# An Analytical Solution for Investigating the Characteristics of Tidal Wave and Surge Propagation Associated with Non-Tropical and Tropical Cyclones in the Humen Estuary, Pearl River

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## Abstract

**:**

## 1. Introduction

## 2. Study Areas

#### 2.1. Overview

^{3}/s in the wet summer to 3600 m

^{3}/s in the dry winter) into the northern South China Sea through eight outlets (Figure 1). Four of the eight outlets (Humen, Jiaomen, Hongqimen, and Hengmen) enter Lingdingyang Bay, which has a trumpet-like shape with a width of 5 km near the northern end and 35 km at the southern end. Among the four outlets, the Humen Estuary is the largest mouth with a large amount of tidal influx and outflux between the estuary and offshore. It is obvious that the trumpet-like bay tends to amplify the tide amplitude in conjunction with the convergent estuary when the tidal wave propagates from the deep sea into the Humen Estuary in the landward direction. Thus, we focus on the characteristics of the tidal wave along the Humen Estuary, specifically the segment from the mouth upstream to approximately 1.5 km downstream from Huangpu Bridge.

#### 2.2. Shape of the Humen Estuary

_{0}, B

_{0}, and h

_{0}are the same variables at the estuary mouth; x is the distance from the estuary mouth; and a, b, and d are convergent lengths of the cross-sectional area, width, and depth.

## 3. Analytical Solution

_{0}is the classical wave celerity of a frictionless progressive wave, $\omega $ is the frequency of the wave, $\zeta =\frac{\eta}{h}$ is the dimensionless tidal amplitude, and $f$ is the dimensionless friction factor defined as

## 4. Numerical Model and Verification

## 5. Results

## 6. Discussion

#### 6.1. The Characteristics of the Tidal Wave Propagation in the Humen Estuary

#### 6.2. Comparison with Other Estuaries

## 7. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 3.**The regression lines for the cross-sectional area A (m

^{2}), width B (m), and depth h (m) along the estuary.

**Figure 5.**Verification of the numerical model in four stations: Nansha, Wanqinsha, Henmeng, and Neigang.

**Figure 6.**Comparison of the analytical results for (

**a**) tidal amplitude and (

**b**) travel time, and the numerical simulation after calibration during 8–9 September 2018. The diamonds denotes the numerical simulation results and the same for the following figures.

**Figure 7.**Comparison of the analytical results for (

**a**) tidal amplitude and (

**b**) travel time, and the numerical simulation for verification under astronomical tide during 16–17 September 2018.

**Figure 8.**Comparison of the analytical tidal amplitude before (solid line) and after (dash line) tuning Manning’s coefficient, and numerical simulation for verification under tide and surge during 16–17 September 2018.

**Figure 9.**The relation between four parameters: (

**a**) velocity number, (

**b**) damping number, (

**c**) celerity number, and (

**d**) phase lag. The estuary shape number $\gamma $ for different friction numbers $\chi $ is indicated by different line types. The bold lines indicate the parameters for the Humen Estuary under astronomical tide (red) and tide plus surge (blue), with the numbers indicating the distance from the estuary mouth in kilometers. The drawn line with the crosses represents the ideal estuary.

**Figure 10.**Positioning of the Humen (red line), Schelde (yellow squares), and Hau (pink triangles) Estuaries in the damping number (

**a**) and celerity number (

**b**) diagrams, with the numbers at the inflection points indicating the distance from the estuary mouth (in kilometers). The other lines are the same as those in Figure 9.

Subsections | Range (km) | A (km) | B (km) | D (km) |
---|---|---|---|---|

Mouth | 0–8.7 | 166.7 | 333.3 | 333.3 |

Middle | 8.7–30.4 | 25 | 71.4 | 40.0 |

Upstream | 30.4–36 | 20 | 8.3 | 208.3 |

Time | Latitude (N) | Longitude (E) | Pressure (hPa) | Maximum Wind Speed (m/s) |
---|---|---|---|---|

00:00 14/09 | 16 | 126.9 | 905 | 56.6 |

06:00 14/09 | 16.7 | 125.7 | 905 | 56.6 |

12:00 14/09 | 17.4 | 124.1 | 905 | 56.6 |

18:00 14/09 | 18 | 122.3 | 905 | 56.6 |

00:00 15/09 | 18 | 120.5 | 940 | 46.3 |

06:00 15/09 | 18.5 | 119.7 | 940 | 46.3 |

12:00 15/09 | 19.2 | 118.3 | 950 | 43.7 |

18:00 15/09 | 19.8 | 117 | 955 | 41.2 |

00:00 16/09 | 20.6 | 115.3 | 960 | 38.6 |

06:00 16/09 | 21.7 | 113.5 | 960 | 38.6 |

12:00 16/09 | 22.2 | 111.6 | 970 | 33.4 |

18:00 16/09 | 22.7 | 109.7 | 980 | 28.3 |

Subsections | Storage Width Ratio r _{s} | Value Range | Manning’s Coefficient n (m^{−1/3}s) | ||
---|---|---|---|---|---|

Astronomical Spring Tide | Considering Cyclone Surge | Value Range | |||

Mouth | 1 | 1–2 | 0.005 | 0.005 | 0.017–0.06 |

Middle | 1.8 | 1–2 | 0.031 | 0.018 | 0.017–0.06 |

Upstream | 1.5 | 1–2 | 0.035 | 0.015 | 0.017–0.06 |

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**MDPI and ACS Style**

Zhang, Z.; Guo, F.; Hu, D.; Zhang, D. An Analytical Solution for Investigating the Characteristics of Tidal Wave and Surge Propagation Associated with Non-Tropical and Tropical Cyclones in the Humen Estuary, Pearl River. *Water* **2021**, *13*, 2375.
https://doi.org/10.3390/w13172375

**AMA Style**

Zhang Z, Guo F, Hu D, Zhang D. An Analytical Solution for Investigating the Characteristics of Tidal Wave and Surge Propagation Associated with Non-Tropical and Tropical Cyclones in the Humen Estuary, Pearl River. *Water*. 2021; 13(17):2375.
https://doi.org/10.3390/w13172375

**Chicago/Turabian Style**

Zhang, Zhuo, Fei Guo, Di Hu, and Dong Zhang. 2021. "An Analytical Solution for Investigating the Characteristics of Tidal Wave and Surge Propagation Associated with Non-Tropical and Tropical Cyclones in the Humen Estuary, Pearl River" *Water* 13, no. 17: 2375.
https://doi.org/10.3390/w13172375