臺灣博碩士論文加值系統

本研究主要是以二維數值模式模擬孤立內波的傳播現象，模式採用美國康乃爾 大學Lynett & Liu (2002)所發展，經鄭等人(2005)修改後之二維內波傳播模式。其理論基礎以動量方程與流體連續方程式做為主要的控制方程式。模式採用上層與下層固定密度跟厚度的兩層流體，因此決定上下層的密度與厚度將會是重要的因素。本文所討論的兩層流體介面深度與密度是以實測溫度資料求其密度、浮力頻率與特徵值，再使用KdV係數法對兩層流體KdV方程式與連續流體KdV方程式計算非線性項與頻散項最小誤差的一組數據。使用KdV係數法計算，若計算的原始資料總水深大於500公尺，計算所得分層介面水深會趨近於底部，因此選用Vlasenko等人(2005)與Xie等人(2010)所提到的理想化浮力頻率公式，將浮力頻率做理想化修正後，再進行計算。此外並對EOF分析與特徵值曲線對照比較，以及最大浮力頻率所處水深與計算的分層深度做整理比較。
內波是呂宋海域及南海海域普遍存在的海洋特徵，本文選用該區域之觀測資料進行計算，最終目的為使用KdV係數法讓兩層流體的精確度提升，進而替代連續流體以加快模式計算。將計算出的分層厚度配合當地之數值地形代入模式，並給予一初始波，模擬衛星影像的內波交互作用現象。海洋中有很多內波的交互作用現象，如可以使用二維模式來模擬並且準確度還有一定水準的話，便可以節省不少的模擬時間。

The main topic of this research is the simulation of internal wave interaction by a two-dimensional numerical model developed by Lynett & Liu (2002) of Cornell University, then modified by Cheng et al. (2005). The governing equation includes two-dimensional momentum and continuity equation. The model uses constant upper and lower layer densities; hence, these factors as well as the upper layer thickness. Should be determined before the simulation. This study discusses the interface depth and the density according to the buoyancy frequency distribution, the EOF, and the eigen-value based on the measured density profile. Besides, a method based on the two-layer KdV equation and the KdV of continuously-stratified fluid. By minimize the difference of linear celeriy, nonlinear and dispersion terms, the upper layer thicknes can also be determined. However, the interface will be much deeper than the depth of max temperature drop in the KdV method if the total water depth is bigger than 500 meters. Thus, the idealization buoyancy frequency formula proposed by Vlasenko et al. (2005) or Xie et al. (2010) are used to modify the buoyancy frequency.
The internal wave in the Luzon Strait and the South China Sea are famous and deserves detailed study. We use the KdV method to find the parameters in the two fluid model to speed up the simulation of internal wave phenomena found in the satellite image.

目錄
章次 頁次
中文摘要 i
英文摘要 ii
目錄 iii
圖目錄 vi
表目錄 x
第一章 緒論
1.1 內波介紹 1
1.2 研究目的 1
1.3 本研究使用之資料 2
1.4 本文架構 3
第二章 內波理論與數值模擬
2.1 內波理論 4
2.1.1兩層流體KdV方程與連續流體KdV方程動力相似 4
2.1.2淺水兩層KdV表示法 5
2.1.3淺水連續分層KdV表示法 5
2.1.4深水連續分層的Benjamin-Ono方程表示法 6
2.1.5深水兩層的Benjamin-Ono方程表示法 7
2.2 內波二維傳播模式 8
第三章 最佳化上下層深度與密度
3.1 KdV係數法 9
3.2 分層結果與最大溫度振盪比較 11
3.2.1 KdV係數法法分析FB1資料與溫度振盪比較 11
3.2.2KdV係數法法分析FB2資料與溫度振盪比較 14
3.2.3使用KdV係數法時改變密度代入規則探討結果 17
3.3 理想化浮力頻率曲線公式Type I 18
3.4 理想化浮力頻率曲線公式Type II 20
3.5 經驗正交函數(EOF) 21
3.6 FB1實測資料分析 22
3.6.1理想化浮力頻率曲線Type I 22
3.6.2理想化浮力頻率曲線Type II 24
3.6.3 EOF分析 27
3.7 FB2實測資料分析 28
3.7.1理想化浮力頻率曲線Type I 28
3.7.2理想化浮力頻率曲線Type II 30
3.7.3 EOF分析 33
3.8 OR3實測資料分析 34
3.8.1 KdV係數法 34
3.8.2理想化浮力頻率曲線Type I 37
3.8.3理想化浮力頻率曲線Type II 39
3.8.4 EOF分析 41
3.9 FR1實測資料分析 42
3.9.1 KdV係數法 42
3.9.2理想化浮力頻率曲線Type I 45
3.9.3理想化浮力頻率曲線Type II 47
3.9.4 EOF分析 49
3.10 CTD淺灘資料分析 50
3.11數據結果 52
第四章 模式應用結果
4.1內波經過海底地形時的交互作用 54
4.2兩波交會產生的交互作用 60
第五章 結論
5.1最佳化分層厚度與密度 69
5.2內波交互作用 72
5.3建議 72
參考文獻 73
附錄、二維內波傳播模式 76
(1)兩層流體之介面波布式方程理論 76
(2) 數值模式 79

參考文獻
1.羅安凱，《西北太平洋夏季季內振盪之多重尺度特性》，國立臺灣大學大氣科學研究所碩士論文，2004。
2.傅科憲，《非線性效應與混合層厚度對非線性內波傳播的影響》，國立中山大學海洋物理研究所碩士論文，2007。
3.吳瑞中，《潮汐引致呂宋海峽內波之數值模擬研究》，國立中山大學海洋物理研究所碩士論文，2007。
4.王啟盟，《以衛星影像估計深海內孤立波的波高》，國立中山大學海洋物理研究所碩士論文，2010。
5.Chen, Guan‐Yu, Cho‐Teng Liu, Yu‐Huai Wang , Ming‐Kuan Hsu, “Interaction and generation of long‐crested internal solitary waves in the South China Sea,”Journal of Geophysical Research, Vol.116, 2011.
6.Cheng, M.H., J.R-C. Hsu, C.Y. Chen,“Numerical model for internal solitary wave evolution on impermeable variable seabad,”Proc.27th Ocean Eng, pp.355-359, 2005.
7.Lee, Chi-Yuan and R. C. Beardsley,“The Generation of Long Nonlinear Internal Waves in a Weakly Stratified Shear Flow”, Journal of Geophysical Research, Vol. 79, 453-462, 1974.
8.Fraedrich, K., J. L. McBride, W. M. Frank, R. Wang,“Extended EOF Analysis of Tropical Disturbances: TOGA COARE,”J. Atmos. Sci., Vol 54, Issue 19, pp.2363–2372, 1997.
9.Grimshaw, R., “Internal Solitary Wave,” Mathematical Science Loughborough University, No. 33, 2000.
10.Grimshaw, R.,“Internal solitary waves,”Topics in Environmental Fluid Mechanics, Vol.3, pp.1-27, 2003.
11.Tsuji, H. and M. Oikawa,“Oblique interaction of internal solitary waves in a two-layer fluid of infinite depth,”Fluid Dynamics Research, Vol.29, pp.251–267, 2001.
12.Ono, H.,“Algebraic solitary waves in stratified fluids,”Journal of The Physical Society of Japan, Vol.39, No.4, October, 1975 .
13.Korteweg, D.J. and G. de Vries,“On the change of form of long waves advancing in a rectangular canal and on a new type of long stationary waves,”Philosophical Magazine, Vol.39(5), pp.422-443, 1895.
14.Liu, J.T. and H.L. Lin,“Sediment dynamics in a submarine canyon,case of river-sea interaction,”Marine Geology, Vol.207,pp. 55-81, 2004.
15.Liu, C.T., R. Pinkel, M.K. Hsu, J.M. Klymak, H.W. Chen, C. Villanoy, “ Non-linear Internal Waves from Luzon Strait,” EOS, Vol.87, No.42, pp.449-451, 2006.
16.Oikawa, M. and H. Tsuji,“Oblique interactions of weakly nonlinear long waves in dispersive systems,”Fluid Dynamics Research, Vol.38, pp.868–898, 2006.
17.Lynett, P.J. and P.L.-F. Liu,“A Two-Dimensional Depth Integrated Model for Internal Wave Propagation over Variable Bathymetry,”Wave Motion ,Vol.36, pp.221-240, 2002.
18.Lueck, R.G. and T.D. Mudge,“Topographically Induced Mixing Around a Shallow Seamount,”Science, New Series, Vol.276, No.5320, pp.1831-1833, 1997 .
19.Vlasenko, V. and W. Alpers,“Generation of secondary internal waves by the interaction of an internal solitary wave with an underwater bank,”Journal of Geophysical Research, Vol. 110, 2005.
20.Vlasenko, V., N. Stashchuk, K. Hutter,“Baroclinic Tides: Theoretical Modeling and Observational Evidence”, 2005.
21.Wang, D.P.,“Long coastal trapped waves off the west coast of United States,”Phys. Oceanogr., Vol.7, pp.856-864, 1973.
22.Choi, W.Y. and R. Camassa,“Fully nonlinear internal waves in a two fluid system,”J.Fluid Mech., Vol.396, pp.1-36, 1999.
23.Xie, Jieshuo, Shuqun Cai, Yinghui He,“A continuously stratified nonlinear model for internal solitary waves in the northern South China Sea,”Vol.28, No. 5, pp.1040-1048, 2010.