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博碩士論文 etd-0528116-175254 詳細資訊
Title page for etd-0528116-175254
論文名稱
Title
兩層流體中界面波之非線性解析
The Analysis of Nonlinear Interfacial Wave in a Two-layer Fluid
系所名稱
Department
畢業學年期
Year, semester
語文別
Language
學位類別
Degree
頁數
Number of pages
72
研究生
Author
指導教授
Advisor
召集委員
Convenor
口試委員
Advisory Committee
口試日期
Date of Exam
2016-05-31
繳交日期
Date of Submission
2016-06-30
關鍵字
Keywords
兩層流體、界面波、波浪交互作用、攝動法
interfacial wave, two-layer fluid, wave interaction, perturbation
統計
Statistics
本論文已被瀏覽 5724 次,被下載 99
The thesis/dissertation has been browsed 5724 times, has been downloaded 99 times.
中文摘要
海洋內波現象近年來已成為熱門研究議題,無論生物、軍事、工程、環境和物理層面,國內外皆有諸多海洋學者投身相關研究,其多以現場觀測及試驗為主,但受限於氣候、成本之考量,較不易取得大量可信之資料。
故本文描述於二度空間裡,前進在兩層流體中之週期性規則表面及界面重力波的問題。對波浪場中各物理量以攝動冪級數展開,將所有的控制方程式展開成系統化的公式,並逐階解析波動流場至第二階解,其中包含上下層流體間之非線性與交互作用項。
解析結果中,對流場提出較為合理的闡述,使得對流場之解析有了更好的描述。二階交互作用項之振幅,隨厚度比提升即自由表面與界面處距離增加,此時流場波動亦隨著距離衰減,使得兩層流體間之交互作用影響減小。
Abstract
More and more oceanographers at home and abroad are devoted to the researches of internal waves. But on-site observation and experiments are the major, and it’s difficult to acquire lots of reliable data with the consideration of weather and cost. In this paper describe the second-order solution for the nonlinear internal and surface progressive water wave in a two-layer fluid. We use the perturbation method to develop a mathematical derivation. The two-order asymptotic solution includes the high-order nonlinear term and interaction term between the two-layer fluid.
The results propose an appropriate elaboration of the fluid field that differ from approximation solution, and describe the features of the wave and the induced. The interaction term of amplitude become weaker when the ratio of upper and lower layers thickness increases, which means the influence between the two-layer decays with the distance of surface and interface.
目次 Table of Contents
目錄
論文審定書 i
論文授權書 ii
致謝 iii
中文摘要 iv
Abstract v
目錄 vi
圖目錄 viii
符號說明 x
第一章 緒論 1
1.1 研究目的 1
1.2 文獻回顧 2
1.3 本文處理方法 4
1.4 本文組織 5
第二章 波動系統之描述 6
2.1 座標系統之描述 6
2.2 波動場之邊界條件 7
2.3 波動系統之攝動展開 10
第三章 波動流場之解析 16
3.1 "ε" _"1" ^"m" 、"ε" _"2" ^"n" ,m=n=1階解 16
3.2 "ε" _"1" ^"m" 、"ε" _"2" ^"n" ,m=n=2階解 19
3.2.1 "ε" _"1" ^"2" 、"ε" _"2" ^"2" 階解 21
3.2.2 "ε" _"1" ^"1" "ε" _"2" ^"1" 階解 23
第四章 理論之檢核與分析 25
4.1 流場解與其波動特性 25
4.2 流場解之檢核 30
4.3 流場解之結果與分析─Surface mode 32
4.3.1 頻散關係式 32
4.3.2 界面波高之變化 36
4.3.3 二階交互作用項之振幅 37
4.4 流場解之結果與分析─Interface mode 39
4.4.1 頻散關係式 39
4.4.2 波高與波形變化 43
4.4.3 二階交互作用項之振幅 50
4.4.4 界面波波動流場 52
第五章 結論與建議 54
5.1 結論 54
5.2 建議 56
第六章 參考文獻 57
參考文獻 References
1. 陳陽益,1988,單一表面規則前進重力波列
2. 陳陽益,1989,兩波交會之系統化與流場機構,港灣技術,第八期,27-60頁。
3. 陳震遠、許榮中、郭青峰、陳信旭、鄭明宏,2005,介面波在兩層流體系統中的運動特性,第27屆海洋工程研討會論文集,236-243頁
4. 王瑋宏、鄭明宏、賴得旺、盧典育、許榮中,2007,實驗室觀測孤立內波傳遞之粒子運動軌跡,第29屆海洋工程研討會論文集,799-804頁
5. 許光明、劉安國,2010,神秘的巨浪─南海內波,國家實驗研究院科技政策研究與資訊中心,科學發展電子期刊,第四百四十六期,52-60頁。
6. 許弘莒、李孟學、程嘉彥、曾文哲,2012,兩層流體中非線性界面波之三階解,海洋工程學刊,第十二卷第二期,219-234頁。
7. Benjamin, T.B., 1966, Internal waves of finite amplitude and permanent form, Journal of Fluid Mechanics, Vol. 25, pp. 241-270.
8. Benjamin T.B., 1967, Internal waves of permanent form of great depth, Journal of Fluid Mechanics, Vol. 29, pp. 559-592.
9. Blair Kinsman, 1984, WIND WAVES:Their Generation and Propagation on the Ocean Surface, pp. 167-172.
10 Hsu, M.K., Liu, A.K., Liu, C., 2000, A study of internal waves in the China Seas and Yellow Sea using SAR, Continental Shelf Res., 20:389-410.
11. Hunt, J.N., 1961, Interfacial waves of finite amplitude, La Houille Blanche, Vol. 4, pp. 515-531.
12. Keulegan, G.H., 1953, Characteristics of internal solitary waves, Journal of Research of the National Bureau of Standards, Vol. 51, pp. 133.
13. Koop, C.G., and Bulter, G., 1981, An investigation of internal solitarywaves in a two-fluid system, Journal of Fluid Mechanics, Vol. 112, pp. 225-251.
14. Lamb, H., 1932, Hydrodynamics, Cambridge University Press, New York.
15. Long, R.R., 1956, Solitary waves in one- and two- fluid systems, Tellus, Vol, 8, pp. 460-471.
16. Song, J.B., 2004, Second-order randon wave solution for internal waves in a two-layer fluid, Geophys. Res. Lett, Vol. 31, pp. L15302.
17. Stokes, G.G., 1847, On the theory of oscillatory waves, Transaction of the Cambridge Philosophical Society, Vol. 8, pp. 441-473
18. Umeyama, M., 2000, Third-Order Stokes Internal Waves for a Density-Stratified Two-Layer Fluid, Memoirs of Graduate School of Engineering 50, pp. 120-136.
19. Umeyama, M., 2002, Experimental and theoretical analyses of internal waves of finite amplitude, Journal of Waterway, Port, Coastal and Ocean Engineering, Vol. 128, pp. 133-141.
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