Influence of Ningbo–Zhoushan Port Main Corridor on the Tidal Current Dynamics in the Zhoushan Sea Area

Gu, Zhanxiong

doi:https://doi.org/10.1155/2022/8485677

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Abstract Introduction Methods Study Area Model Verification Results and Discussion Conclusions Data Availability Conflicts of Interest Acknowledgments References Copyright Related Articles

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Volume 2022 | Article ID 8485677 | https://doi.org/10.1155/2022/8485677

Influence of Ningbo–Zhoushan Port Main Corridor on the Tidal Current Dynamics in the Zhoushan Sea Area

Zhanxiong Gu^1,2

Academic Editor: Yi Xue

Received17 Jun 2022

Revised14 Jul 2022

Accepted16 Jul 2022

Published28 Jul 2022

Abstract

Ningbo–Zhoushan Port Main Corridor project is important in the development of Zhoushan City, but its impact on the hydrodynamic characteristics of the Zhoushan sea area is still unclear. Finite volume method is used in the present study to solve the shallow water equations and establish a plane two-dimensional tidal current numerical model. The measured tidal current data of the Yangtze River Estuary and Hangzhou Bay is utilized to verify the accuracy of the model in simulating the tidal current process. The results indicate the model can numerically reproduce the tidal current process in the Hangzhou Bay–Yangtze River Estuary–Zhoushan sea area (HYZ). In addition, the dynamic characteristics of tidal currents in the Zhoushan sea area with and without piers are compared. The results show that the construction of the project changes the water level near the bridge piers and causes the water obstruction and deficiency in the front and behind the piers, respectively. Tidal flow velocity increases on sides of the piers with while a low velocity area is formed before and after the piers. The project construction exerts a small impact on the tidal currents but a strong influence on the local area near the bridge piers.

1. Introduction

Zhoushan sea area is located in the Donghai Sea, which is an extremely important geographical location and economic status with many estuaries, islands, ports, and docks. The Ningbo–Zhoushan Port Main Corridor project is crucial in the development of Zhoushan because it connects the Zhoushan Mainland–Islands Link Project in the south and Daishan Island in the north as well as joins Changbai Island through the Changbai Interchange constructed in the sea [1, 2]. Large-scale bridge construction usually impacts local hydrodynamic characteristics [3–5].

In recent years, numerical simulation has gradually become an important means to explore the changes of hydrodynamic characteristics with the rapid development of computers [6–13]. For example, Cao et al. [14] analyzed the impact of piers in the tidal reach at the North Branch of the Yangtze River Estuary on the water flow using a two-dimensional flow model and revealed that piers exert the maximum impact on the water level and flow velocity when the tide flow velocity is rapidly rising and falling. Furthermore, the most apparent area of the impact is near the pier or the pier-concentrated area. Zhang et al. [15] constructed a plane two-dimensional tidal-current mathematical model to investigate the influence of fan pile group on hydrodynamic conditions, such as water level, flow velocity, and tidal flux, in the Yangtze River Estuary, Hangzhou Bay, and its adjacent waters. Jin et al. [16] numerically analyzed the impact of the sea-crossing bridge project on Shunhe river course and demonstrated that the construction of a sea-crossing bridge will slightly raise the water level of Shunhe. Wu [17] simulated and analyzed the deep-channel flow structure after the Hangzhou Bay bridge project as well as examined the change in the water flow structure before and after the project; the results showed that the influence of piers on the flow velocity in the downstream is higher than that in the upstream.

Various approaches were applied according to the different pier characteristics [18–20]. Wang [21] calculated the backwater height of piers using an empirical formula and water surface curve method. However, this method is unsuitable for calculating the influencing range of backwater and can only calculate the backwater height of a bridge section. Zhu and Cao [22] simulated the influence of piers through assist correction method and verified that the construction of a bridge in the river course will lead to the rise of water level. The three-dimensional turbulent mathematical model around a vertical cylinder is typically used to examine the influence of sea-crossing bridges on the dynamic characteristics of the ocean. The three-dimensional flow field is obtained by solving the N–S equation on the basis of the standard turbulence model [23].

Although previous studies were carried out in many aspects, they aimed to solve the problem of marine tidal dynamic changes in the small scale. Studies in the large scale are still weak, especially those related to sea-crossing bridges. In particular, investigations on changes in characteristics of the marine hydrodynamic environment coupled with the tidal dynamic process before and after the construction of pier groups are lacking. Three-dimensional models have been increasingly applied and assessed in recent years. However, relevant studies remain insufficient, and the corresponding two-dimensional tidal current numerical model has been extensively investigated. The two-dimensional tidal current numerical model is built by comprehensively considering environmental characteristics, such as terrain and hydrological conditions, which ensure high accuracy and calculation efficiency. Therefore, the present study is aimed at establishing a two-dimensional tidal current numerical model on the basis of the global tide data to examine the influence of the pier group of Ningbo–Zhoushan Port Main Corridor on the tidal current dynamics in the Zhoushan sea area.

2. Methods

2.1. Governing Equations

The tidal current is considered as single-phase continuum, and then, mass and momentum conservation equations are established, which contributes to acquire average Reynolds equations. The following N–S equations based on average Reynolds equations are used as the governing equations of the plane two-dimensional tidal current numerical model in this study [24]: (1)Continuity equation(2)Momentum conservation equationwhere refers to the time; refers to the depth of water; and refer to the Cartesian coordinate system in the horizontal direction; and refer to the depth integral average speed in the and directions, respectively; refers to the gravitational acceleration; refers to the Coriolis parameter; and refer to the bed slope in the and y directions, respectively (Equations (4) and (5)); and refer to the resistance gradient of water flow in the and directions, respectively; , , , and refer to the depth-averaged Reynolds stress (Equations (6)–(8)). where refers to the height of the bed slope; and refer to the resistance gradient of water flow in the and directions, respectively. where refers to the depth-integral average turbulent kinetic energy; refers to the turbulent eddy viscosity coefficient; refers to the kinematic viscosity coefficient of water, which is equal to m²/s.

2.2. Empirical Relationship

The number of unknowns in the aforementioned governing equations is larger than the number of equations. To make the equations closed, some empirical relations of variables are necessary to be introduced. The Chezy coefficient [25] is adopted in the present study to estimate the resistance on the bed bottom as follows: where refers to the Chezy coefficient, which can be calculated using the empirical relationship , and refers to the roughness of the bed surface, which is equal to 0.055 in this study.

One-equation, zero-equation, and models are commonly used calculation methods for the turbulent eddy viscosity coefficient. To simplify the calculation, the zero-equation model is adopted in the present study as follows: where refers to the Karman constant, which is equal to 0.4 in the present study; refers to the drag velocity.

The zero-equation model is discretized by using the finite volume method, and the detailed discretization process is referred to in Hu et al. [26–28].

3. Study Area and Data Acquisition

3.1. Study Area

The study area is located in the Hangzhou Bay–Yangtze River Estuary–Zhoushan sea area (HYZ) with a domain of about 20,800 km² (Figure 1). The overall water depth of Zhoushan sea area is relatively shallow, the water depth of Hangzhou Bay is less than 10 m (theoretical lowest tidal level), and the overall water depth of volcanic islands is still less than 15 m. The silt tidal flat is characterized by fine particle suspended sediment deposits. The distribution characteristics of sediments are coarse and fine mixed without grain size zonation. The surface sediments are mainly silty and clay silty, with a small amount of sandy silty and very small amount of sand. The grain size of the sediments is about 0.01 mm [29].

The coastal tide is irregular and semidiurnal. The tidal current is characterized by the reversing current. The ebb current flows to the east, and the flood current flows to the west. The flow velocity in the bay is not large, and the average flow velocity of flood and ebb tide is less than 0.6 m/s [29]. In addition, the flow velocity of the ebb tide is less than that of the flood tide, and the surface flow velocity is higher than the bottom flow velocity. Therefore, the influence of a bridge engineering group on the overall hydrodynamic variation characteristics of the large-scale sea area is emphasized in the present study. Given that sediment and salinity gradient mainly affect the hydrodynamic forces of local piers through the density baroclinic effect, they are not considered in this study.

Calculation areas include Bohai Sea, Huanghai Sea, Donghai Sea, Hangzhou Bay, and Yangtze River Estuary. The open boundary is set in the open sea, which is far from the islands with evenly and gently variable tidal currents. A sparse grid with a resolution of about 38 km is used in the open sea to enhance the calculation efficiency. The water level and flow velocity change sharply in the area close to the island shoreline, especially in the region near the project. Accordingly, the encrypted grid is adopted in the aforementioned area to ensure the accuracy of the simulation and calculation. Specifically, the minimum spatial step is about 40 m with 64,111 nodes and 122,844 grids when the influence of bridge engineering is not considered (Figure 2).

The maximum resolution of the grid can reach 5 m with a total of 86,485 nodes and 167,757 grids when the influence of bridge projects is considered. In addition, a total of 368 piers with a span of 70 m are set, and the pier shape is generalized as a square with a side length of 5 m (Figure 3). It should be noted that grids are randomly generated by the Surface Water Modeling System (SMS) software, which was developed by United States Army Corps of Engineers Hydraulics Laboratory and Brigham Young University. The layouts of the two sets of grids with and without piers are similar, and the calculation method of Li et al. [30] is adopted. Grid sensitivity analysis was performed in the research of Li et al. [30], which indicated that different grid layouts exert less effect on the calculation results when the size of grids is equivalent.

3.2. Data Acquisition

The measured discharge of Datong Station is adopted in the open boundary at the upper reaches of the Yangtze River (near Sanjiangying, with a distance of about 300 km from the downstream of Datong). A constant flow of 800 m³/s is set in the open boundary at the reaches of Qiantang River. The curved open sea boundary (in the inner side of the continental shelf) is driven by the water level, which mainly considers the tidal components M2, N2, K2, S2, Q1, K1, P1, O1, MF, MM, M4, MS4, and MN4. The tidal level process of each boundary point is calculated as the offshore boundary condition according to the global tide database TPXO.

The initial topography of the model consists of three different data sources: the topography of the south and north branches of the Yangtze River Estuary in 2016; the topography of other areas of the Yangtze River Estuary (upper reaches to Sanjiangying), Hangzhou Bay, adjacent coastal areas, and most of the adjacent waters of the Donghai Sea based on the 2015 electronic chart with a resolution of 10 m; and the topography of other areas based on the ETOPO1 topographic data provided by National Oceanic and Atmospheric Administration (NOAA).

The initial water level and flow velocity of the model are set to 0. The roughness coefficient is calculated by using the formula 0.01+0.01/h.

4. Model Verification

The simulated results of the tidal level are verified by the observation values of the four observation stations in the Yangtze River Estuary (Shidongkou, Jigujiao, east of Nanchao, and middle of Bei Chao) and six stations in the Hangzhou Bay (Yangshan Port, Beilun, Daishan, Lvhua, Shengshan, and Zhenhai). The simulated results of the tidal current are verified by the observation value of the stations of NGN4S, CS9S, and NCH6. The detailed station locations are shown in Figure 4.

4.1. Verification of Tidal Level

Root mean square error (RMSE), correlation coefficient (CC), and skill score (SS) are used to quantify the error to clarify the difference between the simulated and measured tidal current processes. Figures 5 and 6 present that the RMSE ranges from 0.145 m to 0.362 m (RMSE of Shengshan and Shidongkou stations is the minimum and maximum, respectively) according to the available measured data. The tidal level error calculated using the model with a maximum tidal range of about 4.5 m (Yangshan Port) is acceptable.

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4.2. Verification of Tidal Current

The flow velocity and direction of the three stations is used to verify the proposed model (Figure 7, July 21–22, 2016). The range of RMSE between simulated and measured flow velocities is 0.180–0.287 m/s (the RMSE in NCH6 andCS9S stations is the minimum and maximum, respectively). The range of RMSE between the simulated and measured flow direction is 13°37–24°4 (the RMSE in CS9S and NGN4S stations is the minimum and maximum, respectively). The maximum variation range of the flow direction is 180°, and the maximum flow velocity is about 2.2 m/s (CS9S station). Therefore, the errors of the calculated flow velocity and direction using the proposed model are acceptable.

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The CC and SS between simulated and measured values of tidal level, flow velocity, and flow direction are above 0.9 and 0.76, respectively. The coincidence grade is considered “excellent” when according to the evaluation criteria of SS [31]. Skill scores (SSs) between the simulated and measured values of the tidal level, flow velocity, and flow direction are more than 0.65, thereby indicating that the tidal level, flow velocity, and flow direction calculated using the proposed model are consistent with the measured values. Accordingly, the proposed model can be used to simulation calculation of the HYZ.

5. Results and Discussion

The two-dimensional hydrodynamic numerical model is applied to simulate and analyze the characteristics of tidal level and current under the two working conditions of with and without piers. The scale of pies is comparatively small with very dense grids. To reveal the possible influence of the construction of the sea-crossing bridge on the hydrodynamic environment in the nearby sea area, a navigable bridge opening of the Zhoudai bridge and its surrounding piers are selected as examples to clarify and intuitively carry on the detailed researches.

5.1. Comparison of Tidal Level Distribution before and after the Project Construction

5.1.1. Characteristics of Spring Tidal Level

The isopleth of the tidal level at the flood slack and fall of spring tide is nearly parallel under the working condition of no pier (Figures 8(a) and 8(c)). After the construction of project, the tidal level changes near the piers and a large backwater in front of the pier at the flood slack of spring tide (Figure 8(b)). The low tidal level area was replaced by the high tidal level area after the project construction, and the tidal level is increased by approximately 2 cm in the low-value area. The backwater in the direction facing the tide near the piers is evident. The high tidal level area is around 3 cm more than the water chamber area at the rear of the piers. This difference results in the increase of the tidal level gradient in the east–west direction of the pier and the subsequent acceleration of the flow velocity.

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(b)

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(d)

At the flood fall of spring tide, the high tidal level area in front of the west pier is evident (Figure 8(d)). Notably, the tidal level in the original high-value area increases due to the backwater in the pier, while the tidal level in the low-value area behind the east pier reduces and is concentrated in the northeast side of the navigable bridge opening. The tidal level in the backwater area before the piers and navigable bridge opening is high, with a maximum of about −1.469 m. The tidal level gradient near the piers is large due to the existence of backwater and water deficiency. The tidal level in front of the piers is about −1.469 m, while the tidal level at the back of the piers is approximately −1.497 m with a tidal level range of 2–3 cm. This tidal level gradient increases the flow velocity, and a subhigh-tidal level area of about −1.477 m exists between piers.

5.1.2. Characteristics of Neap Tidal Level

The tidal level at the flood slack of neap tide before the project construction declines from northwest to southeast, and the northeast–southwest trend of the isopleth is nearly parallel (Figure 9(a)). At the flood fall of neap tide, the tidal level gradually decreases from the west to east and the isopleth is nearly parallel (Figure 9(c)). After the construction of the project, the tidal level distribution at the flood slack of neap tide shows the same trend as that before the project construction but the isopleth near the pier is curved (Figure 9(b)). Assuming that the direction facing the tide is the front, water deficiency occurs behind the piers and the tidal level decreases to around 1.774 m.

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At the flood fall of neap tide, the isopleth of the tidal level in the navigable bridge opening is nearly parallel, while the isopleth near the piers is clearly curved (Figure 9(d)). A water chamber exists in front of the piers, and a backwater area is observed behind the piers. The difference between tidal levels in front of and behind the piers is about 2 cm. This difference increases the tidal level gradient in the south and north of piers and further results in the acceleration of the flow velocity. From Figures 9(b) and 9(d), we can observe that the tidal level gradient in the front and behind the piers is increased, which results in the acceleration of the flow velocity in the south and north of piers.

5.2. Comparison of Flow Field Distribution before and after the Project Construction

5.2.1. Characteristics of Flow Field of Spring Tide

Assuming that the tide rise (from east to west) is the negative direction, Figure 10(a) illustrates that the flow velocity generally increases from northeast to southwest at the rapid rising of spring tide before the construction of project. On the contrary, the flow velocity shows a generally decreasing trend from southwest to northeast at the rapid falling of spring tide (Figure 10(c)). The isopleth of the flow velocity is inclined and nearly parallel at the rapid rising and falling of spring tide.

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After the construction of the project, the flow velocity increases near the navigable bridge opening and the area of high flow velocity expands at the rapid rising of spring tide (Figure 10(b)). The isopleth of the flow velocity is distributed irregularly and even produces a closed area. The flow velocity in front of and behind the piers significantly decreases at a difference of about 0.3 m/s due to the blocking effect of the piers. The wake zone is located behind the piers and extends into the high-velocity area with a length of 200 m at the rapid rising and falling of spring tide (Figures 10(b) and 10(d)). The velocity in the wake zone is smaller than that of the surrounding flow field with a decrease of about 6%–26% (rapid rising moment) and 10%–40% (rapid falling moment). In addition, Figure 10(d) illustrates that an area with an increased flow velocity of about 0.2 m/s exists in front of the pier at the southwest side of the navigable bridge opening. The flow velocity between piers increases by 15%–20% compared with that before the project construction due to the absence of blocking of piers and narrowed overflow surface. This phenomenon occurs in piers on both sides of the navigable bridge opening.

5.2.2. Characteristics of Flow Field of Neap Tide

The isopleth of flow velocity at the rapid rising of neap tide is inclined and nearly parallel before the project construction (Figure 11(a)). Assuming that the flood tide (from east to west) is the negative direction, the flow velocity gradually increases from northeast to southwest with a maximum of 1.3 m/s. At the rapid falling of neap tide, the flow velocity presents the same tendency as that at the rapid rising of neap tide, with a minimum of around 0.53 m/s (Figure 11(c)). The maximal flow velocity occurs in the southwest with a value of 1 m/s.

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After the construction of the project, the maximum flow velocity near the navigable bridge opening and piers slightly decreases by about 0.1 m/s at the rapid rising of neap tide (Figure 11(b)). The flow velocity of the navigable bridge opening does not vary much. A low-velocity wake zone with a range of about 150 m exists behind piers due to the blocking of the piers near piers. Particularly, the flow velocity in the southwest side of the navigable bridge opening decreases by 25% from about 1.2 m/s to nearly 0.9 m/s. As for the moment of the rapid falling of the neap tide, a wake zone with a range of 150 m exists behind the pier with opposite flow direction compared with the moment of rising tide (Figure 11(d)). The flow velocity in the wake zone decreases to 0.7 m/s, which is 20%–30% lower than the surrounding flow velocity due to the blocking of the piers. A high-velocity zone exists between piers due to the narrow channel effect.

6. Conclusions

The present study establishes a two-dimensional tidal current numerical model using unstructured triangular grids. Then, the proposed model is verified by using the measured tidal current data. Finally, the influence of piers (groups) on the hydrodynamic characteristics of the Zhoushan sea area is further investigated. The following conclusions can be drawn from this study: (1)The tidal current in Hangzhou Bay presents significant characteristics of reversing current. Tide flows from west to east at the falling tide, while moving from east to west at the rising tide with a larger velocity. The isopleth of the tidal level at the flood slack inclines, indicating that the phases of the tidal level in the south and north are asynchronous. The overall structure of the flow field in neap tide is similar to that in spring tide, but the flow velocity is small with a maximum value of about 1 m/s(2)The construction of the bridge will cause the local water level to rise. The backwater and water deficiency occur at the front and back tides of piers, respectively, with a difference of 4–6 cm regardless of the rise or fall of the tide. This water level difference will lead to the increase of the tidal level gradient and subsequent acceleration of the flow velocity between piers(3)The construction of the project has a small influence on the tidal current but a strong influence on local areas. Specifically, the flow field near the piers changes significantly. A low-velocity zone exists in front of the piers, and a wake zone is observed behind the piers. The wake flow is 100–200 m long with a comparatively small flow velocity

The sediment transport and seabed scouring and silting model will be further considered in the future investigation to examine the influence of the project on sediment transport and seabed evolution.

Data Availability

The data used to support the findings of this study are available from the corresponding author upon request.

Conflicts of Interest

The author declares no conflicts of interest.

Acknowledgments

This research was funded by the Zhejiang Key R & D Projects (Grant no. 2021C03180).

References

G. Dong, S. Y. Zheng, and P. T. W. Lee, “The effects of regional port integration: the case of Ningbo-Zhoushan Port,” Transportation Research Part E: Logistics and Transportation Review, vol. 120, pp. 1–15, 2018.
View at: Publisher Site | Google Scholar
H. X. Feng, M. Grifoll, and P. J. Zheng, “From a feeder port to a hub port: the evolution pathways, dynamics and perspectives of Ningbo-Zhoushan port (China),” Transport Policy, vol. 76, pp. 21–35, 2019.
View at: Publisher Site | Google Scholar
M. G. Li, Y. Yan, X. J. Han, and W. D. Li, “Physical model study for effects of the Hong Kong-Zhuhai-Macao Bridge on harbors and channels in Lingdingyang Bay of the Pearl River Estuary,” Ocean and Coastal Management, vol. 177, pp. 76–86, 2019.
View at: Publisher Site | Google Scholar
C. Krautwald, H. Von Häfen, P. Niebuhr et al., “Large-scale physical modeling of broken solitary waves impacting elevated coastal structures,” Coastal Engineering Journal, vol. 64, no. 1, pp. 169–189, 2022.
View at: Publisher Site | Google Scholar
K. Wei, C. Zhou, M. J. Zhang, Z. L. Ti, and S. Q. Qin, “Review of the hydrodynamic challenges in the design of elevated pile cap foundations for sea-crossing bridges,” Advances in Bridge Engineering, vol. 1, no. 1, pp. 1–30, 2020.
View at: Publisher Site | Google Scholar
X. J. Chen and C. H. Hu, “Study on two-dimensional mathematical model simulation of bridge backwater level,” Journal of China Institute Water Resource and Hydropower Research, vol. 1, no. 3, pp. 194–199, 2003.
View at: Google Scholar
W. R. Huang, Q. P. Yang, and H. Xiao, “CFD modeling of scale effects on turbulence flow and scour around bridge piers,” Computers and Fluids, vol. 38, no. 5, pp. 1050–1058, 2009.
View at: Publisher Site | Google Scholar
W. Zhang and X. M. Xie, “Numerical calculation method of backwater of pile pier,” Advance in Science and Technology of Water Resources, vol. 28, no. 5, pp. 25–28, 2008.
View at: Google Scholar
D. F. Xie, S. Gao, Z. B. Wang, and C. Pan, “Numerical modeling of tidal currents, sediment transport and morphological evolution in Hangzhou Bay, China,” International Journal of Sediment Research, vol. 28, no. 3, pp. 316–328, 2013.
View at: Publisher Site | Google Scholar
Z. Defne, K. A. Haas, and H. M. Fritz, “Numerical modeling of tidal currents and the effects of power extraction on estuarine hydrodynamics along the Georgia coast, USA,” Renewable Energy, vol. 36, no. 12, pp. 3461–3471, 2011.
View at: Publisher Site | Google Scholar
P. Li, G. X. Li, L. L. Qiao et al., “Modeling the tidal dynamic changes induced by the bridge in Jiaozhou Bay, Qingdao, China,” Continental Shelf Research, vol. 84, pp. 43–53, 2014.
View at: Publisher Site | Google Scholar
Y. Xue, J. Liu, X. Liang, S. Wang, and Z. Ma, “Ecological risk assessment of soil and water loss by thermal enhanced methane recovery: Numerical study using two-phase flow simulation,” Journal of Cleaner Production, vol. 334, article 130183, 2022.
View at: Publisher Site | Google Scholar
Y. Xue, J. Liu, P. G. Ranjith, Z. Zhang, F. Gao, and S. Wang, “Experimental investigation on the nonlinear characteristics of energy evolution and failure characteristics of coal under different gas pressures,” Bulletin of Engineering Geology and the Environment, vol. 81, no. 1, article 38, 2022.
View at: Publisher Site | Google Scholar
M. X. Cao, X. R. Gan, F. N. Zhou, and X. H. Wang, “Numerical calculation and analysis of the influence of piers on flow in tidal reach,” Yangtze River, vol. 37, no. 4, pp. 81–84, 2006.
View at: Google Scholar
W. Zhang, B. Wang, and H. F. Xia, “Influence of wind turbine pile group layout of offshore wind farm on hydrodynamic conditions in sea area,” China Harbour Engineering, vol. 2, pp. 1–4, 2007.
View at: Google Scholar
X. N. Jin, D. M. Sun, and P. Feng, “Numerical analysis of influence of Shunhe Sea crossing bridge project on river courses,” South-to-North Water Transfers and Water Science & Technology, vol. 15, no. 3, pp. 164–170, 2017.
View at: Google Scholar
Y. K. Wu, “Numerical simulation of flow structure in deep channel of Hangzhou Bay,” master's thesis, Zhejiang University, Hangzhou, 2015.
T. M. Salaheldin, J. Imran, and M. H. Chaudhry, “Numerical modeling of three-dimensional flow field around circular Piers,” Journal of Hydraulic Engineering, vol. 130, no. 2, pp. 91–100, 2004.
View at: Publisher Site | Google Scholar
A. A. Beheshti and B. Ataie-Ashtiani, “Experimental study of three-dimensional flow field around a complex bridge pier,” Journal of Engineering Mechanics, vol. 136, no. 2, pp. 143–154, 2010.
View at: Publisher Site | Google Scholar
M. H. Tseng, C. L. Yen, and C. C. S. Song, “Computation of three-dimensional flow around square and circular piers,” International Journal for Numerical Methods in Fluids, vol. 34, no. 3, pp. 207–227, 2000.
View at: Publisher Site | Google Scholar
C. Y. Wang, “Study on the Impact of Sea Crossing Bridge on Hydrodynamic Environment,” master's thesis, Changsha University of Science & Technology, Changsha, 2011.
J. Z. Zhu and Y. Cao, “Analysis on the influence of several bridges on flood discharge in tidal estuary,” Journal of Hydrodynamics, vol. 21, no. 5, pp. 592–598, 2006.
View at: Google Scholar
J. G. He, H. W. Fang, and R. S. Fu, “Three-dimensional numerical analysis of the influence of pier groups on river flow,” Journal of Hydrodynamics, vol. 22, no. 3, pp. 345–351, 2007.
View at: Google Scholar
J. J. Han, “Water Sediment Coupling Simulation Technology and Numerical Study on Dynamic Geomorphic Process of Estuary/Waterway -- Taking Qiantang River and Dongliu Waterway as an Example,” master's thesis, Zhejiang University, Hangzhou, 2018.
S. Y. Sun, “Discussion on derivation of hydraulic calculation formula (Xie Cai formula),” Railway Standard Design, vol. 6, pp. 41–45, 1988.
View at: Google Scholar
P. Hu, Y. L. Lei, J. J. Han, Z. X. Cao, H. H. Liu, and Z. G. He, “Computationally efficient modeling of hydro-sediment-morphodynamic processes using a hybrid local time step/global maximum time step,” Advances in Water Resources, vol. 127, pp. 26–38, 2019.
View at: Publisher Site | Google Scholar
P. Hu, J. J. Han, and Y. L. Lei, “Mathematical simulation of water sediment coupling based on local time step method,” Journal of Zhejiang University (Engineering Science), vol. 53, no. 4, pp. 743–752, 2019.
View at: Google Scholar
P. Hu, A. F. Ji, and J. Y. Tao, “Research and application of power flow numerical model based on local time step method,” The Ocean Engineering, vol. 38, no. 1, pp. 116–124, 2020.
View at: Google Scholar
Y. F. Gu, “Influence of Island Connecting Project and Sea Level Rise on Sediment Transport Mechanism in Zhoushan Sea Area,” master's thesis, Zhejiang Ocean University, Zhoushan, 2020.
W. Li, J. Y. Zhou, and P. Hu, “High performance urban flood simulation based on porosity and local time step technology,” Journal of Zhejiang University (Engineering Science), vol. 54, no. 3, pp. 1–9, 2020.
View at: Google Scholar
D. Ralston, W. Geyer, and J. Lerczak, “Structure, variability, and salt flux in a strongly forced salt wedge estuary,” Journal of Geophysical Research, Oceans, vol. 115, no. C6, pp. 1–21, 2010.
View at: Publisher Site | Google Scholar

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Copyright © 2022 Zhanxiong Gu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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