Abstract

In a natural basin, the vegetation can change the slope convergence and affect the surface runoff. Vegetation height may vary in an area, showing a two-layer combination of high and low collocation. This study aimed to understand the effects of double-layer vegetation in different submerged states on flow resistance. Plantings of vegetation at different heights may control landslides and contribute to soil and water conservation. This study explored the water flow resistance characteristics of double-layer vegetation at different heights. A plastic bar was used to simulate rigid vegetation, and an indoor channel fixed bed experiment was used to simulate vegetation with different heights of 5 cm and 7 cm, 5 cm and 8 cm, 5 cm and 9 cm, and 5 cm and 10 cm. By analyzing the relationship between the Darcy–Weisbach resistance coefficient (f) and water depth (h), it was concluded that when the vegetation is in a non-submerged state, f and h satisfy f= 5.6427 h+ 0.0245. When the water depth just submerges the low vegetation, f changes abruptly, and f and h satisfy the relationship f= 3.4075 h + 0.0021. When the water depth is the same as the height of high vegetation, f attains the maximum value. In addition, the flow resistance f increases by 0.03 with a 1 cm increase in the vegetation height h. When the vegetation is completely submerged, f is negatively correlated with h.

INTRODUCTION

Slope vegetation changes water flow structure and distribution, increasing water flow resistance, and reducing the water flow rate (Baptist et al. 2007; Cheng 2011; Cheng et al. 2012; Wang et al. 2014b; Liu et al. 2018a, 2018b), thereby increasing the risk of flood disasters during the flood season.

In a natural ecological environment, vegetation height is not consistent. High and low plants grow together in basins, showing some spatial sequencing. This spatial sequence of the vegetation is relatively uniform in time and space. Double-layer vegetation (two different heights of vegetation) can occur in the same watershed. Double-layer vegetation has a considerable impact on water flow and directly affects the surface runoff process.

Vegetation's water flow resistance is an important indicator of soil and water conservation. Flow resistance usually refers to the degree of roughness of the ground and the blocking effect of vegetation on water flow. The premise of studying the surface runoff process is to understand flow resistance (Weltz et al. 1992; Hu & Abrahams 2004, 2005, 2006; Wang et al. 2014a; Liu et al. 2018a, 2018b).

A resistance coefficient should fully reflect the effect of the underlying vegetation on flow resistance. It is important to calculate the resistance coefficient accurately to study slope surface flow (Guo et al. 2011; Jiang et al. 2012; Zheng et al. 2012; Liu et al. 2015). Wang et al. (2012) concluded, through experimental analysis, that the Darcy–Weisbach resistance coefficient can effectively reflect the resistance of slope flow, and the Darcy–Weisbach resistance coefficient was positively correlated with the depth index of the slope flow in their experiment. In addition, f was more suitable for higher flow regimes, and there is still controversy about the flow regime on the slope. Hence, it was reasonable to choose f to represent the flow resistance (Abrahams et al. 1994; Yen 2002). Therefore, this study mainly used the Darcy–Weisbach resistance coefficient f to characterize water flow resistance.

The influence of double-layer vegetation on water flow has attracted the attention of many scholars. Hao et al. (2017) used a three-dimensional Doppler ultrasonic speedometer (ADV) to measure the vertical flow velocity of different regions with short and high rods; Rowiński & Kubrak (2002) used a mixed length model to predict the change in flow velocity when water flowed through a vertical distribution of vegetation; their estimation of Reynolds stress was inseparable from the fluctuation of velocity. In calculating the shear rate, we should first consider the transformation of lateral energy; Yang & Choi (2010) proposed an average velocity expression by using the two-layer method to study the characteristics of submerged vegetation in open channel water flow. They successfully predicted the average velocity distribution of water flow and provided an expression for the vegetation roughness coefficient. The roughness coefficient performed better than other formulas. Li et al. (2014) studied the flow characteristics of a composite layer of vegetation using the three-dimensional numerical simulation method, and they found that the vertical flow velocity had an inflection point. The resulting mixed velocity layer resulted in a combined stream of different speeds. They also showed that the Manning roughness coefficient increased as the density of vegetation increased.

Huai et al. (2013, 2014) studied the flow velocity of double-layer vegetation and analyzed a suitable model, but some scale factors had to be solved. For example, the scale factor and the penetration length scale of the submerged canopy in the model had to be solved, and the flow characteristics required two-layer vegetation with different configurations for in-depth study. In addition, the theory of a large deflection cantilever beam has been used to derive the polynomial velocity distribution of the upper free water layer based on the momentum balance in the vegetation layer. The interaction of high momentum fluids and low momentum fluids resulted in flow folding and created strong vortices in each mixed layer, which is important for studying the riparian environment, especially in downstream areas.

Although there have been many achievements in the research on water flow in double-layer vegetation open channels, there is still no consensus on some issues due to the influence of experimental facilities and experimental conditions. Research questions have focused on flow velocity distribution, and the inflection point problem of the top vegetation velocity distribution between high plants and low plants has been studied. Conclusions drawn from inconsistent experimental conditions have varied. Therefore, this study was based on previous research results. We explored variations in flow resistance with different vegetation height combinations to overcome single height differences used in double-layer vegetation studies. A more detailed study of the relationship between the height difference of double-layer vegetation and water flow resistance may guide vegetation plantings for water and soil conservation and prevent the frequent occurrence of natural disasters.

MATERIALS AND METHODS

The experiment device consisted of a variable slope rectangular water tank, a pressure gauge, a tailgate, an electromagnetic flowmeter, and a slope-adjusting device (Figure 1). The bottom of the tank and both walls were made of Plexiglas. The tank was 5 m long, 0.4 m wide, and 0.3 m deep. There was an experiment laying section in the middle of the rectangular water tank. The length of the experiment laying section was 3 m, and the bottom slope could be varied. The slope was fixed at 1.0% to reduce the number of experiments. In the experiment section, two sections were marked as sections 1 and 2 (1.5 m apart). Piezometer tubes were arranged in the two sections to observe water level changes.

Figure 1

Experimental device.

Figure 1

Experimental device.

Currently, indoor flume drainage experiments are mostly used to study the flow resistance of vegetation. Most experimental materials use various plastic rods to simulate vegetation, and the control variate method is used to study the effect of flow resistance. Therefore, uniform plastic rods and Plexiglas plates were used in this study. This was done to generalize the vegetation and underlying surface, focusing on the difference in the water flow resistance with the change in vegetation height. The experiment laying section was composed of Plexiglas to simulate the underlying surface of vegetation. There were uniform holes in the Plexiglas panels. Plastic rods inserted into the holes were used to simulate rigid vegetation, and the high and low rods were alternated. Because the distribution of double-layer vegetation in a natural watershed is relatively uniform, the row spacing of each small hole was 60 mm by 60 mm, and the diameter of each small hole was 6 mm (Figure 2).

Figure 2

Top view of the experiment laying section.

Figure 2

Top view of the experiment laying section.

The tall and short rods were staggered. The electromagnetic flow meter adjusted the flow rate to control the water depth to simulate different flooding states. A piezometer was used to measure the water depth in sections 1 and 2 ( and , respectively). The flow rates for sections 1 and 2 were calculated as and : 
formula
(1)
where is the flow velocity in section 1 (m/s), is the flow velocity in section 2 (m/s), Q is the flow (m3/s), and B is the open channel width.
The average water flow velocity through section 1 and section 2 was calculated as: 
formula
(2)
where v is the average flow velocity of a stream (m/s).
Because the Darcy–Weisbach resistance coefficient formula has good physical significance and is easy to use, it is the most commonly used formula to characterize slope flow resistance. Its formula is: 
formula
(3)
where is the average flow velocity of a stream (m/s), is the Darcy–Weisbach resistance coefficient, is the average hydraulic radius (m), g is the standard of gravitational acceleration (m/s2), and J is the hydraulic gradient.

DATA ANALYSIS AND DISCUSSION

The results are obtained by using the relevant equations, and the relevant calculation data are summarized in Table 1.

Table 1

Experiment data

SlopeHighly matchedExperiment sequenceHydraulic parameters
Q(m3/s)h1(m)h2(m)V1(m/s)V2(m/s)f
1.0% 0.05 m & 0.07 m 0.000957 0.0059 0.0136 0.405681 0.175994 0.079962 
0.001559 0.0161 0.0273 0.242121 0.142789 0.155178 
0.002054 0.0263 0.0383 0.195219 0.134054 0.209739 
0.003245 0.0485 0.0605 0.167287 0.134106 0.335469 
0.003544 0.0539 0.0660 0.164356 0.134224 0.351879 
0.003775 0.0572 0.0698 0.164991 0.135208 0.307619 
0.004064 0.0624 0.0749 0.162816 0.135644 0.336976 
0.004294 0.0663 0.0787 0.161897 0.136389 0.360601 
0.004571 0.0708 0.0832 0.161416 0.137359 0.372785 
10 0.004921 0.0765 0.0892 0.160827 0.137929 0.349353 
11 0.005422 0.0854 0.0984 0.158730 0.137760 0.331678 
12 0.006586 0.1033 0.1169 0.159393 0.140849 0.260645 
13 0.007125 0.1116 0.1254 0.159610 0.142045 0.234090 
14 0.007935 0.1230 0.1372 0.161284 0.144592 0.169062 
0.05 m & 0.08 m 0.000943 0.0062 0.0163 0.380078 0.144569 0.088916 
0.001498 0.0171 0.0292 0.219028 0.128266 0.157532 
0.002008 0.0284 0.0410 0.176790 0.122459 0.215146 
0.002894 0.0463 0.0588 0.156287 0.123063 0.319627 
0.003186 0.0518 0.0642 0.153770 0.124070 0.354979 
0.003519 0.0579 0.0709 0.151962 0.124099 0.305782 
0.003766 0.0643 0.0772 0.146413 0.121948 0.353688 
0.004289 0.0726 0.0853 0.147689 0.125700 0.396380 
0.004860 0.0787 0.0912 0.154390 0.133229 0.407978 
10 0.005122 0.0874 0.1006 0.146517 0.127292 0.350660 
11 0.005667 0.0959 0.1093 0.147723 0.129613 0.323411 
12 0.006270 0.1048 0.1183 0.149579 0.132510 0.309357 
13 0.007383 0.1211 0.1351 0.152422 0.136627 0.221213 
14 0.007898 0.1281 0.1422 0.154140 0.138856 0.201872 
0.05 m & 0.09 m 0.000935 0.0059 0.0133 0.396265 0.175787 0.081021 
0.001590 0.0161 0.0274 0.246866 0.145056 0.149577 
0.002172 0.0278 0.0395 0.195344 0.137482 0.226525 
0.002713 0.0369 0.0487 0.183805 0.139269 0.270003 
0.003509 0.0506 0.0622 0.173382 0.141047 0.354616 
0.003833 0.0561 0.0686 0.170826 0.139699 0.297617 
0.004236 0.0624 0.0748 0.169716 0.141581 0.324239 
0.004900 0.0744 0.0867 0.164651 0.141292 0.379787 
0.005104 0.0795 0.0919 0.160494 0.138839 0.395820 
10 0.005513 0.0853 0.0975 0.161576 0.141358 0.430114 
11 0.006616 0.1003 0.1131 0.164899 0.146237 0.359786 
12 0.007130 0.1074 0.1204 0.165960 0.148040 0.336297 
13 0.007625 0.1152 0.1287 0.165473 0.148116 0.270016 
14 0.007933 0.1187 0.1323 0.167088 0.149912 0.252952 
0.05 m & 0.10 m 0.000992 0.0064 0.0162 0.387370 0.153035 0.087679 
0.001586 0.0174 0.0292 0.227890 0.135797 0.157671 
0.002112 0.0283 0.0407 0.186576 0.129732 0.209265 
0.002625 0.0380 0.0503 0.172697 0.130467 0.266865 
0.003209 0.0489 0.0609 0.164073 0.131743 0.347963 
0.003449 0.0542 0.0670 0.159090 0.128697 0.298338 
0.004050 0.0635 0.0760 0.159449 0.133224 0.351818 
0.004601 0.0720 0.0843 0.159754 0.136445 0.394827 
0.005167 0.0820 0.0943 0.157520 0.136974 0.428564 
10 0.005728 0.0906 0.1029 0.158051 0.139159 0.445072 
11 0.006596 0.1040 0.1163 0.158565 0.141795 0.469940 
12 0.006824 0.1084 0.1213 0.157382 0.140645 0.386870 
13 0.007335 0.1155 0.1287 0.158770 0.142486 0.340383 
14 0.007951 0.1235 0.1372 0.160950 0.144878 0.255746 
SlopeHighly matchedExperiment sequenceHydraulic parameters
Q(m3/s)h1(m)h2(m)V1(m/s)V2(m/s)f
1.0% 0.05 m & 0.07 m 0.000957 0.0059 0.0136 0.405681 0.175994 0.079962 
0.001559 0.0161 0.0273 0.242121 0.142789 0.155178 
0.002054 0.0263 0.0383 0.195219 0.134054 0.209739 
0.003245 0.0485 0.0605 0.167287 0.134106 0.335469 
0.003544 0.0539 0.0660 0.164356 0.134224 0.351879 
0.003775 0.0572 0.0698 0.164991 0.135208 0.307619 
0.004064 0.0624 0.0749 0.162816 0.135644 0.336976 
0.004294 0.0663 0.0787 0.161897 0.136389 0.360601 
0.004571 0.0708 0.0832 0.161416 0.137359 0.372785 
10 0.004921 0.0765 0.0892 0.160827 0.137929 0.349353 
11 0.005422 0.0854 0.0984 0.158730 0.137760 0.331678 
12 0.006586 0.1033 0.1169 0.159393 0.140849 0.260645 
13 0.007125 0.1116 0.1254 0.159610 0.142045 0.234090 
14 0.007935 0.1230 0.1372 0.161284 0.144592 0.169062 
0.05 m & 0.08 m 0.000943 0.0062 0.0163 0.380078 0.144569 0.088916 
0.001498 0.0171 0.0292 0.219028 0.128266 0.157532 
0.002008 0.0284 0.0410 0.176790 0.122459 0.215146 
0.002894 0.0463 0.0588 0.156287 0.123063 0.319627 
0.003186 0.0518 0.0642 0.153770 0.124070 0.354979 
0.003519 0.0579 0.0709 0.151962 0.124099 0.305782 
0.003766 0.0643 0.0772 0.146413 0.121948 0.353688 
0.004289 0.0726 0.0853 0.147689 0.125700 0.396380 
0.004860 0.0787 0.0912 0.154390 0.133229 0.407978 
10 0.005122 0.0874 0.1006 0.146517 0.127292 0.350660 
11 0.005667 0.0959 0.1093 0.147723 0.129613 0.323411 
12 0.006270 0.1048 0.1183 0.149579 0.132510 0.309357 
13 0.007383 0.1211 0.1351 0.152422 0.136627 0.221213 
14 0.007898 0.1281 0.1422 0.154140 0.138856 0.201872 
0.05 m & 0.09 m 0.000935 0.0059 0.0133 0.396265 0.175787 0.081021 
0.001590 0.0161 0.0274 0.246866 0.145056 0.149577 
0.002172 0.0278 0.0395 0.195344 0.137482 0.226525 
0.002713 0.0369 0.0487 0.183805 0.139269 0.270003 
0.003509 0.0506 0.0622 0.173382 0.141047 0.354616 
0.003833 0.0561 0.0686 0.170826 0.139699 0.297617 
0.004236 0.0624 0.0748 0.169716 0.141581 0.324239 
0.004900 0.0744 0.0867 0.164651 0.141292 0.379787 
0.005104 0.0795 0.0919 0.160494 0.138839 0.395820 
10 0.005513 0.0853 0.0975 0.161576 0.141358 0.430114 
11 0.006616 0.1003 0.1131 0.164899 0.146237 0.359786 
12 0.007130 0.1074 0.1204 0.165960 0.148040 0.336297 
13 0.007625 0.1152 0.1287 0.165473 0.148116 0.270016 
14 0.007933 0.1187 0.1323 0.167088 0.149912 0.252952 
0.05 m & 0.10 m 0.000992 0.0064 0.0162 0.387370 0.153035 0.087679 
0.001586 0.0174 0.0292 0.227890 0.135797 0.157671 
0.002112 0.0283 0.0407 0.186576 0.129732 0.209265 
0.002625 0.0380 0.0503 0.172697 0.130467 0.266865 
0.003209 0.0489 0.0609 0.164073 0.131743 0.347963 
0.003449 0.0542 0.0670 0.159090 0.128697 0.298338 
0.004050 0.0635 0.0760 0.159449 0.133224 0.351818 
0.004601 0.0720 0.0843 0.159754 0.136445 0.394827 
0.005167 0.0820 0.0943 0.157520 0.136974 0.428564 
10 0.005728 0.0906 0.1029 0.158051 0.139159 0.445072 
11 0.006596 0.1040 0.1163 0.158565 0.141795 0.469940 
12 0.006824 0.1084 0.1213 0.157382 0.140645 0.386870 
13 0.007335 0.1155 0.1287 0.158770 0.142486 0.340383 
14 0.007951 0.1235 0.1372 0.160950 0.144878 0.255746 

The Darcy–Weisbach resistance coefficient first increased and then decreased with increasing depth in the open channel (Figure 3). We identified three stages in the experiment. At the beginning of the experiment, the water level in the open channel flume was low because of the small discharge, and the high and low plants were not submerged (the first stage). As the discharge gradually increased, the water level in the flume rose; the low plants were submerged, and the high plants were not submerged (the second stage). When the discharge further increased, the water level increased, and both high and low plants were submerged (the third stage).

Figure 3

Curves of four different heights with f and h.

Figure 3

Curves of four different heights with f and h.

The resistance coefficient f did not start from zero because the bottom of the flume was covered with Plexiglas panels (Figure 3). The resistance coefficient f increased positively with water depth, which is similar to the relationship (the relationship between resistance coefficient and water depth) obtained by Järvelä (2002). When the water depth in the open channel submerged the low plants, the resistance coefficient peaked, and when the water level increased, the resistance coefficient suddenly decreased. When the water just submerged the low plants, the effective water-resisting area of the vegetation reached its maximum. When the water level rose further and the low plants were completely submerged, the vortex generated by the low plants' top layer was gradually submerged. Therefore, the resistance of the vortex decreased, the effect of the low plants on the current was reduced, and the resistance coefficient suddenly decreased. As the water level continued to rise, the high plants in the open channel resisted the water flow, so the resistance coefficient increased. When the water depth just submerged the higher plants, the contact area between the vegetation and water surface was maximized, the specific surface area was maximized, and the effective resistance area to the water flow was maximized; therefore, the resistance coefficient attained the maximum value. This is similar to previous studies on turbulent energy and the Reynolds stress distribution of stratified vegetation. At the top of each vegetation layer, there was an obvious peak (Wang & Wang 2010; Wang & Huai 2014). Then, the flow rate continued to increase, the water level rose, and the vegetation was completely submerged. The resistance of the vegetation to water flow decreased, the water layer thickened, the vortices generated by the vegetation layer were submerged, and the resistance of the vortices was further reduced. The disturbance of vegetation with water flow decreased, so the resistance coefficient decreased with increasing water depth (negative correlation). The difference of height between the high and low plants led to the difference in the peak values of the resistance coefficient. When the difference in vegetation height was 0.01 m, the difference in the resistance coefficient's peak values was 0.03. The overall similarity of the relationship between double-layer vegetation and water depth and the relationship between single-height vegetation and deep water is that they are both positively correlated initially, and negatively correlated after complete submergence of the vegetation. This is consistent with the results of the Yang et al. (2016) study. There is an abrupt change in the law of flow resistance, which agrees with the results of the previous studies on the distribution of velocity and turbulent kinetic energy (Ghisalberti & Nepf 2002; Huai et al. 2009). This relationship can be used to guide plantings in open channels for ecological restoration.

The relationship between the vegetation resistance coefficient and water depth at the same height was also studied. The resistance coefficient of vegetation at the same height first increased and then decreased with increasing water depth. When the water submerged the vegetation, the resistance coefficient reached a maximum, then decreased with increasing water depth. Our results showed that the resistance effect of double-layer vegetation on flow is more complex than uniform height vegetation with different peak values for the drag coefficient.

The resistance coefficient increased with increasing water depth in the first and second stages (Figure 3), and it had a positive correlation with water depth. However, the submerged state of the vegetation differed in these two stages, and the resistance coefficient's increasing trend also differed. The resistance coefficients of the two stages are plotted with water depth in Figure 4. The resistance coefficient in the first stage had a faster rate of increase than in the second stage because the disturbance of the water flow was affected when the water depth completely submerged the low plants; the vegetation and water contact area reduced, resulting in the resistance coefficient's slower rate of increase.

Figure 4

Growth rate of the resistance coefficient for two different submerged states.

Figure 4

Growth rate of the resistance coefficient for two different submerged states.

CONCLUSIONS

In this study, we examined vegetation at a uniform height, either submerged or not submerged, and its effects on water flow. The resistance characteristics represented the slope flow pattern. We used open channel water tank simulation experiments to overcome the single height differences used in previous double-layer vegetation studies. The experiment results show that the variation of the flow resistance coefficient of double-layer vegetation is first positively correlated with the increase in water depth, and negatively correlated with the increase in discharge. These results agree with those of previous studies on the variation of flow resistance of vegetation at a single height. However, we verified that the resistance coefficient of double-decked vegetation changes abruptly in the growth stage, that is, there is an inflection point, which is similar to its velocity distribution. At the same time, the rate of increase of the drag coefficient is different before and after the inflection point, and the rate of increase of the drag coefficient clearly decreases after mutation. In addition, the peak value of the flow resistance coefficient increases by 0.03 with an increase of 1 cm of the vegetation height. The relationship obtained in this experiment can guide the planting of vegetation with different heights for soil and water conservation, landslide prevention, and debris flow management without affecting the flow of water. Further study of this relationship is required in the natural environment as these experiments were conducted with an open channel flume in a laboratory.

ACKNOWLEDGEMENTS

We would like to thank the National Natural Science Foundation of China (Grant No. 41471025) and Innovative Science and Technology Project for Postgraduates of Shandong University of Science and Technology (SDKDYC190315) for support and funding, and thank the help and support of other people in the project group.

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