本研究以數值模擬探討孤立內波之傳播。物理基礎是利用美國Cornell大學Lynett and Liu (2002)所發展，並經Cheng 等人(2005)修改後之二維內波傳播模式。模式中假設內波存在於弱非線性效應、弱頻散效應與黏滯性很小的兩層流體系統。其主要理論基礎是利用流體連續方程式與動量方程式為主要控制方程式，利用深度積分配合有限差分數值方法，並納入實際的地形水深以模擬內波傳播的情況。為了使模擬更符合實際情況，本文進而修改下列幾項初始條件：原本固定之上層混合層厚度改為隨地點不同而改變、原本sech2(x)函數波形納入其他函數波形及以衛星影像拍攝到的波前形狀。模式中模擬內波在東沙島附近傳播產生繞射的現象，並比較變動混合層厚度下與固定混合層厚度的不同。模擬MODIS影像上波前之傳播，利用模式與影像比對找出24小時後同一波源內波的位置。從衛星影像資料發現在呂宋海脊附近內波從波源產生後可以變得相當寬，其能量來源可能來自於波與波之間的非線性效應：大振幅內波吸收小振幅內波的能量。模擬結果也顯示在傳播的過程中大振幅內波的能量有增加的現象。

This thesis applies a numerical model to study the propagation of internal solitary wave based on a two-dimensional model developed by Lynett and Liu (2002) and modified by Cheng et al. (2005).The numerical model derived assumes weak nonlinearity and weak dispersion in a two-layer inviscid fluid system. The governing continuity and momentum equations are solved and the real topography is included in the wave model. In order to improve the accuracy of simulation, mixed-layer thickness is allowed to change from place to place. Initial conditions are modified so that wave forms of non-hyperbolic -secant functions and wave fronts taken by satellite can be used. The diffraction near the island of Dongsha is simulated, and results of both fixed and variable mixed-layer thickness are compared. Simulated waveform in MODIS images after 24 hours are compared with other wave fronts of the same image. Laterally, internal waves can become very wide when it is far away from its origin. The extra energy can be explained by nonlinear wave-wave interaction because the energy of large amplitude internal wave increases after interacting with smaller internal waves.

章次
中文摘要 ………………………………………………………………...................
英文摘要 ………………………………………………………………...................
目錄 …………………………………………………………….......................
圖目錄 ………………………………………………………………...................
表目錄 ………………………………………………………………...................





第一章　緒論 …………………………………………………………...................... 1
1.1 前言 ...............………………………………………………...................... 1
1.2 研究目的 ...…………………………………………………...................... 2
1.3 本文架構 .…………………………………………………........................ 2
第二章 文獻回顧 ……………………………………………………...................... 4
2.1 現場實驗及衛星影像資料研究 ..…………………………. ..................... 4
2.2 KdV方程式 ..………………………………………………...................... 7
2.3 數值模式 ..…………………………………………………. ..................... 9
第三章 數值模式介紹 ……………………………………….................................. 10
3.1 內波二維傳播模式 ..................................................................................... 10
3.2 模式初始條件設定 ..................................................................................... 10
第四章 模式驗證 .........................................……………………………………..... 28
4.1 模式代入波形測試 ..………………………………………………........... 28
4.2 穩定孤立波波形 ....................…………………………………………..... 28
4.3 模式在斜坡上的驗證 ………………………..……………....................... 32
第五章 模式結果、討論與結論 ..…………………………………........................ 35
5.1 模式結果與討論 ….………………………………………........................ 35
5.1.1 變動混合層厚度 ...………...……………………………........................ 35
5.1.2 兩個孤立波波形 ........……………………………………...................... 40
5.1.3模擬MODIS影像上波前傳播的情況 …………..………....................... 41
5.1.4波與波之間的非線性效應 ………………………………....................... 46
5.2 結論 ............................................................................................................... 50
參考文獻 ………………………………………….……………………..................... 51
附錄 ……………………………………………….……………………..................... 55

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