# Numerical Simulation of the Hydraulic Characteristics and Fish Habitat of a Natural Continuous Meandering River

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

## Highlights

- To study the hydraulic characteristics of natural continuous curved river flows;
- To study the influence of the hydraulic characteristics of natural continuous curved river flows on fish habitats;
- To evaluate the impact of channel regulation on the construction of ecological waterways.

## Abstract

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Mathematical Model

#### 2.1.1. Hydrodynamic Control Equations

_{ij}is the transverse stress; and $\tau $ is the riverbed stress.

#### 2.1.2. Boundary Conditions and Model Parameter Settings

#### 2.1.3. Grid Division

#### 2.2. The Shannon Diversity Index

#### 2.3. Experimental Parameter Selection

#### 2.4. Experimental Conditions

^{3}/s), mid-water flow (1520 m

^{3}/s), and dry-water flow (374 m

^{3}/s) during the annual average flow were selected as the main parameters for the numerical simulation. The flood flow represents the flow corresponding to the highest navigable water level (1 in 3 years); the mid-water flow represents the flow corresponding to the 1.2-m-high remediation level; and the dry water flow represents the flow corresponding 95% of the guaranteed minimum navigable water level.

^{3}/s), and six working conditions of mathematical model tests, i.e., natural conditions, L1 (374 m

^{3}/s), L2 (1520 m

^{3}/s), and L3 (3410 m

^{3}/s); and M1 (374 m

^{3}/s), M2 (1520 m

^{3}/s), and M3 (3410 m

^{3}/s) after river regulation. The working condition arrangement is shown in Table 1.

## 3. Results

#### 3.1. Feasibility Analysis of the Mathematical Model

#### 3.2. Numerical Simulation of Natural Rivers

#### 3.2.1. Flow Velocity

#### 3.2.2. Water Level and Depth

#### 3.2.3. Flow Pattern

#### 3.2.4. Fish Living Environment

_{crit}= 25.84L

^{0.63}, where U

_{crit}represents the critical swimming speed (unit: cm/s) and L represents the body length of grass carp (unit: cm). When the current velocity exceeded 60% of the critical swimming velocity of fish, the current conditions were not suitable for the long-term survival of fish, and the upstream migration rate of fish decreased. At the same time, water flow velocities below the induced flow velocity (v < 0.2 m/s) were not within the appropriate flow velocity range for grass carp backflow. The size of adult grass carp is generally between 30 and 80 cm, and the critical swimming speed was calculated to be about 2.2~4.1 m/s. The flow velocity corresponding to 60% of the critical swimming speed was about 1.3~2.5 m/s. Therefore, the flow velocity suitable for fish survival is 0.2 m/s < v < 2.5 m/s.

#### 3.3. Numerical Simulation Analysis after River Regulation

#### 3.3.1. Flow Velocity

#### 3.3.2. Water Level and Depth

#### 3.3.3. Flow Pattern

#### 3.3.4. Fish Living Environment

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- Mao, M. Flow Characteristics and Influence of Geometric Factors in a Bend. Ph.D. Thesis, Xi’an University of Technology, Xi’an, China, 2017. [Google Scholar]
- Liu, X.X.; Bai, Y.C. Turbulent structure and bursting process in multi-bend meander channel. J. Hydrodyn. Ser. B
**2014**, 26, 207–215. [Google Scholar] [CrossRef] - Cao, Y.F. Hydrodynamic Instability and Short-Term Evolution Properties of Bed Surface in Curved Channel. Ph.D. Thesis, Tianjin University, Tianjin, China, 2020. [Google Scholar]
- Van Balen, W.; Blanckaert, K.; Uijttewaal, W.S.J. Analysis of the role of turbulence in curved open-channel flow at different water depths by means of experiments, LES and RANS. J. Turbul.
**2010**, 11, N12. [Google Scholar] [CrossRef] - Stoesser, T.; Ruether, N.; Olsen, N.R.B. Calculation of primary and secondary flow and boundary shear stresses in a meandering channel. Adv. Water Resour.
**2010**, 33, 158–170. [Google Scholar] [CrossRef] - Yang, Y.; Lin, Y.-T.; Ji, X. Hydrodynamic characteristics of flow over emergent vegetation in a strongly curved channel. J. Hydraul. Res.
**2022**, 60, 240–257. [Google Scholar] [CrossRef] - He, Y.; Cheng, H.; Chen, J. Morphological evolution of mouth bars on the Yangtze estuarine waterways in the last 100 years. J. Geogr. Sci.
**2013**, 23, 219–230. [Google Scholar] [CrossRef] - Breen, M.; Dyson, J.; O’Neill, F.G.; Jones, E.; Haigh, M. Swimming endurance of haddock (Melanogrammus aeglefinus L.) at prolonged and sustained swimming speeds, and its role in their capture by towed fishing gears. ICES J. Mar. Sci.
**2004**, 61, 1071–1079. [Google Scholar] [CrossRef] - Bretón, F.; Baki, A.; Link, O.; Zhu, D.; Rajaratnam, N. Flow in nature-like fishway and its relation to fish behaviour. Can. J. Civ. Eng.
**2013**, 40, 567–573. [Google Scholar] [CrossRef] - Winger, P.D.; He, P.; Walsh, S.J. Factors affecting the swimming endurance and catchability of Atlantic cod (Gadus morhua). Can. J. Fish. Aquat. Sci.
**2000**, 57, 1200–1207. [Google Scholar] [CrossRef] - Smith, D.L. The Shear Flow Environment of Juvenile Salmonids. Ph.D. Thesis, University of Idaho, Moscow, ID, USA, 2003. [Google Scholar]
- Haro, A.; Odeh, M.; Noreika, J.; Castro-Santos, T. Effect of water acceleration on downstream migratory behavior and passage of Atlantic salmon smolts and juvenile American shad at surface bypasses. Trans. Am. Fish. Soc.
**1998**, 127, 118–127. [Google Scholar] [CrossRef] - He, D.R. Fish Behavior; Xiamen University Press: Xiamen, China, 1998. [Google Scholar]
- Hammer, C. Fatigue and exercise tests with fish. Comp. Biochem. Physiol. Part A Physiol.
**1995**, 112, 1–20. [Google Scholar] [CrossRef] - Plaut, I. Critical swimming speed: Its ecological relevance. Comp. Biochem. Physiol. Part A Mol. Integr. Physiol.
**2001**, 131, 41–50. [Google Scholar] [CrossRef] - Yang, N.-L.; Dou, X.-P.; Zhang, X.-Z.; Luo, X.-F. Hydrodynamic effect of the regulation project of Yangtze River deepwater channel downstream of Nanjing. China Ocean Eng.
**2013**, 27, 767–779. [Google Scholar] [CrossRef] - Jian, L.; Wang, P.; Wang, M.; Han, L. Experimental study on hydraulic characteristics of new ecological slope protection structure. Mar. Georesources Geotechnol.
**2021**. [Google Scholar] [CrossRef] - Kuhnle, R.A.; Alonso, C.V.; Shields, F.D. Local scour associated with angled spur dikes. Hydraulic Eng.
**2002**, 128, 1087–1093. [Google Scholar] [CrossRef] [Green Version] - Kang, J.; Yeo, H.; Jung, S. Flow characteristic variations on groney types for aquatic habitat. Sci. Res.
**2012**, 4, 811–812. [Google Scholar] [CrossRef] [Green Version] - Liu, C.H.; Liu, S.; Li, D.; Yan, J.; Lu, C. An Analysis of the Impact of Zhonghuan Sewage Outlet on Water Quality of the Yangtze River Based On MIKE21 Model. China Rural. Water Conserv. Hydropower
**2020**, 1, 72–76. [Google Scholar] - Li, T.Y.; Li, Z.H.; Huang, B.B. Simulation on water quantity and quality of Shahe Reservoir by Mike21 model. Acta Sci. Circumstantiae
**2021**, 41, 293–300. [Google Scholar] [CrossRef] - Tan, W.; Hu, S. Implementation of first-order finite-volume Osher scheme in shallow water flow computation. Adv. Water Sci.
**1994**, 5, 262–270. (In Chinese) [Google Scholar] - Zhou, J.G.; Causon, D.M.; Ingram, D.M.; Mingham, C.G. Numerical solutions of the shallow water equations with discontinuous bed topography. Int. J. Numer. Methods Fluids
**2002**, 38, 769–788. [Google Scholar] [CrossRef] - Valiani, A.; Caleffi, V.; Zanni, A.A. Case study: Malpasset dam-break simulation using a two-dimensional finite volume method. J. Hydraul. Eng. ASCE
**2002**, 128, 460–472. [Google Scholar] [CrossRef] - Hu, J.L. Hydraulic Characteristics of a New Permeable Spur Dike and Its Effect on Fish Behavior. Ph.D. Thesis, Chongqing Jiaotong University, Chongqing, China, 2021. [Google Scholar]
- Shannon, C.E. A mathematical theory of communication. Bell Syst. Tech. J.
**1948**, 27, 3–55. [Google Scholar] [CrossRef] [Green Version]

**Figure 1.**Diagram of the continuous curved river channel (① represents an obstruction point; ② represents low depression in the riverbed).

**Figure 8.**Proportion diagram of velocity distribution at all levels of the river channel under different flow conditions.

**Figure 9.**Layout of the treatment scheme (1 indicates dredging; 2 indicates a filling groove; 3 indicates the construction of a submerged dam).

**Figure 11.**Proportion of flow velocity distribution in each layer of the river under different flow conditions.

Prototype Condition | Mathematical Model Test Conditions | ||||
---|---|---|---|---|---|

Natural Conditions | Natural Conditions | After Remediation | |||

Working Condition | Flow (m ^{3}/s) | Working Condition | Flow (m ^{3}/s) | Working Condition | Flow (m ^{3}/s) |

- | - | L1 | 374 | M1 | 374 |

A1 | 1520 | L2 | 1520 | M2 | 1520 |

- | - | L3 | 3410 | M3 | 3410 |

Gradient (‰) | 1.5 | 2 | 3 | 4 | 5 | 6 | 7 |

Velocity (m/s) | 4 | 3.8 | 3.5 | 3.2 | 2.9 | 2.5 | 2.1 |

Location | Error Value | Location | Error Value |
---|---|---|---|

C1 | −0.5% | C6 | 1.2% |

C2 | 0.1% | C7 | 1.8% |

C3 | 0.2% | C8 | 0.6% |

C4 | 0.3% | C9 | 0.9% |

C5 | 3.1% |

H (m) | Error Value | H (m) | Error Value | H (m) | Error Value |
---|---|---|---|---|---|

0 | −3.73% | 876.6821 | 3.69% | 1667.3218 | −5.16% |

101.8836 | −2.96% | 952.0129 | 9.00% | 1709.6348 | 2.45% |

166.9831 | −4.83% | 1022.0596 | 0.28% | 1747.4577 | 4.35% |

237.3158 | −4.38% | 1100.1048 | 13.22% | 1825.6284 | 6.17% |

311.4188 | −6.02% | 1159.6542 | 7.08% | 1868.7288 | 3.21% |

381.3038 | −8.39% | 1210.8155 | 6.25% | 1903.3225 | 3.61% |

420.921 | −8.94% | 1258.7356 | −5.78% | 1973.2406 | −0.97% |

500.7897 | −12.32% | 1337.7123 | −5.63% | 2056.0031 | 0.72% |

569.4314 | 5.71% | 1472.2932 | −8.39% | 2148.2125 | −6.63% |

658.2227 | 5.11% | 1513.4778 | −1.80% | 2210.2138 | 3.66% |

706.4791 | 5.62% | 1552.1245 | −8.57% | 2328.5594 | 7.02% |

785.4862 | −11.08% | 1593.023 | −12.25% | 2394.4765 | 3.48% |

826.5563 | −5.36% | 1632.6447 | 10.85% | 2606.0386 | 6.09% |

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**MDPI and ACS Style**

Wang, P.; Li, J.; Wang, M.; Hu, J.; Zhang, F.
Numerical Simulation of the Hydraulic Characteristics and Fish Habitat of a Natural Continuous Meandering River. *Sustainability* **2022**, *14*, 9798.
https://doi.org/10.3390/su14169798

**AMA Style**

Wang P, Li J, Wang M, Hu J, Zhang F.
Numerical Simulation of the Hydraulic Characteristics and Fish Habitat of a Natural Continuous Meandering River. *Sustainability*. 2022; 14(16):9798.
https://doi.org/10.3390/su14169798

**Chicago/Turabian Style**

Wang, Pingyi, Jian Li, Meili Wang, Jielong Hu, and Fan Zhang.
2022. "Numerical Simulation of the Hydraulic Characteristics and Fish Habitat of a Natural Continuous Meandering River" *Sustainability* 14, no. 16: 9798.
https://doi.org/10.3390/su14169798