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研究生:楊智傑
研究生(外文):Chih-Chieh Yang
論文名稱:泥流經變化河岸的不穩定性分析
論文名稱(外文):Instability for mud flow through meadering rivers
指導教授:劉格非劉格非引用關係
指導教授(外文):Ko-Fei Liu
口試委員:周憲德陳樹群
口試日期:2010-07-23
學位類別:碩士
校院名稱:國立臺灣大學
系所名稱:土木工程學研究所
學門:工程學門
學類:土木工程學類
論文種類:學術論文
論文出版年:2011
畢業學年度:99
語文別:中文
論文頁數:97
中文關鍵詞:賓漢流體不穩定性分析土石流微擾法
外文關鍵詞:Debris flowBingham flowPerturbation methodinstability analyze
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近年來土石流為台灣的一種主要災害。土石流分為許多種,像是粒石流、泥流…等。其中泥流本構關係式可以用賓漢流體來近似。
本文從基本流況開始--穩態(steady)、均勻流(uniform),再給一河岸微小變化的擾動,利用為擾法探討流況的穩定性,之後再針對參數加以研究分析。
由研究結果可知,不管在任何的河寬河深比例、重力與剪力效應比例皆有可能有不穩定的情形發生。不過在所產生的波長極短的假設底下,其穩定性決定於重力與河岸剪力的大小關係,若重力效應大於剪力效應則穩定;在所產生的波長極長的假設底下,其流況為穩定。


In recent years, debris flows have been a major kind of natural disasters in Taiwan. Debris flow can be divided into several categories, such as granular flow, mud flow, etc. Mud flow can often be simulated by Bingham flow theory.
This study started from steady and uniform flow. Then, Perturbation method is used to analyze if it is stable, and I have applied a small perturbation on the wall of channels. The final step is to apply different parameters in the experiment to analyze the result.
From this thesis, we know that no matter what ratio of channel width to channel depth, gravity to shear, it may be unstable. But if we assume that the wavelength of perturbation is very short, it’s stable or not will depend on the ratio of gravity to shear. On the other hand, if we assume the wavelength of perturbation is very long, it will be stable.


摘要 .....................................................................................................................一
目錄 .....................................................................................................................四
第一章 緒論 ...............................................................................................................1
1.1 前言 .............................................................................................................. 1
1.2 前人研究 ...................................................................................................... 2
1.3 研究目的與方法 .......................................................................................... 2
1.4 論文架構 ...................................................................................................... 2
第二章 基本理論 .......................................................................................................3
2.1 座標系統與假設條件 .................................................................................. 3
2.2 控制方程式 .................................................................................................. 3
2.2.1 連續方程式 ...................................................................................... 3
2.2.2 動量方程式 ...................................................................................... 3
2.3 邊界條件 ...................................................................................................... 5
2.3.1 自由表面 .......................................................................................... 5
2.2.3 強剪層與弱剪層交界面 .................................................................. 7
2.3.2 底床 .................................................................................................. 8
2.4 穩態均勻流解 .............................................................................................. 8
2.4.1 河床強剪層 ...................................................................................... 8
2.4.2 弱剪層 ............................................................................................ 10
2.4.3 河岸強剪層 .................................................................................... 10
2.5 方程式積分 ................................................................................................ 13
2.5.1 深度積分 ........................................................................................ 13
2.5.2 斷面積分 ........................................................................................ 20
第三章 不穩定性分析 .............................................................................................33
3.1 特徵參數與尺度分析 ................................................................................ 33
3.2 控制方程式的無因次化與尺度分析 ........................................................ 36
3.2.1 連續方程式 .................................................................................... 38
3.2.2 x 方向動量方程式 ......................................................................... 40
3.2.3 y 方向動量方程式 ......................................................................... 51
3.2.4 z 方向動量方程式 ......................................................................... 59
3.2.5 應變率 ............................................................................................ 70
3.3 邊界條件的無因次化與尺度分析 ............................................................ 71
3.3.1 自由表面 ........................................................................................ 71
3.3.2 強剪弱剪層交界面 ........................................................................ 76
3.4 解方程式 .................................................................................................... 77
3.4.1 方程式的化簡 ................................................................................ 77
3.4.2 假設解的形式並代入方程式中 .................................................... 83
3.4.3 討論各參數與不穩定性的關係 .................................................... 89
第四章 結論與建議 .................................................................................................95
4.1. 結論 ............................................................................................................ 95
4.2. 建議 ............................................................................................................ 95
參考文獻 .....................................................................................................................96


(英文部分)
1.Balmforth, N. J. and Craster, R. V. (1999), A Consistent Thin-LayerTheory For Bingham Fluids, J. Non-Newtonian Fluid Mech., vol. 84,pp. 65-81.
2.Balmforth, N. J. and Mandre, S. (2004), Dynamics of Roll Waves, J.Fluid Mech., vol. 514, pp. 1-33.
3.Balmforth, N. J. and Liu, J. J. (2004), Roll Waves In Mud, J. FluidMech., vol. 519, pp. 33-54.
4.Cornish, V. (1934), Ocean Waves and Kindred GeophysicalPhenomena, Cambridge University Press, London.
5.Dressler, R. F. (1949), Mathematical Solution of The Problem of Roll-Waves In Inclined Open Channels, Communications of Pure andApplied Mathematics, Vol. 2, pp. 149-194.
6.Julien, P. Y. and Hartley, D. M. (1986), Formation of Roll Waves InLaminar sheet flow, J. Hydraulic R., Vol. 24, No. 1, pp. 5-17.
7.Liu, K. F. and Mei, C. C. (1994), Roll Waves On A Layer of a MuddyFluid Flowing Down a Gentle Slope-A Bingham Model, Physics ofFluids, vol. 6, no. 8.97
8.Martin Vide, J. P. (1992), Open Channel Surges and Roll Waves from Momentum Principle, J. Hydraulic R., Vol. 30, No. 2, pp. 183-196.
9.Mei, C. C. and Yuhi, M. (2001), Slow Flow of a Bingham Fluid In a Shallow Channel of Finite Width, J. Fluid Mech., vol. 431, pp.135-159.
10.Mandre, S. (2001), Effect of bottom topography on roll wave instabilities, Proc. 2001 Geophysical Fluid Dynamics Summer Study Program. Woods Hole Oceanographic Institution.
(中文部分)
1.劉格非,(1994),「厚泥流流動特性之數值分析」,中國土木水利工程專刊,第六卷,第二期,第193-203 頁。
2.陳美玲,(2006),「泥流流經變化底床之擾動分析」。


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