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

Published online by Cambridge University Press:  12 January 2026

Yuan Xu Open the ORCID record for Yuan Xu [Opens in a new window] ,
Siyuan Ma ,
Qigang Chen Open the ORCID record for Qigang Chen [Opens in a new window] ,
Qiang Zhong Open the ORCID record for Qiang Zhong [Opens in a new window] ,
Fan Xu Open the ORCID record for Fan Xu [Opens in a new window] ,
Qing He  and
Heidi Nepf
Yuan Xu*
Affiliation:
State Key Laboratory of Estuarine and Coastal Research, East China Normal University , Shanghai 200241, PR China State Key Laboratory of Hydroscience and Engineering, Tsinghua University , Beijing 100084, PR China
Siyuan Ma
Affiliation:
State Key Laboratory of Estuarine and Coastal Research, East China Normal University , Shanghai 200241, PR China
Qigang Chen
Affiliation:
School of Civil Engineering, Beijing Jiaotong University, Beijing 100044, PR China
Qiang Zhong
Affiliation:
College of Water Resource and Civil Engineering, China Agricultural University, Beijing 100083, PR China
Fan Xu*
Affiliation:
State Key Laboratory of Estuarine and Coastal Research, East China Normal University , Shanghai 200241, PR China
Qing He
Affiliation:
State Key Laboratory of Estuarine and Coastal Research, East China Normal University , Shanghai 200241, PR China
Heidi Nepf
Affiliation:
Department of Civil and Environmental Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
*
Corresponding authors: Yuan Xu, yuanxu@sklec.ecnu.edu.cn; Fan Xu, fxu@sklec.ecnu.edu.cn
Corresponding authors: Yuan Xu, yuanxu@sklec.ecnu.edu.cn; Fan Xu, fxu@sklec.ecnu.edu.cn
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Abstract

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.

JFM classification

Boundary Layers: Boundary Layers Turbulent Flows: Turbulent Flows

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JFM Papers
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Journal of Fluid Mechanics , Volume 1026 , 10 January 2026 , A47
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© The Author(s), 2026. Published by Cambridge University Press

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