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| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 蔡宛珊 | zh_TW |
| dc.contributor.advisor | Christina W. Tsai | en |
| dc.contributor.author | 洪毓茹 | zh_TW |
| dc.contributor.author | Yu-Ju Hung | en |
| dc.date.accessioned | 2023-05-18T16:13:19Z | - |
| dc.date.available | 2023-11-09 | - |
| dc.date.copyright | 2023-05-10 | - |
| dc.date.issued | 2022 | - |
| dc.date.submitted | 2023-02-14 | - |
| dc.identifier.citation | Absi, R. (2019). Eddy viscosity and velocity profiles in fully-developed turbulent channel flows. Fluid Dynamics, 54(1):137–147.
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| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/87181 | - |
| dc.description.abstract | 工程實務上，懸浮泥砂的濃度為水質和水庫管理的重要因子。汙染物會附著於懸浮泥砂上，藉由紊流的擴散機制造成汙染的傳播，而懸浮泥砂本身亦會對水質造成影響，其沉降後對水庫造成的淤積也是一大工程問題。若對懸浮泥砂顆粒的運動機制有更深入的探討，便能更準確地估計懸浮泥砂濃度，並且藉由了解泥砂顆粒的運動軌跡，便能對潛在的汙染區域提前進行預防及整治。在科學理論中，泥砂受水流作用發生運動，泥砂運動又會影響水流性質，兩者相互影響，運動機制複雜。在過往研究中，懸浮泥砂顆粒一般使用平流擴散方程(advection-diffusion equation, ADE)或泥砂率定曲線(sediment rating curves)來做定率的懸浮泥砂濃度估計。然而，由於紊流的不穩定，水流中的泥砂不僅僅會順著水流方向運動，也會在水體中進行隨機的擴散。本研究利用序率隨機模擬，更深入地以機率方法描述泥砂顆粒在明渠流中，受到紊流影響的運動行為，並以科學方法量化泥砂濃度和其運輸率的變化及不確定性。本研究考量不同尺度紊流結構對懸浮泥砂運動所造成的影響，提出一序率模型: 非整數布朗運動驅動之隨機擴散粒子追蹤模型(fractional stochastic differential diffusion particle tracking model, FSD-PTM)，此模型旨在模擬明渠流中懸浮泥砂顆粒的隨機運動軌跡，並利用蒙地卡羅方法計算紊流中懸浮泥砂的濃度與輸砂率。此模型為一進階的隨機拉格朗日模型(Lagrangian model)，可以描述底床邊界附近，受到在時間上具有持續性之紊流擬序結構(time-persistent turbulent coherent structures)的影響，懸浮泥砂粒子所反映出的隨機運動行為。本研究利用實驗數據與模型模擬結果(系統平均速度和泥砂濃度等)進行模型驗證。模擬結果除一般定率模型能模擬之懸浮泥砂濃度和輸砂率外，還可量化濃度與輸砂率的變化率及其相對應之不確定性。在水質泥砂濃度標準已知的情況下，方能提供時間和空間上所對應的超越機率值，即為水質汙染風險機率，應用於風險管理範疇中評估風險容忍度與制定應對政策時，可提供決策者有效的風險評估依據。 | zh_TW |
| dc.description.abstract | The study focuses on the Lagrangian particle tracking of suspended sediment particles whose motions are strongly coupled with surrounding turbulent flows. The diffusion of suspended particles is often linked to turbulence diffusion theories. The high irregularity and protean properties of turbulence generally lead to the usage of Brownian diffusion. It implies that the spreading of suspended sediment particles is normally distributed and embeds independent properties in particle motions. However, the non-Gaussian phenomenon in sediment movements has been observed and recognized during the last decades. The sediment-laden flow experiments have suggested that coherent structures in turbulent shear flow strongly impact particles' suspension near the boundary. This study proposes an advanced Lagrangian particle tracking model, whose driven fluctuation process is the fractional Brownian motion (FBM). By introducing the fractional stochastic process to the PTM, the correlated increments aim to describe anomalous suspended sediment particles' movements resulting from intermittent and time-persistent coherent turbulent structures near the boundary. The proposed model is applied to simulate suspended sediment transport in two-dimensional open channel flow. Via Monte Carlo simulation, the ensemble statistics results are presented, including mean, variance, skewness of particle positions, and particle velocity fluctuations. The anisotropic sediment behaviors can be found in the probability density function (PDF) of particle velocity fluctuations at different water depths. Simulation results show improvements in the streamwise particle velocity profiles and in predicting sediment concentrations near the boundary. | en |
| dc.description.provenance | Submitted by admin ntu (admin@lib.ntu.edu.tw) on 2023-05-18T16:13:19Z No. of bitstreams: 0 | en |
| dc.description.provenance | Made available in DSpace on 2023-05-18T16:13:19Z (GMT). No. of bitstreams: 0 | en |
| dc.description.tableofcontents | Verification Letter from the Oral Examination Committee i
Acknowledgements iii 摘要 v Abstract vii Contents ix List of Figures xiii List of Tables xvii Chapter 1 Introduction 1 1.1 Anomalous diffusion in suspended sediment transport . . . . . . . . 1 1.2 Research aim and research objectives . . . . . . . . . . . . . . . . . 4 1.3 Overview of the thesis . . . . . . . . . . . . . . . . . . . . . . . . . 6 Chapter 2 Overview of the physical processes in suspended sediment transport in open channel turbulent flows 9 2.1 Turbulence in open-channel flow . . . . . . . . . . . . . . . . . . . 9 2.1.1 Reynold’s decomposition and RANS equation . . . . . . . . . 10 2.1.2 Flow field in open-channel flows . . . . . . . . . . . . . . . 15 2.2 Coherent structures in turbulent shear flow . . . . . . . . . . . . . . 23 2.2.1 Formation of coherent structures . . . . . . . . . . . . . . . . 24 2.2.2 Quadrant analysis . . . . . . . . . . . . . . . . . . . . . . . . 27 2.3 Lagrangian Particle tracking models . . . . . . . . . . . . . . . . . . 29 2.3.1 Stochastic diffusion particle tracking model (SD-PTM) . . . . 30 2.3.2 Analysis of particle diffusive behaviors . . . . . . . . . . . . 34 Chapter 3 Fractional stochastic diffusion particle tracking model (FSD-PTM) 37 3.1 Anomaly in suspended sediment transport . . . . . . . . . . . . . . . 37 3.1.1 Fractional Brownian motion . . . . . . . . . . . . . . . . . . 39 3.1.2 Memory in correlated increments . . . . . . . . . . . . . . . 41 3.2 Conceptual model of the research . . . . . . . . . . . . . . . . . . . 43 3.2.1 Boundary conditions . . . . . . . . . . . . . . . . . . . . . . 44 3.3 Fractional stochastic diffusion particle tracking model (FSD-PTM) . 46 3.3.1 Governing equation of the FSD-PTM . . . . . . . . . . . . . 47 3.3.2 Determination of the coefficients of drift and random terms . 51 3.3.3 Numerical scheme for FSD-PTM . . . . . . . . . . . . . . . 53 Chapter 4 Fractional suspended sediment transport in open channel flows 55 4.1 Application to suspended sediment transport in fully-developed open-channel flows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 4.1.1 Flow conditions and sediment particle characteristics . . . . . 58 4.1.2 Particle diffusion coefficient . . . . . . . . . . . . . . . . . . 61 4.1.3 Occurrence of coherent structures . . . . . . . . . . . . . . . 64 4.2 Simulation results and discussions . . . . . . . . . . . . . . . . . . . 66 4.2.1 Ensemble statistics of particle positions . . . . . . . . . . . . 67 4.2.2 Anomalous particle diffusion . . . . . . . . . . . . . . . . . . 68 4.2.3 Model validation: sediment concentration . . . . . . . . . . . 73 4.2.4 Model validation: streamwise particle velocity profile . . . . 76 4.2.5 Distributions of particle velocity fluctuations . . . . . . . . . 78 Chapter 5 Interpretation of Hurst parameter value 81 5.1 Estimation of Hurst value . . . . . . . . . . . . . . . . . . . . . . . 83 5.2 Application to suspended sediment transport in a geophysical-scaled flow event . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 5.2.1 Simulation assumptions . . . . . . . . . . . . . . . . . . . . 87 5.2.2 Simulation results and discussions . . . . . . . . . . . . . . . 92 5.2.3 Summaries of the application . . . . . . . . . . . . . . . . . . 97 Chapter 6 Conclusions 99 6.1 Advantages and limitations of the proposed FSD-PTM . . . . . . . . 100 Appendix A — Definition 103 A.1 Markovian property: Memorylessness . . . . . . . . . . . . . . . . . 103 A.2 Memory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104 Appendix B — Stochastic process 105 B.1 Gaussian process . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 B.2 Wiener process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106 B.3 Fractional Brownian motion process (FBM) . . . . . . . . . . . . . . 109 B.4 Poisson process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112 Appendix C — Stochastic differential equation (SDE) 115 C.1 SDE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115 C.1.1 Ito-Stratonovich dilemma . . . . . . . . . . . . . . . . . . . 116 C.1.2 Ito-Stratonovich drift correction formula . . . . . . . . . . . . 118 Appendix D — SDE simulation 119 D.1 Convergence of numerical scheme . . . . . . . . . . . . . . . . . . . 119 D.2 Common numerical scheme . . . . . . . . . . . . . . . . . . . . . . 120 D.2.1 Euler-Maruyama scheme . . . . . . . . . . . . . . . . . . . . 120 D.2.2 Euler-Heun scheme . . . . . . . . . . . . . . . . . . . . . . . 121 D.2.3 Milstein scheme . . . . . . . . . . . . . . . . . . . . . . . . 121 Notation. . . . . . . . 123 Abbreviation. . . . . . . . 129 References. . . . . . . . 131 | - |
| dc.language.iso | en | - |
| dc.subject | 紊流擬序結構 | zh_TW |
| dc.subject | 隨機泥砂傳輸模型 | zh_TW |
| dc.subject | 隨機擴散粒子追蹤模型 | zh_TW |
| dc.subject | 非整數布朗運動 | zh_TW |
| dc.subject | fractional Brownian motion | en |
| dc.subject | turbulent coherent structure | en |
| dc.subject | particle tracking model | en |
| dc.subject | stochastic suspended sediment transport | en |
| dc.subject | anomalous transport by fractional process | en |
| dc.title | 非整數動力學之下的隨機泥砂傳輸 | zh_TW |
| dc.title | Stochastic Suspended Sediment Transport by Fractional Dynamics | en |
| dc.type | Thesis | - |
| dc.date.schoolyear | 111-1 | - |
| dc.description.degree | 博士 | - |
| dc.contributor.oralexamcommittee | Rafik Absi;謝平城;周逸儒;余化龍;游景雲;何昊哲 | zh_TW |
| dc.contributor.oralexamcommittee | Rafik Absi;Ping-Cheng Hsieh;Yi-Ju Chou;Hwa-Lung Yu;Gene Jiing-Yun You;Hao-Che Ho | en |
| dc.subject.keyword | 隨機泥砂傳輸模型,隨機擴散粒子追蹤模型,非整數布朗運動,紊流擬序結構, | zh_TW |
| dc.subject.keyword | particle tracking model,turbulent coherent structure,stochastic suspended sediment transport,anomalous transport by fractional process,fractional Brownian motion, | en |
| dc.relation.page | 141 | - |
| dc.identifier.doi | 10.6342/NTU202300192 | - |
| dc.rights.note | 同意授權(全球公開) | - |
| dc.date.accepted | 2023-02-15 | - |
| dc.contributor.author-college | 工學院 | - |
| dc.contributor.author-dept | 土木工程學系 | - |
| 顯示於系所單位： | 土木工程學系 | |
文件中的檔案：
| 檔案 | 大小 | 格式 | |
|---|---|---|---|
| ntu-111-1.pdf | 6.67 MB | Adobe PDF | 檢視/開啟 |
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