# Characteristics of Shallow Flows in a Vegetated Pool—An Experimental Study

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Theory

#### 2.2. Experimental Setup

_{50}) was 10.4 mm. The smooth surface of the channel bed was carefully prepared to eliminate large-scale variation in the bed topography. The artificial vegetation patch with a height of about 2.5 cm was placed over the middle pool section, which was 1.5 m long (Figure 1).

## 3. Results and Discussions

#### 3.1. Shear Velocity Distribution and Logarithmic Law

^{2}values show in Table 2. According to Figure 3, along the CAF (acceleration flow) section, the velocity data collected for the outer layer of the flow at a depth of 1.0 > z/h > 0.2 (till water surface) are above the regression line, implying a dominant adverse pressure gradient (∂p/∂x > 0). However, a favorable pressure gradient (∂p/∂x < 0) is dominant in the CDF (deceleration flow) and middle pool sections of the pool, where the data points collected for the outer layer of flow (1.0 > z/h > 0.2) are below the regression line. Approaching the sidewall, the validity of the logarithmic law for the velocity data near the bed region has also been confirmed. For flow with a relatively low Reynolds number, the boundary layer tends to be a laminar boundary layer. As the Reynolds number increases, the boundary layer becomes unstable with small disturbances. Further growth of these disturbances results in the transition to a turbulent boundary layer. Most practical flows involve high Reynolds numbers and turbulent boundary layers. Because of the three-dimensional interchanges in momentum, a turbulent boundary layer is thicker and has a larger wall velocity gradient than that of a laminar layer with the same Reynolds number. The increased momentum near the wall allows a turbulent boundary layer to withstand a larger unfavorable pressure gradient than a laminar layer without separating, but results in higher wall shear stress and drag.

#### 3.2. Velocity Distribution along the Pool

_{max}) of each velocity profile. Also, the depth related to a velocity point measurement (z) became dimensionless depth by dividing it to the flow depth (h).

#### 3.3. Quadrant Analysis of Bursting Events

#### 3.4. Distribution of Shear Stress and Longitudinal Turbulence Intensities

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 2.**Distributions of shear velocity determined using two methods: (

**A**) Clauser’s method; (

**B**) the boundary layer method.

**Figure 4.**Distributions of stream-wise velocity profiles. Note: green line: central axis over vegetated bed with w/h = 2; black line: central axis over sandy bed with w/h = 2; gray line: central axis over vegetated bed with w/h= 2.7; blue line: second axis over vegetated bed with w/h = 2.

**Figure 5.**Distributions of velocity profiles. Note: green line: central axis over vegetated bed with w/h = 2; black line: central axis over sandy bed with w/h = 2; gray line: central axis over vegetated bed with w/h = 2.7; blue line: second axis over vegetated bed with w/h = 2.

**Figure 7.**Distribution of Reynolds shear stress. Note: green line: central axis over vegetated bed with w/h = 2; black line: central axis over sandy bed with w/h = 2; gray line: central axis over vegetated bed with w/h = 2.7; blue line: second axis over vegetated bed with w/h = 2.

**Figure 8.**Distribution of stream-wise RMS of turbulence intensity. Note: green line: central axis over vegetated bed with w/h = 2; black line: central axis over sandy bed with w/h = 2; gray line: central axis over vegetated bed with w/h = 2.7; blue line: second axis over vegetated bed with w/h = 2.

Q (L/s) | H (m) | W (m) | U_{avg} (cm/s) | W/H | Re × 10^{4} | Fr |
---|---|---|---|---|---|---|

10 | 0.20 | 0.4 | 12.5 | 2.0 | 2.5 | 0.09 |

10 | 0.15 | 0.4 | 16.7 | 2.7 | 2.5 | 0.13 |

x | Equation | ${\mathbf{R}}^{2}$ | ${\mathbf{U}}_{*}$ | f | |
---|---|---|---|---|---|

Central Axis | CDF Section | $\mathrm{u}/{\mathrm{u}}_{*}=0.0116\mathrm{ln}(\mathrm{z}/{\mathrm{k}}_{\mathrm{s}})+0.0321$ | 0.98 | 0.00464 | 0.011 |

Middle Sect. | $\text{}\mathrm{u}/{\mathrm{u}}_{*}=0.02\mathrm{ln}(\mathrm{z}/{\mathrm{k}}_{\mathrm{s}})+0.0538$ | 0.90 | 0.008 | 0.032 | |

CAF Section | $\mathrm{u}/{\mathrm{u}}_{*}=0.0274\mathrm{ln}(\mathrm{z}/{\mathrm{k}}_{\mathrm{s}})+0.0644$ | 0.96 | 0.0108 | 0.059 | |

Second Axis | CDF Section | $\mathrm{u}/{\mathrm{u}}_{*}=0.0106\mathrm{ln}(\mathrm{z}/{\mathrm{k}}_{\mathrm{s}})+0.0204$ | 0.89 | 0.0042 | 0.009 |

Middle Sect. | $\mathrm{u}/{\mathrm{u}}_{*}=0.0151\mathrm{ln}(\mathrm{z}/{\mathrm{k}}_{\mathrm{s}})+0.0333$ | 0.97 | 0.006 | 0.018 | |

CAF Section | $\mathrm{u}/{\mathrm{u}}_{*}=0.0268\mathrm{ln}(\mathrm{z}/{\mathrm{k}}_{\mathrm{s}})+0.054$ | 0.93 | 0.0105 | 0.058 |

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**MDPI and ACS Style**

Parvizi, P.; Afzalimehr, H.; Sui, J.; Raeisifar, H.R.; Eftekhari, A.R.
Characteristics of Shallow Flows in a Vegetated Pool—An Experimental Study. *Water* **2023**, *15*, 205.
https://doi.org/10.3390/w15010205

**AMA Style**

Parvizi P, Afzalimehr H, Sui J, Raeisifar HR, Eftekhari AR.
Characteristics of Shallow Flows in a Vegetated Pool—An Experimental Study. *Water*. 2023; 15(1):205.
https://doi.org/10.3390/w15010205

**Chicago/Turabian Style**

Parvizi, Parsa, Hossein Afzalimehr, Jueyi Sui, Hamid Reza Raeisifar, and Ali Reza Eftekhari.
2023. "Characteristics of Shallow Flows in a Vegetated Pool—An Experimental Study" *Water* 15, no. 1: 205.
https://doi.org/10.3390/w15010205