# Effects of Submerged Vegetation Density on Turbulent Flow Characteristics in an Open Channel

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

_{S}and change the point where G

_{S}is vertically maximum upwards to the vegetation top.

## 1. Introduction

_{NB}, respectively. Here, λ

_{NB}is the critical density which indicates the change from the free-shear flow to the secondary boundary-shear flow. The value of λ

_{NB}has not been determined yet, but according to the comparison and summary of many investigations, λ

_{NB}might lie in the range between 0.512 and 1.55 [6].

_{NB}), especially the latter one in the vegetated channel. Flow at 0.04 < λ < 0.1 and λ > λ

_{NB}(the secondary boundary-shear flow may appear) have been rarely analyzed. In the present investigation, flow characteristics have been measured and analyzed as λ varies within a large range. Based on vertical distributions of turbulent statistics (velocity, shear stress, skewness coefficients), turbulence kinetic generation rate and turbulence spectra, different flow types have been verified. Furthermore, flow characteristics and velocity distribution laws at 0.04 < λ < 0.1 and λ > λ

_{NB}are discussed specifically.

## 2. Experimental Setup and Measurement

_{v}= 6 cm) aluminum cylinder with diameter d

_{v}= 0.6 cm. In order to place the cylinders in the channel bed, an artificial bottom was constructed with an 8-m-long plate of 0.6-cm-holed pegboard. The streamwise and spanwise spacings between neighboring cylinders were defined as S

_{x}and S

_{y}respectively. The vegetation was linearly arranged at the mid 8 m length of the flume, and λ was calculated by λ = (d

_{v}h

_{v})/(S

_{x}S

_{y}).

_{v}and the mean bulk velocity U

_{m}= Q/(BH) remain constant in the experiment. The flow with Sub = 3 and U

_{m}= 30 cm/s in this study represented the high-speed shallow flow. The experimental λ was selected from a wide range to create different flow conditions. According to [5], the bed-shear flow and free-shear flow may occur in Cases I & II (λ = 0, 0.0056) and Case V (λ = 0.36), respectively (Table 1).

_{x}× S

_{y}It is, thus, believed the spatial averages of the experimental data at these 9 locations can represent the overall flow. A comparison between the averaged velocity at the 9 locations and the averaged velocity at points 1# and 2# was conducted to verify that the measurements for points 1# & 2# are indeed representative.

## 3. Results

#### 3.1. Spatial Variation of the Velocity and Reynolds Stress Profiles

_{a#~i#}and $-{\overline{uw}}_{a\#~i\#}$ represent the overall space-averaged flow characteristics in the experiment.

_{1#}> U

_{a#~d#}, U

_{2#}< U

_{e#~i#}and U

_{1#}< U

_{2#}are shown in Figure 3a. However, $-{\overline{uw}}_{1\#}\approx -{\overline{uw}}_{a\#~d\#}$, $-{\overline{uw}}_{2\#}\approx -{\overline{uw}}_{e\#~i\#}$ and $-{\overline{uw}}_{1\#}<-{\overline{uw}}_{2\#}$ are shown in Figure 4a.

_{1#~2#}≈ U

_{a#~i#}and $-{\overline{uw}}_{1\#~2\#}\approx -{\overline{uw}}_{a\#~i\#}$, respectively, throughout the depth. Hence, it is sufficiently accurate to describe the overall flow dynamics by the averaged velocity of points 1# and 2#. In this study, therefore, we analyze the flow characteristics by the averaged values of points 1# and 2#. The subscript is omitted in the rest sections of this article.

#### 3.2. Turbulent Statistics

#### 3.2.1. Velocity

^{−1}in this region. For Case V, U increases rapidly near the canopy top (55 ≤ z ≤ 65 mm) and dU/dz = 5 s

^{−1}there (Figure 5b & Table 2), which indicates intensive shear exists in this region under this flow condition.

^{−1}near the channel bed and 2 to 3 s

^{−1}around the vegetation top, which are between the ones for Cases I & II (bed-shear flow) and the one for Case V (free-shear flow) (Table 2).

#### 3.2.2. Shear Stress

_{v}(Figure 6b) and the free-shear flow happens because of flow discontinuity at the canopy top [10].

#### 3.2.3. Skewness Coefficients

_{u}and Sk

_{w}are the skewness coefficients of u and w, respectively. Bursting phenomenon manifests in four different manners, i.e., outward interaction (Sk

_{u}> 0, Sk

_{w}> 0), ejection (Sk

_{u}< 0, Sk

_{w}> 0), inward interaction (Sk

_{u}< 0, Sk

_{w}< 0) and sweep (Sk

_{u}> 0, Sk

_{w}< 0) [8]. The absolute values of Sk

_{u}and Sk

_{w}reflect the intensity degree of the bursting actions [13].

_{u}and Sk

_{w}profiles above canopy (Figure 7f) are similar to those throughout depth in the bed-shear flow. Meanwhile, the ejection action is vertically fiercest near the free surface (Figure 7f), indicating that the sidewall effect disappears in Case VI.

_{w}profiles are similar to the one for the free-shear flow; however, Sk

_{u}attains its vertical maximum at the bottom, which is in line with that for the bed-shear flow.

#### 3.3. Turbulence Kinetic Energy Generation Rate

_{S}, ${G}_{S}=-\overline{uw}\frac{\partial U}{\partial z}$, represents the turbulent energy that is drained from the mean flow. We compute G

_{S}by the measured data and plot G

_{S}profiles corresponding to different vegetation densities in Figure 8.

_{S}decreases with z and its vertical maximum appears at the channel bottom. However, for Case II (the bed-shear flow with sparse vegetation), G

_{S}attains its peak both at the flume bottom and at a certain height above the bed (z = 31 mm). Meanwhile, G

_{S}in Case II is larger than that in Case I.

_{S}is slightly below the vegetation top (Figure 8b). G

_{S}within canopy decreases towards the bed but increases suddenly on the bed (see the partially enlarged figure in Figure 8b). The near bed G

_{S}values approximate the ones in Cases I & II.

_{S}is increasing continuously from Cases I & II, Case III & IV, Case V to Case VI (Figure 8), indicating that the change of the turbulent flow type, which is induced by an increase of λ, would intensify the flow turbulence.

#### 3.4. Turbulence Spectra

_{S}among different cases (Figure 8). The intermediate frequency in this study except z = 51 mm in Case VI ranges from 0.4 to 4 Hz where the −5/3 power law is satisfied, which is characteristic of the systematic cascade of turbulence energy within the inertial subrange (ISR).

#### 3.5. Distribution Law of the Velocity Profiles

_{c1}where the U profile deviates from the logarithmic law toward the bed. Figure 10a shows that the inertial layer starts from the channel bed (i.e., h

_{c1}= 0), when there is no-vegetation (Case I, the red line); while it locates above the bed (i.e., h

_{c1}> 0) in case of a sparsely vegetated condition (Case II, the black line). For the roughness layer (0 < z < h

_{c1}) below in Case II, the exponential function [17] has been adopted to fit the measured U data, which leads to the coefficients of determination R

^{2}= 0.9229.

_{max}and the region from z = Z

_{max}to the free surface as the velocity dip layer, respectively. The U profile in the velocity dip layer could be described by a power law, with R

^{2}= 0.9015 for Case II (Figure 10a).

_{p}), the intermediate free-shear layer (h

_{p}< z< h

_{o}) and the surface layer (h

_{o}< z < H) [9]. h

_{p}and h

_{o}are the boundaries of the free-shear layer that could be estimated by the displacement height and the turbulent kinetic energy balance, respectively [19,20]. Experimental U data in the free-shear layer and the surface layer were fitted by the hyperbolic tangent function with R

^{2}= 0.9986 and logarithmic function with R

^{2}= 0.986 (see the blue dash line in Figure 10b), respectively. The U data in the lower canopy layer was compared with the power, exponential and logarithmic functions, of previous studies [17,18,21], separately. An exponential distribution law is satisfied in this region with R

^{2}= 0.9328 (see Figure 10b).

^{2}= 0.9987 (Case III) and 0.9985 (Case IV) (hyperbolic tangent distribution law in the free-shear layer), and R

^{2}= 0.8372 (Case III) and 0.8993 (Case IV) (exponential law in the lower canopy layer) (see the blue lines in Figure 11a,b). We find that U profiles throughout the region above canopy could be described by the hyperbolic tangent law. Therefore, one could assume that the free-shear layer is unconfined and the surface layer “disappears” in these cases.

^{2}= 0.9811 (Case III) and 0.997 (Case IV) (logarithmic law in the inertial layer) and 0.9247 (Case III) and 0.8213 (Case IV) (exponential law in the roughness layer) (see the red lines in Figure 11a,b). We find that the velocity dip layer disappears in this condition, since U profile near the water surface could also be described approximately by the logarithmic law.

_{c2}< z < H in Figure 11c) fits well with logarithmic function (R

^{2}= 0.9947) (Figure 11c). The dense stems did not allow access of the ADV probes hence U profile in the zone where z < 0.7h

_{v}could not be presented in this case. Nezu & Sanjou [9] have shown that U is small there in this condition. Therefore, only the U profile from z = 0.7h

_{v}to z = h

_{c2}was considered. Results of the Least Square Fitting by the exponential function seems to be fine with R

^{2}= 0.9641.

## 4. Discussion

_{NB}, with the bed-shear flow and free-shear flow being laid out as the backdrop. Three-dimensional velocities were collected using ADV devices, and turbulent statistics (velocity, shear stress, skewness coefficients), turbulence kinetic energy generation rate, turbulence spectra and the velocity distribution laws were analyzed in the research.

#### 4.1. Horizontal Heterogeneity in the Flow Field

#### 4.2. Flow at 0.04 < λ < 0.1

_{S}profile attains its vertical maximum both near the bed and at the canopy top; (2) the maximum $-\overline{uw}$ appears between the one for the bed-shear flow and the one for the free-shear flow; (3) Sk

_{w}profile is similar to the one for the free-shear flow; however, Sk

_{u}attains its vertical maximum at the bottom, which is in line with that for the bed-shear flow and (4) some slight humps are observed and the F(f) tends to decrease with f within the low-frequency range. Experimental U data could be fitted to comply with either the free-shear flow feature or the bed-shear flow feature. Since G

_{S}at the bed surface is considerably smaller than the one near vegetation top, we conclude that the vegetation drag plays a dominant role to turbulent motion.

#### 4.3. The Secondary Boundary-Shear Flow

_{S}are vertically maximum near canopy top; (3) the Sk

_{u}and Sk

_{w}profiles above canopy are similar to those throughout depth in the bed-shear flow, except that the sidewall effect disappears in the secondary boundary-shear flow; and (4) the spectral curve fluctuates intensely within the low-frequency range and spectral densities of low-frequency eddies are small within canopy.

_{c2}) nearly coincides with the point where bursting phenomenon changes, and the portion of the roughness layer above canopy occupies about 10% of the region from vegetation top to the free surface in Case VI (i.e., h

_{c2}− h

_{v}≈ 0.1(H – h

_{v})). These two points are similar to features of the bed-shear flow, since the vegetation top acts as a new boundary in this extremely dense vegetation condition. However, the secondary boundary-shear flow is significantly fiercer than the bed-shear flow, according to the profiles of turbulent statistics and G

_{S}in different cases.

## 5. Conclusions

_{NB}have been conducted, according to vertical distributions of turbulent statistics (velocity, shear stress, skewness coefficients), turbulence kinetic generation rate and turbulence spectra. The findings are summarized as follows:

- It is sufficiently accurate to represent overall flow characteristic by an average of velocities measured at Locations 1# & 2#;
- For a modest value of 0.04 < λ < 0.1, characteristics of profiles for turbulent statistics are similar to both the bed-shear flow one and the free-shear flow one. U profile could be described to comply with either the free-shear flow or the bed-shear flow features;
- The secondary boundary-shear flow occurs in Case VI with λ = 1.44. U profile could be described to comply with the bed- shear flow feature, and the boundary between the roughness layer and the inertial layer locates above the canopy;
- The change of turbulent flow type induced by an increase of λ would intensify the turbulence with large maximum value of G
_{S}. The point where turbulence is vertically fiercest moves upwards gradually with λ; - The ISRs of spectral curves range from 0.4 to 4 Hz at different heights except within canopy in the secondary boundary-shear flow. For spectral curves of the low-frequency eddies, there are some slight humps at 0.04 < λ < 0.1, and the curves fluctuate intensely while λ > λ
_{NB}.

_{NB}should be determined by large series of experiments, with variations in vegetation configuration (stiffness, shape and arrangement pattern), flow velocity and submergence depth being considered. Turbulence structures in different conditions should also be studied basing on flow field measurement in the future.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 2.**The arrangement of measurement points for analysis of spatial variations and representative locations of the flow field.

**Figure 3.**(

**a**) Spatial variations of the velocity profiles and (

**b**) the comparison between U

_{1#~2#}profile and the U

_{a#~i#}one in Case V.

**Figure 4.**(

**a**) Spatial variations of the Reynolds stress profiles and (

**b**) the comparison between $-{\overline{uw}}_{1\#~2\#}$ profile and the $-{\overline{uw}}_{a\#~i\#}$ one in Case V.

**Figure 5.**U profiles with different vegetation densities, (

**a**) from Case I to Case IV and (

**b**) from Case III to Case VI.

**Figure 6.**$-\overline{uw}$ profiles with different vegetation densities, (

**a**) from Case I to Case III and (

**b**) from Case IV to Case VI.

**Figure 7.**Sk

_{u}and Sk

_{w}with different vegetation densities, in (

**a**) Case I, (

**b**) Case II, (

**c**) Case III, (

**d**) Case IV, (

**e**) Case V and (

**f**) Case VI.

**Figure 8.**G

_{S}profiles with different vegetation densities, in (

**a**) Cases I & II, (

**b**) Cases III & IV and (

**c**) Cases V & VI.

**Figure 9.**Turbulence spectra F(f) at different heights in (

**a**) Case I, (

**b**) Case II, (

**c**) Case III, (

**d**) Case IV, (

**e**) Case V and (

**f**) Case VI.

Case | λ | S_{x} (cm) | S_{y} (cm) | H (cm) | Sub | Q (L/s) | U_{m} (cm/s) |
---|---|---|---|---|---|---|---|

I | 0 | 0 | 0 | 18 | — | 32.44 | 30.04 |

II | 0.0056 | 40 | 16 | 18 | 3 | 32.34 | 29.94 |

III | 0.045 | 10 | 8 | 18 | 3 | 32.43 | 30.03 |

IV | 0.09 | 5 | 8 | 18 | 3 | 32.35 | 29.95 |

V | 0.36 | 5 | 2 | 18 | 3 | 32.4 | 30 |

VI | 1.44 | 2.5 | 1 | 18 | 3 | 32.48 | 30.07 |

Case I | Case II | Case III | Case IV | Case V | Case VI | |
---|---|---|---|---|---|---|

0 < z< 10 mm | 2.99 | 3.462 | 2.407 | 2.03 | −0.068 | — |

55 ≤ z ≤ 65 mm | 1.126 | 1.38 | 2.025 | 3.077 | 4.978 | 19.764 |

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## Share and Cite

**MDPI and ACS Style**

Zhao, H.; Yan, J.; Yuan, S.; Liu, J.; Zheng, J.
Effects of Submerged Vegetation Density on Turbulent Flow Characteristics in an Open Channel. *Water* **2019**, *11*, 2154.
https://doi.org/10.3390/w11102154

**AMA Style**

Zhao H, Yan J, Yuan S, Liu J, Zheng J.
Effects of Submerged Vegetation Density on Turbulent Flow Characteristics in an Open Channel. *Water*. 2019; 11(10):2154.
https://doi.org/10.3390/w11102154

**Chicago/Turabian Style**

Zhao, Hanqing, Jing Yan, Saiyu Yuan, Jiefu Liu, and Jinyu Zheng.
2019. "Effects of Submerged Vegetation Density on Turbulent Flow Characteristics in an Open Channel" *Water* 11, no. 10: 2154.
https://doi.org/10.3390/w11102154