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完整後設資料紀錄
DC 欄位 | 值 | 語言 |
---|---|---|
dc.contributor.advisor | 黃良雄 | |
dc.contributor.author | Yuan-Ching Kuo | en |
dc.contributor.author | 郭遠錦 | zh_TW |
dc.date.accessioned | 2021-06-13T06:36:37Z | - |
dc.date.available | 2011-07-27 | |
dc.date.copyright | 2011-07-27 | |
dc.date.issued | 2011 | |
dc.date.submitted | 2011-07-25 | |
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dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/34907 | - |
dc.description.abstract | 本研究的主旨在釐清時間尺度以探討二維緩慢底床變形。在本研究中,底床之控制方程式乃修改自Biot (1956)所提出之多孔彈性介質動量方程式。本研究先以量階分析修改Biot方程式使其適用於研究緩慢底床變形,再搭配Hsieh et al. (2001) 所提出之簡化邊界條件,以解析方式探討水波、流及底床變形間之時間尺度差異。由時間尺度分析顯示,此系統中存在四個明顯不同之時間尺度:水波、砂波、水流及底床變形 (砂波即彈性波中的雷利波 (Rayleigh wave))。時間尺度差異表示系統中之各種運動間存在速度差異並顯示量階分析的可行性,即水波、流與底床之交互作用並不需迭代計算,僅需計算主要驅動模式後以修正方式計算次要項即可。採用量階方析之主要優點在於避免以數值方法模擬緩慢底床變形時,因迭代計算無法收斂而導致之數值發散問題。
本研究接著以首階方程式及邊界積分方程式法建立一數值水槽,以數值水槽模擬李鴻源等(1991) 之緩慢底床變形試驗並得到合理的一致性。數值水槽之建立係採用邊界積分方程式法,邊界積分方程式法以積分方式將控制方程式離散於邊界點上,此一數值方法同時兼具計算效率及適應不規則邊界。 總結本研究之主要貢獻有三:一、本研究以量階分析探討Biot(1956)式於緩慢底床變化中的量階項並以Hsieh et al. (2001) 所提出之簡化邊界條件建立可用於探討緩慢底床變形之首階控制方程式與邊界條件。二、本研究發現緩慢底床變形之時間尺度比。三、本研究以量階分析及邊界積分方程式法建立一數值水槽,此數值水槽克服了江百祥(1996)及施宛平(1998)所提出之數值困難並模擬了緩慢底床變形。 | zh_TW |
dc.description.abstract | The primary object of this study aims at clarifying the time scales for analyzing the two dimensional slowly deforming bed forms. In the study, we modified the momentum equations of Biot (1956) with an order of magnitude analysis and made the equations suitable for modeling the slowly deforming beds. Together with the simplified boundary conditions proposed by Hsieh et al. (2001), we analyzed the time scales of the water waves, flows, sand waves and the slowly deforming bed analytically and we discovered that there are four different time scales, i.e. the time scales of water waves, sand waves, water flows and the deformation of bed (the sand waves are the Rayleigh waves of the elastic waves). The differences in time scales imply the differences between each phenomenon and validated the feasibility of the order of magnitude analysis. With the order of magnitude analysis, the iteration between the computation of water and the bed are no longer required and the computations may be done by calculating the major driven terms and modified the minor terms and hence the numerical approaches to the slowly deformation of bed forms shall no longer be suffering from the numerical divergences.
After we established the leading order analysis for the slowly deforming bed, we constructed a numerical water tank. Moreover, we verified the model with the flume experiment of Li et al. (1991) and obtained reasonable agreement. The numerical water tank was constructed with the boundary integral equation method which transforms the governing equations into discrete grids on the boundaries with integral equations and the boundary integral equation method is efficient and flexible for irregular boundaries. The major achievements of the present study are threefold: 1. we conducted an order of magnitude analysis to the equations of Biot (1956) and adopted the simplified boundary conditions of Hsieh et al. (2001) for establishing the suitable formulations for modeling the slowly deforming beds. 2. We discovered the time scale ratio of the slowly deforming bed. 3. We constructed a numerical water tank with the leading order formulations and the boundary integral equation method and the numerical water tank conquered the numerical difficulties reported by Chiang (1996) and Shih (1998) and modeled the slowly deforming bed forms. | en |
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dc.description.tableofcontents | 中文摘要..................................i
Abstract.................................ii Content..................................iv List of Tables..........................vii List of Figures........................viii List of Symbols........................xiii Chapter 1. Introduction 1 1.1 Background 1 1.2 Literature review 2 1.3 Objects and Methodologies 5 1.4 Outline 7 Chapter 2. Governing equations and boundary conditions 8 2.1 Formulations of the water and the soil 9 2.1.1 Governing equations 9 2.1.2 Boundary conditions 11 2.2 Simplification of the governing equation and boundary conditions 12 2.2.1 Order of magnitude analysis on the governing equations of the soil bed 13 2.2.2 Simplification of the boundary conditions 14 Chapter 3. Analytical solutions and time scales 17 3.1 Exact solutions and the leading order solutions 17 3.1.1 The linear water waves with a constant current U passing over a soil bed 17 3.1.2 Verifications with Song’s solutions 20 3.1.3 Leading order analysis on the linear water waves passing over a soil bed 26 3.1.4 The soil waves passing under water 33 3.1.5 Leading order analysis on the soil waves passing under water 35 3.2 Discussion on the time scales of the system 41 Chapter 4. Two dimensional numerical water tank 44 4.1 Mathematical formulations of the numerical water tank 45 4.1.1 The governing equations of the water and of the pressure in the soil 46 4.1.2 The governing equations of the soil 47 4.1.3 The free surface boundary conditions of water and their finite difference equation form 48 4.1.4 The dissipative boundary condition (the sponge layer) 49 4.1.5 The lateral boundary conditions 49 4.1.6 The boundary conditions of pressure and the soil displacement 50 4.1.7 The computational flow chart of the model 51 4.2 Preliminary verifications 55 4.2.1 Linear soil waves passing under water 55 4.2.2 Linear water waves propagating over a soil bed 64 4.2.3 Generation of a uniform current 68 Chapter 5. Application of the numerical water tank and some numerical experiments 73 5.1 Verifications with the flume experiments 73 5.1.1 Introduction to the flume experiments 73 5.1.2 Model calibrations 75 5.2 Illustrative cases for flow over uneven beds 79 5.2.1 Uniform flow over a sand pit 79 5.2.2 Uniform flow over a sand pile 84 Chapter 6: Conclusions and suggestions 90 6.1 The achievements of the study 90 6.2 Recommendations for future works 91 List of Tables Table 3.1 The parameters of case 1 (silt) employed for verification with Song (1993) 21 Table 3.2 The parameters of case 2 (fine sand) employed for verification 22 Table 3.3 The parameters of water and soil employed for verifying the leading order algorithm 29 Table 3.4 The parameters of water and soil employed for verifying the leading order algorithm 37 Table 3.5 The parameters of water and soil employed for verifying the frequency of water and soil wave versus different wave length 41 Table 4.1 The parameters of water and soil employed for verification 56 Table 4.2 The parameters of water and soil employed for verification 65 Table 4.3 The parameters of water for studying the initial disturbance 69 Table 5.1 The parameters of the experiment 75 Table 5.2 The parameters of water and soil employed for case 1 80 Table 5.3 The parameters of water and soil employed for case 2 85 List of Figures Figure 2.1 Schematization of the two dimensional x-z domain 8 Figure 3.1 Verification of the potential of water of case 1 22 Figure 3.2 Verification of the water wave induced bed form of case 1 23 Figure 3.3 Verification of the leading order pressure inside the bed of case 1 23 Figure 3.4 Verification of the attenuation of the leading order pressure along the z axis at x = 5m of case 1 24 Figure 3.5 Verification of the potential of water of case 2 24 Figure 3.6 Verification of the water wave induced bed form of case 2 25 Figure 3.7 Verification of the leading order pressure inside the bed of case 2 25 Figure 3.8 Verification of the attenuation of the leading order pressure along the z axis at x = 5m of case 2 26 Figure 3.9 Verification of the potential of water at t = 0 30 Figure 3.10 Verification of the water wave induced bed form at t = 0 30 Figure 3.11 Horizontal velocity distribution along the z axis with the interface at z = 0 m. Solid line : Exact solution, Symbols : Leading order solution. 31 Figure 3.12 Vertical velocity distribution along the z axis with the interface at z = 0 m. Solid line : Exact solution, Symbols : Leading order solution. 32 Figure 3.13 Verification of the potential of water at t = 0 38 Figure 3.14 Verification of the soil wave induced water surface at t = 0 38 Figure 3.15 Horizontal velocity distribution along the z axis with the interface at z = 0 m. Solid line : Exact solution, Symbols : Leading order solution. 39 Figure 3.16 Vertical velocity distribution along the z axis with the interface at z = 0 m. Solid line : Exact solution, Symbols : Leading order solution. 40 Figure 3.17 Frequency versus wave number of free water waves 41 Figure 3.18 Frequency versus wave number of free soil waves 42 Figure 4.1 Schema of the numerical water tank 45 Figure 4.2 The flow chart for calculating the water flow/waves over a soil bed 52 Figure 4.3 The flow chart for calculating the soil waves under water 54 Figure 4.4 The setting of the nodal points 56 Figure 4.5 Amplitude of the soil waves at t=T 57 Figure 4.6 Amplitude of the water waves induced by the soil waves at t=0.2T 57 Figure 4.7 Amplitude of the water waves induced by the soil waves at t=0.4T 57 Figure 4.8 Amplitude of the water waves induced by the soil waves at t=0.6T 58 Figure 4.9 Amplitude of the water waves induced by the soil waves at t=0.8T 58 Figure 4.10 The potential of the water induced by the soil waves at t=0.25T 58 Figure 4.11 The potential of the water induced by the soil waves at t=0.5T 59 Figure 4.12 The potential of the water induced by the soil waves at t=0.75T 59 Figure 4.13 The potential of the water induced by the soil waves at t=T 59 Figure 4.14 The pressure distribution inside the soil bed at t=0.25T 60 Figure 4.15 The pressure distribution inside the soil bed at t=0.5T 60 Figure 4.16 The pressure distribution inside the soil bed at t=0.75T 60 Figure 4.17 The pressure distribution inside the soil bed at t=T 61 Figure 4.18 The velocity of the water at t=0.25T 61 Figure 4.19 The velocity of the water at t=0.5T 61 Figure 4.20 The velocity of the water at t=0.75T 62 Figure 4.21 The velocity of the water at t=T 62 Figure 4.22 The displacement potential of the soil at t=0.25T 62 Figure 4.23 The displacement potential of the soil at t=0.5T 63 Figure 4.24 The displacement potential of the soil at t=0.75T 63 Figure 4.25 The displacement potential of the soil at t= T 63 Figure 4.26 The setting of the nodal points 65 Figure 4.27 Amplitude of the water waves at t = 97 sec to t = 100 sec 66 Figure 4.28 Amplitude of the water waves at t = 100 sec 66 Figure 4.29 Amplitude of the soil induced by water waves at t = 100 sec 66 Figure 4.30 The potential of water at t = 100 sec 67 Figure 4.31 The pressure distribution inside the bed at t = 100 sec 67 Figure 4.32 The displacement potential of the soil at t = 100 sec 67 Figure 4.33 The velocity of the water at t = 100 sec 68 Figure 4.34 The setting of the nodal points 70 Figure 4.35 The water surface at t=1s 70 Figure 4.36 The water surface at t=10s 70 Figure 4.37 The water surface at t=50s 71 Figure 4.38 The water surface at t=100s 71 Figure 4.39 The flow velocity at t=1s 71 Figure 4.40 The flow velocity at t=100s 72 Figure 4.41 The flow velocity at t=100s – a close view 72 Figure 5.1 Side view of the flume (Li et al. (1991)) 73 Figure 5.2 Top view of the flume (Li et al. (1991)) 74 Figure 5.3 Bed form at t=40 min, solid line – experiment, delta – G=100 N/ m2, square – G=1000 N/ m2, circle – G=10000 N/ m2, Dash line- t=30min 76 Figure 5.4 Bed form at t=50 min, solid line – experiment, square – G=1000 N/ m2, Dash line- t=30min 77 Figure 5.5 Bed form at t=60 min, solid line – experiment, square – G=1000 N/ m2, Dash line- t=30min 77 Figure 5.6 Bed form at t=70 min, solid line – experiment, square – G=1000 N/ m2, Dash line- t=30min 78 Figure 5.7 Bed form at t=80 min, solid line – experiment, square – G=1000 N/ m2, Dash line- t=30min 78 Figure 5.8 The setting of the nodal points of case 1 80 Figure 5.9 The surface of the soil of case 1 at t=120s 81 Figure 5.10 The surface of the soil of case 1 at t=300s 81 Figure 5.11 The surface of the soil of case 1 at t=600s 81 Figure 5.12 The deformation of surface of the soil of case 1 82 Figure 5.13 The water surface of case 1 at t=120s 82 Figure 5.14 The water surface of case 1 at t=300s 82 Figure 5.15 The water surface of case 1 at t=600s 83 Figure 5.16 The flow velocity of case 1 83 Figure 5.17 The displacement of the soil of case 1 at t=120s 83 Figure 5.18 The displacement of the soil of case 1 at t=300s 84 Figure 5.19 The displacement of the soil of case 1 at t=600s 84 Figure 5.20 The setting of the nodal points of case 2 85 Figure 5.21 The surface of the soil of case 2 at t=120s 86 Figure 5.22 The surface of the soil of case 2 at t=300s 86 Figure 5.23 The surface of the soil of case 2 at t=600s 86 Figure 5.24 The deformation of surface of the soil of case 2 87 Figure 5.25 The water surface of case 2 at t=120s 87 Figure 5.26 The water surface of case 2 at t=300s 87 Figure 5.27 The water surface of case 2 at t=600s 88 Figure 5.28 The flow velocity of case 2 88 Figure 5.29 The displacement of the soil of case 2 at t=120s 88 Figure 5.30 The displacement of the soil of case 2 at t=300s 89 Figure 5.31 The displacement of the soil of case 2 at t=600s 89 | |
dc.language.iso | en | |
dc.title | 水下長時間尺度之底床變形研究 | zh_TW |
dc.title | A study on the slowly deforming bed form under water | en |
dc.type | Thesis | |
dc.date.schoolyear | 99-2 | |
dc.description.degree | 博士 | |
dc.contributor.oralexamcommittee | 劉格非,丁肇隆,謝平城,許泰文 | |
dc.subject.keyword | 緩慢底床變形,量階分析,長時間尺度,首階控制方程式,邊界積分方程式法,數值水槽, | zh_TW |
dc.subject.keyword | Slowly deforming bed form,order of magnitude analysis,long time scale,leading order formulations,Boundary Integral Equation Method,numerical water tank, | en |
dc.relation.page | 131 | |
dc.rights.note | 有償授權 | |
dc.date.accepted | 2011-07-25 | |
dc.contributor.author-college | 工學院 | zh_TW |
dc.contributor.author-dept | 土木工程學研究所 | zh_TW |
顯示於系所單位: | 土木工程學系 |
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