State Key Laboratory of Simulation and Regulation of Water Cycle in River Basin, China Institute of Water Resources and Hydropower Research, Beijing, 100038, China.
Department of Water Environment, China Institute of Water Resources and Hydropower Research, Beijing, 100038, China.
Sci Rep. 2019 Mar 26;9(1):5178. doi: 10.1038/s41598-019-41477-7.
The need for operational models describing the friction factor f in streams remains undisputed given its utility across a plethora of hydrological and hydraulic applications concerned with shallow inertial flows. For small-scale roughness elements uniformly covering the wetted parameter of a wide channel, the Darcy-Weisbach f = 8(u/U) is widely used at very high Reynolds numbers, where u is friction velocity related to the surface kinematic stress, U = Q/A is bulk velocity, Q is flow rate, and A is cross-sectional area orthogonal to the flow direction. In natural streams, the presence of vegetation introduces additional complications to quantifying f, the subject of the present work. Turbulent flow through vegetation are characterized by a number of coherent vortical structures: (i) von Karman vortex streets in the lower layers of vegetated canopies, (ii) Kelvin-Helmholtz as well as attached eddies near the vegetation top, and (iii) attached eddies well above the vegetated layer. These vortical structures govern the canonical mixing lengths for momentum transfer and their influence on f is to be derived. The main novelty is that the friction factor of vegetated flow can be expressed as f = 4C(U/U) where U is the spatially averaged velocity within the canopy volume, and C is a local drag coefficient per unit frontal area derived to include the aforemontioned layer-wise effects of vortical structures within and above the canopy along with key vegetation properties. The proposed expression is compared with a number of empirical relations derived for vegetation under emergent and submerged conditions as well as numerous data sets covering a wide range of canopy morphology, densities, and rigidity. It is envisaged that the proposed formulation be imminently employed in eco-hydraulics where the interaction between flow and vegetation is being sought.
鉴于摩擦系数 f 在涉及浅层惯性流的众多水文和水力应用中具有实用性，因此需要用能够描述其特性的操作模型。对于小尺度粗糙度元素均匀覆盖宽通道的湿周，达西-魏斯巴赫 f=8(u/U) 在非常高的雷诺数下被广泛使用，其中 u 是与表面运动应力相关的摩擦速度，U=Q/A 是整体速度，Q 是流量，A 是垂直于流动方向的横截面面积。在自然河流中，植被的存在给量化 f 带来了额外的复杂性，这是本工作的主题。植被中紊流的特征是存在许多相干的旋涡结构：（i）植被冠层下部的卡门涡街，（ii）靠近植被顶部的开尔文-亥姆霍兹以及附着涡旋，以及（iii）在植被层上方的附着涡旋。这些旋涡结构控制着动量传递的典型混合长度，它们对 f 的影响有待推导。主要的新颖之处在于，植被流动的摩擦系数可以表示为 f=4C(U/U)，其中 U 是冠层体积内的空间平均速度，C 是每单位迎风面积的局部阻力系数，该系数用于包括冠层内和上方的层状旋涡结构的影响以及关键的植被特性。将所提出的表达式与为出露和淹没条件下的植被得出的许多经验关系以及涵盖广泛的冠层形态、密度和刚性的许多数据集进行了比较。设想在所寻求水流与植被相互作用的生态水力学中立即采用所提出的公式。
