Resistance of Open-Channel Flow under the Effect of Bending Deformation of Submerged Flexible Vegetation

The resistance of an open-channel flow under the influence of bending deformation of submerged flexible vegetation canopy was experimentally studied in an indoor water flume. Altogether, 27 tests under the cross-combinations of three bulk flow velocities ($V$), three vegetation elastic moduli ($E$), and three vegetation stem thicknesses ($b$) were conducted. The total drag force experienced by the vegetation stem was accurately calculated based on the measured vertical profiles of flow velocity and the second order turbulent momentum in front of an individual plant, and this enabled the estimation of the overall drag coefficient ($C_D$) for bulk flow. The results show that the bending deformation of vegetation helps to transfer momentum downward toward the channel bed, thus helping to reduce the overall resistance to flow. The Cauchy number ($C_Y$) is an important parameter representing the bending property of the vegetation in open-channel flow; it’s functionally related to the resistance of flow. For small deformation configurations, the bending angle ($\theta$) and the relative bending displacement (${\delta }_z/h_p$) are linearly dependent on $C_Y$ and ${(C_Y)}^2$, respectively. The $C_D$ and Manning’s $n$ for the bulk flow are both power law functions of $C_Y$. The semiempirical formulas of $C_D$ and $n$ proposed in this study are expected to apply to further experimental studies and river engineering.