# Numerical Analysis of the Impact Factors on the Flow Fields in a Large Shallow Lake

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Methodology

#### 2.1. Study Area

^{2}. In recent years, the area of the Momoge Wetland has shrunk significantly. The local government has developed a series of wetland restoration projects. Baihe Lake is one of the largest lakes in the Momoge Wetland. The area of the lake is 15 km

^{2}and the eastern region of the lake is next to the Nenjiang River. The lake is also the main fishing area for local fishermen and its upstream is surrounded by local farmland. Every year a large amount of irrigation water recedes to Baihe Lake as a replenishment. At the same time, the lake also plays a role in purifying the water quality. The lake’s outlet is next to the Taoer River. Therefore, Baihe Lake plays an extremely important role in local services such as economic activities, water quality purification, hydrological connectivity, and ecological protection.

#### 2.2. Governing Equations

_{j}and u

_{j}are the distance and instantaneous velocity components in the j direction; g is the gravitational acceleration and equals 9.81 m

^{2}/s; ν is the kinematic viscosity; and F

_{i}is the external force term.

#### 2.3. External Force Term

**is the force term and can be expressed as:**

_{i}^{3}. Z

_{b}is the bed elevation; τ

_{bi}is the bed friction and can be expressed as:

_{b}= gn

^{2}/h

^{1/3}; n is Manning’s coefficient; and τ

**is the wind shear stress that can be expressed as:**

_{wi}_{a}is the air density; c

_{w}is the resistance coefficient; and u

**and u**

_{wi}**are the wind velocities in the i and j directions.**

_{wj}**is the average velocity on the vegetation elements in the i direction; C**

_{vi}_{d}is the drag force coefficient and is usually in the range of 1 and 1.5 [31]; and λ is the projected area (normal to the flow) of vegetation per unit volume of water and is calculated by:

_{v}represents the shape factor; c is the density of the vegetation zones and represents the projected area of vegetation per unit bed area; D

_{v}is the vegetation stems diameter; and u

**is equal to the average velocity u**

_{vi}**.**

_{i}#### 2.4. Lattice Boltzmann Method (LBM)

_{α}is the particle distribution function; ∆x is the lattice size; ∆t is time step; the external force F

**is calculated by:**

_{α}**is force term computed by Equation (3); e = Δx/Δt; ω**

_{i}_{α}is the weight factor: ω

_{α}= 4/9 for α = 0; ω

_{α}= 1/9 for α = 1, 3, 5, 7; and ω

_{α}= 1/36 for α = 2, 4, 6, 8.

_{αi}is the particle velocity in the i direction. The nine-velocity square lattice is shown in Figure 3. Each particle moves one lattice unit at its velocity along the eight links represented by numbers 1–8, while 0 represents a particle at rest with zero speed. The velocity vector of the particles is defined by:

**can be expressed as:**

_{i}#### 2.5. Rainfall

#### 2.6. Boundary Conditions

## 3. Results

#### 3.1. Initial Conditions

^{3}/s from 11 May to 25 June, and at an average rate of 14.4 m

^{3}/s from 10 October to 21 November. The average wind speed was equal to 1.78 m/s in the northeast (132°) from 11 May to 25 June, and average wind speed was equal to 2.36 m/s in the northeast (110°) from 10 October to 21 November.

_{d}are equal to 1.0 [28].

#### 3.2. Numerical Tests

#### 3.3. Sensitivity Analysis

#### 3.3.1. Wind Speed

#### 3.3.2. Inflow Discharge

#### 3.3.3. Vegetation Density

#### 3.3.4. Rain Density

#### 3.4. Scenario Simulation

^{3}/s. The monthly rainfall was 184 mm; the average wind speed was 2.13 m/s in the northeast direction (132°); and the vegetation density was 0.26. When the simulation was stable and the result was steady, the outflow rate was 0.54 m/s. The change in velocity and depth is shown in Figure 8a.

^{3}/s in the receding trough of the farmland drainage. The monthly rainfall was 38 mm; the average wind speed was 2.85 m/s in the northeast direction (110°); and the vegetation density was 0.12. The change in velocity and depth is shown in Figure 8b.

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Geographical location and topographic conditions of Baihe Lake (Datum: 45°56’ N, 122°45’ E).

**Figure 3.**D2Q9 lattice pattern (D2 represent two-dimensional and Q9 represent nine velocity directions in each particle).

**Figure 8.**Comparison of the simulated results with different initial conditions: (

**a**) Case 1 (water velocity); (

**b**) Case 2 (water depth).

Variation Range | Wind Speed (m/s) | Outflow Velocity (m/s) | Outflow Velocity Variation | Average Velocity (m/s) | Average Velocity Variation |
---|---|---|---|---|---|

−30% | 1.25 | 0.0381 | −5.93% | 0.00149 | −7.18% |

−20% | 1.42 | 0.0386 | −4.69% | 0.00152 | −5.01% |

−10% | 1.60 | 0.0395 | −2.47% | 0.00155 | −2.98% |

0% | 1.78 | 0.0405 | 0.00% | 0.00160 | 0.00% |

10% | 1.96 | 0.0411 | 1.48% | 0.00164 | 2.55% |

20% | 2.14 | 0.0433 | 6.91% | 0.00172 | 7.81% |

30% | 2.31 | 0.0457 | 12.84% | 0.00184 | 14.98% |

Variation Range | Inflow Discharge (m^{3}/s) | Outflow Velocity (m/s) | Outflow Velocity Variation | Average Velocity (m/s) | Average Velocity Variation |
---|---|---|---|---|---|

−30% | 18.55 | 0.0338 | −16.56% | 0.00125 | −21.99% |

−20% | 21.20 | 0.0358 | −11.53% | 0.00137 | −14.58% |

−10% | 23.85 | 0.0370 | −8.71% | 0.00144 | −10.24% |

0% | 26.50 | 0.0405 | 0.00% | 0.00160 | 0.00% |

10% | 29.15 | 0.0436 | 7.66% | 0.00178 | 11.42% |

20% | 31.80 | 0.0467 | 15.23% | 0.00188 | 17.63% |

30% | 34.45 | 0.0503 | 24.11% | 0.00204 | 27.65% |

Variation Range | Vegetation Density | Outflow Velocity (m/s) | Outflow Velocity Variation | Average Velocity (m/s) | Average Velocity Variation |
---|---|---|---|---|---|

−30% | 0.14 | 0.0424 | 4.71% | 0.00165 | 2.97% |

−20% | 0.16 | 0.0417 | 3.03% | 0.00164 | 2.57% |

−10% | 0.18 | 0.0411 | 1.49% | 0.00162 | 1.09% |

0% | 0.20 | 0.0405 | 0.00% | 0.00160 | 0.00% |

10% | 0.22 | 0.0399 | −1.57% | 0.00158 | −1.23% |

20% | 0.24 | 0.0392 | −3.11% | 0.00155 | −2.98% |

30% | 0.26 | 0.0385 | −4.88% | 0.00154 | −3.72% |

Variation Range | Rainfall (mm) | Outflow Velocity (m/s) | Outflow Velocity Variation | Average Velocity (m/s) | Average Velocity Variation |
---|---|---|---|---|---|

−30% | 50.82 | 0.0347 | −14.23% | 0.00137 | −14.17% |

−20% | 58.08 | 0.0370 | −8.56% | 0.00147 | −8.34% |

−10% | 65.34 | 0.0385 | −4.78% | 0.00153 | −4.66% |

0% | 72.60 | 0.0405 | 0.00% | 0.00160 | 0.00% |

10% | 79.86 | 0.0433 | 6.97% | 0.00171 | 6.85% |

20% | 87.12 | 0.0446 | 10.23% | 0.00176 | 9.98% |

30% | 94.38 | 0.0490 | 21.11% | 0.00193 | 20.44% |

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**MDPI and ACS Style**

Liu, H.; Zhu, Z.; Liu, J.; Liu, Q.
Numerical Analysis of the Impact Factors on the Flow Fields in a Large Shallow Lake. *Water* **2019**, *11*, 155.
https://doi.org/10.3390/w11010155

**AMA Style**

Liu H, Zhu Z, Liu J, Liu Q.
Numerical Analysis of the Impact Factors on the Flow Fields in a Large Shallow Lake. *Water*. 2019; 11(1):155.
https://doi.org/10.3390/w11010155

**Chicago/Turabian Style**

Liu, Haifei, Zhexian Zhu, Jingling Liu, and Qiang Liu.
2019. "Numerical Analysis of the Impact Factors on the Flow Fields in a Large Shallow Lake" *Water* 11, no. 1: 155.
https://doi.org/10.3390/w11010155