臺灣博碩士論文加值系統

本文以水力學角度，將流場分為兩個區域(水層與土層)，推求水流流經裸露地之水、土二層水平與垂直流速分布。不同於以往，本研究並未忽略垂直流速，因此增加了慣性力項，故以新的方式來推求水平與垂直流速分布，對裸露地水流有更深一層的探討。文中將土層視為一具有透水性的孔隙介質，因此水、土交介面上之水平與垂直流速不為零，此結果更能貼近真實現象。
流場之求解過程中，水層之動量方程式以 Navier-Stokes 方程式來描述水層之運動現象，土層則使用宋長虹(1993)改進 Biot (1956b)之多孔彈性介質理論，配合 Desseaux (1999)的流速設定型式，可導出一組耦合之非線性常微分方程式，利用 Arikoglu & Ozkol (2006)所提出之微分變換運算法求解，最後得到流場水平與垂直流速分布與各項物理量。
求得流場各項物理量之解析解後，選定並代入相關參數即可觀察流速、剪應力、正向應力等物理量之分布情形，發現垂直流速確實遠小於水平流速，且垂直流速約只有水平流速之千分之一。此外，亦發現在x=0處，考量慣性力之水層水平流速，比採用忽略慣性力之水層水平流速約增加0.3倍 本研究特別著重於水平與垂直流速之分布，並與前人資料進行比較、驗證，結果尚可接受。本研究未忽略垂直流速，不僅解析之難度更甚以往，求解的方法與技巧亦需配合許多相關文獻及理論，故對坡地漫地流之水理解析提供新的想法，開闢新的研究方向。

In this study, the flow field is divided into two regions (the water layer and soil layer). By additionally considering the vertical velocity and the inertia force, we were aimed at having a deeper discussion on the water flow down a slope. Considering the vertical velocity of the flow, we searched for a new way to derive horizontal and vertical velocity distribution both in the water and soil layers. In this article, the soil layer is regarded as a porous media so that the nonzero velocity at the ground surface could be expected.
In the water layer, we adopt the Navier-Stokes equation to describe the motion of the water flow, while in the soil layer, Song’s (1993) laminar model based on Biot’s poroelastic theory (1956b) is chosen. With the velocity type set by Desseaux (1999), we derive a couple of nonlinear ordinary differential equations which are solved by taking the Differential Transform Method (DTM) proposed by Arikoglu & Ozkol (2006). Finally, we derive the horizontal and vertical velocity distributions and some other physical quantities.
After the analytical solution is obtained, we select the relevant parameters and then the velocity, shear stress, and normal stress distributions can be discussed. We find that the vertical velocity is actually far less than the horizontal velocity, and is about 0.1% of the horizontal one. Besides, we also find that at x=0 , the horizontal velocity considering inertia force is 0.3 time more than neglecting the inertial force. In this research, we focus on the distribution of horizontal and vertical velocity, and the results compared with the previous research are acceptable. Because we don’t neglect the vertical velocity of flow, as a result, not only the difficulty is more than ever, but also we have to search more relevant methods and theories in the literature. The results of this study are inspiring and show a new way of the future research on the overland flow.

摘要 I
Abstract II
目錄 IV
圖目錄 VI
表目錄 VII
符號定義表 VIII
第一章 緒論 1
1.1 研究緣起 1
1.2 研究動機 1
1.3 研究目的 2
第二章 文獻回顧 3
2.1 多孔彈性介質理論之相關研究 3
2.2 孔隙層非等向性之相關研究 4
2.3 以解析解求垂直與水平速度之相關研究 5
2.4 地表入滲之相關研究 6
2.5 微分變換法(D.T.M.)之相關研究 7
第三章 理論推導 8
3.1 水層之控制方程式 9
3.2 微分變換法後之水層控制方程式 12
3.3 土層之控制方程式 16
3.4 邊界條件 25
3.5 解析解 29
3.5.1 等向性有限厚土層 29
3.5.2 非等向性有限厚土層 34
第四章 結果與討論 40
4.1 等向性有限厚土層 40
4.1.1 各項參數之選用 40
4.1.2 垂直流速分布之探討 41
4.1.3 水平流速分布之探討 45
4.1.4 壓力分布之探討 51
4.1.5 各項應力分布之探討 53
4.2 非等向性有限厚土層 59
4.2.1 各項參數之選用 59
4.2.2 非等向性有限厚土層垂直流速分布之探討 60
4.2.3 非等向性有限厚土層水平流速分布之探討 61
4.2.4 非等向性有限厚土層壓力分布之探討 62
4.3 理論驗證 64
4.3.1 水平流速分布之驗證 64
4.3.2 坡地入滲速率之驗證 68
第五章 結論與建議 72
5.1 結論 72
5.2 建議 73
參考文獻75
附錄 A 坡地斜面坐標軸之坐標變換推導證明 81
附錄 B 以 6 階 DTM 法求解流速之 MAPLE 程式 88

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