# Effect of Rigid Aquatic Bank Weeds on Flow Velocities and Bed Morphology

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

_{v}) for emerged weeds (Table 1).

^{2}, there was no significant difference between the scouring stage and the development stage.

_{50}equal to 0.50 mm. The results concluded that bank vegetation reduced scour near banks. Also, Vargas-Luna et al. [24] experimentally concluded that, at variable discharge, vegetation establishment on floodplains reduced bank erosion. Azarisamani et al. [25] studied the physical effects of rigid vegetation distribution on bed scouring at the toe and bank slope of a meandering river. The results concluded that, in the presence of vegetation, the core of maximum velocity diverted toward the centerline of the flume, reducing erosion risk.

## 2. Methods and Materials

#### 2.1. Dimensional Analysis

_{u}, V

_{d}, V

_{in}, u, ū, (ds)

_{max}, g, ρ, μ, y

_{o}) = 0

_{o}d

^{2}/4, (N

_{o}is the number of stems per unit side area, and d is the stem diameter (m)), V

_{u}is the upstream velocity (m/s), V

_{d}is the downstream velocity (m/s), V

_{in}is the velocity in the middle of the infested reach (m/s), u is the smooth velocity (m/s), ū is the average velocity in the smooth case (m/s), (ds)

_{max}is the maximum scour depth inside the weedy reach (m), g is the gravitational acceleration (m/s

^{2}), ρ is the density of water, μ is the dynamic viscosity of water, and y

_{o}is the smooth water depth (m). By using Buckingham’s Pi theorem, the general equation can be modified as follows:

_{u}/u, V

_{d}/u, V

_{in}/u, (ds)

_{max}/y

_{o}) = (λ,F

_{ro})

_{ro}is the approached Froude number, F

_{ro}= ū/(g y

_{o})

^{1/2}. R

_{n}is the Reynolds number, where R

_{n}= [(ρ g

^{1/2}y

_{o}

^{3/2})/μ] for free-surface open-channel flow; R

_{n}is in the fully turbulent zone and has a negligible effect.

#### 2.2. Experimental Setup

^{2}and three weed densities, λ, of 0.013, 0.0028, and 0.0013/m were used.

_{50}= 0.65 mm. The geometrical standard deviation of the used sand, σ

_{g}= (D

_{84}/D

_{16})

^{1/2}= 1.37 < 1.40, indicated that the used bed material was uniform; Dey et al. [43]. The grain size distribution for the used sand was presented in Figure 2. A drainage system was installed on the bottom of the sand basin to drain excess water before surveying sand surface levels at the end of each run. Before each run, the basin was refilled with the sand and leveled to the bed level—i.e., all runs had the same experimental work conditions and started with the same sediment bed height.

- The sand basin was filled with the tested sand and leveled to the channel bed level.
- The vegetation density and tail-water depth were adjusted according to the study run.
- The flume was filled to the required level by making the pumps circulate the flow very slowly until the flow was adjusted to the required value (25, 30, 35, and 40 L/s) using the control valve.
- The experiment was run for the equilibrium time, which was estimated later, and then the feeding pump was turned off.
- Water was drained out slowly until the formed sand holes became visible.
- Bed scour holes were surveyed every 0.16 and 0.12 m in the longitudinal and transverse directions, respectively.

## 3. Results and Discussion

#### 3.1. Vertical Velocity Profile

_{u}, V

_{in}, and V

_{d}were decided according to the essential location at which the behavior of the water surface changed due to vegetation (see Figure 3). The vertical velocity profile was measured every 2 cm to predict the vertical profiles. In some cases, three distributed cross-sections of the velocity profile were measured at the center of the infested reach, with one in the middle, one near the right bank, and the other near the left bank. These measurements aimed to visualize the effect of the bank vegetation on velocities near the bank.

_{o}≤ 0.5), where bank weed presence produced secondary flow that increased the velocity near the channel bed. As a result of that, the approach of logarithmic distribution was achieved only until y/h

_{o}≤ 0.5 for W/h ≤ 3, “where W/h is the ratio between the channel width and the flow height”. These results agreed with the findings of [9,11,12,13,15,30,44], which concluded that, in the presence of vegetation on the channel walls, the level of maximum velocity and maximum shear stress is below the water surface and occurs near the channel bed. Also, Afzalimehr and Dey [9] observed that the maximum velocity is located at y/h

_{o}= 0.2, near the vegetated bank, and at y/h

_{o}= 0.56 in the flume center under uniform flow and an aspect ratio of (W/h = 3). Also, it was found that for all weed densities, the maximum velocity V

_{max}was higher than that in the smooth case (no weeds). The maximum velocity-increasing ratios (V

_{max}/u

_{max}) were recorded in Table 4.

_{ro}).

_{in}) was examined using 36 data points to re-determine it using the predictor equations of James et al. [16], Hirschowitz and James [10], Huai et al. [17], Valyrakis et al. [14], and Liu and Shan [18]. Figure 7 plots the measured velocities inside the weedy reach and those calculated by the above-mentioned equations in Table 1.

#### 3.2. Bed Morphology

#### 3.3. Relative Velocity and Maximum Scour Depth Estimation

^{2}was used as a measure of goodness of fit, where the predicted value indicates how well the model predicts responses to new observations. Before regression, a correlation matrix was produced to show the significant effect of the chosen independent variables on velocity and maximum scour depth (Table 6).

_{ro}) ranged between 0.11 and 0.3. Empirical equations were developed to assess and understand the impact of aquatic bank weed density on changes in velocities and scour depth. Table 7 shows the estimated equations and their adjusted coefficient of multiple determination (R

^{2}), which is higher than 80%, i.e., there is good fitting quality for the experimental data. Figure 15 shows the fitting curves, where the measured data were plotted against the predicted data. The curves show good fitting for the data, and all data points fall within ±20%. So, these equations can be used to estimate the change in the velocity and the scour depth.

#### 3.4. Research Application

## 4. Conclusions

_{ro}). The maximum velocity occurred within the weedy reach and was close to that measured just downstream of the weedy reach.

_{o}≤ 0.5).

_{ro}) ranged from 0.11 to 0.30, eight empirical equations were developed to assess and understand the impact of aquatic bank weed density on changes in velocities and scour. These equations can contribute to irrigation channel management and rehabilitation, offering a chance to carry them out with the minimum expenditure of time and money.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Artificial flume, rigid vegetation on the channel side slopes: (

**a**) bilateral weeds; (

**b**) unilateral weeds.

**Figure 5.**Vertical velocity profiles for both bilateral and unilateral arrangements at F

_{ro}= 0.15.

**Figure 6.**Vertical velocity profiles for both bilateral and unilateral arrangements at F

_{ro}= 0.30.

**Figure 10.**Scour contour map for bilateral weeds at different densities, Q = 40 L/s, and F

_{ro}= 0.30.

**Figure 11.**Scour wireframe map for bilateral weeds at different densities, Q = 40 L/s, and F

_{ro}= 0.30.

**Figure 12.**Scour contour map for unilateral weeds at different densities, Q = 40 L/s, and F

_{ro}=0.30.

**Figure 13.**Scour wireframe map for unilateral weeds at different densities, Q = 40 L/s, and F

_{ro}= 0.30.

**Figure 14.**Scour depth along the middle of the vegetation at different densities and Q = 40 L/s for (

**a**,

**c**) bilateral infestation and (

**b**,

**d**) unilateral infestation.

Authors | Equation | Remark |
---|---|---|

James et al., 2004 [16] | ${V}_{v}=\frac{1}{F}\sqrt{S}$ $F=\sqrt{\frac{2g}{{C}_{d}Nd}}\sqrt{\left(1-\frac{N\pi {d}^{2}}{4}\right)}$ | F: resistance coefficient accounting for stem drag; S: channel slope; N: number of stems per unit area; d: stem diameter; C _{d}: drag coefficient. |

Hirschowitz and James 2009 [10] | ${V}_{v}={\left(\frac{gA}{\frac{{f}_{b}}{8}B+2\frac{{f}_{V}}{8}h}\right)}^{0.5}{S}^{0.5}$ | A: cross-sectional area of the un-vegetated zone; B: bed width; h: flow depth at the interface; f _{b}: friction factor of the bed;f _{v}: friction factor of the vegetation interface. |

Huai et al., 2009 [17] | ${V}_{v}=\sqrt{\frac{2gi}{{C}_{d}mD}}$ | D: cylinder diameter. m: number of stems in the control volume = 1/(x _{a} y_{a});i: energy slope. |

Valyrakis et al., 2021 [14] | ${V}_{v}=u\text{}\left(1-0.143\text{}\varnothing \right)$ | φ: solid volume fraction (φ = mπD^{2}/(4LW_{v});u: mean velocity in the no-weeds case. |

Liu and Shan 2022 [18] | ${V}_{v}=\sqrt{\left(\frac{ghS}{{C}_{f}+0.5({C}_{d}ah\left(1-\varnothing \right)}\right)}$ | S: water surface slope; Φ: solid volume fraction (=(π/4)nd ^{2});C _{f}: bed friction coefficient;C _{d}: drag coefficient;a: frontal area per patch volume (=nd); h: flow depth. |

Authors | Stem Simulation | ||||
---|---|---|---|---|---|

Shaped | Material | Diameter (mm) | Spacing (Δx) | Distribution | |

James et al. [16] | Cylindrical | Steel | 5 | 2.5, 5, and 7.5 cm | Staggered |

Stone and Shen [28] | Wood | 3.18, 6.35 and 12.7 | 3.8, 4.6 and 7.6 cm | Staggered | |

Meftah et al. [29] | Steel | 3 | 10 cm | Linear | |

Kothyari et al. [30] | Stainless steel | 10 | 3.2 to 20.3 cm | Staggered | |

Cheng and Nguyen [31] | Steel | 3.2, 6.6 and 8.3 | 3 and 6 cm | Staggered | |

Panigrahi [32] | Steel | 6.5 | 10 cm | Both linear and staggered | |

Ahmed and Hady [33] | PVC | 10 | 22.72, 11.9, and 9.61 cm | Linear | |

Chakraborty and Sarkar [34] | PVC | 6 | Random Distribution | ||

Tong et al. [35] | PVC | 8 | 10 cm | Linear | |

D’Ippolito et al. [36] | Wood | 8 and 10 | 4.24 and 8.48 cm | Both linear and staggered | |

Lee et al. [37] | Acrylic | 10 | 4 and 8 cm | staggered | |

Wang et al. [38] | PVC | 6 | 6 cm | Linear | |

Huang et al. [39] | Wood | 6 | 2.5 and 5 cm | Linear | |

Current study | Steel | 3 | 2.5, 5, and 7.5 cm | Staggered |

Weeds Configuration | Bed Condition | Discharge (L/s) | Tail Water Depth | No of Runs | ||
---|---|---|---|---|---|---|

Density/m | Arrangement | Spacing cm | ||||

No weeds | n/a | n/a | concrete | 40,35,30,25 L/s | Three different tail depths for each discharge | 12 |

High (λ~0.013) | Staggered both bilateral and unilateral weeds | 2.5 | 40,35,30,25 L/s | 24 | ||

Medium (λ~0.0028) | 5.0 | 40,35,30,25 L/s | 24 | |||

Low (λ~0.0013) | 7.5 | 40,35,30,25 L/s | 24 | |||

No weeds | n/a | n/a | Sandy soil with D_{50} = 0.65 | 40,35,30,25 L/s | 12 | |

High (λ~0.013) | Staggered both bilateral and unilateral weeds | 2.5 | 40,35,30,25 L/s | 24 | ||

Medium (λ~0.0028) | 5.0 | 40,35,30,25 L/s | 24 | |||

Low (λ~0.0013) | 7.5 | 40,35,30,25 L/s | 24 | |||

Total Number of Runs | 168 |

Arrangement | Density | Velocity Position | ||
---|---|---|---|---|

Upstream | Middle | Downstream | ||

Bilateral infestation | High | 9% | 50% | 43% |

Medium | 4% | 32% | 28% | |

Low | 2% | 27% | 24% | |

Unilateral infestation | High | 4% | 24% | 17% |

Medium | 2% | 12% | 9% | |

Low | 1.4% | 12% | 8% |

Authors/Model | Average Error | Maximum Error | Minimum Error | Variance | RMSE |
---|---|---|---|---|---|

James et al. [16] | −0.189 | 0.080 | −0.043 | 0.018 | 0.080 |

Hirschowitz and James [10] | −0.322 | 0.068 | −0.098 | 0.018 | 0.141 |

Huai et al. [17] | −0.014 | 0.493 | 0.259 | 0.053 | 0.299 |

Valyrakis et al. [14] | −0.165 | −0.055 | −0.095 | 0.019 | 0.100 |

Liu and Shan [18] | −0.400 | 0.247 | −0.062 | 0.022 | 0.175 |

λ | F_{ro} | (V_{u}/u)_{max} | (V_{d}/u)_{max} | (V_{in}/u)_{max} | $(\mathit{d}{\mathit{s}}_{\mathit{m}\mathit{a}\mathit{x}}$/y_{o}) | |
---|---|---|---|---|---|---|

λ | 1.00 | |||||

F_{ro} | 0.00 | 1.00 | ||||

(V_{u}/u)_{max} | 0.31 | 0.86 | 1.00 | |||

(V_{d}/u)_{max} | 0.55 | 0.72 | 0.93 | 1.00 | ||

(V_{in}/u)_{max} | 0.63 | 0.67 | 0.90 | 0.98 | 1.00 | |

($d{s}_{max}$/y_{o}) | 0.37 | 0.71 | 0.73 | 0.73 | 0.72 | 1.00 |

Term | Bilateral Weeds | Unilateral Weeds |
---|---|---|

Upstream relative velocity | ${(\frac{{V}_{u}}{u})}_{max}=1.10{\left(\lambda \right)}^{0.05}{\left(8.82\right)}^{{F}_{ro}}$ ${R}^{2}=0.88\left(3\right)$ | ${(\frac{{V}_{u}}{u})}_{max}=1.10{\left(\lambda \right)}^{0.04}{\left(5.53\right)}^{{F}_{ro}}$ ${R}^{2}=0.80\left(4\right)$ |

Downstream relative velocity | ${(\frac{{V}_{d}}{u})}_{max}=1.80{\left(\lambda \right)}^{0.1}{\left(8.10\right)}^{{F}_{ro}}$ ${R}^{2}=0.88\left(5\right)$ | ${(\frac{{V}_{u}}{u})}_{max}=1.10{\left(\lambda \right)}^{0.03}\text{}{\left(7.10\right)}^{{F}_{ro}}$ ${R}^{2}=0.85\left(6\right)$ |

Relative velocity inside the weedy patch | ${(\frac{{V}_{in}}{u})}_{max}=2.24{\left(\lambda \right)}^{0.13}{\left(9.71\right)}^{{F}_{ro}}$ ${R}^{2}=0.90\left(7\right)$ | ${(\frac{{V}_{in}}{u})}_{max}=1.30{\left(\lambda \right)}^{0.05}{\left(6.57\right)}^{{F}_{ro}}$ ${R}^{2}=0.86\left(8\right)$ |

Relative maximum scour depth | $\left(\frac{d{s}_{max}}{{y}_{o}}\right)=2.70{\left(\lambda \right)}^{0.21}{\left({F}_{ro}\right)}^{0.96}$ ${R}^{2}=0.91\left(9\right)$ | $\left(\frac{d{s}_{max}}{{y}_{o}}\right)=1.69{\left(\lambda \right)}^{0.20}{\left({F}_{ro}\right)}^{0.84}$ ${R}^{2}=0.90\left(10\right)$ |

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## Share and Cite

**MDPI and ACS Style**

Elzahry, E.F.M.; Eltoukhy, M.A.R.; Abdelmoaty, M.S.; Eraky, O.M.; Shaaban, I.G.
Effect of Rigid Aquatic Bank Weeds on Flow Velocities and Bed Morphology. *Water* **2023**, *15*, 3173.
https://doi.org/10.3390/w15183173

**AMA Style**

Elzahry EFM, Eltoukhy MAR, Abdelmoaty MS, Eraky OM, Shaaban IG.
Effect of Rigid Aquatic Bank Weeds on Flow Velocities and Bed Morphology. *Water*. 2023; 15(18):3173.
https://doi.org/10.3390/w15183173

**Chicago/Turabian Style**

Elzahry, Elzahry Farouk M., Mahmoud Ali R. Eltoukhy, Mohamed S. Abdelmoaty, Ola Mohamed Eraky, and Ibrahim G. Shaaban.
2023. "Effect of Rigid Aquatic Bank Weeds on Flow Velocities and Bed Morphology" *Water* 15, no. 18: 3173.
https://doi.org/10.3390/w15183173