# Study on the Spillover of Sediment during Typical Tidal Processes in the Yangtze Estuary Using a High-Resolution Numerical Model

^{1}

^{2}

^{*}

## Abstract

**:**

^{4}t/day, accounting for 37.5–34.9% of the landward floodtide CSSF. The mechanics of sediment spillover in Yangtze Estuary are clarified in terms of a successive process comprising the source, transport, and drainage of the spillover sediment.

## 1. Introduction

^{8}m

^{3}/year) and periodical tides from the ocean meet in the estuary and interact with each other, leading to complicated hydrodynamics and sediment transport. The landward floodtide flow often spills over from the North to the South Branches, carrying a lot of sediment. The estuarine circulations of water and sediment fluxes, characterized by the spillover of water and sediment, play an important role in shaping the morphology of the Yangtze Estuary [1,2,3,4,5].

^{8}m

^{2}, as shown in Figure 2. Second, the computational grid should be fine enough to describe well the local river regimes in the Yangtze Estuary and simulate the estuarine mesoscale structures and transport process correctly [7,8]. Corresponding to fine grids, a small time step of 1–2 min is often required to ensure the stability and accuracy in simulating the fully unsteady flows and sediment transport. Third, simulations of long-term tidal flows, sediment transport, and riverbed evolution are often required in studies of the morphological dynamics. When the domain of the entire Yangtze Estuary is divided using a high-resolution grid, a huge computational cost is required. These requirements challenge almost all existing 2D or 3D numerical models [9]. As a result, in real applications of the Yangtze Estuary, researchers often have to use coarse grids, establish local models [10,11,12], or adopt simplified methods, such as the method of the morphological scale factor [13,14].

## 2. Numerical Formulation

#### 2.1. Governing Equations

^{2}); η(x, y, t) is the water level measured from an undisturbed reference water surface, (m); υ

_{t}is the coefficient of the horizontal eddy viscosity, (m

^{2}/s); f is Coriolis factor; n

_{m}is Manning’s roughness coefficient, (m

^{−1/3}s); ρ is the water density, (kg/m

^{3}); and τ

_{sx}and τ

_{sy}are the wind stress in the x- and y-directions, respectively, (N/m

^{2}).

^{−5}rad/s) is the angular velocity of rotation of the Earth; ϕ (31.38724°) is the latitude of the reference location (x

_{c}, y

_{c}) which is shown in Figure 2.

^{4}tons, accounting for 1–2% of the total sediment load [15]. The bed-load transport therefore contributes little to the horizontal circulations of global water–sediment fluxes in the Yangtze Estuary, and is not solved by the present model. The suspended sediment is regarded to be nonuniform and is described by a fraction method. The vertically averaged 2D advection–diffusion equation, with a source term describing sediment exchange between flow and riverbed, is used to describe the transport of nonuniform suspended load:

_{s}(N

_{s}is the number of fractions); C

_{k}and S

_{*k}= sediment concentration and the sediment-carrying capacity of flows for the k

_{th}fraction of the nonuniform suspended load, respectively, kg/m

^{3}; w

_{sk}= settling velocity of sediment particles for the k

_{th}fraction of the suspended load, m/s; α = sediment recovery coefficient, which is set to 1.0 and 0.25, respectively, in case of erosion and deposition [16].

_{s}) of the fine particles according to field data, experiments or their experience [11,12,17,18,19,20]. In the present model, the w

_{s}of fraction 1 is set according to field data in the Yangtze Estuary, while the primitive settling velocity is directly used for other fractions.

_{th}fraction of the nonuniform suspended load is described by

_{bk}= riverbed deformation caused by the k

_{th}fraction sediment, m; ρ′ = dry density of bed materials, kg/m

^{3}. The gradation state of the bed materials is also updated using the method of [22].

_{m}, in the HDM and the coefficient of the sediment-carrying capacity, K, in the STM are determined by calibration tests with field data. Because the Yangtze Estuary is large and includes various regions with different characteristics of flows and sediment transports (e.g., river reach, tidal reach, coast sea area, and sea region), non-constant model parameters are used in different regions.

#### 2.2. Computational Grid and Model Formulation

#### 2.2.1. Computational Grid

_{i}is the area of cell i; (2) i(j,l) are two cells that share side j, where l = 1, 2; δ

_{j}is the distance between two adjacent cell centroids that are separated by side j; L

_{j}is the length of side j; (3) s

_{i}

_{,l}is a sign function associated with the orientation of the normal velocity defined on side l of cell i. Specifically, s

_{i}

_{,l}= 1/−1 if a positive velocity on side l of cell i corresponds to outflow/inflow (of cell i).

#### 2.2.2. Numerical Discretizations

_{bt}and v

_{bt}. The horizontal momentum equations in the local horizontal x-, y-directions of unstructured grids are then discretized as follows (at side j)

_{bt}and v

_{bt}to enhance computation stability. The explicitly discretized horizontal diffusion term is not expanded here for simplicity, and denoted by E

_{X}and E

_{Y}in x- and y-directions, respectively. The η at nodes is regarded as auxiliary variables, which are interpolated from water-level values of neighboring cells.

_{j}

^{n}

^{+1}and v

_{j}

^{n}

^{+1}of Equation (8a,b) into the discrete depth-integrated continuity equation. This substitution results in a wave propagation equation with cell water levels (η) as unknowns. Using the topology relations among the cells, the resulting discrete wave propagation equation is given by (at cell i)

_{bt}is the solution to the advection subequation. The C

_{bt}is calculated using a recently developed finite-volume ELM (FVELM) [28], where mass is conserved and large time steps (for which the Courant-Friedrichs-Lewy number (CFL) can be much greater than 1) are allowed.

#### 2.3. Parallelization of the Model Code

_{1}= runtime of a sequential run using one working core; T

_{nc}= runtime of a parallel run using n

_{c}working cores.

## 3. Model Parameters and Tests

#### 3.1. Computational Grid and Boundary Conditions

#### 3.2. Calibration and Validation Tests of HDM

^{3}/s during 6–16 December 2012.

_{m}, was calibrated using the spring-tide condition from 14 December at 0:00 to 16 December at 0:00. The inflow discharge was set to 19,000 m

^{3}/s. The n

_{m}of sub regions was adjusted so that the simulated tide-level histories would agree with field data. The n

_{m}was then corrected slightly so that the simulated velocity histories would agree with field data at the same time. The n

_{m}was finally calibrated as 0.022–0.021 from Station Datong to Jiangyin, 0.021–0.015 from Station Jiangyin to Xuliujing, and 0.014–0.011 for the North and South Branches. The n

_{m}in the North and South Branches was similar to the values reported in previous research [31,32].

_{m}, the histories of the simulated tidal levels and depth-averaged velocities were shown to agree well with field data. Generally, the mean absolute error in simulated tide levels was less than 0.15 m compared with the field data, while the mean absolute relative error in simulated velocity at survey positions was less than 10%. The accuracy of the model was then verified by simulating a full spring-neap tide process on 6–16 December 2012, and the simulation results are shown in Figure 4 and Figure 5.

#### 3.3. Calibration and Validation Tests of STM

^{3}/s and 0.112 kg/m

^{3}. The parameter K is calibrated as 0.11–0.08 from Datong to Jiangyin, 0.07–0.04 from Jiangyin to Xuliujing, 0.05–0.02 for the North and the South Branches. Similar to the calibrated n

_{m}, the calibrated K in coast sea regions of the Yangtze Estuary (0.07–0.02) also appears to be smaller than that of inland rivers (0.1–0.2), but approaches the values (about 0.07) reported by [32].

^{8}m

^{3}and 2.854 × 10

^{8}tons. The daily river discharge and sediment concentration are imposed at the upstream boundary, while the seaward open boundaries are forced by tide levels of one-hour intervals. The measured topographical data in December 2011 is used to set the initial topography. The elevations of the nodes in the area of reclamations (or regulations) are modified to be consistent with the design, and the cells there are set to be non-erodible. Then, the model steps forward to November 2013 to get the final topography.

^{4}tons in the simulation, and has an error of +11.1% relative to field data.

#### 3.4. Sensitivity Study of Model Parameters and Coefficients

_{m}, and K).

_{bt}) is, respectively, set to 6, 8, 9, 10, and 12.

_{m}) is performed by changing the n

_{m}in the North and the South Branches which are considered as the most important regions in this case study. The distribution of the n

_{m}, obtained by the calibration test, is taken as the reference and is denoted by “original friction (nm)”. The tests, with the n

_{m}being reduced (−0.001) and increased (+0.001), are denoted by “nm −0.001” and “nm +0.001”, respectively.

_{m}, the histories of the simulated tide level and survey-point velocity are, respectively, shown in Figure 9 (taking Station QLG and Survey Point A1 as examples). It is found that the smaller the n

_{m}of the North and South Branches are, the stronger the landward floodtide flow in these reaches will be (characterized by higher tidal levels and large velocities). It is obvious that the variation of water levels with respect to the n

_{m}is just opposite for the estuary tidal flows and for the inland river flows. The variation of the peak water level in Station QLG is +0.15 m when the n

_{m}is reduced by 0.001, and is −0.04 m when the n

_{m}is increased by 0.001. The variation of the peak velocity in Survey Point A1 is +0.12 m/s when the n

_{m}is reduced by 0.001, and is −0.25 m/s when the n

_{m}is increased by 0.001.

^{3}when the K is reduced by 0.002, and is +0.25 kg/m

^{3}when the K is increased by 0.002.

#### 3.5. Efficiency Tests of HDM and STM

^{3}/s) and a downstream spring tide, is tested to clarify the speedup property of the modeling system. The total runtime of the HDM and the STM is 1550.7 s in sequential runs, and is reduced to 131.1 s in parallel runs (n

_{c}= 16) with a speedup of 11.8. The unsteady flow and sediment transport in 1999 are then tested. It takes the modeling system 12.2 h (using 16 cores) to complete the simulation of a 1-year unsteady flow, sediment transport, and riverbed evolution in the Yangtze Estuary.

## 4. Results

#### 4.1. Simulation Conditions

^{3}/s and 0.112 kg/m

^{3}, respectively. The flow and sediment fluxes at Datong are then respectively calculated to be 16.41 × 10

^{8}m

^{3}and 18.39 × 10

^{4}tons per day. The seaward boundaries are forced by the tide-level histories of a spring tide and a neap tide, respectively, which leads to two tests of 1-day simulation. Nine cross-sections are arranged to record the histories of the flow rates and the sediment transport rates (see Figure 3). For the sake of convenience, the divisions of North Branch are defined as follows: the upper reach (from the bifurcation of North and South Branches to Station QLG); the middle reach (from Station QLG to SHG); the lower reach (from Station SHG to STG); the tail reach (from Station STG to LXG).

#### 4.2. Horizontal Circulation of Water Flux

^{8}m

^{3}/day, accounting for 24.2–28.8% of the landward floodtide CSWF. The CSWF difference of the North Branch runs downstream along South Branch during ebbtide durations, and a horizontal anticlockwise circulation of water flux is formed.

#### 4.3. Sediment Spillover from North to South Branches

^{3}in the reach between QLG and SHG of during floodtide duration in field data. The landward floodtide high-concentration flow, going through cross-section QLG, provides sediment input for the upper reach of North Branch, some of which spillovers from the North to the South Branches.

^{4}t/day, accounting for 37.5–34.9% of the landward floodtide CSSF. The CSSF difference of the North Branch is caused by the sediment which spills over from the North to the South Branches. The sediment, arising from the spillover, runs downstream toward the coast along with the ebbtide flow of the South Branch, and a horizontal anticlockwise circulation of sediment flux is formed.

#### 4.4. Balances of Water and Sediment Fluxes

^{8}m

^{3}/day). Inflow runoff from Datong (16.31 × 10

^{8}m

^{3}/day) contributes to the second part. The water spillover from the North Branch (0.6 × 10

^{8}m

^{3}/day) contributes to the third part, accounting for 1.24% of the ebbtide CSWF at cross-section SE. The ebbtide CSSF at the entrance cross-section of the South Branch (SE) also comprises three parts. Sediment flux, which intrudes upstream of cross-section SE from the South Branch during the floodtide duration, returns during the ebbtide duration, and contributes to the first part (85.76 × 10

^{4}t/day). Sediment input at Datong is 18.39 × 10

^{4}t/day and it evolves to 25.35 × 10

^{4}t/day at cross-section XLJ after a long-distance adjustment of erosion and deposition, which contributes to the second part. The sediment spillover from North Branch (30.89 × 10

^{4}t/day) contributes to the third part, accounting for 21.75% of the ebbtide CSSF at cross-section SE.

^{8}m

^{3}/day, accounting for 1.39% of the CSWF at cross-section SE during the ebbtide duration. At the same time, the sediment spillover from the North Branch reduces to 7.88 × 10

^{4}t/day, accounting for 18.46% of the CSSF at cross-section SE during the ebbtide duration.

#### 4.5. Analysis of Spillover on Morphological Dynamics

## 5. Discussion

#### 5.1. Calculation of Hydrodynamics in Estuaries

#### 5.2. Calculation of Sediment Transport in Estuaries

_{b}is riverbed elevation). However, the effects of these additional terms are still open issues. Some researchers [47,48] included both of the two kinds of additional terms in their models. Wu [49] pointed out that the effect of the $\partial {z}_{b}/\partial t$ term, added into the continuity equation, is dominant relative to the effect of other additional terms. This point is supported in Cao et al. [50], where only the enhanced continuity equation is used together with the momentum equations from the original SWEs. Generally, the Level-1 model is mainly used when the flow, sediment transport, and morphological evolution are strongly coupled to each other (the rate of bed deformation being considerable compared to that of flow evolution), such as the dam-break flows on a moveable riverbed.

#### 5.3. Differences between the Spillover of Saltwater and Sediment

^{3}/s and the tidal range at Station QLG was greater than 2 m, and became remarkable when the upstream runoff was less than 20,000 m

^{3}/s and the tidal range at Station QLG was greater than 2.5 m. The mechanics and quantitative studies on the spillover of saltwater from the North to the South Branches can be found in [5]. These research results provide references for our study on the spillover of sediment-carrying flow.

## 6. Conclusions

^{8}m

^{3}/day, accounting for 24.2–28.8% of the landward floodtide CSWF. The difference of the cross-sectional sediment flux (CSSF) between the floodtide and the ebbtide durations is 43.85–11.26 × 10

^{4}t/day, accounting for 37.5–34.9% of the landward floodtide CSSF.

## Supplementary Materials

## Author Contributions

## Funding

## Conflicts of Interest

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**Figure 1.**The location of the Yangtze Estuary and the study area (a Google Map diagram showing the geographical features of the location). (

**a**) Location; (

**b**) Tidal reaches and estuary.

**Figure 2.**Description of the bound, the three-level bifurcations and the strong river-coast-sea coupling in Yangtze Estuary (computational domain and grid are also given).

**Figure 4.**Comparisons of the simulated tide-level histories and field data. (

**a**) at Station Xuliujing (XLJ), (

**b**) at Station Qinglonggang (QLG), (

**c**) at Station Lianxingang (LZG), (

**d**) at Station Nanmen (NM), (

**e**) at Station Hengsha (HS).

**Figure 5.**Comparisons of simulated histories of velocity with field data (negative velocity is landward velocity, which appears during the flood duration). (

**a**) at Survey Point B1, (

**b**) at Survey Point A1, (

**c**) at Survey Point A3, (

**d**) at Survey Point A5, (

**e**) at Survey Point B7.

**Figure 6.**Comparisons of simulated sediment concentration histories and field data at survey locations. (

**a**) at Survey Point B1, (

**b**) at Survey Point A1, (

**c**) at Survey Point A3, (

**d**) at Survey Point A5, (

**e**) at Survey Point B7.

**Figure 7.**Comparisons of the simulated riverbed evolutions and field data at cross-sections. (

**a**) at CS2, (

**b**) at CS5, (

**c**) at CS7, (

**d**) at CS9.

**Figure 8.**Comparisons of the simulated histories and field data. (

**a**) Tide-level histories at Station Qinglonggang (QLG), (

**b**) velocity histories at Survey Point A1, and (

**c**) sediment concentration histories at Survey Point A1.

**Figure 9.**Comparisons of the simulated histories and field data. (

**a**) Tide-level histories at Station Qinglonggang (QLG) and (

**b**) velocity histories at Survey Point A1.

**Figure 10.**Comparisons of the histories of the simulated sediment concentration and field data (at Survey Point A1).

Region | Length (km) | Area (km ^{2}) | Resolution of Bathymetry Graph | Grid Scale (m × m) |
---|---|---|---|---|

Tidal reach | 533 | 2066 | 1/10,000 | 200 × 80 |

North Branch | 80 | 366 | 1/10,000 | 200 × 80–400 × 200 |

South Branch | 88 | 1132 | 1/25,000 | 400 × 200 |

Coast region | - | 8746 | - | 500–2000 |

East Sea | - | 105,993 | - | 2000–5000 |

Region | Cross-Section | Spring Tide | Neap Tide | ||
---|---|---|---|---|---|

Flood | Ebb | Flood | Ebb | ||

River | JY | −7.72 ^{1} | 24.20 | −3.25 | 19.68 |

XLJ | −28.26 | 44.57 | −15.03 | 31.39 | |

North Branch | QLG | −2.48 | 1.88 | −1.63 | 1.16 |

SHG | −5.73 | 5.14 | −3.22 | 2.76 | |

STG | −11.06 | 10.48 | −6.26 | 5.80 | |

South Branch | SE | −31.41 | 48.35 | −16.34 | 33.18 |

NM | −38.79 | 55.64 | −18.96 | 35.82 | |

North C. | −28.52 | 36.05 | −13.09 | 21.15 | |

South C. | −25.32 | 34.61 | −11.36 | 20.21 |

^{1}Note: In the table, a negative value means the direction of the flux is landward, while a positive value means the direction of the flux is seaward. Arrangements of the cross-sections are shown in Figure 3.

Region | Cross-Section | Spring Tide | Neap Tide | ||
---|---|---|---|---|---|

Flood | Ebb | Flood | Ebb | ||

River | JY | −10.62 ^{1} | 33.92 | −3.31 | 20.60 |

XLJ | −55.76 | 81.11 | −15.28 | 30.76 | |

North Branch | QLG | −116.73 | 72.88 | −32.28 | 21.02 |

SHG | −244.80 | 204.47 | −56.09 | 50.97 | |

STG | −190.93 | 198.84 | −42.65 | 46.96 | |

South Branch | SE | −85.76 | 142.00 | −19.33 | 42.69 |

NM | −157.33 | 218.09 | −31.61 | 57.77 | |

North C. | −130.29 | 164.43 | −20.87 | 36.27 | |

South C. | −82.05 | 109.83 | −13.83 | 25.29 |

^{1}Note: In the table, a negative value means the direction of the flux is landward, while a positive value means the direction of the flux is seaward. Arrangements of the cross-sections are shown in Figure 3.

© 2019 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 (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Hu, D.; Wang, M.; Yao, S.; Jin, Z.
Study on the Spillover of Sediment during Typical Tidal Processes in the Yangtze Estuary Using a High-Resolution Numerical Model. *J. Mar. Sci. Eng.* **2019**, *7*, 390.
https://doi.org/10.3390/jmse7110390

**AMA Style**

Hu D, Wang M, Yao S, Jin Z.
Study on the Spillover of Sediment during Typical Tidal Processes in the Yangtze Estuary Using a High-Resolution Numerical Model. *Journal of Marine Science and Engineering*. 2019; 7(11):390.
https://doi.org/10.3390/jmse7110390

**Chicago/Turabian Style**

Hu, Dechao, Min Wang, Shiming Yao, and Zhongwu Jin.
2019. "Study on the Spillover of Sediment during Typical Tidal Processes in the Yangtze Estuary Using a High-Resolution Numerical Model" *Journal of Marine Science and Engineering* 7, no. 11: 390.
https://doi.org/10.3390/jmse7110390