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博碩士論文 etd-0620106-154041 詳細資訊
Title page for etd-0620106-154041
論文名稱
Title
孤立內波於變動地形之數值模擬
Numerical modeling for internal solitary wave evolution on variable topography
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
147
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
2006-05-17
繳交日期
Date of Submission
2006-06-20
關鍵字
Keywords
數值模擬、內波
internal wave, numerical model
統計
Statistics
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中文摘要
本研究以數值模擬探究孤立內波通過不透水海底障礙物之波形雨季本物理特性的演變。本研究之理論基礎是利用美國Cornell大學Lynett and Liu (2002)所發展之內波數值模式,因原文數學式展開恐有遺漏,本研究乃重新推導,並修正原方程以及原始數值模擬之電腦程式得正確的數值解與理論比較,再將數值結果與內波實驗室試驗結果比較(Kuo, 2005),以瞭解該數值模擬之精確度與適用性。
本模式假定內波存在於弱非線性、弱分散性與忽略黏滯性作用之流體。此模式的理論基礎是利用流體連續方程式與Euler方程式為主要控制方程式,並利用水深積分配合有限差分數值方法,計算內波在變動底床上的波形變化。在此數值實驗中的邊界設定除模擬現場情況外,均以已知實驗室成果之設備條件為主。其中數值水槽上下層水深比(H1/H2),障礙物高度(hs)、種類(三角形與梯形)、前後間距,以及孤立內波初始振幅(a)為基本數值實驗的主要控制變因。在各種不同實驗條件配合下,探討數值計算結果及比較以上變因對孤立內波之透射後振幅(at)、波速(Ct)與能量(Et)的影響。本研究更進一步與實驗室試驗之結果相比較,進而歸納出內波波動特性與本數值模式之精確度。
單一障礙物對於內波傳遞影響的程度可以由障礙比(ζ= (a1+h1)/(h1+h2-hs))決定,此可分成微量影響、中度影響與碎波。在內波通過兩個連續障礙物時,兩障礙物間距越小則其總能量在微量作用下下損耗最大。而在孤立內波通過兩個前後高低不一的障礙物時,則障礙物對波浪傳遞的影響程度,在微量作用下,前高後低情況下之內波能量損耗小於前低後高者;而在中度作用與碎波狀態下,則前高後低之內波能量損耗大於前低後高者。
由修正的數值模式及原數值模式與實驗室試驗資料相較,得知前者的相似度優於後者。故研究所提出的修正數值模式,應有利於模擬與探究孤立內波在海洋中傳遞及受到海底障礙物影響之波形與基本物理參數演化。
Abstract
The good of this thesis is to apply a numerical model for studying waveform of an internal solitary wave (ISW) on variable seabed topography. The numerical model developed by Lynett and Liu (2002) is adopted for this work but with modification to improve its accuracy, both mathematically and in programming codes. Numerical experiments using the modified model are then performed and the results compared with laboratory experiments of Kuo (2005), in order to validate its accuracy.
The mathematical model derived in the present study is based on the assumption that an internal wave is weakly nonlinear and weakly dispersive in an inviscid fluid. The governing equations based on the continuity equation and Euler equations are solved for ISW propagation over variable topography. The input conditions for the numerical experiments include physical parameters related to water depth and geometry of submarine obstacle, such as depth ratio between upper and lower layers (H1/H2), height (hs) and type (triangular ridge and trapezoidal shelf) of obstacles, in addition to the amplitude (ai) of an incident ISW. From the results of numerical experiments, wave amplitude, phase speed, and wave energy of a transmitted ISW are obtained and compared with that of laboratory experiments. (Kuo, 2005)
ISW propagation over a single obstacle is affected by a dimensionless parameter called “blockage parameter", ζ= (a1+h1)/(h1+h2-hs). Three types of interaction may be classified (weak interaction, moderate interaction, and wave breaking) depending on the value ofζ . For an ISW propagating over two consecutive obstacles, the interval between them is significant in reducing its amplitude and energy, as the interval reduces. Moreover, the effect of relative height between two obstacles may also be classified into two types: (i) within the range of weak interaction, energy dissipation is less for a high obstacle first than for it as the second; (ii) within the range of moderate interaction, the energy dissipation is higher for a high obstacle first than for it as the second.
Further comparisons have shown that the modified numerical model is in better agreement with the results of laboratory experiments (Kuo, 2005) than the original model of Lynett and Liu (2002). The results obtained from the present numerical experiments for ISW evolution on variable topography is encouraging which could benefit other who may be interested in internal wave propagation for practical applications in oceanography.
目次 Table of Contents
Contents

謝誌 I
Abstract (English) II
中文摘要 IV
Contents V
List of Symbols VIII
List of Figures X
List of Tables XV
Chapter 1 Introduction
1.1 Background 1
1.2 Literature Review 2
1.2.1 Field investigation 3
1.2.2 Theoretical analysis 3
1.2.2.1 theoretical formulations 3
1.2.2.2 Korteweg-deVries equations 5
1.2.3 Laboratory experiments on wave over submerged ridge 10
1.2.4 Numerical model 12
1.3 Motivation 19
1.4 Organization in this thesis 20
Chapter 2 Basic Characteristics of Internal Gravity Wave
2.1 Background 23
2.2 Internal Wave Generation, Propagation and Dissipation 24
2.2.1 IGW generation 25
2.2.2 IGW propagation 25
2.2.3 IGW dissipation 25
2.3 IGW Type and Velocity Field 26
2.3.1 IGW type 26
2.3.2 IGW flow field 28
2.4 IGW Interaction with Submarine Obstacle 30
2.4.1 Interaction with continental shelf 31
2.4.2 Reflection and transmission 32
2.4.3 Diffraction 32
2.4.4 Breaking 36
2.4.5 Energy dissipation 36
Chapter 3 Mathematical Theories for Internal Solitary Wave
3.1 Physical Variables and Boundary Conditions 37
3.2 Derivation of Combined Equation by Perturbation 42
3.3 Governing Equations 49
3.4 Simplified Governing Equations 54
Chapter 4 Numerical Modeling for Internal Solitary Wave Propagation
4.1 Finite-Difference Scheme 59
4.2 Boundary Condition of Numerical Model 61
4.3 Initial Condition for Numerical Model 63
4.4 Preliminary Results of Numerical Experiments 64
4.4.1 Numerical results of ISW characteristics 67
4.4.2 Evoultion of an ISW profile on a variable seabed 75
Chapter 5 Analysis of Numerical Results and Comparison with Experimental Data
5.1 Effecy of an ISW Propagating over an Obstacle 93
5.1.1 ISW propagation over single triangular ridge 93
5.1.2 ISW of depression propagation over single ridge 95
5.2 Characteristics of an ISW Propagating over Single Obstacle 97
5.2.1 Position of wave probes in a wave flume 97
5.2.2 Waveform 99
5.2.3 Wave amplitude 102
5.2.4 Wave phase speed 104
5.2.5 Wave energy 107
5.3 Characteristics of an ISW Propagating over Double Obstacles 111
5.3.1 Locations of wave probes 111
5.3.2 Waveform 112
5.3.2.1 effect of interval between two obstacles 112
5.5.2.2 effect of relative height in double-obstacles arrangement 115
5.3.3 Wave amplitude 117
5.3.2.1 effect of interval between two obstacles 117
5.5.2.2 effect of relative height in double-obstacles arrangement 119
5.3.3 Wave energy 120
5.3.2.1 effect of interval between two obstacles 120
5.5.2.2 effect of relative height in double-obstacles arrangement 123

Chapter 6 Conclusions and Suggestions
6.1 Conclusions 125
6.2 Suggestions 127
References
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