Drag Coefficient of Emergent Flexible Vegetation in Steady Nonuniform Flow

Flexible vegetation plays key roles in the natural channel and riparian ecology. This paper investigates the drag coefficient C-df of an emergent flexible vegetation array in a steady nonuniform flow. Laboratory flume tests of five vegetation densities exposed to a constant flow rate were conducted, and the variation in the water surface was accurately measured. The Saint-Venant equation was applied to explore vegetation hydrodynamics under nonuniform conditions, and a more widely applicable formula for the vegetated drag of nonuniform flow was proposed. Furthermore, the flexible drag coefficient factor alpha(b) was used to represent the flexibility and drag reconfiguration, which were explored from the perspective of material mechanics. The results reveal that the calculated values of C-df exhibit nonmonotonic variation with increasing Reynolds number along the streamwise direction due to the flow nonuniformity. There are two effects of blockage and sheltering in the emergent vegetated patch: The blockage effect increases the drag coefficient, while the sheltering effect-especially at the leading edge and tail of the vegetated patch-reduces the drag of the flexible canopy due to bending deformation. These two effects achieve equilibration in dense flexible canopies. Finally, by relating alpha(b) to flexibility through the slenderness Cauchy number C-YS, a nonmonotonic pattern can be obtained for each test. A fitting formula was proposed based on alpha(b) as a function of C-YS. The results presented in this study can potentially support applications related to the plant flexible dams and vegetated filter strips for river ecosystems.