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## Mathematical Models of Bending Curve and Velocity Distribution in Flow Through Flexible Vegetation

Author(s): Weijie Wang; Wenqi Peng; Wenxin Huai; Xiaobo Liu; Fei Dong

Linked Author(s): Weijie Wang, Wenxin Huai, Wenqi Peng

Keywords: No Keywords

Abstract: Vegetation in channel or wetland alters the structure of water flow, forming a fast flow region in surface layer and a slow flow region in vegetation layer when vegetation is submerged, which generates different sizes of vortex in each layer and affects transportation for sediment and solute. Turbulent eddies such as Von Karman streets are generated by vegetation elements near channel bottom, and mixing layer is developed near the vegetation top due to velocity jump between vegetation layer and surface layer, while boundary layer develops in the region above mixing layer where flowing water moving freely without obstructions. The interaction between flexible vegetation and flow is much complicated compared with rigid vegetation. Here, mathematical methods including analytical and numerical solutions for predicting the bending of flexible element and vertical distribution of streamwise velocity in flow affected by submerged flexible vegetation are illustrated here. For the prediction of bending status for vegetation in flowing water, deflection cantilever beam theory is adopted for calculating the bending degree of flexible elements, and different approaches are used based on the extent of bending degree. Analytical solution of bending curve is derived under the uniform load based on depth-averaged velocity in canopy layer, giving a reasonable prediction of bending angle for small-deflection, which was verified in our previous work. For large deflection, numerical solution with finite difference scheme for calculating bending curve is widely adopted. For the prediction of velocity distribution in vegetated flow, analytical solution of momentum equations is obtained under consideration of formula solvability, which adopts exponential distribution of shear stress in this situation. For the numerical solution of velocity profile, it is derived by adopting shear stress expressed by mixing length theory with constant value of mixing length in canopy layer and linear increasing mixing length in surface layer from vegetation top to flow surface. In this paper, mathematical models for describing bending curve and velocity profile in flow with flexible vegetation are summarized.

DOI:

Year: 2018