當孤立波在寬渠道中傳遞,由於透射波會先繞過內側轉角點,波高分佈將形成弧形曲面分佈。寬度越大,則透射波恢復一維性所需的時間越久。當下游區寬度變窄,透射波波形可維持良好一維性。當下游渠道寬度變寬時,透射波在達到最大溯上波高時以弧形曲面分佈的情形與通過寬渠道的情況相近。
Until now the characteristics of solitary wave propagating in a straight channel with uniform water depth have been studied extensively and a lot of remarkable achievements have been obtained, including those extended to a channel with arbitrary cross section or with mild bottom slope. On the other hand, the studies on solitary waves propagating in a curved channel are less discussed.
To develop a two-dimensional long-wave model capable to analyze a solitary wave motion with an arbitrary incident angle, this thesis intended to solve the generalized Boussinesq (briefly, gB) equations numerically and assessed the numerical result by examining various boundary conditions. When using this model to simulate a solitary wave propagating through a right-angled channel, one found that the effects of changes in converting direction and transition width on the wave transmission, reflection and diffraction around a sharp internal corner could be reasonably analyzed. During the interaction near the corner, the channel width variation at the turning end presents different phase delays on the waveform across the internal and external walls after one compared with the evolved waveform, amplitude and kinetic energy. The induced flow varied greatly as the wave passed by the internal corner. Furthermore, the interaction with the reflected wave enhances the dispersive wave pattern there. Numerical error also pollutes the simulated result at different degrees as various corner conditions are used. This analysis suggests us on which condition would be most reasonable to be employed in the model.
中文摘要 I
Abstract II
謝誌 III
目錄 IV
圖目錄 VI
表目錄 VIII
符號說明 IX
第一章 緒論 1
1-1 研究目的 1
1-2 文獻回顧 3
1-3 本文組織 5
第二章 理論背景 6
2-1 水深積分平均方程式 6
2-2 Boussinesq型態長波理論 10
2-2-1 不同水平速度分量Boussinesq型態方程組 11
2-2-2 傳統一維Boussinesq方程組之頻散分析 12
2-3 Boussinesq方程組與水深平均式的壓力平均項比較 14
第三章 數值方法 15
3-1離散方法 15
3-2 數值疊代 18
3-3 初始與邊界條件 20
3-3-1 說明條件 20
3-3-2邊界上差分精度 21
3-4 計算流程 23
第四章 模式測試 25
4-1計算效率 25
4-2 邊界條件與入射角度 27
第五章 計算結果與討論 29
5-1轉角點測試 29
5-2 通過等寬度直角彎曲渠道 32
5-3 通過上下游不等寬度直角彎曲渠道 35
第六章 結論與建議 37
6-1 結論 37
6-2 建議 38
參考文獻 39
參考附圖 41
1.張志華、唐啟釗 (1996) “兩孤立子互撞低階解析解之數值驗證”,成功大學學報第31卷 科技.醫學 第89-106頁
2.張志華 (1997) 「孤立波與結構物在黏性流體中互制作用之研究」,博士論文,國立成功大學水利及海洋工程研究所,中華民國,台灣,台南
3.林德昌 (1997) 「非線性長波與離岸潛堤互制作用分析」,碩士論文,國立成功大學水利及海洋工程研究所,中華民國,台灣,台南
4.張登林 (1999) 「應用不同波浪型態方成祖數值解析初始孤立波傳現象」,碩士論文,國立成功大學水利及海洋工程研究所,中華民國,台灣,台南
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