# Interaction of Irregular Distribution of Submerged Rigid Vegetation and Flow within a Straight Pool

^{1}

^{2}

^{*}

## Abstract

**:**

_{50}= 23.3 mm. Plastic cylinders planted in an irregular pattern in the channel beds were used to model rigid submerged vegetation. The velocity components were recorded by using an ADV at 200 Hz. In this study, the distributions of velocity, Reynolds stress, and TKE were investigated for flows in the presence of submerged rigid vegetation in channel beds with various area densities of vegetation. Results show that the shape of Reynolds stress distribution depends on the entrance and exit slopes of the pool, as well as the irregular distribution pattern of vegetated elements. Inside the pool with the presence of submerged vegetation in the channel bed, the maximum TKE appears above the bed surface with a larger distance depending on the area density of vegetation in the channel bed. However, the momentum exchange and turbulent energy are likely influenced by the secondary circulation of the flows associated with the irregular distribution of vegetated elements in the channel bed. Results of the quadrant analysis show that the momentum between the flow, bedform, and vegetated elements is mostly transferred by sweep and ejection events. The outward event tends to grow toward the water surface, reaching the highest amount near the water surface. At the pool entrance section where the flow is decelerating, the ejection event is dominant near the bed while the sweep event is strong near the water surface. With the decrease in the vegetation density in the pool bed, both the ejection and outward events become dominant.

## 1. Introduction

## 2. Materials and Methods

#### 2.1. The Field Study

^{3}, the average flow velocity U = 1.0 m/s, the Reynolds number $Re=UH/{\vartheta}_{m}=424,620$, and the Froud number $Fr=U/{\left(gH\right)}^{0.5}=0.5$. The values of $Re$ and $Fr$ indicate a fully turbulent and sub-critical flow at the pool entrance.

#### 2.2. Experimental Study

^{−3}, 4.7 × 10

^{−3}, and 7 × 10

^{−3}, (Figure 3e–g), where $\varnothing ={A}_{r}\pi {D}^{2}/4$ is defined as the area density of vegetation and ${A}_{r}=N/\left({L}_{veg}\times {B}_{veg}\right)$, $N$ is the total number of vegetation elements, and ${L}_{veg}=2.4\mathrm{m}$ and ${B}_{veg}=0.6\mathrm{m}$ are the length and width of the vegetated area along with the streamwise and spanwise directions, respectively. Additionally, the measurements were conducted in the bare pool (without vegetation) to compare results with the presence of vegetation to those without vegetation in the pool.

_{50}= 23.3 mm, d-i

_{6}= 14 mm, and d

_{84}= 40 mm (Figure 2). However, since the geometric standard deviation (${\sigma}_{g}={\left({d}_{84}/{d}_{16}\right)}^{0.5}$) = 1.69 > 1.4, the gravel bed materials are not uniformly graded in bed flume. As described in Section 2.1 (Figure 3d), the entrance and exit slopes were 7.4 and 4 degrees, respectively.

## 3. Theory

#### 3.1. Statistical Description of Velocity

_{0}), ${u}^{*}$ is the shear velocity, and $\kappa $ is the Von Karman coefficient ($\kappa =0.4$ in uniform flow). Additionally, ${z}_{0}$was $0.2{d}_{50}$ in this study. The inner layer has been found to extend to a relative depth of $z/H=0.2$ in uniform and nonuniform flow [49], but the upper layer is variable [50]. Bed shear stress is a critical parameter for the prediction of sediment transport. Although sediment transport is not within the aim of this paper, it is crucial to qualify the spatial variability of shear stress as a means of assessing the effect of the redistribution of flow and turbulence on the channel boundary. Typical formulae to estimate shear stress from velocity measurements use either the gradient of mean velocity near the bed or some measure of turbulence such as the Reynolds stress or turbulent kinetic energy. Shear velocity is the most fundamental scale with which to normalize mean velocity. However, since its measurement is not trivial, several methods have been proposed to estimate this parameter [51]. Following previous studies of non-uniform flows [52,53] the wake parameter ($\mathsf{\Pi}$) was determined at each measurement location from a fit of the velocity profile to the wake law [54] following the relation:

#### 3.2. Shear Velocity (Friction Velocity)

## 4. Results and Discussion

#### 4.1. Streamwise Velocity and Shear Velocity along the Channel Centerline

#### 4.2. The Reynolds Stress along the Channel Centerline

#### 4.3. Turbulence Kinetic Energy

#### 4.4. Quadrant Analysis

## 5. Conclusions

- The variations in velocity along the pool section with the submerged vegetation in the channel bed are different from that in the bare pool. In the entrance section of the pool where the flow is decelerating, a regular velocity distribution pattern is observed without any reversal flow even though the pressure gradient is unfavorable. However, in the exit section of the pool where the flow is accelerating and the pressure gradient is favorable, a reverse flow near the bed is observed. This is due to the appearance of a positive pressure gradient developed in this section. This difference in velocity pattern shows the influence of the submerged vegetation on the velocity distribution.
- A suitable method for estimating the shear velocity for the flow with the presence of submerged vegetation in the channel bed is the TKE method (${u}^{*}{}_{TKE})$, since all the fluctuation components of turbulence have been used in this method. In fact, the strong lateral component of turbulence fluctuation ${v}^{\prime 2}$ does not appear in the Reynolds stress method. In addition, when the area density of vegetation decreases, the location of the maximum ${u}^{*}{}_{TKE}$ changes along with the pool.
- The shape and the location of the maximum value of the Reynolds stress distribution depend on the slopes of the entrance and the exit section of the pool. In addition, the distribution pattern of vegetated elements in the channel bed also affects the shape and the location of the maximum value of the Reynolds stress distribution. In general, the Reynolds stress distribution in the pool with the presence of vegetation in the bed is irregular and is considerably different from that in the bare pool.
- For all investigated Cases within the pool, the maximum Reynolds stress and TKE occur at a larger distance above the bed surface, depending on the area density of vegetation. The irregular distributions of Reynolds stress and TKE result from the secondary circulations associated with the irregular distribution pattern of vegetated elements in the channel bed.
- Results of the quadrant analysis show that the momentum between flow, bedform and vegetated elements are mostly transferred by sweep and ejection events. Toward the water surface, the outward event becomes the dominant event. At the pool entrance where the flow is decelerating, the ejection event is dominant near the bed while the sweep event is strong near the water surface. In the presence of an irregular distribution of submerged vegetated elements in the pool-bed, ejections become dominant (for Case I, II, and III) and then the outward event becomes stronger as the area density of vegetation decreases (for Cases IV).

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 3.**Laboratory set up. (

**a**) The vegetation elements and prefabricated wooden templates, (

**b**) instantaneous velocity measurements using an ADV, (

**c**) the tool for topographical bed survey, (

**d**) side view of the riffle-pool-riffle bedform, (

**e**) the irregular array pattern of vegetation elements with $\varnothing =7\times {10}^{-3}$, (

**f**) $\varnothing =4.7\times {10}^{-3}$, (

**g**) $\varnothing =2.3\times {10}^{-3}$, and (

**h**) bed topographic contours. Note: the green-color circles are vegetated elements and red-color rectangles represent the location of the velocity measurements.

**Figure 4.**Profiles of streamwise velocity along the channel centerline for all Cases. (

**a**) The upstream section of the pool ($\mathrm{X}/\mathsf{\lambda}=0.017$, (

**b-i**,

**b-j**) the pool entrance ($\mathrm{X}/\mathsf{\lambda}=0.21$), (

**c-i**,

**c-j**) the middle of the pool ($\mathrm{X}/\mathsf{\lambda}=0.5$), (

**d-i**,

**d-j**) the pool exit ($\mathrm{X}/\mathsf{\lambda}=0.78$), and (

**e-i**,

**e-j**) the downstream section of the pool ($\mathrm{X}/\mathsf{\lambda}=0.98$).

**Figure 5.**(

**a**) Shear velocity according to the law of wall (${u}^{*}{}_{Lw}$), (

**b**) shear velocity according to the Reynolds stress (${u}^{*}{}_{RS}$ ), (

**c**) shear velocity according to the turbulent kinetic energy (${u}^{*}{}_{TKE}$ ), and (

**d**) Coles wake parameter ($\mathsf{\Pi}$) along the channel centerline from upstream to downstream of the bedform.

**Figure 6.**Profiles of the Reynolds stress $-\overline{{u}^{\prime}{w}^{\prime}}$ along the channel centerline for all Cases. (

**a**) The upstream section of the pool ($\mathrm{X}/\mathsf{\lambda}=0.017$), (

**b-i**,

**b-j**) the pool entrance ($\mathrm{X}/\mathsf{\lambda}=0.21$), (

**c-i**,

**c-j**) the middle of the pool ($\mathrm{X}/\mathsf{\lambda}=0.5$), (

**d-i**,

**d-j**) the pool exit ($\mathrm{X}/\mathsf{\lambda}=0.78$), and (

**e-i**,

**e-j**) the downstream section of the pool ($\mathrm{X}/\mathsf{\lambda}=0.98$).

**Figure 7.**Profiles of the TKE values along the channel centerline for all Cases. (

**a**) The upstream section of the pool ($\mathrm{X}/\mathsf{\lambda}=0.017$), (

**b-i**,

**b-j**) the pool entrance ($\mathrm{X}/\mathsf{\lambda}=0.21$), (

**c-i**,

**c-j**) the middle of the pool ($\mathrm{X}/\mathsf{\lambda}=0.5$), (

**d-i**,

**d-j**) the pool exit ($\mathrm{X}/\mathsf{\lambda}=0.78$), and (

**e-i**,

**e-j**) the downstream section of the pool ($\mathrm{X}/\mathsf{\lambda}=0.98$).

**Figure 8.**Quadrant analysis using the bursting cycle detection method at (

**a**) the upstream section of the pool ($\mathrm{X}/\mathsf{\lambda}=0.017$), (

**b**) the pool entrance ($\mathrm{X}/\mathsf{\lambda}=0.21$), (

**c**) the middle of the pool ($\mathrm{X}/\mathsf{\lambda}=0.5$), (

**d**) the pool exit ($\mathrm{X}/\mathsf{\lambda}=0.78$), and (

**e**) the downstream section of the pool ($\mathrm{X}/\mathsf{\lambda}=0.98$) for all Cases.

Case | $\mathbf{Vegetation}\mathbf{Density}\varnothing $ | Q (L/s) | Bedform Amplitude ∆(m) | Ratio ∆/λ |
---|---|---|---|---|

I | $7\times {10}^{-3}$ | 31.7 ± 0.1 | 0.1428 | 0.051 |

II | $4.7\times {10}^{-3}$ | 31.7 ± 0.1 | 0.1428 | 0.051 |

III | $2.3\times {10}^{-3}$ | 31.7 ± 0.1 | 0.1428 | 0.051 |

IV | bare pool | 31.7 ± 0.1 | 0.1428 | 0.051 |

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**MDPI and ACS Style**

Nosrati, K.; Afzalimehr, H.; Sui, J.
Interaction of Irregular Distribution of Submerged Rigid Vegetation and Flow within a Straight Pool. *Water* **2022**, *14*, 2036.
https://doi.org/10.3390/w14132036

**AMA Style**

Nosrati K, Afzalimehr H, Sui J.
Interaction of Irregular Distribution of Submerged Rigid Vegetation and Flow within a Straight Pool. *Water*. 2022; 14(13):2036.
https://doi.org/10.3390/w14132036

**Chicago/Turabian Style**

Nosrati, Kourosh, Hossein Afzalimehr, and Jueyi Sui.
2022. "Interaction of Irregular Distribution of Submerged Rigid Vegetation and Flow within a Straight Pool" *Water* 14, no. 13: 2036.
https://doi.org/10.3390/w14132036