# The Impact of Tidal Straining and Advection on the Stratification in a Partially Mixed Estuary

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

^{3}/s in the dry season, Qingcaosha Reservoir may be threatened by saline intrusion [15], so this study focuses on the dry season.

## 2. Research Area and Research Methods

#### 2.1. Research Area

^{3}/s (Datong gauging station) from 1950 to 2010 [18]. The monthly averaged discharge of the Changjiang River varies from 10

^{4}m

^{3}/s during the dry season (from May to October) to 4 × 10

^{4}m

^{3}/s during the wet season (from November to April) [17]; 51.03% of the Yangtze River fresh water is exported from the North Channel [19]. Tides are irregular semidiurnal, with a mean and maximum tidal range of about 2.67 m and 4.62 m at Zhongjun station [20]. The main tidal constituents are O

_{1}, K

_{1}, M

_{2}and S

_{2}, with amplitudes of 0.2 m, 0.3 m, 1.3 m and 0.6 m at Niupijiao station [21]. The average flood and ebb duration are 5 and 7.5 h, respectively [22]. The salinity of the North Channel increases from the river to the sea. The North Channel is greatly affected by saltwater intrusion and is characterized as a partially stratified estuary [23].

#### 2.2. Research Data

#### 2.3. Data Analysis

#### 2.3.1. Gradient Richardson Number (Ri)

#### 2.3.2. Simpson Number (Si)

_{d}= 0.0025 is the drag coefficient, U

_{bottom}is amplitude of bottom tidal current velocity,$\overline{\rho}$ is the depth-mean density, $\frac{\partial \overline{\rho}}{\partial x}$ is the longitudinal gradient of depth-mean density, and h is the water depth. According to the evaluation criteria of Becherer et al., $Si$ ≤ 0.088 represents a completely mixed state, 0.088 < $Si$ < 0.84 represents SIPS state, and $Si$ ≥ 0.84 represents permanently stratified [27].

#### 2.3.3. Potential Energy Anomaly (Φ)

^{3}) is the amount of energy per unit volume required to instantaneously homogenize the water column with a given density stratification [3]:

_{x}is the depth-mean straining term, A

_{x}is the longitudinal advection term, N

_{x}is the non-mean straining term, T

_{x}is the tidal stirring term, t is the time, $\overline{u}$ is the depth-mean horizontal velocity, $\tilde{u}$ is the deviation from the depth-mean horizontal velocity, and $\frac{\partial \tilde{\rho}}{\partial x}$ is the deviation from the longitudinal gradient of depth-mean density. The parameter ε = 0.004 is related to the mixing efficiency, and $\left|\overline{u}\right|$ is the amplitude of the depth-mean velocity. If the contribution term S

_{x}, A

_{x}, N

_{x}, or T

_{x}is positive, it indicates that this mechanism induces the increase in ${\varphi}_{t}$ and stabilization of the stratification. On the contrary, if the contribution term is negative, it indicates that this mechanism drives water mixing.

## 3. Results

#### 3.1. Characteristics of Tides

#### 3.2. Characteristics of Salinity

^{4}, 0.33 kg/m

^{4}, 0.23 kg/m

^{4}during the neap, mean and spring tide, respectively, which is the largest in neap tide and the smallest in spring tide, and the former is 7.43 times that of the latter (Table 2). The mean longitudinal salinity gradients are 0.31 × 10

^{−3}kg/m

^{4}, 0.49 × 10

^{−3}kg/m

^{4}, and 0.62 × 10

^{−3}kg/m

^{4}during the neap, mean and spring tide, respectively, which is the largest in spring tide and the smallest in neap tide.

#### 3.3. Characteristics of Mixing and Stratification

#### 3.3.1. Characteristics of Mixing and Stratification Indicated by Ri

#### 3.3.2. Characteristics of Mixing and Stratification Indicated by Φ

#### 3.3.3. Characteristics of Mixing and Stratification Indicated by Si

#### 3.4. Physical Mechanisms of Mixing and Stratification Processes

_{x}, the longitudinal advection term A

_{x}, the non-mean straining term N

_{x}and the tidal stirring term T

_{x}. As mentioned in Section 2.3.3, if the contribution term is positive, it indicates that this mechanism increases the time derivative of Φ and promotes stratification. To the contrary, if the contribution term is negative, it indicates that this mechanism drives water mixing.

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Sketch of the Changjiang Estuary and observation stations in the North Channel. CX and HS denote Changxing Island and Hengsha Island, respectively.

**Figure 2.**Longitudinal–vertical distribution of tidal mean salinity during neap tide (

**a**), mean tide (

**b**), spring tide (

**c**) in the North Channel.

**Figure 3.**Time variation of velocity (

**a**–

**c**), salinity (

**d**–

**f**), and Ri (

**g**–

**i**) at (

**A**) G1, (

**B**) G2 and (

**C**) G3 stations in the North Channel.

**Figure 4.**Time series of water depth and depth mean velocity (a–c), Φ (d–f), and surface–bottom density difference Δρ, and forcing terms in the Φ−equation (g–i) at (

**A**) G1, (

**B**) G2 and (

**C**) G3 stations in the North Channel.

Station | Tide | Water Depth (m) | Tidal Range (m) | Flood Tide | Ebb Tide | |||||
---|---|---|---|---|---|---|---|---|---|---|

Duration (h) | Mean Longitudinal Velocity (m/s) | Mean Lateral Velocity (m/s) | Maximum Longitudinal Velocity (m/s) | Mean Longitudinal Velocity (m/s) | Mean Lateral Velocity (m/s) | Maximum Longitudinal Velocity (m/s) | ||||

G0 | Neap | 14.31 | 1.20 | 7.00 | 0.27 | 0.05 | 0.42 | 0.23 | 0.06 | 0.40 |

G1 | 13.35 | 1.40 | 7.00 | 0.41 | 0.02 | 0.56 | 0.46 | 0.04 | 0.59 | |

G2 | 8.49 | 1.60 | 7.00 | 0.41 | 0.16 | 0.69 | 0.33 | 0.12 | 0.51 | |

G3 | 13.14 | 1.70 | 7.00 | 0.24 | 0.21 | 0.38 | 0.34 | 0.29 | 0.61 | |

G0 | Mean | 14.22 | 1.60 | 5.50 | 0.70 | 0.07 | 1.19 | 0.64 | 0.02 | 1.09 |

G1 | 13.78 | 2.10 | 5.50 | 0.70 | 0.05 | 1.23 | 0.93 | 0.99 | 1.34 | |

G2 | 8.73 | 2.60 | 5.50 | 0.74 | 0.15 | 1.19 | 0.92 | 0.11 | 1.39 | |

G3 | 13.10 | 3.00 | 5.50 | 0.49 | 0.27 | 0.80 | 0.70 | 0.19 | 0.93 | |

G0 | Spring | 14.58 | 2.40 | 4.50 | 0.61 | 0.05 | 1.17 | 0.98 | 0.04 | 1.42 |

G1 | 13.82 | 3.50 | 4.50 | 0.75 | 0.05 | 1.18 | 1.27 | 0.09 | 1.83 | |

G2 | 8.84 | 3.80 | 4.50 | 0.79 | 0.21 | 1.30 | 1.03 | 0.14 | 1.58 | |

G3 | 13.01 | 4.30 | 6.50 | 0.56 | 0.27 | 0.96 | 0.63 | 0.26 | 0.81 |

Station | Vertical Gradient of Salinity | Longitudinal Gradient of Salinity | ||||
---|---|---|---|---|---|---|

Neap Tide | Mean Tide | Spring Tide | Neap Tide | Mean Tide | Spring Tide | |

G1 | 0.48 | 0.45 | 0.09 | 0.30 × 10^{−3} | 0.42 × 10^{−3} | 0.31 × 10^{−3} |

G2 | 2.93 | 0.38 | 0.29 | 0.55 × 10^{−3} | 0.51 × 10^{−3} | 0.62 × 10^{−3} |

G3 | 1.71 | 0.14 | 0.31 | 0.69 × 10^{−3} | 0.65 × 10^{−3} | 0.83 × 10^{−3} |

Station | Neap Tide | Mean Tide | Spring Tide | |||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Flood- Mean | σ | Ebb- Mean | σ | Tidal Mean | σ | Flood- Mean | σ | Ebb- Mean | σ | Tidal Mean | σ | Flood- Mean | σ | Ebb- Mean | σ | Tidal Mean | σ | |

G0 | 1.43 | 0.06 | 1.34 | 0.12 | 1.40 | 0.10 | 0.87 | 0.43 | 0.84 | 0.33 | 0.84 | 0.38 | 0.05 | 0.03 | 0.18 | 0.22 | 0.12 | 0.18 |

G1 | 4.97 | 3.00 | 0.89 | 0.07 | 1.85 | 2.78 | 9.55 | 1.73 | 8.84 | 2.45 | 9.16 | 2.17 | 1.13 | 0.53 | 3.38 | 1.78 | 2.68 | 1.91 |

G2 | 15.13 | 4.11 | 12.18 | 1.00 | 12.27 | 1.90 | 19.48 | 1.21 | 18.03 | 2.29 | 18.16 | 2.36 | 12.80 | 4.66 | 14.79 | 5.39 | 14.18 | 5.52 |

G3 | 28.53 | 0.65 | 27.07 | 0.87 | 27.46 | 1.07 | 32.15 | 1.02 | 30.87 | 0.82 | 31.82 | 1.13 | 29.40 | 1.32 | 29.65 | 1.23 | 29.62 | 1.29 |

Station | Neap Tide | Mean Tide | Spring Tide |
---|---|---|---|

G1 | 1.21 | 1.07 | 0.78 |

G2 | 1.02 | 0.59 | 0.53 |

G3 | 1.31 | 0.79 | 0.74 |

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**MDPI and ACS Style**

Zhang, J.; Cheng, L.; Wang, Y.; Jiang, C. The Impact of Tidal Straining and Advection on the Stratification in a Partially Mixed Estuary. *Water* **2023**, *15*, 339.
https://doi.org/10.3390/w15020339

**AMA Style**

Zhang J, Cheng L, Wang Y, Jiang C. The Impact of Tidal Straining and Advection on the Stratification in a Partially Mixed Estuary. *Water*. 2023; 15(2):339.
https://doi.org/10.3390/w15020339

**Chicago/Turabian Style**

Zhang, Jin, Li Cheng, Yajun Wang, and Chenjuan Jiang. 2023. "The Impact of Tidal Straining and Advection on the Stratification in a Partially Mixed Estuary" *Water* 15, no. 2: 339.
https://doi.org/10.3390/w15020339