Abstract
Floating vegetation islands (FVIs) have been widely utilized in various river ecological restoration projects due to their ability to purify pollutants. FVIs float at the surface of shallow pools with their roots unanchored in the sediment. Biofilm formed by roots under islands filters nutrients and particles in the water flowing through it. Flow field disturbance will occur, and transverse distribution of flow velocity will change due to the existence of FVIs. Transport efficiency of suspended solids, nutrients, and pollutants will also be altered. A modified analytical model that considers the effects of boundary friction, drag force of vegetation, transverse shear turbulence, and secondary flow is established to model the transverse distributions of depth-averaged streamwise velocity for the open-channel flow with FVIs using the Shiono and Knight Method. The simulation results with suitable boundary conditions successfully modeled the lateral profile of the depth-averaged streamwise velocity compared with the experimental results of symmetrical and unsymmetrical arrangements of FVIs. Hence, the presented model is of guiding significance to investigate the flow characteristics of rivers with FVIs.
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Data availability
The datasets used or analyzed during the current study are available from the corresponding author on reasonable request.
Abbreviations
- A 1–A 8 :
-
integration constants in Eqs. (12)–(15)
- A v :
-
projected area of canopy per unit volume in the longitudinal direction (m−1)
- A d :
-
area of the entire cross section (m2)
- b :
-
width of floating vegetated islands (m)
- B :
-
flume width (m)
- C b :
-
bed friction coefficient (-)
- C d :
-
drag force coefficient (-)
- D :
-
canopy diameter (m)
- f d :
-
Darcy–Weisbach comprehensive friction factor (-)
- F v :
-
drag force, as defined by Eq. (2) (N/m3)
- g :
-
gravitational acceleration (m/s2)
- h c :
-
height of the root canopy (m)
- h g :
-
height of the gap region (m)
- H :
-
flow depth (m)
- \( \overline{K} \) :
-
secondary flow coefficient (-)
- m :
-
number of columns per bed area (rods/m−2)
- n :
-
Manning’s roughness coefficient (-)
- P u :
-
scale parameter between \( {U}_{d_c} \) and Ud (-)
- \( {P}_u^{\prime } \) :
-
scale parameter between \( {U}_{d_c} \) and \( {U}_{d_g} \) (-)
- Q :
-
flow rate (m3/s)
- R :
-
hydraulic radius (m)
- S 0 :
-
channel bed slope (-)
- u΄, v΄, w΄ :
-
fluctuating velocities in x, y, and z directions (m/s)
- U d :
-
depth-averaged streamwise velocity (m/s)
- \( {U}_{d_c} \) :
-
depth-averaged streamwise velocity in the canopy region (m/s)
- \( {U}_{d_g} \) :
-
depth-averaged streamwise velocity in the gap region (m/s)
- U ∗ :
-
local shear velocity (m/s)
- V column :
-
volume of the water depth column per unit vegetated bottom area (m)
- V vegetation :
-
volume occupied by the vegetation per unit vegetated bottom area (m)
- x, y, z :
-
streamwise, lateral, and vertical directions (-)
- X D :
-
velocity adjustment length (m)
- α :
-
coefficients in Eq. (5) (-)
- β :
-
shape factor (-)
- δ :
-
porosity (-)
- λ :
-
lateral dimensionless eddy viscosity (-)
- κ :
-
Karman constant (-)
- γ 1 − 8, w 1 − 4 :
-
coefficients in Eqs. (12)–(15)
- τ yx, τ zx :
-
Reynolds shear stresses on planes perpendicular to y- and z-directions, respectively (N/m2)
- \( \overline{\tau_{yx}} \) :
-
depth-averaged Reynolds shear stresses on planes perpendicular to the y-direction (N/m2)
- τ d :
-
boundary shear stress (N/m2)
- χ :
-
dimensionless wetted perimeter per unit width (-)
- \( \overline{\varepsilon_{yx}} \) :
-
depth-averaged eddy viscosity (m2/s)
- g, c :
-
abbreviations of lower gap and upper canopy regions
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Acknowledgements
The authors gratefully acknowledge their family, teachers, and classmates for their help in making this study more meaningful.
Funding
This work was financially supported by the National Natural Science Foundation of China [grant numbers 52020105006 and 11872285].
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Wenxin Huai proposed the idea of this study. Xuecheng Fu did the majority of calculations, writing, and editing. Feifei Wang revised the manuscript. The experiment was designed by Wenxin Huai and Mengyang Liu and performed by Xuecheng Fu and Feifei Wang. All authors read and approved the final manuscript.
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Highlights
An analytical model of depth-averaged streamwise velocity for open-channel flow with floating vegetated islands is proposed.
The modeled results indicate good predictions in depth-averaged streamwise velocity.
The new calculation method of comprehensive friction factor is derived.
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Fu, X., Wang, F., Liu, M. et al. Transverse distribution of the streamwise velocity for the open-channel flow with floating vegetated islands. Environ Sci Pollut Res 28, 51265–51277 (2021). https://doi.org/10.1007/s11356-021-14353-z
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DOI: https://doi.org/10.1007/s11356-021-14353-z