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標題: Hydraulic analysis of a 2-D water flow down a slope
作者: 徐培原
Pei-Yuan Hsu
關鍵字: 孔隙介質流
porous media flow
overland flow
vertical velocity
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摘要: 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.
其他識別: U0005-2606201509323500
文章公開時間: 2018-07-16
Appears in Collections:水土保持學系



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