Hostname: page-component-68c7f8b79f-lvtpz Total loading time: 0 Render date: 2026-01-15T04:37:06.037Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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

Information

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

Aliaga, J. & Aberle, J. 2024 Bed shear stress and near-bed flow through sparse arrays of rigid emergent vegetation. Water Resour. Res. 60 (4), e2023WR035879.10.1029/2023WR035879CrossRefGoogle Scholar
Beltrán-Burgos, M., Esposito, C.R., Nepf, H.M., Baustian, M.M. & Di Leonardo, D.R. 2023 Vegetation-driven seasonal sediment dynamics in a freshwater marsh of the Mississippi river delta. J. Geophys. Res.: Biogeosci. 128 (4), e2022JG007143.10.1029/2022JG007143CrossRefGoogle Scholar
Biron, P.M., Robson, C., Lapointe, M.F. & Gaskin, S.J. 2004 Comparing different methods of bed shear stress estimates in simple and complex flow fields. Earth Surf. Proc. Land. 29 (11), 1403–1415.10.1002/esp.1111CrossRefGoogle Scholar
Caroppi, G., Vastila, K., Järvelä, J., Lee, C., Ji, U., Kim, H.S. & Kim, S. 2022 Flow and wake characteristics associated with riparian vegetation patches: results from field-scale experiments. Hydrol. Process. 36 (2), e14506.10.1002/hyp.14506CrossRefGoogle Scholar
Chen, Q., Duan, Y., Zhong, Q., Wang, Z. & Huang, L. 2021 On the method of determining instantaneous wall shear stress from near-wall velocity measurements in wall turbulence. Phys. Fluids 33 (12), 125105.10.1063/5.0068077CrossRefGoogle Scholar
Cheng, Y., Peng, Z., Xu, Y., Zhao, Y. & He, Q. 2025 Longitudinal and vertical evolution of wave-induced turbulence within vegetation. Coast. Engng 199, 104737.10.1016/j.coastaleng.2025.104737CrossRefGoogle Scholar
Conde-Frias, M., Ghisalberti, M., Lowe, R., Abdolahpour, M. & Etminan, V. 2023 The near-bed flow structure and bed shear stresses within emergent vegetation. In Water Resources Research, pp. e2022WR032499.Google Scholar
Dey, S. 2014 Fluvial Hydrodynamics. Springer.10.1007/978-3-642-19062-9CrossRefGoogle Scholar
Dey, S. & Das, R. 2012 Gravel-bed hydrodynamics: double-averaging approach. J. Hydraul. Engng 138 (8), 707–725.10.1061/(ASCE)HY.1943-7900.0000554CrossRefGoogle Scholar
van Driest, E.R. 1956 On turbulent flow near a wall. J. Aeronaut. Sci. 23 (11), 1007–1011.10.2514/8.3713CrossRefGoogle Scholar
Etminan, V., Ghisalberti, M. & Lowe, R.J. 2018 Predicting bed shear stresses in vegetated channels. Water Resour. Res. 54 (11), 9187–9206.10.1029/2018WR022811CrossRefGoogle Scholar
Etminan, V., Lowe, R.J. & Ghisalberti, M. 2017 A new model for predicting the drag exerted by vegetation canopies. Water Resour. Res. 53 (4), 3179–3196.10.1002/2016WR020090CrossRefGoogle Scholar
Fang, H., Han, X., He, G. & Dey, S. 2018 Influence of permeable beds on hydraulically macro-rough flow. J. Fluid Mech. 847, 552–590.10.1017/jfm.2018.314CrossRefGoogle Scholar
Fourqurean, J.W., et al. 2012 Seagrass ecosystems as a globally significant carbon stock. Nat. Geosci. 5 (7), 505–509.10.1038/ngeo1477CrossRefGoogle Scholar
Gambi, M.C., Nowell, A.R.M. & Jumars, P.A. 1990 Flume observations on flow dynamics in Zostera marina (eelgrass) beds. Mar. Ecol. Prog. Ser. 1 (2), 159–169.10.3354/meps061159CrossRefGoogle Scholar
Hamilton, J.F., Kelley, B.Z., Monismith, S.G. & Koseff, J.R. 2025 On the use of simplified geometries to represent turbulent flow over coral reefs. J. Fluid Mech. 1004, A11.10.1017/jfm.2024.1179CrossRefGoogle Scholar
Huai, W., Li, S., Katul, G.G., Liu, M. & Yang, Z. 2021 Flow dynamics and sediment transport in vegetated rivers: a review. J. Hydrodyn. 33 (3), 400–420.10.1007/s42241-021-0043-7CrossRefGoogle Scholar
Huai, W., Xue, W. & Qian, Z. 2015 Large-eddy simulation of turbulent rectangular open-channel flow with an emergent rigid vegetation patch. Adv. Water Resour. 80, 30–42.10.1016/j.advwatres.2015.03.006CrossRefGoogle Scholar
Kähler, C.J., Astarita, T., Vlachos, P.P., Sakakibara, J., Hain, R., Discetti, S., La Foy, R. & Cierpka, C. 2016 Main results of the 4th international PIV challenge. Exp. Fluids 57 (6), 97.10.1007/s00348-016-2173-1CrossRefGoogle Scholar
von Karman, T. 1930 Mechanische Ähnlichkeit und turbulenz. In Proceedings of Third International Congress for Applied Mechanics, vol. 1, pp. 79–93. Sveriges Litografiska Tryckerier.Google Scholar
Kemp, J.L., Harper, D.M. & Cross, G.A. 2000 The habitat-scale geohydraulics of rivers. Ecol. Engng 16 (1), 17–29.10.1016/S0925-8574(00)00073-2CrossRefGoogle Scholar
Kennedy, H., Beggins, J., Duarte, C.M., Fourqurean, J.W., Holmer, M., Marbà, N. & Middelburg, J.J. 2010 Seagrass sediments as a global carbon sink: isotopic constraints. Global Biogeochem. Cycles 24 (4), GB4026.10.1029/2010GB003848CrossRefGoogle Scholar
Kim, H. & Lee, S. 2002 Performance improvement of two-frame particle tracking velocimetry using a hybrid adaptive scheme. Meas. Sci. Technol. 13 (4), 573.10.1088/0957-0233/13/4/321CrossRefGoogle Scholar
King, A.T., Tinoco, R.O. & Cowen, E.A. 2012 A $k-\epsilon$ turbulence model based on the scales of vertical shear and stem wakes valid for emergent and submerged vegetated flows. J. Fluid Mech. 701, 1–39.10.1017/jfm.2012.113CrossRefGoogle Scholar
Kothyari, U.C., Hashimoto, H. & Hayashi, K. 2009 Effect of tall vegetation on sediment transport by channel flows. J. Hydraul. Res. 47 (6), 700–710.10.3826/jhr.2009.3317CrossRefGoogle Scholar
Kuwata, Y. & Kawaguchi, Y. 2019 Direct numerical simulation of turbulence over systematically varied irregular rough surfaces. J. Fluid Mech. 862, 781–815.10.1017/jfm.2018.953CrossRefGoogle Scholar
Leonard, L.A., Hine, A.C. & Luther, M.E. 1995 Surficial sediment transport and deposition processes in a Juncus roemerianus marsh, west-central Florida. J. Coast. Res. 11 (2), 322–336.Google Scholar
Li, C., Peng, Z., Zhao, Y., Fang, D., Chen, X., Xu, F. & Wang, X. 2024 Seasonal variations in drag coefficient of salt marsh vegetation. Coast. Engng 193, 104575.10.1016/j.coastaleng.2024.104575CrossRefGoogle Scholar
Lightbody, A.F. & Nepf, H.M. 2006 Prediction of velocity profiles and longitudinal dispersion in salt marsh vegetation. Limnol. Oceanogr. 51 (1), 218–228.10.4319/lo.2006.51.1.0218CrossRefGoogle Scholar
Liu, C., Shan, Y., He, L., Li, F., Liu, X. & Nepf, H. 2024 Plant morphology impacts bedload sediment transport. Geophys. Res. Lett. 51 (12), e2024GL108800.10.1029/2024GL108800CrossRefGoogle Scholar
Liu, C., Yan, C., Sun, S., Lei, J., Nepf, H. & Shan, Y. 2022 Velocity, Turbulence and Sediment Deposition in a Channel Partially Filled with a Phragmites Australis Canopy. Water Resources Research.10.1029/2022WR032381CrossRefGoogle Scholar
Liu, D., Dumas, P., Fairbanks, J.D. & Hodges, C.C. 2008 An experimental study of flow through rigid vegetation. J. Geophys. Res.: Earth Surface 113 (F4), F04015.Google Scholar
Manners, R.B., Wilcox, A.C., Kui, L., Lightbody, A.F., Stella, J.C. & Sklar, L.S. 2015 When do plants modify fluvial processes? Plant-hydraulic interactions under variable flow and sediment supply rates. J. Geophys. Res.: Earth Surface 120 (2), 325–345.10.1002/2014JF003265CrossRefGoogle Scholar
Mass, T., Genin, A., Shavit, U., Grinstein, M. & Tchernov, D. 2010 Flow enhances photosynthesis in marine benthic autotrophs by increasing the efflux of oxygen from the organism to the water. Proc. Natl Acad. Sci. 107 (6), 2527–2531.10.1073/pnas.0912348107CrossRefGoogle ScholarPubMed
Maza, M., Adler, K., Ramos, D., Garcia, A.M. & Nepf, H. 2017 Velocity and drag evolution from the leading edge of a model mangrove forest. J. Geophys. Res.: Oceans 122 (11), 9144–9159.10.1002/2017JC012945CrossRefGoogle Scholar
Naden, P., Rameshwaran, P., Mountford, O. & Robertson, C. 2006 The influence of macrophyte growth, typical of eutrophic conditions, on river flow velocities and turbulence production. Hydrol. Process. 20 (18), 3915–3938.10.1002/hyp.6165CrossRefGoogle Scholar
Nepf, H.M. 2012 Flow and transport in regions with aquatic vegetation. Annu. Rev. Fluid Mech. 44 (1), 123–142.10.1146/annurev-fluid-120710-101048CrossRefGoogle Scholar
Nepf, H.M. & Koch, E.W. 1999 Vertical secondary flows in submersed plant-like arrays. Limnol. Oceanogr. 44 (4), 1072–1080.10.4319/lo.1999.44.4.1072CrossRefGoogle Scholar
Nepf, H.M. & Vivoni, E.R. 2000 Flow structure in depth-limited, vegetated flow. J. Geophys. Res.: Oceans 105 (C12), 28547–28557.10.1029/2000JC900145CrossRefGoogle Scholar
Nezu, I. & Nakagawa, H. 1993 Turbulence in Open-Channel Flows. Balkema.Google Scholar
Nikora, V., McEwan, I., McLean, S., Coleman, S., Pokrajac, D. & Walters, R. 2007 Double averaging concept for rough-bed open-channel and overland flows: theoretical background. J. Hydraul. Engng 133 (8), 873–883.10.1061/(ASCE)0733-9429(2007)133:8(873)CrossRefGoogle Scholar
Nowell, A.R.M. & Jumars, P.A. 1984 Flow environments of aquatic benthos. Annu. Rev. Ecol. Syst. 15, 303–328.10.1146/annurev.es.15.110184.001511CrossRefGoogle Scholar
Poggi, D., Borgorato, A., Ridolfi, L., Albertson, J.D. & Katurji, G.G. 2004 The effect of vegetation density on canopy sub-layer turbulence. Boundary-Layer Meteorol. 111 (3), 565–587.10.1023/B:BOUN.0000016576.05621.73CrossRefGoogle Scholar
Pope, S.B. 2000 Turbulent Flows. Cambridge University Press.Google Scholar
Prandtl, L. 1925 Bericht über untersuchungen zur ausgebildeten turbulenz. Z. Angew. Math. Mech. 5, 136–139.10.1002/zamm.19250050212CrossRefGoogle Scholar
Ranjan, P., Mittal, K., Chamorro, L.P. & Tinoco, R.O. 2022 Impact of gaps on the flow statistics in an emergent rigid canopy. Phys. Fluids 34 (6), 066601.10.1063/5.0088527CrossRefGoogle Scholar
Raupach, M.R. & Shaw, R.H. 1982 Averaging procedures for flow within vegetation canopies. Boundary-Layer Meteorol. 22 (1), 79–90.10.1007/BF00128057CrossRefGoogle Scholar
Ricardo, A.R., Franca, M.J. & Ferreira, R.M.L. 2016 Turbulent flows within random arrays of rigid and emergent cylinders with varying distribution. J. Hydraul. Engng 142 (9), 04016022.10.1061/(ASCE)HY.1943-7900.0001151CrossRefGoogle Scholar
Rousseau, G. & Angey, C. 2020 Scanning PIV of turbulent flows over and through rough porous beds using refractive index matching. Exp. Fluids 61 (8), 172.10.1007/s00348-020-02990-yCrossRefGoogle Scholar
Shan, Y., Zhao, T., Liu, C. & Nepf, H. 2020 Turbulence and bed load transport in channels with randomly distributed emergent patches of model vegetation. Geophys. Res. Lett. 47 (12), e2020GL087055.10.1029/2020GL087055CrossRefGoogle Scholar
Stoesser, T., Kim, S.J. & Dumas, P. 2010 Turbulent flow through idealized emergent vegetation. J. Hydraul. Engng 136 (12), 1003–1017.10.1061/(ASCE)HY.1943-7900.0000153CrossRefGoogle Scholar
Tanino, Y. & Nepf, H.M. 2008 Lateral dispersion in random cylinder arrays at high Reynolds number. J. Fluid Mech. 600, 339–371.10.1017/S0022112008000505CrossRefGoogle Scholar
Tinoco, R.O. 2011 An experimental investigation of drag and the turbulent flow structure in simulated and real aquatic vegetation. PhD thesis, Cornell University.Google Scholar
Tinoco, R.O., San Juan, J.E. & Mullarney, J.C. 2020 Simplification bias: lessons from laboratory and field experiments on flow through aquatic vegetation. Earth Surf. Proc. Land. 45 (1), 121–143.10.1002/esp.4743CrossRefGoogle Scholar
Tseng, C.-Y. & Tinoco, R.O. 2020 A model to predict surface gas transfer rate in streams based on turbulence production by aquatic vegetation. Adv. Water Resour. 143, 103666.10.1016/j.advwatres.2020.103666CrossRefGoogle Scholar
Tseng, C.-Y. & Tinoco, R.O. 2021 A two-layer turbulence-based model to predict suspended sediment concentration in flows with aquatic vegetation. Geophys. Res. Lett. 48 (3), e2020GL091255.10.1029/2020GL091255CrossRefGoogle Scholar
Tseng, C.-Y. & Tinoco, R.O. 2022 From substrate to surface: a turbulence-based model for gas transfer across sediment-water–air interfaces in vegetated streams. Water Resour. Res. 58 (1), e2021WR030776.10.1029/2021WR030776CrossRefGoogle Scholar
Wang, X., Gualtieri, C. & Huai, W. 2023 Grain shear stress and bed-load transport in open channel flow with emergent vegetation. J. Hydrol. 618, 129204.10.1016/j.jhydrol.2023.129204CrossRefGoogle Scholar
Wilcock, R.J., Champion, P.D., Nagels, J.W. & Croker, G.F. 1999 The influence of aquatic macrophytes on the hydraulic and physico-chemical properties of a New Zealand lowland stream. Hydrobiologia 416 (0), 203–214.10.1023/A:1003837231848CrossRefGoogle Scholar
Xu, F., et al. 2024 Anomalous scaling of branching tidal networks in global coastal wetlands and mudflats. Nat. Commun. 15 (1), 9700.10.1038/s41467-024-54154-9CrossRefGoogle ScholarPubMed
Xu, Y., Esposito, C.R., Beltram-Burgos, M. & Nepf, H.M. 2022 Competing effects of vegetation density on sedimentation in deltaic marshes. Nat. Commun. 13 (1), 4641.10.1038/s41467-022-32270-8CrossRefGoogle ScholarPubMed
Xu, Y. & Nepf, H. 2020 Measured and predicted turbulent kinetic energy in flow through emergent vegetation with real plant morphology. Water Resour. Res. 56 (12), e2020WR027892.10.1029/2020WR027892CrossRefGoogle Scholar
Xu, Y. & Nepf, H. 2021 Suspended sediment concentration profile in a Typha Latifolia canopy. Water Resour. Res. 57 (9), e2021WR029902.10.1029/2021WR029902CrossRefGoogle Scholar
Yang, J.Q., Kerger, F. & Nepf, H.M. 2015 Estimation of the bed shear stress in vegetated and bare channels with smooth beds. Water Resour. Res. 51 (5), 3647–3663.10.1002/2014WR016042CrossRefGoogle Scholar
Zhang, Y., Lai, X., Ma, J., Zhang, Q., Yu, R., Yao, X. & Deng, H. 2021 Field study on flow structures within aquatic vegetation under combined currents and small-scale waves. Hydrol. Process. 35 (4), e14121.10.1002/hyp.14121CrossRefGoogle Scholar
Zhao, T. & Nepf, H. 2024 Turbulence and bedload transport in submerged vegetation canopies. Water Resour. Res. 60 (12), e2024WR037694.10.1029/2024WR037694CrossRefGoogle Scholar
Zhao, Y., Peng, Z., Chen, X., Fang, D., Liu, S., Wang, X. & He, Q. 2024 Parameterisation and evolution of non-breaking wave nonlinearity over flexible vegetation. Coast. Engng 192, 104543.10.1016/j.coastaleng.2024.104543CrossRefGoogle Scholar
Supplementary material: File

Xu et al. supplementary material

Xu et al. supplementary material
Download Xu et al. supplementary material(File)
File 4.6 MB