# Hydraulic Features of Flow through Emergent Bending Aquatic Vegetation in the Riparian Zone

^{1}

^{2}

^{*}

## Abstract

**:**

_{s}was a key determinant of those influences. Manning coefficient n varied greatly with the variation of vegetation densities, relative depth ratio of water depth h to stem height h

_{s}, Re and Fr. Manning coefficient n increased with increasing vegetation density, particularly in cases when h/h

_{s}> 1. The velocity distributions did not follow logarithmic profiles, but they instead exhibited double logarithmic profiles. In addition, vegetation characteristics were shown to influence the height of maximum velocity. The position of maximum velocity is further away from the bed in cases with denser vegetation distribution. Finally, turbulence intensity showed more significant variation in the stem part and peaked near the middle of the stem, at z/h

_{s}= 0.5, where z was the distance from the bottom.

## 1. Introduction

## 2. Laboratory Experiments

#### 2.1. Materials

#### 2.2. Experimental Setup and Measurement Technique

^{3}), which is 5 cm away from the sensing elements. The probe was connected to the computer via a processing card. Real-time data could be recorded using a data acquisition program installed in the sampling computer. For each measurement, the sample-reporting rate was 25 Hz, and the acoustic frequency was 10 MHz. The velocity components, u, v, and w, correspond to the stream-wise (x), lateral (y), and vertical (z) directions, respectively. A 180-second sampling period was set for each test run. The WinADV-program, a post-processing program, was used to filter and post-process the sampled data. Data with average correlations less than or equal to 70% were filtered out.

#### 2.3. Test Series Description

_{s}and h/h

_{s}, as well as the influence of the vegetation density, δ, on Manning coefficient n and the velocity distribution. Data for the 5 test series, with a total of 44 test runs, have been obtained in this study. A summary of the test series is presented in Table 1. In all the test series, the Reynolds numbers, Re, ranged from approximately 5600–48,000, indicating that all of the test runs are within the range of turbulent flow. The Froude numbers, Fr, ranged from 0.070 to 0.604, which means that all test runs can be considered subcritical flow. The plants exhibited no bending but instead oscillated slightly with low discharge. Conversely, because the leaves are flexible, the stems bend somewhat, and the leaves are streamlined with higher discharge. Furthermore, for each vegetation distribution pattern, the greatest discharge run (circled data in Table 1) has been selected to investigate flow velocity distribution and turbulence by water depth.

Series | Description | Test runs | Q(m^{3}/s) | Re | Fr | h(cm) | u(m/s) |
---|---|---|---|---|---|---|---|

V0 | No vegetation | V0-1 | 0.00650 | 12996 | 0.502 | 4.09 | 0.318 |

V0-2 | 0.00796 | 15918 | 0.527 | 4.53 | 0.351 | ||

V0-3 | 0.01090 | 21792 | 0.533 | 5.55 | 0.393 | ||

V0-4 | 0.01347 | 26942 | 0.532 | 6.40 | 0.421 | ||

V0-5 | 0.01900 | 38000 | 0.514 | 8.23 | 0.462 | ||

V0-6 | 0.02140 | 42781 | 0.510 | 8.95 | 0.478 | ||

V0-7 | 0.02520 | 50394 | 0.566 | 9.32 | 0.541 | ||

V0-8 | 0.03095 | 61801 | 0.604 | 10.22 | 0.605 | ||

V1 | 45 cm, 40 plants | V1-1 | 0.00616 | 12324 | 0.267 | 6.01 | 0.205 |

V1-2 | 0.00804 | 16072 | 0.278 | 6.98 | 0.230 | ||

V1-3 | 0.01040 | 20805 | 0.269 | 8.47 | 0.246 | ||

V1-4 | 0.01208 | 24159 | 0.263 | 9.51 | 0.254 | ||

V1-5 | 0.01514 | 30273 | 0.248 | 11.50 | 0.263 | ||

V1-6 | 0.01612 | 32246 | 0.238 | 12.34 | 0.261 | ||

V1-7 | 0.01879 | 37571 | 0.224 | 14.20 | 0.265 | ||

V1-8 | 0.02204 | 44080 | 0.221 | 15.95 | 0.276 | ||

V1-9 | 0.02391 | 47922 | 0.216 | 17.10 | 0.280 | ||

V2 | 30 cm, 60 plants | V2-1 | 0.00498 | 9957 | 0.226 | 5.82 | 0.171 |

V2-2 | 0.00606 | 12127 | 0.233 | 6.51 | 0.186 | ||

V2-3 | 0.00843 | 16861 | 0.227 | 8.25 | 0.205 | ||

V2-4 | 0.00902 | 18044 | 0.224 | 8.72 | 0.207 | ||

V2-5 | 0.01154 | 23074 | 0.217 | 10.49 | 0.220 | ||

V2-6 | 0.01381 | 27610 | 0.214 | 11.93 | 0.231 | ||

V2-7 | 0.01405 | 28103 | 0.207 | 12.35 | 0.228 | ||

V2-8 | 0.01854 | 37077 | 0.188 | 15.85 | 0.234 | ||

V2-9 | 0.02056 | 41121 | 0.170 | 18.13 | 0.227 | ||

V3 | 15 cm, 240 plants | V3-1 | 0.00288 | 9320 | 0.130 | 5.75 | 0.100 |

V3-2 | 0.00369 | 7372 | 0.118 | 7.36 | 0.100 | ||

V3-3 | 0.00466 | 5752 | 0.133 | 8.06 | 0.116 | ||

V3-4 | 0.00530 | 10600 | 0.121 | 9.23 | 0.115 | ||

V3-5 | 0.00610 | 12195 | 0.122 | 10.05 | 0.121 | ||

V3-6 | 0.00750 | 14999 | 0.107 | 12.56 | 0.119 | ||

V3-7 | 0.00980 | 19602 | 0.090 | 16.73 | 0.117 | ||

V3-8 | 0.01158 | 23152 | 0.081 | 20.26 | 0.114 | ||

V3-9 | 0.01290 | 25758 | 0.070 | 22.80 | 0.113 | ||

V4 | 15 cm, 280 plants | V4-1 | 0.00298 | 5955 | 0.104 | 6.94 | 0.086 |

V4-2 | 0.00305 | 6100 | 0.104 | 7.05 | 0.087 | ||

V4-3 | 0.00350 | 6999 | 0.108 | 7.55 | 0.093 | ||

V4-4 | 0.00420 | 8397 | 0.118 | 8.01 | 0.105 | ||

V4-5 | 0.00550 | 10996 | 0.121 | 9.45 | 0.116 | ||

V4-6 | 0.00618 | 12357 | 0.114 | 10.63 | 0.116 | ||

V4-7 | 0.00640 | 12785 | 0.109 | 11.22 | 0.114 | ||

V4-8 | 0.00736 | 14714 | 0.098 | 13.22 | 0.111 | ||

V4-9 | 0.01090 | 21801 | 0.079 | 19.86 | 0.101 |

## 3. Analytical Method

#### 3.1. Vegetation Density

^{−1}; N is the total number of plants; D is the diameter of stem, m; A is the area of testing reach, m

^{2}; h is the water depth, m; h

_{s}is the height of stem, m; and L

_{w}is the width of wetted foliage, m.

_{w}) can be easily obtained. However, because L

_{w}mainly depends on the bending degree, it cannot be directly determined. In this study, L

_{w}is determined statistically using the geometric mean after measuring the wetted foliage widths of 20 plants for each test run.

#### 3.2. Resistance Coefficient

_{d}is the effective vegetal drag coefficient; A

_{veg}is the frontal area of the vegetation; and k

_{n}is the units term.

#### 3.3. Turbulence Intensity

_{u}, RMS

_{v}and RMS

_{w}are turbulence intensities corresponding to streamwise, lateral and vertical flow, respectively.

## 4. Results and Discussion

#### 4.1. Vegetation Density

_{s}> 1, while the V1 cases have the least increase rate of δ.

#### 4.2. Manning Coefficient n

_{w}and n

_{b}, respectively. Because the flume wall is glass, its resistance can be considered negligible compared to that of vegetation. In other words, the flow resistance in a vegetated flume is dominated by the vegetation bottom resistance. The flow resistance n = n

_{b}can be evaluated by applying Equation (2). After investigating various test runs, it may be concluded how Manning coefficient n varies with the relative depth ratio of water depth h to stem height h

_{s}, the vegetation density and the Reynolds number. These are shown in Figure 5a–d.

**Figure 4.**Profiles of vegetation densities against water depth in different vegetation distribution patterns, where h is the water depth and δ is the vegetation density.

**Figure 5.**Manning coefficient n for each series: (

**a**) n against relative depth ratio, h/h

_{s}, where h is the water depth and h

_{s}is the plant stem height; (

**b**) n against vegetation density, δ(m

^{−1}); (

**c**) n against Reynolds number, Re; (

**d**) n against Froude number, Fr.

_{s}. However, the increment of change in n below the stem height (h/h

_{s}= 1.0) is less than that above the stem height. When the ratio of flow depth to plant stem height, h/h

_{s}< 1, the n increment is approximately 3%. Conversely, when h/h

_{s}> 1, the Manning n increments are approximately 5.7%, 7.7%, 16.4%, 23.2% at V1, V2, V3 and V4, respectively. It illustrates that the contribution of foliage with flexible leaves is significantly greater than that of plant stems without leaves. Thus, variations in Manning n depend on the position of the separating point between the stem and foliage. The leaf is found to be an important factor in the analyses, and properties such as rigidity are found to influence the drag exerted by leaves. This can also be illustrated by Figure 5b. When the vegetation density is less than approximately 6.5 m

^{−1}, an increasing trend of Manning n is not apparent. However, when the vegetation density is greater than 6.5 m

^{−1}, the Manning n increases more significantly with increasing vegetation density. Manning coefficient is almost uniform up to the critical plant density and then increases [6].

#### 4.3. Velocity Distribution

^{3}/s for V1, 0.02056 m

^{3}/s for V2, 0.01290 m

^{3}/s for V3 and 0.01090 m

^{3}/s for V4), are used to investigate velocities and turbulence intensities in x, y and z directions. The sampling vertical line stands at the center of four neighboring plants. The surveyed velocity profiles are shown on the plane z/h

_{s}against u/u* (Figure 6), where z is the distance from the bed, h

_{s}is the plant stem height and u* is the shear velocity estimated using , where J is the flume slope [26].

_{s}< 1) and the foliage part (z/h

_{s}> 1). However, because both profiles in the stem and foliage parts almost follow logarithmic behavior, the whole velocity profile can be characterized as a double logarithmic profile. Furthermore, both the stem and foliage parts have significant variations in mean velocities and exhibit the generation of a horizontal shear layer. The magnitude of the mean velocity in the foliage part is less than that in the stem part because the foliage consumes much more energy and momentum from the flow through the generation of turbulence. A local velocity maximum can be observed near the bed in the stem part. In addition, Figure 6 shows that vegetation densities have some influence on the vertical velocity distribution. The vertical velocities of V3 and V4 are much lower than those of V1 and V2, as expected. Figure 6 also shows that the position of maximum velocity is farther from the bed in the denser vegetation distributions. This result is similar to the report by Afzalimehr, et al. [27].

#### 4.4. Turbulence

_{u}, RMS

_{v}, RMS

_{w}) and Reynolds stress (u'w') for V3 (Q = 0.0129 m

^{3}/s) and V4 (Q = 0.0109 m

^{3}/s) are shown in Figure 7a,b, respectively.

**Figure 7.**Turbulence intensities and Reynolds stress against relative depth ratio of vertical distance from bed z to stem height h

_{s}: (

**a**) represents V3 pattern and Q = 0.0128 m

^{3}/s; (

**b**) represents V4 pattern and Q = 0.0109 m

^{3}/s.

_{s}> 1, turbulence intensity has little variation and can be considered constant. However, the turbulence intensity varies dramatically for 0 < z/h

_{s}< 1. The turbulence intensity peaks near the middle of the stem. In another words, turbulence intensity increases for z/h

_{s}< 0.5 and decreases for 0.5 < z/h

_{s}< 1. Afzalimhr, et al. [27] reported similar results of approximately constant turbulence intensity above the stem height. When the water depth is higher than the stem height, the flexible leaves bend over in the flow when the discharge is high. As the leaves become parallel to the flow, the momentum flux is absorbed, decreasing the turbulence intensity of the flow within the canopy. While the foliage induces a greater drag force, the turbulence generated by shear is reduced due to the inhibition of momentum exchange by the plant frontal area. In conclusion, the stem and foliage of emergent bending aquatic vegetation have quite different effects on the turbulence intensity of the flow, with more intense turbulence in the stem regime.

## 5. Conclusions

_{s}was a key factor for investigating the hydraulic features of this species. For instance, Manning coefficient n varied greatly with the variation of vegetation densities δ, relative depth ratio h/h

_{s}, Re and Fr. Manning coefficient n increased with the increasing vegetation density and increased more rapidly in cases with h/h

_{s}> 1.

_{s}= 0.5. This result indicates the presence of strong turbulence intensity around the stem and that bending flexible foliage weakened the turbulence intensities.

## Acknowledgments

## Conflicts of Interest

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**MDPI and ACS Style**

Xia, J.; Nehal, L.
Hydraulic Features of Flow through Emergent Bending Aquatic Vegetation in the Riparian Zone. *Water* **2013**, *5*, 2080-2093.
https://doi.org/10.3390/w5042080

**AMA Style**

Xia J, Nehal L.
Hydraulic Features of Flow through Emergent Bending Aquatic Vegetation in the Riparian Zone. *Water*. 2013; 5(4):2080-2093.
https://doi.org/10.3390/w5042080

**Chicago/Turabian Style**

Xia, Jihong, and Launia Nehal.
2013. "Hydraulic Features of Flow through Emergent Bending Aquatic Vegetation in the Riparian Zone" *Water* 5, no. 4: 2080-2093.
https://doi.org/10.3390/w5042080