A Numerical Model of the Pollutant Transport in Rivers with Multi-Layer Rigid Vegetation

Abstract

River water pollution is a key environmental issue to human society. How to effectively simulate the flow velocity and pollution transport in a vegetated river can provide a theoretical basis for solving such problems. Based on previous experimental data, this article uses the lattice Boltzmann method and random displacement method to simulate the velocity distribution and nutrient transport in multi-layer rigid vegetated rivers. The simulation results indicate that incorporating the drag force of the vegetation into the model according to different vegetation layers can effectively simulate the velocity in a multi-layer vegetated river. Incorporating the turbulent diffusion and mechanical diffusion effects of nutrients caused by vegetation into the model can effectively simulate the effects of multi-layer vegetation on nutrient transport. This model can provide effective predictions of the flow velocity and pollution transport in multi-layer vegetation.

1. Introduction

With the development of society, the river water environment is receiving more and more attention from people [1,2]. The main reason for the deterioration of rivers’ water quality is that people discharge excessive production waste and domestic sewage into the river, causing eutrophication or heavy metal pollution, and so on. Rivers often contain a large amount of vegetation, including floating vegetation, submerged vegetation, and emergent vegetation. Vegetation is an important factor affecting the water environment of rivers [3,4]. It not only absorbs excess pollutants in the river, but also affects the hydrodynamics of the river [5,6]. At the same time, river vegetation also affects the hydrological conditions of rivers, including having an impact on the curvature of rivers, and so on. Studying the impact of vegetation on river hydrodynamics and pollutant transport can effectively provide theoretical assistance for the retention of river pollution.

The research and development of river flow dynamics have been improved a lot recently, and many scholars have made significant contributions to the study of the distribution of river flow dynamics. The research on river hydrodynamics can be divided into several methods: indoor laboratory flume velocity simulation, outdoor river hydrodynamic measurement, and numerical model simulation. For rivers without vegetation, the N-S equation can be directly used for the solution. Later, many studies also incorporated the influence of vegetation on river water dynamics into the solution. Vegetation has a certain drag effect on the water flow, and different vegetation types have different drag effects on the water flow [7,8]. Some scholars previously unified the resistance of vegetation to the water flow into a comprehensive roughness coefficient [9], but this was clearly a poor conceptual basis, in which the changes in flow structures that are caused by vegetation cannot be reflected appropriately. Some scholars express the resistance of vegetation to the water flow as an equation related to the drag coefficient [10]. The drag coefficient is expressed as a parameter related to hydraulic conditions, vegetation distribution patterns, and vegetation morphology [11,12]. On the basis of determining the impact of vegetation on water flow, the distribution pattern of the flow velocity in water flow affected by vegetation can be obtained. There are several analytical methods and numerical modeling methods for solving the velocity distribution in vegetated rivers. The analytical solution mainly solves the N-S equation with a vegetation drag force term through determined river boundary conditions [13]. Zhang et al. [14] defined two depth-averaged velocities for vegetation areas (including the depth-averaged velocity and vegetation-height-averaged velocity) and obtained analytical solutions for predicting the lateral distribution of the water depth averaged flow velocity. Numerical models mainly discretize the N-S equations through different methods, among which the most common are the finite volume method, finite element method, and finite integration method [15]. Shi et al. [16] used a fluid volume model combined with a porous medium model to conduct numerical simulations using numerical model to study the influence of partially nonsubmerged rigid vegetation on the free surface flow of curved open channels. Asif et al. [17] studied the effects of various vegetation patch configurations and inundation conditions on flow characteristics using numerical model and obtained good simulation results. Conventional research on vegetation and water flow mainly focuses on rigid or flexible vegetation of the same height, studying the vertical or horizontal distribution of velocity [18,19]. However, in nature, the vegetation height in rivers is usually not uniform, so some studies tend to explore the impact of vegetation combinations at different levels on hydrodynamics [20,21,22]. Huai et al. [23] studied the vertical distribution of the velocity in double-layered vegetation flows and found that the vertical velocity distribution can be divided into three layers. Based on the lattice Boltzmann model, Xuan and Bai [24] defined the drag force of vegetation in different layers and established a numerical model that can simulate the vertical distribution of the flow velocity in double-layered vegetation. Tang et al. [25] conducted an experiment with rigid vegetation of two heights in one side of a channel and found that a strong shear layer existed between non-vegetated and vegetated zones, indicating the reductive effect of vegetation on the flow velocity.

The transport of pollutants in rivers is not only affected by the flow velocity, but also by the vegetation in the river. There are many types of nutrients, most of which can be absorbed by vegetation and algae, leading to water blooms and other phenomena, which greatly affect the water quality and environment of rivers. Therefore, studying the transport laws of pollutants in rivers can effectively provide a scientific basis for reducing water blooms. The presence of vegetation accelerates the disturbance of the water flow, thereby increasing the turbulent diffusion of pollutants. Many researchers have studied the impact of vegetation on pollution diffusion through experiments. The influence of vegetation on pollutant transport is also reflected in the change in the pollutant diffusion coefficient. Due to the presence of vegetation, it causes a significant disturbance to the water flow and can also cause changes in the pollutant diffusion coefficient. The diffusion coefficients that generally have a significant impact on the diffusion of pollutants are the longitudinal and transverse diffusion coefficients. The lateral diffusion coefficient can be represented by the plant stem diameter, distance between plants (stem density), flow velocity, and resistance coefficient [26]. The coefficient increases with the increase in the vegetation density, but this effect disappears when the Reynolds number exceeds 240 [27]. Nepf [28] found that the obstruction of vegetation affects the diffusion of solutes, leading to mechanical dispersion. Taking these factors into consideration, some scholars have provided specific equations for the diffusion coefficient of pollutants in vegetated rivers. These equations have played a significant role in studying and simulating pollutant transport. Zhang et al. [29] recently developed a mathematical model considering mechanical dispersion. There are already many widely used models for the study of pollutant transport, which are mainly based on the material continuity equation to study the convective diffusion process of pollutants in rivers. Lu and Dai [30] studied the effect of submerged vegetation on pollution transport in an open channel using large eddy simulation. The model quantitatively predicts the trend of decrease in the concentration distribution along the flow direction with the increase in the vegetation density. How to define the boundary between vegetation and water flow in the model of vegetated river channels is also a very important part, because the hydrodynamic forces and diffusion coefficients of pollutants in the water flow layer and vegetation layer are different. Accurately defining the boundary between the vegetation layer and water flow layer can help improve simulation accuracy. Okamoto and Nezu [31] calculated the vegetation elements as the non-slip condition by using fine grids without introducing any additional drag force terms and provided a large eddy simulation of the 3-D flow structure and mass transport in open-channel flows with submerged vegetation.

Some studies have been conducted on the flow velocity in multi-layer vegetated rivers, but how the complex impact of vegetation on the water flow affects the pollutant transport in such channels has not yet been discovered. Meanwhile, previous research has focused on studying the longitudinal and transverse diffusion coefficients of pollutants in vegetated rivers. For multi-layered vegetation flows, due to the significant changes in vertical hydrodynamic forces, the difference in the vertical diffusion coefficients is also the main factor affecting pollutant transport. The changes in velocity caused by multiple layers of vegetation are more complex, and on this basis, they can also have a significant impact on the transport of pollutants. At this point, defining the transport laws of pollutants in different flow velocity layers is the key to solving such problems. Based on previous experimental data, this article establishes a numerical model for pollutant transport in multi-layer vegetation channels using the lattice Boltzmann method and random displacement method, which can provide a theoretical basis for the treatment of pollutants in multi-layer vegetation channels.

2. Materials and Methods

2.1. Numerical Model

2.1.1. Hydraulic Model

To solve the hydrodynamic distribution of rivers, it is necessary to first construct a continuous hydrodynamic equation under the same conditions. The impact of multi-layer vegetation on the water flow velocity is mainly reflected in the drag force of different vegetation layers, and the hydrodynamic control equation in a multi-layer vegetated channel can be obtained by using the method described by Xuan and Bai [24]:

$$\frac{\partial u_i}{\partial t}+\frac{\partial \left(u_i{u}_j\right)}{\partial t}=\left(\nu +{\nu }_e\right)\frac{{\partial }^2{u}_i}{\partial x_j{x}_j}-g\frac{\partial z_b}{\partial x_i}-S_{bi}$$

(1)

$$\frac{\partial u_i}{\partial t}+\frac{\partial \left(u_i{u}_j\right)}{\partial t}=\left(\nu +{\nu }_e\right)\frac{{\partial }^2{u}_i}{\partial x_j{x}_j}-g\frac{\partial z_b}{\partial x_i}-S_{bi}-S_{fi}$$

(2)

where the Einstein summation convention over Latin indices is adopted; $t$ denotes the time; $u_i$ is the velocity; $\nu$ and ${\nu }_e$ represent kinematic and eddy viscosity, respectively; and $z_b$ is the bed elevation.

$S_{bi}$ is the bed shear stress term in $i$ direction and expressed as a Manning formula.

$$S_{bi}=\frac{g{n}^2}{h^{1/3}}{u}_i\sqrt{u_j{u}_j}$$

(3)

where $n$ refers to Manning’s coefficient, and $h$ is the water depth.

There have been many studies on the effect of the drag force of vegetation on water flow, which is related to the drag force coefficient, vegetation density, and flow velocity. $S_{fi}$ is the drag force of vegetation, which can be obtained by [22]

$$S_{fi}=\frac{1}{2}{C}_{D}a{u}_i^2$$

(4)

where $C_D$ is the coefficient of the rigid vegetation, which can be assumed to be 1 [23]; $a$ is the vegetation density coefficient, and $a=\alpha \times d$; $\alpha$ is the vegetation density, and $d$ is the diameter of the vegetation.

The lattice Boltzmann model is a mesoscale hydrodynamic model that has been widely used in river flow velocity simulation due to its ability to handle complex boundary problems [32,33]. The lattice Boltzmann method (LBM) is a computational fluid dynamics method based on mesoscopic simulation scales. Compared with other traditional CFD calculation methods, this method has the characteristics of a mesoscopic model that lies between the micromolecular dynamics model and the macroscale continuous model. Therefore, it has advantages such as a simple description of fluid interactions, easy setting of complex boundaries, ease of parallel computation, and easy implementation of programs. The LBM has been widely recognized as an effective means of describing fluid motion and dealing with engineering problems. The lattice Boltzmann method is adopted to simulate the velocity distribution in multi-layer vegetated channels, and there are two processes (collision process and migration process) in the lattice Boltzmann method [33,34]. These two processes can be expressed by the following equation:

$$f_{\epsilon }\left(x+e_{\epsilon }∆t, t+∆t\right)=f_{\epsilon }\left(x, t\right)-\frac{1}{{\tau }_t}\left[f_{\epsilon }\left(x, t\right)-f_{\epsilon }^{eq}\left(x, t\right)\right]+\frac{∆t}{N_{\epsilon }{e}^2}{e}_{\epsilon i}{F}_i$$

(5)

where $f_{\epsilon }$ represents the distribution function of particles; $f^{eq}$ is the local equilibrium distribution function; $x$ is the space vector in Cartesian coordinates; $e=∆x/∆t$; $∆x$ is the lattice size; $∆t$ is the time step; ${\tau }_t$ is the total relaxation time parameter; and $F_i$ denotes the external forces.

For a water flow layer with vegetation, it is necessary to add a term describing the impact of the drag of vegetation on the water flow. The external forces $F_{\epsilon i}$ can be expressed in the flow layer and vegetation layer as follows:

$$\left\{\begin{array}{c}{F}_i=-g\frac{\partial z_b}{\partial x_i}-\frac{g{n}^2}{h^{\frac{1}{3}}}{u}_i\sqrt{u_j{u}_j} Non-vegetation layer\\ F_i=-g\frac{\partial z_b}{\partial x_i}-\frac{g{n}^2}{h^{\frac{1}{3}}}{u}_i\sqrt{u_j{u}_j}-\frac{1}{2}{C}_D{a}_n{u}_i^2 Vegetation layer\end{array}\right.$$

(6)

where $a_n$ is the vegetation density coefficient of different vegetation layers.

$N_{\epsilon }$ is a constant and can be defined by the following formula:

$$N_{\epsilon }=\frac{1}{e^2}{{\displaystyle \sum }}_a{e}_{\epsilon i}{e}_{\epsilon i}$$

(7)

The lattice Boltzmann method simulates the movement of particle clusters, including one-dimensional, two-dimensional, and three-dimensional models. For the problem simulated in this paper, as it simulates the vertical distribution of flow velocity, a two-dimensional (D2Q9) lattice model can be used. In the D2Q9 model, $e_{\epsilon i}$ and $f_{\epsilon }^{eq}$ can be calculated by the following equation:

$$e_{\epsilon i}=\left\{\begin{array}{cc}\left(0, 0\right),\hfill & \alpha =0\\ e\left[cos\frac{\left(\alpha -1\right)\pi }{4},sin\frac{\left(\alpha -1\right)\pi }{4} \right],\hfill & \alpha =1, 3, 5, 7\\ \sqrt{2}e\left[cos\frac{\left(\alpha -1\right)\pi }{4},sin\frac{\left(\alpha -1\right)\pi }{4} \right],\hfill & \alpha =2, 4, 6, 8\end{array}\right.$$

(8)

$$f_{\epsilon }^{eq}=\left\{\begin{array}{cc}1-\frac{5g}{6e^2}-\frac{2}{3e^2}{u}_i{u}_i,\hfill & \alpha =0\\ \frac{g}{6e^2}+\frac{1}{3e^2}{e}_{\alpha i}{u}_i+\frac{1}{2e^4}{e}_{\alpha i}{e}_{\alpha j}{u}_i{u}_j-\frac{1}{6e^2}{u}_i{u}_i,\hfill & \alpha =1, 3, 5, 7\\ \frac{g}{24e^2}+\frac{1}{12e^2}{e}_{\alpha i}{u}_i+\frac{1}{8e^4}{e}_{\alpha i}{e}_{\alpha j}{u}_i{u}_j-\frac{1}{24e^2}{u}_i{u}_i,& \alpha =2, 4, 6, 8\end{array}\right.$$

(9)

For the relaxation time parameter ${\mathrm{\tau }}_{\mathrm{t}}$, the following formula can be used:

$${\tau }_t=\frac{\tau +\sqrt{{\tau }^2+18C_s^2/\left(e^2\right)\sqrt{\prod ij\prod ij}}}{1}$$

(10)

$$\prod ij={{\displaystyle \sum }}_a{e}_{\alpha i}{e}_{\alpha j}\left(f_{\alpha }-f_{\alpha }^{eq}\right)$$

(11)

The boundary conditions under different forms are shown in Figure 1. For submerged vegetation, the velocity layer is divided into a water flow velocity layer and a vegetation velocity layer. For emergent vegetation, the velocity layer is only the vegetation velocity layer. For a multi-layer vegetation flow, the velocity layer is divided into the first vegetation velocity layer, the second vegetation velocity layer, and the third vegetation velocity layer. For the entrance of the channel, this article adopts a constant flow rate entrance condition and defines the boundary condition equation at the entrance of the D2Q9 model as follows:

$$f_1=f_3+\frac{2u}{3}rhow$$

(12)

$$f_5=f_7+\frac{u}{6}rhow$$

(13)

$$f_8=f_6+\frac{u}{6}rhow$$

(14)

$$rhow=\left(f_9+f_2+f_4+2\left(f_3+f_6+f_7\right)\right)/\left(1-u\right)$$

(15)

For the boundary conditions at the outlet, this article adopts free outflow boundary conditions. The free boundary outflow equation of the D2Q9 model is defined as follows:

$$f_1=2f_1\left(x-1\right)-f_1\left(x-2\right)$$

(16)

$$f_5=2f_5\left(x-1\right)-f_5\left(x-2\right)$$

(17)

$$f_8=2f_8\left(x-1\right)-f_8\left(x-2\right)$$

(18)

Using free surface boundary conditions near the water surface, the boundary condition formula of the D2Q9 model is defined as follows:

$$f_i=f_i\left(y-1\right)$$

(19)

2.1.2. Pollution Transport Model

There are many methods for simulating pollutant transport, among which the random displacement method is one of the most widely used. It is based on the random walk of pollutant particles in the water flow under the influence of flow velocity and pollutant diffusion, simulating the transport law of pollutants in vegetated rivers. Finally, by counting the total number of pollutant particles at different heights, the vertical distribution pattern of the pollutant concentration is given. The random displacement method can be used to simulate the convective diffusion process of particles in fluids, and due to its high accuracy, it is often used to simulate the diffusion of pollutants in rivers [35]. The random displacement method is applied to the simulation of pollutant transport in a multi-layer vegetated channel, and the equation to simulate the particle position is expressed as follows [36]:

$$x_{i+1}=x_i+u\left(z_i\right)∆t$$

(20)

$$z_{i+1}=z_i+\left(\frac{d{D}_t}{dz}\left(z_i\right)\right)∆t+R\sqrt{2D_t\left(z_i\right)∆t}$$

(21)

where $∆t$ denotes the time step, and $R$ represents a random number showing a normal distribution with mean 0 and standard deviation 1; $C$ refers to the nutrient concentration in the water (mg/L), and $D_t$ is the total diffusion coefficient of the pollution (m²/s).

The diffusion law of pollutants in different layers can be given based on the diffusion coefficient of pollutants. The diffusion coefficient of pollutants in the water flow layer only has a single molecular diffusion coefficient, while for the vegetation layer, the influence of different vegetation densities on the pollutant coefficient needs to be considered. The diffusion of pollutants in vegetation channels is more complex than in conventional channels, and the impact of the disturbance caused by vegetation on pollutant diffusion needs to be considered. The total dispersion in the vegetation can be described by the vegetation resistance and vegetation density as follows [37]:

$$D_t=D_l+\epsilon {\left(C_{df}\alpha b^2\right)}^{1/3}{u}_{m}b+\frac{{\beta }^2}{2}\alpha u_m{b}^3$$

(22)

where $\epsilon =0.81$ and $\beta =\sqrt{2}$ are constants used by Nepf [38] and Lu and Dai [37], $b$ is the stalk width, an average projection width within a 1 cm interval is used in this paper, and $D_l$ is the molecular diffusion coefficient.

In the simulation of pollutant diffusion, it is also very important to define the boundary conditions of the model. Pollutants cannot diffuse through the bottom of the riverbed and water surface, so it is necessary to define the boundaries of the model. Boundary conditions should be set at the bottom of the sink and the free water surface to prevent particles from swimming out of the sink boundary:

$$z_i=-z_i, z_i<0$$

(23)

$$z_i=2h-z_i, z_i>h$$

(24)

2.2. Validation Data

The validation data in this article come from previous experiments and are mainly used to verify the accuracy of the model in simulating the flow velocity and pollutant transport of multi-layer vegetation. The data are derived from Lou et al. [39], and the basic parameters of the experiment are shown in

Table 1. Experimental parameters.

Treatment	Discharge (L/s)	Vegetation Height (cm)	Stem Number	Vegetation Density	Vegetation Diameter (mm)
Case A	0.9	5	95	317	8
Case E	0.9	20	95	317	8
Case H	0.9	5 + 10 + 20	32 + 32 + 31	317	8

. The data include hydrodynamic and pollutant transport experiments at different vegetation heights, as well as hydrodynamic and pollutant transport experiments at different vegetation height combinations (Figure 1). The solute discharge system consisted of a peristaltic pump and a backpressure valve. The discharge outlet was placed at a height of 10 cm (shown in Figure 2). Non-adsorptive solute dye tracer carmine was discharged at 10.54 mL/s in all tests.

3. Results

The simulation results for the flow velocity are shown in Figure 3, and it can be seen that the simulated values are very close to the measured values. The flow velocity of the submerged vegetation flow is clearly divided into two layers, while that of the emergent vegetation flow is relatively uniform. The flow velocity of the multi-layer vegetation flow is divided into three layers. In Figure 3, we can see that the velocity distribution pattern of the emergent vegetation flow is low at the bottom, gradually increasing, and finally stabilizing, which is consistent with previous research [40,41]. The velocity distribution of the submerged vegetation flow shows a two-layer distribution, with the velocity distribution of the lower layer being the same as that of the emergent vegetation, and the velocity distribution of the upper layer being similar to that of the non-vegetation, which is consistent with previous research [8,42].

The simulation diagram of pollutant transport is shown in Figure 4, and it can be seen that the simulation accuracy is very high. In all treatments, pollutants are lower on the upper and lower sides and higher in the middle. Because the random displacement method is a simulation method for counting the number of particles, it differs from traditional convection diffusion models by plotting curves between each point based on the statistical quantity of pollutants. Due to a certain degree of randomness, although the trend of pollutant concentration does not change, the concentration between each point is not a smooth curve, but there are certain fluctuations. This is consistent with previous research [35].

4. Discussion

The flow velocity in a multi-layer vegetation flow exhibits a three-layer distribution, with each layer having a similar flow velocity to the submerged vegetation. It can be inferred that the stratification of the flow velocity is the same as the number of layers of vegetation. In the numerical simulation that we use, we mainly define the vegetation drag force for different vegetation layers, which also proves that our numerical model can be applied to more layers of vegetation flow. The vegetation arrangement in the experiment is a parallel arrangement, and the vegetation drag force coefficient given at this time is 1. However, for different forms of vegetation arrangements, such as a cross-arrangement and random arrangement, the drag force coefficient of the rigid vegetation will change and can be obtained from previous research results [43].

The simulated vegetation used in this article is rigid vegetation, but flexible vegetation often exists in natural river channels. The hydrodynamic study of multi-layer flexible vegetation is more complex [44]. Firstly, we need to consider the deformation of flexible vegetation under hydrodynamic conditions, where the definition of a vegetation layer boundary is a function related to the elastic modulus and shape of the vegetation [45]. At the same time, it is necessary to consider that the shape of flexible vegetation is not uniform, and the projection area of flexible vegetation in different vegetation layers needs to be incorporated into the simulation [46]. Finally, for flexible vegetation, its drag coefficient is often smaller than that of rigid vegetation, and its determination should also be analyzed based on actual conditions [47]. So if we want to study the distribution of the flow velocity in multi-layer flexible vegetation, we need to thoroughly consider the above issues, which is also the focus of our next research work.

Moreover, the transport of pollutants is influenced by both the flow velocity and turbulent diffusion, which is also the reason for the different changes in pollutant concentration under different vegetation cover conditions. Therefore, incorporating turbulent diffusion and mechanical diffusion caused by vegetation into the diffusion coefficient makes our model simulation results more accurate, which is consistent with previous research [48]. Due to the severe impact of vegetation layers on the transport of pollutants, especially the more complex impact of multi-layer vegetation, this is also the main reason why the distribution pattern of pollutants in multi-layer vegetation channels is different from conventional channels [49].

Because the study of the retention effect of channels on pollutants mainly involves the retention of pollutants by vegetation roots, we are more concerned with the concentration of pollutants close to the bottom of the riverbed [50]. From Figure 3, we can see that the relative concentration of pollutants in the riverbed is the highest in the emergent vegetation channel, which is also the most favorable solution for vegetation to remove excess pollutants. For studying the efficiency of vegetation in removing pollutants, we can add a pollutant retention module to the model, defining the adsorption of pollutants by sediment as different adsorption equation modes. This can lay the foundation for simulating the retention of pollutants by vegetation channels.

The transport of nutrients is mainly influenced by the flow velocity and diffusion coefficient [51]. The distribution of the flow velocity in different vegetation flows is different, which is also one of the reasons for the different distribution patterns of nutrients. Vegetation can cause an increase in the diffusion coefficient, which also affects the transport of nutrients. The more vegetation layers there are, the more uniform the vertical distribution of the nutrient concentration is (Figure 4), which should be caused by differences in the flow velocity and diffusion coefficient. For a vegetation water flow, understanding the vertical concentration distribution of nutrients is very useful, as the main removal method of nutrients is composed of sediment adsorption, vegetation absorption, and microbial transformation between vegetation [52,53,54], which can provide a theoretical reference for nutrient retention in vegetation channels.

Compared to analytical solutions, numerical models can be more conveniently applied in practical engineering, because analytical solutions require more precise control conditions, which are rarely achieved in natural environments. The lattice Boltzmann method can be applied to more complex boundary conditions and complex natural environments. The random displacement method can simulate the transport of nutrients well, and the accuracy of the transport is mainly affected by the distribution of the flow velocity and the accuracy of the nutrient diffusion coefficient. The diffusion coefficient given in this article mainly refers to the diffusion coefficient of nutrients in rigid vegetation channels. There are also many flexible vegetation channels in nature, and further discussion is needed on the diffusion coefficient of pollutants in flexible vegetation channels. Meanwhile, more outdoor validation experiments need to be conducted to determine the outdoor application accuracy of our model.

There are also certain research limitations in this study. Firstly, all experiments are based on indoor experiments, and the outdoor river environment is more complex. Outdoor rivers do not always have flat bottoms, and there may be uneven bottoms or multiple cross-sections. In this case, the vertical flow velocity distribution of the river will exhibit significant differences from the results of this study. This study should also obtain validation from outdoor experimental data on these types of rivers. At the same time, there are a large number of animals and microorganisms living in the river, and their presence can also affect the transport of pollutants in the river. This has not been discussed in this article yet and should be carried out as soon as possible in the following work.

5. Conclusions

Based on previous experimental data and numerical models, this article studied the vertical distribution of the flow velocity and nutrient concentration in a multi-layer vegetation water flow and obtained the following results:

(1)

The distribution pattern of the flow velocity in a multi-layer vegetation flow is related to the number of vegetation layers, and the flow velocity layering is consistent with the number of vegetation layers. For simulating the vertical distribution of the flow velocity in a multi-layer vegetation flow, the drag force of vegetation can be layered according to the number of vegetation layers, which is mainly related to the density of vegetation in different layers. The simulation model has a high simulation accuracy.

(2)

The distribution pattern of nutrients in a multi-layer vegetation water flow is related to the number of vegetation layers. The more vegetation layers there are, the more uniform the distribution of nutrient concentrations is. The diffusion of nutrients caused by vegetation is mainly turbulent diffusion and mechanical diffusion. By substituting the diffusion coefficient caused by vegetation into the model, the model simulation has high accuracy.

(3)

At the same time, there are also some shortcomings in this research. Firstly, all the validation data come from indoor experiments. The conditions of outdoor river channels are more complex, and the types and arrangements of vegetation are also significantly different from indoor experiments. The organisms and microorganisms in the river channels also have a significant impact on the transport of pollutants. These situations should be further studied in future applications.