## Abstract

Vegetation is a vital part of the natural environment. Variations in vegetation morphology produce changes in the mechanical and fluid characteristics of overland flow. Determining the effects of vegetation lodging on the overland runoff flow regime and resistance is a prerequisite for accurately simulating overland runoff and convergence, revealing the mechanism of overland flow propagation, and the design and management of vegetation protection, soil consolidation, and ecological slope engineering. To systematically study the effects of vegetation lodging on overland runoff, four planting vegetation lodging angles (*α*) and 10 test water depths were used to simulate experimental research with a 1.0% slope ratio. Experimental results show that the depth and state of vegetation inundation and the degree of lodging significantly influence the flow regime and resistance. Under the same water depth, higher values of *α* are associated with higher values of the flow velocity, Reynolds number, Froude number, and Darcy–Weisbach resistance coefficient (*f*), and lower values of the drag coefficient (*C _{D}*). The overall result is enhanced turbulence in the flow field and weaker flow resistance. Numerical statistics and difference analysis indicate that, when the vegetation is non-submerged, a 10° increase in

*α*produces a 9.30% decrease in

*f*. In the submerged state, a 10° increase in

*α*causes a 26.70% decrease in

*f*.

*C*is greatly affected by the boundary water depth. Below some critical water depths, an increase of 10° in

_{D}*α*reduces

*C*by 8.48%. Above the critical depth, a 10° increase in

_{D}*α*decreases

*C*by 41.10%.

_{D}## INTRODUCTION

Vegetation is a vital component of the natural environment. As such, it is an important factor in maintaining the integrity and health of slope ecosystems, and has a very high ecological service value (Wang *et al.* 2015a, 2015b; Ding & Li 2016; Mohammadiun *et al.* 2016; Yasi & Ashori 2016; Zhang *et al.* 2018). The existence of slope vegetation can effectively reduce sediment transport and slow down the erosion process (Huthoff *et al.* 2007; Cheng & Nguyen 2011; Cheng *et al.* 2012; Zhang *et al.* 2014; Li *et al.* 2015; Vargas-Luna *et al.* 2015), while simultaneously increasing the overland slope resistance (Gabarrón-Galeote *et al.* 2013; Lieskovsky & Kenderessy 2014; Zhao *et al.* 2015; Li *et al.* 2018; Zhu *et al.* 2018). As a result, vegetation is widely used in slope protection, soil and water conservation, and other aspects of hydraulic design. However, studies of overland runoff are complicated by morphological changes in vegetation (Armanini *et al.* 2005; Wilson 2007), and so it is particularly important to study the turbulence and resistance mechanisms of overland runoff. This will provide a scientific basis for accurately simulating the process of slope production and convergence, identifying the mechanism of overland flow movement, predicting and controlling regional catastrophic floods, and designing and managing soil slope protection and ecological slope engineering.

Vegetation can be characterized according to its flexibility or rigidity. For example, flexible vegetation plunges its roots into mud while the relative height of the vegetation is submerged in water. Thus, flexible vegetation can easily tilt and fall under the action of overland flow. Palmer (1945) studied the behavior of vegetation stems and leaves under three characteristic flow rates and different submergence states. The results showed that non-submerged aquatic plants did not bend under a low-speed water flow, whereas in the submerged state, the plants tended to bend in the direction of water flow during medium-speed water flow and tilt under a high-speed flow at a fixed oblique angle. These results are consistent with the findings of Carollo *et al.* (2005) and Busari & Li (2015). Kouwen *et al.* (1981) argued that the resistance of flexible plants to overland flow is also constrained by the shape of the plant itself and the flow regime. The concept of the bending stiffness of vegetation over a unit area was proposed, and a semi-empirical formula for Manning's roughness coefficient was derived using the empirical coefficient of deflection characteristics. Velasco *et al.* (2003) conducted experimental studies on various densities of flexible submerged vegetation. The results showed that vegetation roughness is directly related to the height offset value, relative roughness is negatively correlated with flow rate, and its resistance coefficient tends to a certain value. These conclusions are similar to those of Cantalice *et al.* (2013), who found that the flow resistance decreases after plant deflection in the non-submerged state, and Schoelynck *et al.* (2013), who concluded that vegetation under the impact of water flow will be deformed into a streamlined shape to reduce the resistance. Armanini *et al.* (2005) argued that under non-submerged conditions plant deflection does not result in a change in the water-blocking area, and so the water flow resistance coefficient can be assumed to be constant.

Although the hydrodynamic characteristics of vegetation lodging have been studied, there are still many areas that need to be explored in greater depth (Velasco *et al.* 2003; Li *et al.* 2014; Busari & Li 2015; Han *et al.* 2016). The effect of vegetation lodging on the overland flow field complicates the flow turbulence and resistance law. Research on the complexity of the overland flow characteristics and the hysteresis of the measurement technique under lodging conditions is relatively undeveloped (Järvelä 2002; Carollo *et al.* 2005; Wang *et al.* 2015a, 2015b). The effect and extent of vegetation lodging changes the resistance characteristics of the flow, resulting in a significant stagnant sand retention effect and a certain impact on the slope production and convergence. To accurately describe this effect, it is necessary to conduct an in-depth study of the flow characteristics of this particular fluid.

In this paper, the hydrodynamic characteristics of water flowing overland under the action of vegetation lodging are systematically studied by combining vegetation discharge simulations with the theory of fluid mechanics. Variations in the vegetation lodging degree and submergence under different water depth conditions are analyzed to clarify the differences between the flow characteristics and resistance characteristics, thus promoting the expansion of open-channel hydraulics theory to overland flow through vegetation. Moreover, this research lays the theoretical foundations for studies on the mechanism by which vegetation blocks the transport of water and sediment.

## METHODS AND MATERIALS

### Design of the experimental installation

The overland flow study reported here mainly used the basic theory of flow in an open channel (Hsieh 1964; Li & Shen 1973). Many studies on the effects of vegetation on a slope during water erosion have used variable slopes involving rectangular flume experiments. To enhance the experimental effect and improve the efficiency, single-plant vegetation was generalized into an effective water-blocking cylinder in the experiment (Huthoff *et al.* 2007; Yagci *et al.* 2010). The structure of the test tank is shown in Figure 1. The following design points were determined according to the purpose of the test:

- (1)
The test area was a polymethyl methacrylate flume with a slope of 1.0% that is divided into three sections: an upstream flat water section, an experimental procedure section, and a downstream water measuring section. The structural dimensions of the test plot were 5.0 m long, 0.4 m wide, and 0.3 m high.

- (2)
Light aluminum cylindrical rods were used to simulate the vegetation. The height of the simulated vegetation was set at 0.1 m and the stem diameter was 0.004 m. Combined with the height of the test structure, the lodging angle

*α*was set to 20°, 40°, 60°, or 80° in each of the four working conditions (as shown in Figure 2), and the adjacent vegetation was uniformly arranged over an area of 0.06 × 0.06 m^{2}. - (3)
To systematically study the internal relationship between the vegetation inundation state and vegetation lodging angle (i.e. quantitative analysis of water depth and lodging angle), the final design was subjected to 10 test treatments in which the water depth ranged from 0.01 to 0.10 m at intervals of 0.01 m.

- (4)
Two longitudinal observation sections were set up from top to bottom along the experimental laying section with a spacing of 1.5 m. Three measuring points were set for each observation section, and the velocity and water depth of each section were observed. The lateral measuring point was positioned between two plants to avoid the high and low points of the water surface in the drop zone of the vegetation wake, thus minimizing the influence of lateral variations in the flow velocity on the test results.

### Hydraulic parameter calculation

- (1)
Overland runoff is typically analyzed by measuring flow properties, flow velocity, erosion caused by the flow, and sediment transportation. Two important hydraulic parameters are the Reynolds number (

*Re*) and Froude number (*Fr*) (Horton*et al.*1934; Woolhiser*et al.*1970; Sidorchuk*et al.*2008).

*Fr*lies in determining the ratio of the inertial force of the flow due to gravity. From an energy perspective,

*Fr*represents the ratio of average kinetic energy per unit weight of a liquid to the average potential energy. For open-channel flow,where

*V*is the water velocity (m/s),

*h*is the water depth (m), and

*g*is the acceleration due to gravity (m/s

^{2}).

*Re*is an essential parameter used to reflect flow patterns. This important parameter measures the ratio of the inertial force of a viscous fluid flow to the viscous force. Inertial forces act as a disturbance to the body of water, causing it to break away from regular motion. Viscous forces weaken the effect of blocking the disturbance and maintaining the regular flow.

*Re*can be calculated aswhere is the motion viscosity coefficient (m

^{2}/s) and

*R*is the hydraulic radius. Using the Poiseuille formula,where

*T*is the temperature of the water (°C).

- (2)Resistance is the retardation effect that the vegetation and roughness of the surface of the ground impose on the water flow. Studying the flow resistance is an integral part of investigations into overland flow (Weltz
*et al.*1992; Barros & Colello 2001). In this study, the Darcy–Weisbach resistance coefficient (*f*) and the drag coefficient (*C*) reflect the overall underlying surface resistance and vegetation flow resistance characteristics, respectively. Generally speaking, the overland flow resistance is composed of the surface roughness, flow around the vegetation, internal flow retardation, and boundary effects, and thus reflects the effect of the overall underlying surface on flow resistance (Zhang_{D}*et al.*2010; Wang*et al.*2014).*C*reflects the resistance of the vegetation on the flow (Liu_{D}*et al.*2008; Cheng 2013; Liu & Zeng 2016). If the overland flow friction factor can be calculated precisely, the mechanism by which the overland flow varies may be better understood (Zheng*et al.*2012). The Darcy–Weisbach resistance coefficient,*f*, is expressed as follows:where*h*is the frictional head loss (m) and_{f}*L*is the length of the test section (m).*C*is expressed as follows:where is equal to 3.14,_{D}*d*is the stem roughness (m), and is the coverage per unit area, calculated as:where*L*is the distance between adjacent plants (m).

The experimental calculation data corresponding to the different values of *α* are presented in Table 1.

*Note*: is 20° non-submerged point, is 20° submerged point, is 40° non-submerged point, is 40°submerged point, is 60° non-submerged point, is 60° submerged point, is 80° non-submerged point, and is 80° non-submerged point.

## EXPERIMENTAL RESULTS AND ANALYSES

### Flow pattern and regime

The pattern and regime of the overland flow are determined in terms of open-channel two-dimensional flow, whereby the flow pattern can be divided into a laminar flow zone, transition zone, and turbulent flow zone. The turbulent zone can be subdivided into a turbulent smooth zone, turbulent transition zone, and turbulent rough zone. The law of flow resistance is different in different flow zones, and *Re* is an important indicator for judging the flow pattern. The flow pattern is generally divided into laminar flow, transitional flow, and turbulent flow. The flow regime refers to whether the vegetation water flow is slow or rapid. Generally, there are three kinds of flow states, namely slow flow, critical flow, and rapid flow.

According to the above analysis, the flow can be divided into six flow states: (1) slow laminar flow, (2) slow transitional flow, (3) slow turbulent flow, (4) rapid laminar flow, (5) rapid transient flow, and (6) rapid turbulent flow. Let us approximate = 1 × 10^{−6}m^{2}/s and take the hydraulic radius *R* = *h.* Then, finding simultaneous solutions to *Re**=**VR*/*ν* and *Fr**=**V*/ and plotting them in the logarithmic coordinates of water depth *h* and average flow velocity *V*, we obtain two clusters of parallel lines where *Re* and *Fr* are constant, respectively. The values *Re**=* 500, *Re**=* 5,000, and *Fr**=* 1 are used as the boundaries, and the six-zone flow regime can be determined.

Figure 3 plots the flow regime under the various test conditions. As can be seen from Figure 3, an increase in water depth produces an upward trend in the average velocity of water flow. The reason is shown in Figures 4 and 5. The water depth is positively correlated with *Re* and negatively correlated with *Fr*. As the water depth increases, the inertial force of the fluid dominates the viscous force and the average potential energy; this result is complementary to the conclusions of Li *et al.* (2013). When the vegetation is in the non-submerged state, the rate of increase in velocity is small; however, when the vegetation is completely submerged, the rate of increase in velocity gradually rises. This may be because the completely submerged vegetation reduces the flow resistance. It can be seen from Figures 6 and 7 that when the vegetation is submerged, *f* and *C _{D}* decrease as the water depth increases. This decrease in the overall flow resistance of the underlying surface and vegetation ensures the smooth flow of overland fluid and increases the velocity. Under the test conditions, the flow regime is in the slow transition flow and slow turbulent flow regions. As the water depth increases, the proportion of fluid inertial force gradually becomes greater than the viscous force (see Figure 5). The turbulence of the flow destabilizes the flow field, causing the flow regime to move from the slow transition regime to slow turbulent flow.

It can also be seen from Figure 3 that for the same water depth condition, a larger vegetation lodging angle *α* results in a greater flow velocity *V*. The reason is inseparable from the flow regime and flow resistance response. Under the same water depth conditions, Figures 4 and 5 show that *Fr*_{20°} < *Fr*_{40°} < *Fr*_{60°} < *Fr*_{80°} and *Re*_{20°} < *Re*_{40°} < *Re*_{60°} < *Re*_{80°}, respectively. This indicates that a larger vegetation lodging angle results in a greater kinetic energy and inertia force in the flowing water body and a smaller average potential energy and viscous force. The overall result is a larger flow velocity and stronger flow turbulence.

Under the same water depth conditions, Figures 6 and 7 show that *f*_{20°} > *f*_{40°} > *f*_{60°} > *f*_{80°} and *C _{D}*

_{20°}>

*C*

_{D}_{40°}>

*C*

_{D}_{60°}>

*C*

_{D}_{80°}, respectively. The larger the lodging angle of the vegetation, the smaller the corresponding

*f*and

*C*values, and a lower water-blocking capacity leads to an increase in the flow capacity. Both the flow regime and the resistance response explain why a larger vegetation lodging angle has a larger corresponding flow velocity.

_{D}In general, the flow pattern of the water changes from the slow transition to the slow turbulent flow as the water depth increases. At the same time, as the vegetation lodging angle increases, the turbulence of the flow strengthens. These are important factors affecting the flow regime.

### Resistance characteristics

Flow resistance refers to the roughness of the bed surface and the blocking effect of vegetation on the flow of water. The resistance to overland flow is often represented by the hydraulic roughness coefficient (Smith *et al.* 2007). Most scholars use the Darcy–Weisbach resistance coefficient *f* and the drag coefficient *C _{D}* to characterize the resistance. For most slopes containing vegetation, the dominant component of flow resistance is assumed to be generated by coarse vegetation, and so the comprehensive resistance of overland flow can be replaced by vegetation resistance. However, the comprehensive flow resistance is mainly composed of the circumfluence resistance, boundary resistance, or particle resistance generated by the flow through the vegetation. There are many influencing factors, making it difficult to accurately simulate the hydraulic characteristics of overland flow using suitable approximations. This study therefore systematically compared the composite resistance

*f*and the vegetation flow resistance

*C*to determine the change in comprehensive resistance caused by vegetation flow.

_{D}Figure 6 illustrates the relation between *h* and *f* under four different lodging states. There is a critical water depth (*h**=* 0.03 m) below which the test points are mostly non-submerged. In this domain, *f* increases with *h*, albeit relatively gently. When *h* is greater than the critical depth, *f* increases with *h* in the non-submerged state, but decreases as *h* increases in the fully submerged state. The peak value of *f* is attained when the vegetation is just completely submerged. This conclusion is consistent with the research results of Armanini *et al.* (2005) regarding the flow resistance of flexible vegetation. It can be inferred that, under the non-submerged condition, increasing the water depth effectively increases the solid interface between the water body and the bottom boundary, the lateral boundary, and the vegetation. This increases the solid–liquid contact and the collision probability. Therefore, the frictional resistance under the corresponding conditions increases, resulting in an increase in the comprehensive resistance of the flow. As the vegetation becomes completely submerged, the solid–liquid contact ratio decreases with any further increase in the water depth, so that the comprehensive resistance of the flow gradually decreases.

Figure 7 plots the relation between *h* and *C _{D}* under four different lodging states. Again, there is a critical water depth (

*h*

*=*0.03 m) below which

*C*decreases rapidly with water depth. When

_{D}*h*is greater than the boundary water depth,

*C*rises slowly with the water depth in the non-submerged state, but declines slowly with the water depth in the submerged state. The overall law is consistent with the research results of Ishikawa

_{D}*et al.*(2000). The experimental phenomenon suggests that when the initial water depth is small (

*h*

*=*0.01 m), the overland flow covers the entire test floor to form a thin layer of flow. Under the action of surface tension, the extremely thin flow is fully in contact with the solid surface of vegetation, test floor, and air, making the three-phase solid–liquid–gas medium heavily doped. The vegetation therefore has a water-blocking and circumfluence effect on the thin-layer flow. In this way, a backwater wave of a certain height is formed upstream of the vegetation, and the flow lines on the back surfaces separate to form a wake vortex. This increases the degree of undulation of the free surface of the fluid and increases the resistance of the vegetation to the water flow, resulting in a larger

*C*. Below the critical depth, an increase in the water depth strengthens the turbulence of the flow, and the momentum exchange inside the liquid promotes the uniformity of the velocity distribution. In this case, the ratio of solid and air doping in the solid–liquid–gas medium is greatly reduced, and the subsequent decrease in backwater and wake intensity leads to a rapid decrease in

_{D}*C*. When the water depth exceeds the critical depth, the contact area between the vegetation and the flow increases with

_{D}*h*under the non-submerged condition, and

*f*increases slowly. Once the vegetation is submerged, the behavior is completely the opposite.

Both Figures 6 and 7 give the same critical depth of water, but there are still differences between the two kinds of flow resistance with water depth. The reason may be related to the composition of flow resistance. As mentioned earlier, *f* reflects the effect of the overall underlying surface on comprehensive flow resistance. The experimental conditions mainly include boundary resistance and vegetation resistance, and neglect particle resistance. *C _{D}* only reflects the effect of vegetation on flow resistance. When

*h*is less than the critical depth, that is, the thin-layer flow is spread out across the whole slope, the boundary effect of the fluid increases under the action of surface tension, and the vegetation resistance decreases under the influence of the flow structure. Figure 6 shows that

*f*increases slowly with

*h*below the critical depth. This further shows that boundary resistance is the main flow resistance and that vegetation resistance is secondary. Moreover, the increment in boundary resistance is greater than that of vegetation resistance. When the water depth exceeds the critical water depth, the boundary effect of the slope is weakened and the vegetation resistance is enhanced. Figures 6 and 7 also suggest that under the same water depth, a larger lodging angle is associated with smaller corresponding

*f*and

*C*values and lower water-resisting capacity. In fact, the average velocity and resistance are two expressions of the same problem.

_{D}From the above analysis, it can be seen that the flow resistance characteristics of lodging vegetation are mainly related to the degree of lodging, the submerged state of vegetation, and the boundary water depth. Under the same water depth, larger lodging angles give smaller *f* and *C _{D}* and weaker water-resisting ability, which is consistent with the conclusion of Schoelynck

*et al.*(2013). The Darcy–Weisbach resistance coefficient,

*f*, is greatly affected by vegetation submergence. Through numerical statistics and difference analysis (Tables 2 and 3), it can be concluded that when the vegetation is in the non-submerged state, every 10° increase in lodging angle produces a decrease of 9.30% in

*f*. In the submerged state, every 10° increase in lodging angle causes

*f*to decrease by 26.70%.

*C*is greatly influenced by the critical depth of water. Numerical statistics and difference analysis (Table 4) show that an increase of 10° in the lodging angle produces a decrease in

_{D}*C*of 8.48% (below critical water depth) and 41.10% (above the critical depth).

_{D}Parameter . | Experiment number . | |||||||||
---|---|---|---|---|---|---|---|---|---|---|

1 . | 2 . | 3 . | 4 . | 5 . | 6 . | 7 . | 8 . | 9 . | 10 . | |

h (m/s) | 0.01 | 0.02 | 0.03 | 0.04 | 0.05 | 0.06 | 0.07 | 0.08 | 0.09 | 0.10 |

f_{20°} | 0.1104 | 0.1233 | 0.1300 | 0.1551 | 0.1989 | 0.2384 | 0.2612 | 0.2833 | — | — |

f_{40°} | 0.1016 | 0.1068 | 0.1119 | 0.1218 | 0.1550 | 0.1906 | — | — | — | — |

f_{60°} | 0.0882 | 0.0898 | 0.0914 | 0.0933 | 0.1081 | — | — | — | — | — |

f_{80°} | 0.0681 | 0.0725 | — | — | — | — | — | — | — | — |

(f_{40°} − f_{20°})/f_{20°} | −8.04% | −13.42% | −13.90% | −21.43% | −22.10% | −20.05% | — | — | — | — |

(f_{60°} − f_{40°})/f_{40°} | −13.20% | −15.89% | −18.33% | −23.40% | −30.26% | — | — | — | — | — |

(f_{80°} − f_{60°})/f_{60°} | −22.71% | −19.21% | — | — | — | — | — | — | — | — |

Parameter . | Experiment number . | |||||||||
---|---|---|---|---|---|---|---|---|---|---|

1 . | 2 . | 3 . | 4 . | 5 . | 6 . | 7 . | 8 . | 9 . | 10 . | |

h (m/s) | 0.01 | 0.02 | 0.03 | 0.04 | 0.05 | 0.06 | 0.07 | 0.08 | 0.09 | 0.10 |

f_{20°} | 0.1104 | 0.1233 | 0.1300 | 0.1551 | 0.1989 | 0.2384 | 0.2612 | 0.2833 | — | — |

f_{40°} | 0.1016 | 0.1068 | 0.1119 | 0.1218 | 0.1550 | 0.1906 | — | — | — | — |

f_{60°} | 0.0882 | 0.0898 | 0.0914 | 0.0933 | 0.1081 | — | — | — | — | — |

f_{80°} | 0.0681 | 0.0725 | — | — | — | — | — | — | — | — |

(f_{40°} − f_{20°})/f_{20°} | −8.04% | −13.42% | −13.90% | −21.43% | −22.10% | −20.05% | — | — | — | — |

(f_{60°} − f_{40°})/f_{40°} | −13.20% | −15.89% | −18.33% | −23.40% | −30.26% | — | — | — | — | — |

(f_{80°} − f_{60°})/f_{60°} | −22.71% | −19.21% | — | — | — | — | — | — | — | — |

Parameter . | Experiment number . | |||||||||
---|---|---|---|---|---|---|---|---|---|---|

1 . | 2 . | 3 . | 4 . | 5 . | 6 . | 7 . | 8 . | 9 . | 10 . | |

h (m/s) | 0.01 | 0.02 | 0.03 | 0.04 | 0.05 | 0.06 | 0.07 | 0.08 | 0.09 | 0.10 |

f_{20°} | — | — | — | — | — | — | — | — | 0.2869 | 0.2688 |

f_{40°} | — | — | — | — | — | — | 0.2145 | 0.2113 | 0.1896 | 0.1699 |

f_{60°} | — | — | — | — | — | 0.1173 | 0.1115 | 0.0937 | 0.0816 | 0.0725 |

f_{80°} | — | — | 0.0731 | 0.0640 | 0.0592 | 0.0590 | 0.0509 | 0.0362 | 0.0265 | 0.0248 |

(f_{40°} − f_{20°})/f_{20°} | — | — | — | — | — | — | — | — | −33.91% | −36.79% |

(f_{60°} − f_{40°})/f_{40°} | — | — | — | — | — | — | −48.02% | −55.66% | −56.94% | −57.34% |

(f_{80°}-f_{60°})/f_{60°} | — | — | — | — | — | −49.71% | −54.37% | −61.30% | −67.60% | −65.82% |

Parameter . | Experiment number . | |||||||||
---|---|---|---|---|---|---|---|---|---|---|

1 . | 2 . | 3 . | 4 . | 5 . | 6 . | 7 . | 8 . | 9 . | 10 . | |

h (m/s) | 0.01 | 0.02 | 0.03 | 0.04 | 0.05 | 0.06 | 0.07 | 0.08 | 0.09 | 0.10 |

f_{20°} | — | — | — | — | — | — | — | — | 0.2869 | 0.2688 |

f_{40°} | — | — | — | — | — | — | 0.2145 | 0.2113 | 0.1896 | 0.1699 |

f_{60°} | — | — | — | — | — | 0.1173 | 0.1115 | 0.0937 | 0.0816 | 0.0725 |

f_{80°} | — | — | 0.0731 | 0.0640 | 0.0592 | 0.0590 | 0.0509 | 0.0362 | 0.0265 | 0.0248 |

(f_{40°} − f_{20°})/f_{20°} | — | — | — | — | — | — | — | — | −33.91% | −36.79% |

(f_{60°} − f_{40°})/f_{40°} | — | — | — | — | — | — | −48.02% | −55.66% | −56.94% | −57.34% |

(f_{80°}-f_{60°})/f_{60°} | — | — | — | — | — | −49.71% | −54.37% | −61.30% | −67.60% | −65.82% |

Parameter . | Experiment number . | |||||||||
---|---|---|---|---|---|---|---|---|---|---|

h ≦ Critical depth of water. | h > Critical depth of water. | |||||||||

1 . | 2 . | 3 . | 4 . | 5 . | 6 . | 7 . | 8 . | 9 . | 10 . | |

h (m/s) | 0.01 | 0.02 | 0.03 | 0.04 | 0.05 | 0.06 | 0.07 | 0.08 | 0.09 | 0.10 |

C_{D}_{20°} | 2.7959 | 1.8296 | 1.1497 | 1.0426 | 1.1100 | 1.1583 | 1.1279 | 1.1095 | 1.0358 | 0.9017 |

C_{D}_{40°} | 2.6778 | 1.8864 | 1.0950 | 0.8214 | 0.8665 | 0.9258 | 0.9258 | 0.8302 | 0.6838 | 0.5228 |

C_{D}_{60°} | 2.4668 | 1.6280 | 0.7891 | 0.6285 | 0.6051 | 0.5749 | 0.4825 | 0.3671 | 0.2948 | 0.2417 |

C_{D}_{80°} | 2.3502 | 1.4341 | 0.7554 | 0.3545 | 0.2962 | 0.2948 | 0.2199 | 0.2077 | 0.0955 | 0.0818 |

(C_{D}_{20°} − C_{D}_{40°})/C_{D}_{40°} | 4.41% | −3.01% | 4.99% | 26.92% | 28.10% | 25.11% | 21.82% | 33.63% | 51.47% | 72.48% |

(C_{D}_{40°} − C_{D}_{60°})/C_{D}_{60°} | 8.55% | 15.87% | 38.76% | 30.71% | 43.20% | 61.02% | 91.86% | 126.17% | 131.97% | 116.27% |

(C_{D}_{60°} − C_{D}_{80°})/C_{D}_{80°} | 4.96% | 13.52% | 4.47% | 77.28% | 104.28% | 95.01% | 119.46% | 76.71% | 208.80% | 195.66% |

Parameter . | Experiment number . | |||||||||
---|---|---|---|---|---|---|---|---|---|---|

h ≦ Critical depth of water. | h > Critical depth of water. | |||||||||

1 . | 2 . | 3 . | 4 . | 5 . | 6 . | 7 . | 8 . | 9 . | 10 . | |

h (m/s) | 0.01 | 0.02 | 0.03 | 0.04 | 0.05 | 0.06 | 0.07 | 0.08 | 0.09 | 0.10 |

C_{D}_{20°} | 2.7959 | 1.8296 | 1.1497 | 1.0426 | 1.1100 | 1.1583 | 1.1279 | 1.1095 | 1.0358 | 0.9017 |

C_{D}_{40°} | 2.6778 | 1.8864 | 1.0950 | 0.8214 | 0.8665 | 0.9258 | 0.9258 | 0.8302 | 0.6838 | 0.5228 |

C_{D}_{60°} | 2.4668 | 1.6280 | 0.7891 | 0.6285 | 0.6051 | 0.5749 | 0.4825 | 0.3671 | 0.2948 | 0.2417 |

C_{D}_{80°} | 2.3502 | 1.4341 | 0.7554 | 0.3545 | 0.2962 | 0.2948 | 0.2199 | 0.2077 | 0.0955 | 0.0818 |

(C_{D}_{20°} − C_{D}_{40°})/C_{D}_{40°} | 4.41% | −3.01% | 4.99% | 26.92% | 28.10% | 25.11% | 21.82% | 33.63% | 51.47% | 72.48% |

(C_{D}_{40°} − C_{D}_{60°})/C_{D}_{60°} | 8.55% | 15.87% | 38.76% | 30.71% | 43.20% | 61.02% | 91.86% | 126.17% | 131.97% | 116.27% |

(C_{D}_{60°} − C_{D}_{80°})/C_{D}_{80°} | 4.96% | 13.52% | 4.47% | 77.28% | 104.28% | 95.01% | 119.46% | 76.71% | 208.80% | 195.66% |

## CONCLUSIONS

Vegetation lodging can change the regime and resistance characteristics of overland flow. To investigate the flow characteristics of this special flow type, this study conducted various experimental simulations. The following conclusions can be stated:

- (1)
Under the given test conditions, the water depth and lodging angle are important factors affecting the flow regime.

*V*and*Re*are positively correlated with*h*, whereas*Fr*is negatively correlated with*h*. As the water depth increases, the flow regime changes from slow transition flow to slow turbulence flow. For the same water depth, a larger lodging angle results in larger values of*V*,*Fr*, and*Re*, and stronger turbulence in the flow. - (2)
The flow resistance characteristics of lodging vegetation are related to the degree of vegetation lodging, submerged state, and critical water depth. The relations between

*f*,*C*, and_{D}*h*indicate the same critical water depth, but there are still differences between how the flow resistance varies with water depth. In the non-submerged state,*f*is positively correlated with*h*, whereas in the submerged state, it is negatively correlated.*C*decreases rapidly with_{D}*h*when it is below the critical depth, whereas the submerged vegetation plays a greater role when*h*is above the critical depth, but*C*changes steadily with_{D}*h*. - (3)
At the same water depth, a larger lodging angle produces smaller values of

*f*and*C*and weaker water resistance. The Darcy–Weisbach resistance coefficient,_{D}*f*, is greatly affected by vegetation submergence. Statistical analysis of the numerical difference shows that in the non-submerged state,*f*will decrease by 9.30% for every 10° increase in the lodging angle; in the submerged state,*f*decreases by 26.70% for every 10° increase in lodging angle.*C*is greatly affected by the critical water depth. Up to the critical depth, when the lodging angle increases by 10°,_{D}*C*will decrease by 8.48%. When_{D}*h*is greater than the critical depth, every 10° increase in lodging angle causes*C*to decrease by 41.10%._{D}

Note that these conclusions are based on the premise of controlling for other influencing factors. To simplify the study, this experiment unified the simulated vegetation height and lodging angle. However, in reality, the slope surface is complex and changeable, and the elastic modulus of vegetation leads to different morphological characteristics, as well as bending and swinging under the action of water flow, and so the mechanism of water flow needs to be further explored. In addition, the effect of the movement of vegetation on overland flow is a multidisciplinary problem, and the transport of sediment, pollutants, and organisms should be considered. It is therefore necessary to further study the influence of slope vegetation on the transport characteristics of sediment and pollutants. The reliability and adaptability of these conclusions should also be explored in further detail.

## ACKNOWLEDGEMENTS

The authors would like to thank the National Natural Science Foundation of China (Grant no. 41471025), the Natural Science Foundation of Shandong Province (Grant no. ZR2017MEE055), and the Major Research and Development Program of Shandong Province (Grant no. 2016GSF117027 and 2016GSF117036) for supporting this project.