# Numerical Modeling of the Dispersion Characteristics of Pollutants in the Confluence Area of an Asymmetrical River

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Mathematical Models and Verification

#### 2.1. Control Equations

^{2};

^{3};

^{3};

^{3};

^{2}; and

^{2}[25].

_{w}is the volume fraction of water. For α

_{w}= 0, the calculation cells all occur in the gas phase; for α

_{w}= 1, the calculation units all occur in the water phase; and for 0 < α

_{w}< 1, the calculation units comprise both the water and gas phases [26].

#### 2.2. Model Validation

#### 2.2.1. Verification Model Overview

^{3}/h, and the inlet flow of the branch channel is 4.12 m

^{3}/h. The initial water level both upstream and downstream is 0.16 m. The pollutant concentration at the inlet of the main channel is 0 μg/L, and the pollutant concentration at the inlet of the branch channel is 2000 μg/L. The model structure is shown in Figure 1a. A structured orthogonal grid is selected. At the same time, considering the computational cost, only a part of the solid sidewall is selected during meshing. The specific grid diagram is shown in Figure 1b.

#### 2.2.2. Numerical Method

#### 2.2.3. Model Verification

_{si}is the measured value at the study measurement point, mg/L; $\overline{\mathrm{C}}$ is the average measured value; and n is the number of valid measured and simulated values.

## 3. Program Design

#### 3.1. Overview of the River Model

#### 3.2. Measurement Point Placement and Cross-Sectional Monitoring

_{1}= 0.15, S

_{2}= 0.3, S

_{3}= 0.45, S

_{4}= 0.61, and S

_{5}= 0.75. A measurement cross section is set every 0.8 m from the intersection along the water flow direction, located in a total of 12 cross sections of B

_{1}= 0, B

_{2}= 0.8, B

_{3}= 1.6, B

_{4}= 2.4, B

_{5}= 3.2, B

_{6}= 4, B

_{7}= 4.8, B

_{8}= 5.6, B

_{9}= 6.4, B

_{10}= 7.2, B

_{11}= 8, and B

_{12}= 8.8. The calculation area boundary and section settings are shown in Figure 5.

#### 3.3. Calculation and Setting Conditions

#### 3.3.1. Calculation Conditions

_{1}is the upstream flow of the main stream, Q

_{2}is the incoming flow of the tributary, and R = Q

_{2}/Q

_{1}is the discharge ratio, i.e., the ratio of the incoming flow of the tributary to that of the main stream. Among them, the tributary flow is constant at Q

_{2}= 36.29 m3/h. The concentration difference is the difference between the pollutant concentration at the tributary inlet (C

_{2}) and that at the main stream inlet (C

_{1}), denoted as Cg = C

_{2}− C

_{1}. A clean water simulation is conducted with this model, with the pollution concentration set to C1 = 0 μg/L in the main stream input section. For more information, refer to Table 3.

#### 3.3.2. Establishing the Boundary Conditions

## 4. Analysis of Results

#### 4.1. Analysis of the Horizontal Diffusion Characteristics of Pollutants

^{2}in size. For R = 0.187, the pollutant concentration was 2000–1667, 1667–1333, 1333–1000 and 1000–667 μg/L, respectively, and the size of the resulting pollution zone was 3.90 m

^{2}, which is 15.61% smaller than that for R = 0.267. For R = 0.187, the pollutant concentration distribution was the same as that for R = 0.187, but the pollution zone proportion in the 1000–667 μg/L range increased, and the size of the resulting pollution zone was 2.97 m

^{2}, which is 10.82% smaller than that for R = 0.187. In summary, the discharge ratio greatly impacts the pollution zone. The higher the discharge ratio is, the wider the formed pollution zone and the higher the concentration gradient in each section.

^{2}; for b/h = 3, the size of the pollution zone is 3.90 m

^{2}, which is 13.66% smaller than that for b/h = 3.75. For b/h = 2.5, the size of the pollution zone is 3.65 m

^{2}, which is 7.43% smaller than that for b/h = 3. In summary, the width-depth ratio exerts an impact on the horizontal diffusion of pollutants. The higher the width-depth ratio is, the wider the pollution zone, but the impact is not as notable as that of the discharge ratio.

#### 4.2. Trajectory Line of Pollutant Mixing Interface Changes along the Path

_{p}of the two rivers after complete mixing can be calculated, as shown in Table 5, and the trajectory of the mixing interface is visualized.

_{p}= (Q

_{1}C

_{1}+ Q

_{2}C

_{2})/(Q

_{1}+ Q

_{2})

_{1}and C

_{2}are the tributary and main stream pollution concentrations, respectively, and Q

_{1}and Q

_{2}are the tributary and main stream inflows, respectively.

#### 4.2.1. Influence of the Discharge Ratio on Trajectory Line Variation along the Pollutant Mixing Interface

#### 4.2.2. Influence of the Width-Depth Ratio on Trajectory Line Variation along the Pollutant Mixing Interface

#### 4.2.3. Influence of the Concentration Difference on the Trajectory along the Pollutant Mixing Interface

#### 4.3. Mixing Characteristics of the Pollutant Concentration

_{i}− C

_{p})/C

_{p}

_{i}is the average mass concentration of pollutants in the section, and C

_{p}is the weighted average predicted concentration value of pollutant flow, which can be calculated by Equation (11).

#### 4.3.1. Effect of the Discharge Ratio on the Pollutant Mixing Characteristics

#### 4.3.2. Effect of the Width-Depth Ratio on the Mixing Characteristics of Pollutants

#### 4.3.3. Effect of the Concentration Difference on the Mixing Characteristics of Pollutants

## 5. Discuss

## 6. Conclusions

- (1)
- The dependability of the numerical model is simulated and assessed. According to the verification findings, the flow rate and pollutant content in each section occur within tolerable limits. The numerical model may be used to explore the diffusion mechanism of contaminants in the asymmetric river junction region and to better capture hydrodynamic and water quality changes in the river intersection area.
- (2)
- The three-dimensional properties of the pollutant concentration distribution in the junction area are analyzed. The findings indicate that the discharge ratio and the aspect-to-width-depth ratio significantly impact the distribution of pollutants in the junction region. This is mostly manifested in the horizontal distribution of pollutants, the trajectory of the mixing interface, and the degree of mixing homogeneity. The horizontal diffusion range of pollutants increases with increasing discharge ratio and width-depth ratio, and the mixing homogeneity in each section increases. Pollutants in the bottom plane Z = 0.05 m are totally mixed in the downstream exit section for R = 0.267 and b/h = 3.75. In general, the trajectory line of the mixing interface of pollutants in the junction region exhibits a logarithmic growth tendency, and it progresses along the direction of water flow development. The mixing interface expands to the center axis point after progressively moving to the other side of the interchange.
- (3)
- The concentration difference affects the horizontal distribution and mixing degree of pollutants. The degree of influence, however, is not as high as that of the discharge ratio or width-depth ratio, with only a slight impact. However, the mixing interface trajectory line still exhibits a logarithmic development pattern, and with increasing concentration difference, the mixing interface slightly deviates to the opposite side of the interchange. Molecular diffusion due to concentration variations causes subtle changes in the mixing interface and inhomogeneity index. In summary, the concentration difference only affects the concentration in the pollution belt, but does not influence its width, length, or size.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Wang, M.; Chen, X.; Lin, X.; Wang, P. Study on river channel characteristics of confluence of main and branch streams in the upper reaches of the Yangtze River. Hydro-Sci. Eng.
**2014**, 4, 58–64. (In Chinese) [Google Scholar] [CrossRef] - Zhou, J. Three-Dimensional Numerical Simulation of Open Channel Confluence Flow. Master’s Thesis, Sun Yet-sen University, Guangzhou, China, 2010. (In Chinese). [Google Scholar]
- Best, J.L. Flow Dynamics at River Channel Confluences: Implications for Sediment Transport and Bed Morphology. In Recent Developments in Fluvial Sedimentology. Special Publication 39; Ethridge, F.G., Flores, R.M., Harvey, M.D., Eds.; Society of Economic Paleontologists and Mineralogists: Tulsa, OK, USA, 1987; pp. 27–35. [Google Scholar]
- Lan, B. The comprehensive analysis of the special property at the tributary junction of mountain river. J. Chongqing Jiaotong Inst.
**1998**, 17, 93–98. (In Chinese) [Google Scholar] - Zhang, Q.; Wang, P.; Liu, Q. Reclassification of confluence forms of river branches and tributaries in mountainous areas. J. Chongqing Jiaotong Univ. Nat. Sci. Ed.
**2010**, 29, 458–460. (In Chinese) [Google Scholar] - Mosley, M.P. An Experimental Study of Channel Confluences. J. Geol.
**1976**, 84, 535–562. [Google Scholar] [CrossRef] - Liu, Z.; Liu, W.; Li, Z. Analysis of technical and economic significance of estuary management. Water Resour. Econ.
**2007**, 5, 64–67+78. (In Chinese) [Google Scholar] - Riley, J.D.; Rhoads, B.L. Flow structure and channel morphology at a natural confluent meander bend. Geomorphology
**2012**, 163, 84–98. [Google Scholar] [CrossRef] - Zhang, Y.F.; Wang, P.; Wu, B.S.; Hou, S.Z. An experimental study of fluvial processes at asymmetrical river confluences with hyperconcentrated tributary tributary flows. Geomorphology
**2015**, 230, 26–36. [Google Scholar] [CrossRef] - Gao, Y.; Ye, L.; Wang, Y.; Xu, Z.; Wang, X. Three-dimensional numerical simulation of flow in the confluence of Shenxigou and Baisha River. Adv. Eng. Sci.
**2020**, 52, 78–85. (In Chinese) [Google Scholar] [CrossRef] - Lv, M.; Zhu, X.; Wang, T.; Zhang, Y. Study on drainage drainage pollutant reduction based on TMDL concept. J. North China Univ. Water Resour. Electr. Power Nat. Sci. Ed.
**2020**, 41, 18–23. (In Chinese) [Google Scholar] - Gillibrand, P.A.; Balls, P.W. Modelling salt intrusion and nitrate concentrations in the Ythan Estuary. Estuar. Coast. Shelf Sci.
**1998**, 47, 695–706. [Google Scholar] [CrossRef] - Biron, P.M.; Ramamurthy, A.S.; Han, S. Three-dimensional numerical modeling of mixing at river confluences. J. Hydraul. Eng.
**2004**, 130, 243–253. [Google Scholar] [CrossRef] - Isabel, C.A.; Adriano, A.B.; Pedro, M.D. Influence of river discharge patterns on the hydrodynamics and potential contaminant dispersion in the Douro estuary. Water Res.
**2010**, 44, 3133–3146. [Google Scholar] [CrossRef] - Liu, X.-L. Numerical Simulation of Flow Field and Water Quality of Two Rivers Confluence in Chongqing. Master’s Thesis, Chongqing University, Chongqing, China, 2005. (In Chinese). [Google Scholar]
- Mao, Z.; Zhao, S.; Zhang, L. Experimental study on 3D flow characteristics at the confluence of open channel. J. Hydraul. Eng.
**2004**, 35, 1–7. (In Chinese) [Google Scholar] - Mao, Z.; Zhao, S.; Luo, S.; Zhang, L. Study on separation zone in open channel junction. Adv. Water Sci.
**2005**, 16, 7–12. (In Chinese) [Google Scholar] - Wei, J.; Li, R.; Kang, P.; Liu, S. Transport and diffusion characteristics of pollutants in water flow confluence area. Adv. Water Sci.
**2012**, 23, 822–828. (In Chinese) [Google Scholar] [CrossRef] - Gu, L.; Zhao, X.; Dai, B.; Wu, J.; Chu, K. Influence of confluence ratio on dispersion coefficient of pollutants in U-shaped curved intersection river. J. Hohai Univ. Nat. Sci. Ed.
**2018**, 46, 189–195. (In Chinese) [Google Scholar] - Yuan, S.; Tang, H.; Xiao, Y.; Qiu, X.; Zhang, H.; Yu, D. Turbulent flow structure at a 90-degree open channel confluence: Accounting for the distortion of the shear layer. J. Hydro-Environ. Res.
**2016**, 12, 130–147. [Google Scholar] [CrossRef] - Wu, Z. Numerical Simulation of Hydraulic Characteristics of Jialing River Interchange of Yangtze River. Master’s Thesis, Chongqing Jiaotong University, Chongqing, China, 2012. (In Chinese). [Google Scholar]
- Wang, X. A review of research on force characteristics of sink drooling water. China Rural. Water Resour. Hydropower
**2007**, 10, 82–86. (In Chinese) [Google Scholar] - Xu, H.; Qu, K. Numerical Calculation and Analysis of solid-liquid two-phase flow in a two-channel pump. J. Guangxi Univ. Nat. Sci. Ed.
**2010**, 35, 249–253. (In Chinese) [Google Scholar] [CrossRef] - Feng, Z.; Liu, P.; He, R. Effect of section shape on turbulent flow and field coordination in spiral channel. J. Guangxi Univ. Nat. Sci. Ed.
**2016**, 41, 1960–1967. (In Chinese) [Google Scholar] [CrossRef] - Yang, P.; Cai, D.-S.; Mo, C. Research on Hydraulic characteristics of vertical slit fishway based on FLOW-3D. J. Guangxi Univ. Nat. Sci. Ed.
**2018**, 43, 1675–1683. (In Chinese) [Google Scholar] [CrossRef] - Zhang, J.; Zhan, J.; Gong, Y. Large eddy simulation of aeration process of sliding flow in stepped spillway dam. J. Guangxi Univ. Nat. Sci. Ed.
**2017**, 42, 1572–1580. (In Chinese) [Google Scholar] [CrossRef] - Zhang, T. Study on Flow Structure and Pollutant Transport Law in Asymmetric River Confluence Area. Ph.D. Thesis, Xi’an Industry University, Xi’an, China, 2021. (In Chinese) [Google Scholar] [CrossRef]
- Chen, K.; Feng, M.; Zhang, T.; Teng, S. Study on distribution law of pollutant concentration field in open channel intersection area. J. Hydropower
**2019**, 38, 86–100. (In Chinese) [Google Scholar] - Chen, K. Experimental Study on Hydrodynamic Characteristics and Pollutant Concentration Field in Open Channel Intersection Area. Master’s Thesis, Xi’an University of Technology, Xi’an, China, 2019. (In Chinese). [Google Scholar]
- Tan, M.I.; Jian, Y.A.O. Simulation of pollutant diffusion in Y-shaped river confluence area. Environ. Sci. Technol.
**2020**, 43, 9–16. (In Chinese) [Google Scholar] [CrossRef] - Zhao, Z. Study on Dynamic Characteristics and Water Quality Variation of City Artificial Lake Water -Taking Yanming Lake as an example. Master’s Thesis, Xi’an University of Technology, Xi’an, China, 2018. (In Chinese). [Google Scholar]
- Hua, Z. Environmental Hydraulics; Science Press: Beijing, China, 2020. (In Chinese) [Google Scholar]
- Quinn, W.L.; Bruce, L. Rhoads. Rates and patterns of thermal mixing at a small stream confluence under variable incoming flow conditions. Hydrol. Process.
**2015**, 29, 4442–4456. [Google Scholar] - Teng, S. Study on Transport and Diffusion Characteristics of Transversal Jet Pollutants in Vegetation Open Channels. Ph.D. Thesis, Xi’an University of Technology, Xi’an, China, 2019. (In Chinese). [Google Scholar]
- Kamotani, Y.; Greber, I. Experiments on a Turbulent Jet in a Cross Flow. AIAA J.
**1972**, 10, 1425–1429. [Google Scholar] [CrossRef] - Gaudet, J.M.; Roy, A.G. Effect of bed morphology on flow mixing length at river confluences. Nature
**1995**, 373, 138–139. [Google Scholar] [CrossRef] - Wei, W.; Shao, S.-P.; Liu, Y.-L. Large eddy Simulation of three-dimensional hydraulic characteristics of open channel interchanges at different intersection angles. Chin. J. Appl. Mech.
**2015**, 32, 57–63+172. (In Chinese) [Google Scholar] - Pascale, B.; Antoine, R.; Alistair, K.; Roy, A.G.; Han, S.S. Spatial patterns of water surface topography at a river confluence. Earth Surf. Process. Landf.
**2002**, 27, 913–928. [Google Scholar] [CrossRef] - Claudine, B.; Andre, G.R.; James, L.B. Dynamic of a river channel confluence with discordant beds: Flow turbulence, bed load sediment transport, and bed morphology. J. Geophys. Res. Earth Surf.
**2006**, 111, 1–22. [Google Scholar] [CrossRef] - Bruce, L.R.; Alexander, N.S. Field investigation of three-dimensional flow structure at stream confluences: 1. Thermal mixing and time-averaged velocities. Water Resour. Res.
**2001**, 37, 2392–2410. [Google Scholar] [CrossRef] - Bruce, L.R.; Stephen, T.K. Time-averaged flow structure in the central region of a stream confluence. Earth Surf. Process. Landf.
**1998**, 23, 171–191. [Google Scholar] [CrossRef] - James, L.B. Sediment transport and bed morphology at river channel confluences. Sedimentology
**1988**, 35, 481–498. [Google Scholar] [CrossRef] - Alexander, N.S.; Bruce, L.R. Field investigation of three-dimensional flow structure at stream confluences: 2. Turbulence. Water Resour. Res.
**2001**, 37, 2411–2424. [Google Scholar] [CrossRef] - Shabayek, S.; Steffler, P.; Hicks, F.E. Dynamic Model for Subcritical Combining Flows in Channel Junctions. J. Hydraul. Eng.
**2002**, 128, 821–828. [Google Scholar] [CrossRef] - Signell, R.P.; Jenter, H.L.; Blumberg, A.F. Predicting the Physical Effects of Relocating Boston’s Sewage Outfall. Estuar. Coast. Shelf Sci.
**1999**, 50, 59–71. [Google Scholar] [CrossRef] - Ng, S.M.Y.; Wai, O.W.H.; Li, Y.S.; Jiang, Y. Integration of Agis and a complex three-dimensional hydrodynamic, sediment and heavy metal transport numerical model. Adv. Eng. Softw.
**2009**, 40, 391–401. [Google Scholar] [CrossRef] - Xing, Y.; Ai, C.; Jin, S. A three-dimensional hydrodynamic and salinity transport model of estuarine circulation with an application to a macrotidal estuary. Appl. Ocean. Res.
**2013**, 39, 53–71. [Google Scholar] [CrossRef] - Yang, Z.; Mi, T.; Yao, J.; Zhang, T. Rivers confluence area pollutant diffusion numerical simulation study. J. North China Univ. Water Hydropower Nat. Sci. Ed.
**2021**, 42, 86–92. (In Chinese) [Google Scholar] [CrossRef] - Lu, W.; Zhou, X. Theoretical study on horizontal diffusion of soluble pollutants in river channels. J. Yangzhou Univ. Nat. Sci. Ed.
**2012**, 15, 79–82. (In Chinese) [Google Scholar] [CrossRef] - Yuan, H. Study on Pollutant Mixing Law and Transverse Coefficient Distribution of Inclined Branch Confluence River. Master’s Thesis, Hohai University, Nanjing, China, 2016. (In Chinese). [Google Scholar]
- Hua, Z.L.; Wei, J.; Shan, N.N.; Wu, W. Pollutant mixing and transport process via diverse transverse release positions in a multi-anabranch river with three braid bars. Water Sci. Eng.
**2013**, 6, 250–261. [Google Scholar] [CrossRef] - Wu, D.; Yan, Y.; Li, R. Simulation of pollutant migration trajectory at Xuliujing control node. J. Oceanogr. Chin. Ed.
**2009**, 31, 158–166. (In Chinese) [Google Scholar]

**Figure 3.**Comparison of the pollutant concentrations along each measurement line in the transverse section.

**Figure 6.**Surface pollutant concentration distribution in the intersection area under different discharge ratios.

**Figure 7.**Trajectory of the pollutant mixing interface in the intersection area under various discharge ratios.

**Figure 8.**Trajectory of the pollutant mixing interface in the intersection area under various width-depth ratios.

**Figure 9.**Trajectory of the pollutant mixing interface in the intersection area under various concentration difference.

**Figure 10.**Inhomogeneity index of pollutants in the intersection area under different discharge ratios.

**Figure 11.**Inhomogeneity index of pollutants in the intersection area under different width-depth ratios.

**Figure 12.**Inhomogeneity index of pollutants in the intersection area under different concentrations.

NS Value | Result Evaluation |
---|---|

NSE < 0 | Measured values outperform the simulated values |

0.5 < NSE < 0.65 | Acceptable value |

0.65 < NSE < 0.75 | Improved simulation results |

NSE > 0.75 | Excellent simulation results |

NSE = 1 | Perfect match between the simulated and measured values |

Variables | Cross-Section | MRE (%) | NSE |
---|---|---|---|

Velocity of flow (m/s) | X = 5 cm | 4.13 | 0.899 |

X = 15 cm | 3.20 | 0.998 | |

X = 25 cm | 3.37 | 0.934 | |

Concentration of pollutant (μg/L) | Y = 11 cm | 4.49 | 0.992 |

Y = 32 cm | 4.95 | 0.983 | |

Y = 53 cm | 4.68 | 0.962 | |

Y = 74 cm | 3.16 | 0.959 | |

Y = 116 cm | 4.84 | 0.975 |

Working Conditions | Number | Investigation Factors | Mainstream Flow Q _{1}(m^{3}/h) | Discharge Ratio R | Water Depth h(m) | Width-Depth Ratio b/h | Concentration of Tributary C _{2} (μg/L) | Concentration Difference C _{g} (μg/L) |
---|---|---|---|---|---|---|---|---|

1 | 1(a) | Discharge ratio | 136.08 | 0.267 | 0.3 | 3 | 2000 | 2000 |

1(b) | 194.40 | 0.187 | 0.3 | 3 | 2000 | 2000 | ||

1(c) | 272.16 | 0.133 | 0.3 | 3 | 2000 | 2000 | ||

2 | 2(a) | Width-depth ratio | 194.40 | 0.187 | 0.24 | 3.75 | 2000 | 2000 |

2(b) | 194.40 | 0.187 | 0.3 | 3 | 2000 | 2000 | ||

2(c) | 194.40 | 0.187 | 0.36 | 2.5 | 2000 | 2000 | ||

3 | 3(a) | Concentration difference | 194.40 | 0.187 | 0.3 | 3 | 500 | 500 |

3(b) | 194.40 | 0.187 | 0.3 | 3 | 1000 | 1000 | ||

3(c) | 194.40 | 0.187 | 0.3 | 3 | 2000 | 2000 |

**Table 4.**Statistics of the pollutant concentration distribution range under different incoming flow conditions.

Number | Pollutant Concentration Distribution Area (m^{2}) | Proportion of the Intersection Area (%) |
---|---|---|

1(a) | 5.25 | 60.77% |

1(b) | 3.90 | 45.16% |

1(c) | 2.97 | 34.34% |

2(a) | 5.08 | 58.82% |

2(b) | 3.90 | 45.16% |

2(c) | 3.65 | 42.27% |

3(a) | 3.77 | 43.68% |

3(b) | 3.86 | 44.66% |

3(c) | 3.90 | 45.16% |

Number | Investigation Factors | Mainstream Flow Q _{1} (m^{3}/h) | Concentration of Mainstream C _{1} (μg/L) | Tributary Flow Q _{2} (m^{3}/h) | Concentration of Tributary C _{2} (μg/L) | Average Concentration C _{p} (μg/L) |
---|---|---|---|---|---|---|

1(a) | R = 0.267 | 136.08 | 0 | 36.29 | 2000 | 421.05 |

1(b) | R = 0.187 | 194.40 | 0 | 36.29 | 2000 | 314.61 |

1(c) | R = 0.133 | 272.16 | 0 | 36.29 | 2000 | 235.29 |

2(a) | b/h = 3.75 | 194.40 | 0 | 36.29 | 2000 | 314.61 |

2(b) | b/h = 3.00 | 194.40 | 0 | 36.29 | 2000 | 314.61 |

2(c) | b/h = 2.50 | 194.40 | 0 | 36.29 | 2000 | 314.61 |

3(a) | Cg = 500 | 194.40 | 0 | 36.29 | 2000 | 78.65 |

3(b) | Cg = 1000 | 194.40 | 0 | 36.29 | 2000 | 157.30 |

3(c) | Cg = 2000 | 194.40 | 0 | 36.29 | 2000 | 314.61 |

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |

© 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Wang, X.; Yang, J.; Wang, F.; Xu, N.; Li, P.; Wang, A.
Numerical Modeling of the Dispersion Characteristics of Pollutants in the Confluence Area of an Asymmetrical River. *Water* **2023**, *15*, 3766.
https://doi.org/10.3390/w15213766

**AMA Style**

Wang X, Yang J, Wang F, Xu N, Li P, Wang A.
Numerical Modeling of the Dispersion Characteristics of Pollutants in the Confluence Area of an Asymmetrical River. *Water*. 2023; 15(21):3766.
https://doi.org/10.3390/w15213766

**Chicago/Turabian Style**

Wang, Xu, Jiening Yang, Fan Wang, Na Xu, Peixuan Li, and Ai Wang.
2023. "Numerical Modeling of the Dispersion Characteristics of Pollutants in the Confluence Area of an Asymmetrical River" *Water* 15, no. 21: 3766.
https://doi.org/10.3390/w15213766