Sustainable development is an important issue in the world. The presence of vegetation in river systems contributes to the sustainability of rivers and enhances the self-cleaning capacity of water (Lozanovska et al., 2020). However, the existence of vegetation will change the channel resistance and raise the water level (Rivaes et al., 2017). Ecological discharge is an important parameter in the ecological channel. The existence of vegetation causes some interference on the flow field and flow monitoring. Therefore, it is necessary to study the velocity distribution of the channel with flexible vegetation.

The effect of vegetation distribution on mean flow velocity and turbulence characteristics in a channel is generally studied by model experiments. Järvelä (2002) used natural aquatic grass, sedge, and willows as test material to study the influence of plants on flow velocity distribution by introducing plant parameters that characterize the flexibility and morphology of plants in flow. Bennett et al. (2002) analyzed the influence of vegetation belts arranged at intervals between two sides of water channel on flow characteristics by model test. It was found that vegetation belts carried flow to the other side and the intensity of flow were related to the density of vegetation. Wilson et al. (2005) developed a three-dimensional numerical model and compared it with a standard turbulent flow model to analyze the effect of willows on flow, pointing out that determining the degree of plant bending in flow is important for the study of the interaction mechanisms between vegetation and flow. Bouma et al. (2005) analyzed the influence of vegetation belt with specific shape on flow rate and turbulence and proposed that the distribution of flow rate is closely related to the spacing of vegetation belt. Neumeier (2005) measured the flow velocity and turbulence characteristics of the wake after it crossed the marsh vegetation and inferred that the larger vertical flow velocity and higher turbulence in front of the vegetation could reduce sediment deposition. Helmiö (2002) developed a one-dimensional model to solve the problem of composite channels with vegetation, in which the effect of flow distribution caused by vegetation was considered and the model was validated by using data from the Rhine river. He pointing out that vegetation density and the width of the diffuse zone have a large effect on the transport capacity of the main channel and significantly reduce the flood flow capacity of the channel. Leu et al. (2008) established a two-dimensional model to study the velocity distribution of five different submerged plants in different water depths, pointing out that the submerged plants can reduce the velocity and can meet the requirements of flood control. Zong and Nepf (2009) carried out model tests on flow in semi-covered vegetated river and discussed the changes of flow velocity and turbulence characteristics in vegetation and non-vegetation areas and found that flow can be divided into adjustment areas and fully developed areas. Siniscalchi et al. (2012) measured the flow characteristics of submerged flexible vegetation by flow channel experiment. It was found that the turbulence intensity corresponding to the front of vegetation and the top of vegetation increased and a negative Reynolds stress appeared in the vegetation layer, reflecting the influence of vegetation morphology on the flow velocity and turbulent flux. Wang et al. (2015) proposed a method to calculate the analytical solution of the vertical distribution of the mean flow velocity in the flow direction of an open channel containing flexible vegetation when a large bend occurs and derived a formula for the mean flow velocity of the linear flow resistance in the momentum equation. Okamoto et al. (2016) study how plant motions were coupled to strong oscillations in flow velocity associated with the “monami” phenomenon and its vertical extent in an open channel with flexible vegetation. Wang et al. (2016) simulated the water flow due to wind action on the water surface in a shallow lake through experiments. The effects of different densities of aquatic flexible vegetation on the hydrodynamic characteristics at different wind speeds were investigated. By analyzing the changes of vegetation drag (C_d) and friction (C_f) coefficient with flow and vegetation conditions under different test conditions, Pu et al. (2019) obtained a model of velocity distribution in open channel with flexible vegetation.

Although there are many studies on the hydrodynamic characteristics of flow with flexible vegetation, most of them are still limited to the corresponding hydrodynamic characteristics of specific vegetation. The characteristics of the flow field in the upper layer of vegetation have not been recognized after the flows through the vegetation and most of the current studies focused on the hydrodynamic characteristics of the flow in the center of the open channel. In fact, the hydrodynamic characteristics of the channel center and the open channel sidewalls are not the same. There are fewer studies on the phenomenon of downward shift of the maximum flow velocity point for the channel sidewall. The division of velocity zoning of channel section is not clear. The research results are not universal, so the research needs to be further strengthened.

This article studies on the velocity distribution law of ecological river with vegetation. Based on the vegetation riverbed theory and bursting phenomenon, the velocity distribution law of the whole section of the flow is established. Combined with the physical model test of ecological channel, the correctness of velocity distribution law is verified. Meanwhile, the flow velocity zoning phenomenon of the ecological open channel is discussed with the test results. It provides a solution for the flow measurement of ecological river.

The model experiment was carried out on the open channel device in the hydraulic public test hall of the China Agricultural University. The rectangular channel is 6 m long, 0.8 m wide, 0.6 m high, and the slope is 5‰ (Figure 1). In order to ensure that the flow at the water inlet is as uniform as possible, the water inlet tank is aligned with the center line of the channel and a turbulent honeycomb is arranged at the water inlet of the tank. This experiment controls the water depth in the channel by controlling the valve system on the return water pipeline, so that the flow in the whole channel section can easily reach the uniform flow state in the open channel.

In this experiment, the flexible vegetation was simulated by plastic water plants; every plant was 0.06 m high, 0.03 m in diameter, and the total length of the vegetation section was 4 m. The vegetation is glued to the prefabricated perforated plastic plate, which is laid at the bottom of the sink. The vegetation strip was a single row of vegetation and equidistant (Figure 2); then, the position of the vegetation above the vegetation was measured with the plant as the reference.

The three-dimensional ultrasonic acoustic Doppler velocimetry (ADV) is used in this experiment to measure the velocity and ADV can measure the three-dimensional flow field information. The velocity range of ADV is from 0.001 to 4.5 m/s, the resolution can reach 0.0001 m/s, and the relative error is <1% of the measured velocity. To minimize the influence of ADV noise, the sample size of each measurement point in this experiment is about 2,000 times and the experiment time is 200 s. The downstream position is selected to ensure the stability of vegetation flow conditions.

The section of rectangular channel is symmetrical and the velocity distribution of the section is also symmetrical, so only half of the test data with the vertical line as the boundary line in the open channel need to be measured. Each measuring point is a predivided grid node. It is proposed to arrange one measuring line from the center vertical line to the right at every 0.04 m and one measuring point at every 0.01 m and to encrypt appropriately when close to vegetation (Figure 3), so as to ensure that the measured data can accurately reflect the actual flow field. Four flow conditions are set in the test. The specific test conditions are shown in Table 1.

The experiment is completed based on the experimental platform in section “Experiment” and the measured data under different flow conditions are drawn into the contour (Figure 4). It can be seen from Figure 4 that the shape of the velocity curve is similar under each condition. The velocity distribution near the vertical line in the open channel generally decreases more evenly from the water surface to the vegetation as shown in Figure 4A; in other words, the maximum velocity point appears near the water surface. In the region near the sidewall, for the same z-coordinate of the velocimetric plumb line, it can be found that the velocity near the water surface is not the maximum and the maximum velocity point moves downward. There is also an appeal phenomenon in Figures 4B–D. It shows that it is not well considered to use a velocity formula to describe the velocity distribution of the whole section (Yang et al., 2004). Based on the antecedent analysis of contour, we use the experimental data to verify the theoretical formula derived in section “Modeling the Velocity Distribution in Channel With Flexible Vegetation.”

In fact, it is because the flexible vegetation is inverted with the flow, which is equivalent to forming a “vegetation riverbed” with flexible vegetation as the bottom wall, so the flow in most non-vegetated areas still conforms to the logarithmic law. The biggest difference between the logarithmic velocity distribution formula of vegetated channel and smooth channel is the difference of “riverbed,” which is also reflected in the VRL. In the VRL, it is obvious that the denominator of logarithmic term is the height of deflected vegetation (h_v), while the denominator of logarithmic term of traditional velocity distribution is the boundary layer separation point (Nikuradse, 1930). It shows that the height of deflected vegetation (h_v) is the characteristic length of open channel with vegetation. The characteristic length has also been mentioned in the study by Ghisalberti and Nepf (2002) and they believe that it can be expressed by using the momentum thickness. The momentum thickness needs to be obtained from the flow velocity calculations at the upper and lower boundaries of the mixed layer. In contrast, the calculation of the VRL is simpler.

Similarly, the VRL and the BPL have some similarities. The first term of the two equations is the same; it shows that the BPL also reflects the influence of flexible vegetation on flow. The difference appears in the following expressions. In the VRL, only one-dimensional mainstream velocity is used for calculation. The experimental results show that the flow near the center of the channel is closer to uniform flow and only the influence of the main flow direction can be considered. Most of the flow velocity equations proposed by researchers nowadays only consider the effect of flow velocity in the mainstream direction. For example, the flow velocity equation proposed by Nepf (2011) is partitioned for the vertical direction, but not for the cross-sectional flow velocity of the channel. However, there is a significant downward shift of the maximum velocity point in the region close to the sidewall. It is usually considered that the flow is influenced by the sidewall and produces a secondary flow. The manifestation of secondary flow is that there is a vortex near the water surface, which has a strong horizontal flow pointing to the center. This is the main reason for the location of the maximum flow velocity below the free surface (Nezu and Rodi, 1986). So, the vertical velocity should be included in the calculation. The BPL has a coefficient A, which includes the influence of mainstream velocity and vertical velocity.

Through the above analysis, it can be found that the flow velocity of open channel has obvious zoning phenomenon in the cross section. Take the maximum velocity point on the velocity measuring vertical line as the dividing point, next connect the dividing points on each vertical line and draw the red dividing line in Figure 8. The region above the dividing line is the region affected by the sidewall and the velocity in this region can be calculated by the BPL. The velocity in the area below the dividing line can be calculated by the VRL. The form of the theoretical partition line proposed by Daido (1992) and Yang and Lim (1997), who considered that the form of the dividing line is related to the roughness ratio of the sidewall to the sidewall and is plotted in their proposed theoretical dividing line in the figure (blue and brown lines). Figure 8 shows that there is a gap between the theoretical dividing line and the actual dividing line clearly. The theoretical dividing line is a straight line near the sidewall, while the actual dividing line is a curve. Taking Figure 8A as an example, the dividing line in the near sidewall region has two particularly obvious inflection points, which is the same as that in Figures 8B–D. It shows that the split line is not a simple primary function form, but has a more complex function form, which will be discussed in depth in future studies.

This article studies the flow velocity distribution law with flexible vegetation theoretically and verifies the vegetation riverbed theory and the bursting phenomenon theory based on specific experimental data. The similarities and differences between the VRL and the BPL are also discussed. Based on the section dividing theory, the velocity dividing line of open channel with flexible vegetation is discussed. The main conclusions can be summarized as follows:

The raw data supporting the conclusions of this article will be made available by the authors, without undue reservation.

SW contributed to the conceptualization, methodology, formal analysis, investigation, resources, data curation, writing—original draft, and visualization. YZ contributed to the investigation, resources, and data curation. TL contributed to the conceptualization, resources, writing—review and editing, and supervision. SL contributed to the investigation and resources. MZ contributed to the writing—review and editing. YH contributed to the conceptualization, validation, writing—review and editing, supervision, and funding acquisition. All authors contributed to the article and approved the submitted version.

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

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