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研究生:陳清煌
研究生(外文):Ching-Huang Chen
論文名稱:孤立波經直立壁防波堤繞射反射波場分析
論文名稱(外文):On Diffraction and Reflection of a plane Solitary Wave by a Vertical-wallBreakwater
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:98
中文關鍵詞:孤立波非線性
外文關鍵詞:solitary wavenonlinear
相關次數:
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本文應用平面二維數值模式模擬孤立波經一直立式防波突堤互制波埸的有趣現象。模擬波浪之模式係根據Wu(1981)所推導的弱非線性、弱頻散一般化Boussinesq(gB)方程組建立。然後以二階精度之時空中央差分與時間平均法離散gB模式,並由矩陣法連續疊代求解收斂後,獲得具時間精度之數值結果。本文首先考量初始孤立波振幅演變等不同物理量之效能評估與誤差量測試,而獲得計算分析之最佳格網尺寸。再利用這個模式,模擬初始波高為0.3倍靜水深之孤立波,經半開放式垂直壁防波堤或離岸式防波堤之波埸。初始孤立波受堤的作用被分解成部分反射波與部分繞射波,並表現出非均勻振幅往遮蔽區分散傳遞的時變特性。因數值模式的尾波(誤差波)同時也參與此互制過程,使平面波埸之波峰線呈高低分佈,並發生以堤端為中心之柱狀孤立波,向外傳遞的調變(modulation)現象。當改變堤寬以比較水面之影響變化時,反射區波埸溯升之瞬時等高線分佈並未受堤寬影響而有差異;但繞射區除了因堤寬之波傳時差外,波峰明顯隨堤寬加大後有微弱衰減狀況。應用本模式考量另一種流況時,當孤立波經離岸式防波堤互制產生繞波埸,亦發現柱狀波傳與堤後側兩繞射波會合後使波峰倍增之現象。這些近埸之互制經長距離傳遞後,因兩波系(即反射波與繞射波)的內部非線性量與頻散量再次重新調整而終各自達平衡狀態,最終遠離堤身而水面再次形成平面孤立波的有趣現象。最後,本文亦數值解析兩相向對稱孤立波對撞於半開放式防波堤處,能同時獲得堤兩側溯升水位高度與對撞過程波峰演變之一致性,兩波相撞最大峰高與最大溯上高度幾乎相同但因堤寬而產生相位差,且波埸亦呈對稱性的孤立波傳遞特性。
This thesis discussed the application of a two-dimensional numerical model to simulate the interesting wave phenomena for a solitary wave interacting with a vertical-faced breakwater in uniform water depth. The model applied in the present study is based on the weakly nonlinear, weakly dispersive wave theory described by generalized Boussinesq (gB) equations (Wu, 1981). With the second-order accuracy of central differences for spatial and temporal derivatives and of time-averaged for those linearized coefficients in nonlinear terms, the discretized formulation is then solved iteratively by the LSOR matrix method. Since a fully converged solution is required at each time step, the numerical result is declared as time accurate. To validate this model the author first considered the evolution of a solitary wave propagating at a certain incident angle into a three-dimensional shallow water field. The optimal grid size can then be evaluated from testing the calculated quantities by the error assessment and computing economics. By using this optimal grid size in model, the diffracted and reflected wave fields are investigated for an initial plane solitary wave of moderate strength, namely, of 0.3 water depth, interacting with a semi-open breakwater and with an isolated breakwater. In the first kind of breakwater, the non-stationary reflection and diffraction of cylindrical-type solitary wave is generated and scattered around the tip of breakwater during interaction, and two wave systems moving in the opposite directions are independently combined either with the reflected wave or the transmitted wave to evolve their individual solitary waveforms with distorted crest line. During the wave-structure interaction, these lines of wave crests, which illustrate the wave modulating and damping behaviors in amplitude, vary timely with the width of a breakwater. The wave reflected from the front part of a breakwater does not present any difference in phase and waveform for various breakwaters stood at the same location. However, for the diffracted and transmitted waves, the relative phase lag delayed with the width of breakwater is reasonably shown while the decreasing in wave peak, although weak, become clearer as the width of this breakwater increases accordingly. For an isolated breakwater in a uniform shallow water region, the wave reflection by the breakwater is much weaker than that by the semi-open breakwater. The constructive interference of the cylindrical scattering waves diffracted around two corners of the breakwater amplifies the wave amplitude, and this wave connects itself with the transmitted wave side by side to form a distorted solitary wave system as well. Far from the breakwater, this distorted solitary wave will be seen to evolve gradually into a final plane solitary wave after the lateral balance of nonlinearity and dispersion within the wave system is reached. The final case study in this thesis is that two symmetry solitary waves head-on collide right at the site of a semi-open breakwater with various widths. The consistent wave characteristics during its run-up and reflection, on the one hand, with those during collision and transmission, on the other hand, are obtained in association with the suitable phase lags according to the related breakwater widths. These results discussed in all verify the present numerical model to be reliable and useful in practical applications of coastal engineering.
中文摘要 I
英文摘要 II
致謝 IV
目錄 V
表目錄 VII
圖目錄 VII
符號說明 X

第一章 緒論 1
§1-1 前言 1
§1-2 前人研究與本文研究動機 2
§1-3 本文組織 5

第二章 數學模式 6
§2-1 頻散波(dispersive wave) 6
§2-2 水深平均積分法 8
§2-3 緩變底床之generalized Boussinesq方程組(Wu 1981) 9
§2-4 初始條件及邊界條件 13

第三章 數值方法 17
§3-1 有限差分法 17
§3-2 數值技巧 20
§3-3 數值安定性分析 23
§3-4 計算流程 26

第四章 模式驗證 28
§4-1 合理格網尺寸 28
4-1-1 孤立波沿x方向正向入射測試 28
4-1-2 孤立波沿x軸成 入射測試 30
§4-2 邊界測試 31
4-2-1 開放邊界測試 31
4-2-2 不可穿透邊界測試 32
§4-3 兩孤立波對撞互制作用 33
4-3-1兩相向非對稱孤立波碰撞 33
4-3-2兩相向對稱孤立波碰撞 34

第五章 結果與討論 36
§5-1非線性長波經單一半開放式防波堤 36
5-1-1 波經堤互制的波埸分析 37
5-1-2 堤寬效應對波場影響 40
§5-2 非線性長波入射經離岸式防波堤 41
5-1-1 非線性長波正向入射經單一離岸式防波堤互制 41
5-1-2 非線性長波 角入射經單一離岸式防波堤互制 42
§5-3 兩相向對稱孤立波於半開放防波堤處對撞互制 43

第六章 結論與建議 45
參考文獻 47
附表附圖 49
附錄 94
自述 98
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