# Impact of Vegetation Density on the Wake Structure

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

_{0}, could be evaluated. Figure 1 illustrates the pattern of the vegetation community and the arrangement of the measuring points.

_{0}denote the flow depth and the average velocity in a cross-section; D denote the diameter of patch. In this experiment, repeated trials for each test case were conducted.

## 3. Results and Discussion

#### 3.1. Longitudinal Distribution of the Turbulent Kinetic Energy with Different Vegetation Density

_{0}is the average flow velocity, which is measured at a half depth of the upstream section (X/D = −4). Figure 2 presents the longitudinal distribution of dimensionless turbulent energy along the path.

_{d}= u

_{p}× d/$\nu $, and a function of the flow blockage. Notably, u

_{p}and $\nu $ denote the average velocity within the patch and the kinematic viscosity coefficient, respectively. Furthermore, as Re

_{d}increases, the peak also increases [13].

^{−1}and the range between the first peak and trough was longer. Here, the range is the steady wake region, which is the distance between the patch and the formation point of the vortex street [5]. In addition, the rebounding momentum from the line bottom correlated with the denseness and there existed a minimum turbulence level between the two peaks which was lower than the turbulence level of the undisturbed upstream flow [13].

^{−1}), the subsequent peak appeared near 15 D. As the density changed, the position of the second peak increased gradually and the peak increased. The analysis presented above demonstrates that the higher the vegetation density, the earlier the appearance position of the Von Karman vortex street and the greater the turbulence peak caused by the Von Karman vortex street, suggesting that the strength of the Von Karman vortex street was increasing.

_{max1}and TKE

_{max2}) was defined as L

_{TKE}. We analyzed the correlation between L

_{TKE}and the vegetation group density, a. Figure 3 shows that the density, a, of the vegetation group increased, but L

_{TKE}gradually decreased. When a = 0.5 cm

^{−1}, the length of the L

_{TKE}tended to be stable. In addition, the position of the peak was basically stable at x = 9 D, suggesting the formation of the Von Karman vortex. The position of the street initially moved forward with the increase of the density of the vegetation group. When a reached a certain level, the position of the Von Karman vortex street was no longer affected by a. Figure 3 and Figure 4 show that the position where the valley TKE

_{max1}appears coincides with the positional trend of the peak TKE

_{max2}. In particular, it gradually moved forward and finally became stable. Furthermore, Figure 4 shows that the speed at which TKE

_{max2}advanced was faster than TKE

_{max1}; thus, the slope between the valley and the second peak TKE

_{max2}becomes increasingly steeper. Moreover, when the vortex street was delayed downstream, it also degraded more slowly.

_{max1}and TKE

_{max2}) and the vegetation group density a. The first turbulent peak (TKE

_{max1}) after the vegetation group was distributed in a wave manner with the increase in the density, a, of the vegetation group. Figure 4 suggests that the fluctuation range of TKE

_{max1}was short, whereas the second turbulent peak (TKE

_{max2}) presented a large fluctuation range. Furthermore, TKE

_{max1}increased as the density a increased. The growth rate of TKE

_{max2}decreased first and then increased. When a = 0.8 cm

^{−1}, the turbulent kinetic energy reached its peak value.

_{max1}was higher than that of TKE

_{max2}in the low-density vegetation group and the turbulence intensity after the vegetation group predominated. As the density of vegetation groups increased, the role of the Von Karman vortex street became pivotal, which led to a rapid increase in the peak value TKE

_{max2}. Figure 4 suggests that when a ≈ 0.38 cm

^{−1}, two values of TKE were equal. With the denser vegetation, the turbulence effect generated by the Von Karman vortex street took the main advantage, making the value of TKE

_{max2}much higher than that of TKE

_{max1}.

_{max2}and TKE

_{max1}had opposing tendencies with increasing density (Figure 4), the following transition occurred. For low densities (a ≤ 0.3 cm

^{−1}), the turbulence reached the highest value immediately downstream of the patch; however, for a denser patch, the turbulence intensity was highest at some distance far from the patch [13,33].

#### 3.2. Lateral Distribution of Stream-Wise TKE with Different Vegetation Densities

^{−1}). We observed a positive correlation between the maximum turbulent kinetic energy of the patch and the density. Compared with the brink of the patch, the turbulent kinetic energy was marginally smaller at the centerline behind the patch. Furthermore, beyond the range from centerline to Y/D = 1.2, the value of TKE was stable. As the measured section became farther away from the patch, the difference in TKE between low and high density patches increased.

#### 3.3. Vertical Distribution of the Turbulent Intensity with Altered Plant Patch Density

^{−1}, their dense structure led to backwater, which affected the turbulent energy in the range of H/H

_{0}= 0.2–0.3; the turbulent energy decreased. Hence, for plants with relatively high densities, the law of change describes an initial increase, then a decrease, and then a rise as the water depth increases.

_{0}= 0.25. In the wake region, the peak of $\sigma /{U}_{0}$ occurred far from the channel bed and irregular variation of the peak value of $\sigma /{U}_{0}$ was attributed to detached eddies from upstream cylinders [36].

#### 3.4. Reynolds Stress Distribution of Different Vegetation Density

^{−1}. Figure 8a shows the Reynolds shear stress, defined as ${T}_{uv}=-\overline{{u}^{\prime}{v}^{\prime}}$. Figure 8a indicates that the Reynold shear stress exhibits significant fluctuations. The sign of the shear stress suggests the direction of the momentum flux. In a Cartesian coordinate system, negative values depict momentum flux toward the bed [15]. We observed a maximum in the shear stress distribution of H/H

_{0}= 0.25. The difference in the Reynolds shear stresses increased gradually at X/D = −1 and X/D = 1 from line Y/D = −1.17 to Y/D = 0.58. The difference reached the maximum value on the centerline, behind the plant group. Furthermore, the difference gradually declined toward the left bank. Perhaps, the scatter in the profile of Y/D = ±0.58 is attributable to irregular detachment of wake vortices.

_{0}, varying from 0.2 to 0.3, which could be the most intense place for the bleed flow and the recirculated flow, suggesting that the bed influence on the vertical distribution of the Reynolds stress is limited.

_{0}> 0.3), the distribution of the shear stress at the upper and lower parts of the cross-section is comparable and the shear stress is uniformly distributed. At the range of H/H

_{0}= 0–0.3, starting from the line adjacent to the right bank of the water tank, the upstream shear stress is higher than the one from the downstream. Meanwhile, as it approaches the centerline, the downstream shear stress slowly increases because of the impact of the plant group and attains the maximum value of Y/D = 0.

_{uw}is related to the water depth change at X/D = ±1 and Y/D = 0, demonstrating that u

_{0}w

_{0}is positive at X/D = 1. Hence, momentum transport is upward into the water column. Furthermore, we found extremum Reynolds stress values behind the patch with low densities (a < 0.3 cm

^{−1}) at H/H

_{0}= 0.25, while the highest values of u

_{0}w

_{0}always took place near the bed.

_{0}= 0.25, the difference between the upper and lower shear stresses of above and below the boundary line is small; this difference below the boundary line becomes larger as the water depth increases or decreases. From another perspective, the denser group offers the vegetation group more control over the back-shear stress, also implying that the dense vegetation group exerts more impact on the upstream flow.

## 4. Impact of Turbulence with Altered Vegetation Densities on the Sedimentation

_{1}and $\rho $ are real constants (c

_{1}≈ 0.2) and the water density respectively [37]. Although it is not an accurate method to derive absolute values of ${\tau}_{0}$ from the ADV data, a strong correlation exists between the near-bed turbulence and bed shear stress. In addition, research has highlighted that the turbulence might dislodge individual sediment particles and could affect the net deposition [38,39,40,41,42]. Hence, a study was proposed to compare spatial patterns of the near-bed Reynolds stress and the turbulence intensity in the model [15].

_{TKE}than a high-density patch. However, increasing turbulence and associated elevated vertical diffusivity might enhance resuspension and facilitate sediment transport. Furthermore, the deposition is depressed beyond this region because of the enhanced TKE associated with the Von Karman vortex street [13,19,30]; however, it can dominate the situation through the vortex street.

## 5. Conclusions

_{0}= 0.25 as the boundary, as the shear stress nears the bed surface, the turbulence intensity increases. This study shows that dense patched exert a significant impact on the rear turbulence. Meanwhile, distributions of the Reynolds shears stress are considered for further study of various density vegetation patches. The rear deposition is symmetrically distributed along the centerline, similar to the turbulent energy distribution of the transverse section. Finally, this study deduces that a dense plant group could weaken shear forces from the upstream.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**The schematic pattern of the vegetation community arrangement. The patch model is arranged in the center of the flume. (

**a**) Vertical view (Detail drawing) (

**b**) Front view (

**c**) Vertical view.

**Figure 3.**The distribution of L

_{TKE}and the vegetation group density, a, on the stream-wise direction.

**Figure 5.**The lateral distribution of the dimensionless TKE. (

**a**) X/D = −3 (

**b**) X/D = −1.5 (

**c**) X/D = 0.8 (

**d**) X/D = 1.2 (

**e**) X/D = 1.5 (

**f**) X/D = 2 (

**g**) X/D = 2.5 (

**h**) X/D = 3 (

**i**) X/D = 4.

**Figure 8.**Comparison of lateral stream-wise shear stress distributions on sections at X/D = ±1. (

**a**) T

_{uw}, (

**b**) T

_{uv}, and (

**c**) T

_{vw}.

**Figure 10.**Longitudinal distributions of the main flow velocity and turbulent kinetic energy at the centerline of the vegetation community for different densities: (

**a**) a = 0.3 cm

^{−1}; (

**b**) a = 0.5 cm

^{−1}; and (

**c**) a = 0.8 cm

^{−1}.

**Figure 11.**Variations of the bed topography with different vegetation densities: (

**a**) a = 0.3 cm

^{−1}; (

**b**) a = 0.5 cm

^{−1}; and (

**c**) a = 0.8 cm

^{−1}.

Condition | a (cm^{−1}) | n (cm^{−2}) |
---|---|---|

A1 | 0 | 0 |

A2 | 0.2 | 0.5 |

A3 | 0.25 | 0.625 |

A4 | 0.3 | 0.75 |

A5 | 0.4 | 1 |

A6 | 0.5 | 1.25 |

A7 | 0.6 | 1.5 |

A8 | 0.7 | 1.75 |

A9 | 0.8 | 2 |

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**MDPI and ACS Style**

Yu, Z.; Wang, D.; Liu, X. Impact of Vegetation Density on the Wake Structure. *Water* **2019**, *11*, 1266.
https://doi.org/10.3390/w11061266

**AMA Style**

Yu Z, Wang D, Liu X. Impact of Vegetation Density on the Wake Structure. *Water*. 2019; 11(6):1266.
https://doi.org/10.3390/w11061266

**Chicago/Turabian Style**

Yu, Zijian, Dan Wang, and Xingnian Liu. 2019. "Impact of Vegetation Density on the Wake Structure" *Water* 11, no. 6: 1266.
https://doi.org/10.3390/w11061266