# Comparison of Velocity and Reynolds Stress Distributions in a Straight Rectangular Channel with Submerged and Emergent Vegetation

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

_{p}) where h is water depth and y

_{p}is the deflected plant height in vegetated flow [15]. However, Shucksmith et al. carried out their experiments in various submerged and emergent natural vegetation. They found that vegetation causes uniform velocity distribution in vertical direction, and the velocity shear in submerged vegetation is more than an emergent one due to faster flow conditions over submerged vegetation [17]. Kumar and Sharma showed that the vertical velocity reduces in regions of free stream, but at the central axis of channel cross-section and Reynolds shear stress and turbulent intensity are weaker in magnitude at vegetation region. Accordingly, vegetation decreases the flow velocity, Reynolds shear stress and turbulence intensities, showing that vegetation plays an effective role to reduce the resistance in the flow [18]. Much less is understood on the comparison between vegetation in banks and vegetation over the bed for the same aspect ratio (the ratio of the width to flow depth) and flow discharge. Barahimi and Sui [3] found that over submerged vegetation, a high velocity gradient is observed near the bed up to z/h = 0.1, and a decreasing trend towards the water surface. In addition, the Reynolds stress distribution is influenced by the aspect ratio (W/h), showing an irregular distribution in the vertical direction [3].

## 2. Materials and Methods

^{3}/s and water depth was fixed between 11 and 15 cm.

_{50}the median gravel size (Afzalimehr) [32]. Since the experiments in this study were conducted for (h/${\mathrm{d}}_{50}$) > 5, the change of flow depth has no effect on the results. In addition, for runs 1 and 2, y

_{p}is the plant height.

^{−1}and a sampling volume with a height of 5.5 mm. After measurements, the data were filtered with a WinADV program. WinADV helps to select suitable series data for velocity to draw reliable results. Accordingly, the coefficiency of determination (R

^{2}) for most data collection was over 95 percent, and signal to noise ratio (SNR) was over 15. Data with SNR lower than or equal to 5 and an average correlation of less than 70% were removed from data set. Collecting data with sampling frequency f = 200 Hz and sampling time 120 sec leads to more than 24,000 observations at each point of velocity and Reynolds stress profile. This shows a great repeatability of data at each point. Accordingly, even if 10% of data were not suitable at each point, the analysis was done with more than 21,000 data points, resulting in high certainty in results.

^{3}/s over an artificially vegetated and non-vegetated pool, with 5° slope in the entrance and exit section of the pool. Their experiments were conducted in a laboratory flume with W = 0.4 m, h = 0.20 m, an aspect ratio of 2, and a d

_{50}of 10.4 mm. The vegetation cover over the examined pool was almost the same as the present grass canopy. The comparison of results of Parvizi et al. [2] with the present study is presented in the discussion section.

_{50}under tops of gravel particles where y = 0. Therefore, addition of 0.1d

_{50}in numerator of (3) causes a better fitness of the log law to the velocity points in the logarithmic region. C is a constant that depends on the flow conditions and roughness size. The value of C has been reported 8.5 by Graf and Altinakar [23], however, there is no universal value for C.

_{50}for this study is different from the one used in other studies. For example, Graf and Altinakar use 0.2d

_{50}in order to show a better presentation of data fitness by the log law. The reason for not using any modification factor in Equation (2) such as 0.1y

_{p}is the insignificant change in the presentation of the log- law fitness by this modifying factor.

## 3. Results

#### 3.1. Comparison of Velocity Distributions for Submerged and Emergent Vegetation Covers

^{2}) between u/u

_{max}and Ln(y/d

_{50}) or Ln (y/y

_{p}). In this study, the value of R

^{2}≥ 0.98 in the logarithmic zone was considered as the deviation point where the data are deviated from the log law zone. The value of R

^{2}decreases after the selected deviation point towards the water surface.

_{50}for the gravel bed has some uncertainties. In other words, if one uses a plot with constant particle diameter, there is less uncertainty in application of the log law compared to gravel bed streams.

#### 3.2. Comparison of Reynolds Shear Stress for Submerged and Emergent Vegetation

## 4. Discussion

## 5. Conclusions

- In emergent vegetation, the velocity distribution is influenced by a small aspect ratio (W/h < 5) forcing the maximum velocity to move towards the bed. However, in the submerged vegetation, the velocity distribution is less influenced by the aspect ratio, showing the location of maximum velocity far from the bed.
- The log law is valid up to y/h = 0.23 for the flow over submerged vegetation in different aspect ratios. However, for emergent vegetation, the validation zone depends on the distance from the vegetation bank; at small aspect ratio and the central axis of the flume, this law is valid up to y/h = 0.75.
- Reynolds stress (RS) distributions show a convex form for submerged and emergent vegetation covers at different aspect ratios. However, approaching the bank vegetation (emergent case), the power of secondary currents increases, forcing the maximum RS shifts towards the bed.
- For the aspect ratio of W/h = 4 and flow over submerged vegetation, the location of zero shear stress superposes that of maximum velocity. However, in emergent vegetation, such a superposition is not considered. Further, approaching the bank vegetation and shifting the maximum velocity towards the bed, the location of zero shear stress approaches the bed.
- The results of this research show that estimation of key parameters of fluvial projects, velocity and Reynolds stress is influenced by the vegetation arrangements, submerged or emergent. Therefore, a better estimation of these parameters influences drag coefficient and sediment determinations, improving bank stability with reasonable channel design, reducing the cost of project and modifying the input data for hydraulic models.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

d_{50} | Median diameter of sediment particles |

C | Constant of the log law |

D | Distance from the wall |

y_{p} | Plant height (for run 1 and 2) |

h | Water depth above the vegetation (for run 1 and run 2) and water depth over gravel bed (for run 3 and run 4) |

W | Flume width |

ks | Roughness scale (equivalent sand roughness) |

Q | Flow discharge |

u | Mean point velocity |

u_{ave} | Average velocity at a section; |

u_{max} | Maximum velocity |

u’ | Turbulence intensity in longitudinal direction |

w’ | Turbulence intensity in vertical direction |

u* | Shear velocity |

y | Distance from top of gravel or vegetation cover |

Y | Distance from the bed |

κ | von Karman constant |

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**Figure 1.**(

**a**). Experimental set up showing: (1 and 2) Wheat sprout canopy; (3 and 4) Wheat stems on bank. (

**b**). Measured velocity points of experimental set up, at the distance of 12.9, 13.1, 13.3 m from the entrance of the channel.

**Figure 3.**(

**a**) The log-law validation for different conditions for submerged vegetation (run 2). (

**b**,

**c**) The log-law validation for different conditions: (

**b**) for the gravel bed without vegetation in bed and banks in the central axis (run 3); (

**c**) for the emergent vegetation in banks and gravel bed (run 4).

**Figure 5.**Reynolds stress distributions: (

**a**) for emergent vegetation with gravel bed; (

**b**) over submerged vegetation. (y) is normalized by the total flow depth (h).

**Figure 6.**(

**a**) Location of zero Reynolds stress over submerged vegetation cover. (

**b**) Location of maximum point velocity over submerged vegetation cover.

**Figure 7.**Velocity distributions in pool bed by Parvizi et al. [2].

**Figure 8.**Flow over Pool with submerged vegetation by Parvizi et al. [2]: (

**a**) Distribution of Reynolds shear stress over gravel bed and vegetated canopy; (

**b**) Validation of logarithmic law in vegetated pool.

Exp. | Q (m^{3}/s) | h (cm) | W (cm) | U_{avg} (m/s) | W/h | Covered Area |
---|---|---|---|---|---|---|

Run 1 | 0.037 | 11 | 60 | 0.56 | 5.45 | Bed |

Run 2 | 0.055 | 15 | 60 | 0.61 | 4 | Bed |

Run 3 | 0.037 | 11 | 60 | 0.56 | 5.45 | Bank |

Run 4 | 0.055 | 15 | 60 | 0.61 | 4 | Bank |

_{avg}= the flow velocity average for each run, covered area by vegetation in each run.

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**MDPI and ACS Style**

Mofrad, M.R.T.; Afzalimehr, H.; Parvizi, P.; Ahmad, S.
Comparison of Velocity and Reynolds Stress Distributions in a Straight Rectangular Channel with Submerged and Emergent Vegetation. *Water* **2023**, *15*, 2435.
https://doi.org/10.3390/w15132435

**AMA Style**

Mofrad MRT, Afzalimehr H, Parvizi P, Ahmad S.
Comparison of Velocity and Reynolds Stress Distributions in a Straight Rectangular Channel with Submerged and Emergent Vegetation. *Water*. 2023; 15(13):2435.
https://doi.org/10.3390/w15132435

**Chicago/Turabian Style**

Mofrad, Mohammad Reza Tabesh, Hossein Afzalimehr, Parsa Parvizi, and Sajjad Ahmad.
2023. "Comparison of Velocity and Reynolds Stress Distributions in a Straight Rectangular Channel with Submerged and Emergent Vegetation" *Water* 15, no. 13: 2435.
https://doi.org/10.3390/w15132435