Hydraulic Analysis of Flow Passing Vegetative Ground

Abstract

In this study, we aim to figure out how vegetation influences streamwise velocity by analyzing the velocity of flow passing vegetative ground and dividing the flow field into three regions: homogenous water-layer (the flow over vegetation), vegetation-layer (the flow inside vegetation) and permeable soil-layer (the flow inside the soil). The soil and vegetation are both regarded as porous media and the flow inside the two layers is porous media flow. Thus the nonzero velocity at the ground surface could be estimated. The velocity distribution of the submerged vegetation is solved first, and then degenerate the former solution into unsubmerged vegetation and no vegetative ground. The velocity in laminar flow is solved by simplified Navier-Stokes equations and Song's (1993) laminar model based on Biot's poroelastic theory. And in turbulent flow, the governing equation is modified from Navier-Stokes equations and Biot's poroelastic theory. After solving velocity distribution under any possible situations, we compare the profiles of velocity with the experiment data of Rowiński and Kubrak (2002). As expected, we find it fit well and this reveals that the present solutions of velocity distribution can describe appropriately the flow passing vegetative ground in the turbulent flow.

本文嘗試從水力學的角度，將流場分成三個區域（均質水層、植生層及可透水土層），推求各種流況下水流流經植被地表時之速度解析，希望藉此瞭解植生存在對水流流速的影響。文中除了將植物體下方之土壤視為具滲透性之多孔介質，考慮其透水地表之流速不為零的真實現象外，亦將植物體本身視為一多孔介質，而植被內與土壤中流動的水流則以孔隙介質流視之。 各流況之求解過程，皆是先針對水深漫過植生高度之情況，對其整體流速分佈進行求解，再依據此解分別退化至水深不及植生高度與不具植生覆蓋之裸露地之情況。具體作法如下：在層流流況中，以簡化之那維爾-史拖克斯方程式(Navier-Stokes equation)搭配宋長虹(1993)根據Biot多孔彈性介質理論所建立之多孔介質層流模式為控制方程式；而紊流流況時，則分別對那維爾-史拖克斯方程式及Biot多孔彈性介質理論進行修正，再予以求解。 在求得各種情況之流速分佈後，曾與Rowiński and Kubrak (2002)的實驗數據做一比較，結果十分吻合，這充分顯示本研究的流速解析解，可貼切地描述紊流流況中水流流經植生層的流速分佈。