Near-bed velocity law and bed shear stress in vegetated flows

By generating drag and turbulence away from the bed, aquatic vegetation shapes the mean and turbulent velocity profile. However, the near-bed velocity distribution in vegetated flows has received little theoretical or experimental attention. This study investigated the near-bed velocity profile and bed shear stress using a coupled particle image velocimetry and particle tracking velocimetry system, which enabled the acquisition of flow-field measurements at very high spatial and temporal resolution. A viscous sublayer with a linear velocity profile was present, but this sublayer thickness was much smaller in vegetated flows than in bare flows with the same channel velocity. However, the dimensionless viscous sublayer thickness was the same in vegetated and bare flows, $z_v^+ = z_v \langle u_*\rangle / \nu = 6.1 \pm 0.7$ . In addition, in vegetated flow, the horizontally averaged velocity profile above the viscous sublayer did not follow the classic logarithmic law found for bare beds. This deviation was attributed to the violation of two key assumptions in the classic Prandtl mixing length theory. By modifying the mixing length theory for vegetated conditions, a new theoretical power law profile for near-bed velocity was derived and validated with velocity data from both the present and previous studies, with mean percent errors of 4.9 % and 7.8 %, respectively. Using the new velocity law, the spatially averaged bed shear stress (and friction velocity) can be predicted from channel-average velocity, vegetation density and stem diameter, all of which are conveniently measured in the field.