Engineering Regulation of the Weird Branches in a Branching Estuary and its Mechanics: Using the North Branch of the Yangtze Estuary as an Example

Abstract

Weird horizontal shapes of branches, in large branching estuaries, often cause significant flood risks and environment-related problems. People usually resort to engineering methods to improve the horizontal shape of the weird branches and solve related issues. The responses of the riverbed evolution of a branching estuary to anthropogenic activity are complicated because of complex estuarine hydrodynamics and sediment transports, especially when the project locates specially (e.g., at estuary outlets). The North Branch of the Yangtze Estuary has a narrow upper reach which is almost orthogonal to the South Branch and has a trumpet-shaped lower reach with a wide outlet. The weird horizontal shape of the North Branch brings significant flood risks to cities along this branch, the shrinkage of its entrance, and other problems. In this study, a regulation of the North Branch, which is launched at Guyuan Sand (GYS) just outside the exit of the North Branch, is taken as an example. The GYS regulation aims to improve the weird horizontal shape of the North Branch by building new layouts of outlets, by which people decrease the flood risk of the surrounding cities. The GYS regulation is studied using a 2D numerical model. The riverbed evolution of the Yangtze Estuary in a typical hydrological year is simulated, while the water/sediment fluxes at cross-sections of branches in the estuary during a spring/neap tide are quantitatively calculated. It is found that the regulation changes the rotational flows near the shore, and further reshapes the estuarine circulations of mass inside the outlets, especially exchanges of water/sediment between different branches. The regulation directly changes the riverbed evolution at the outlet of the North Branch, and meanwhile has significant indirect influences on the riverbed evolution of the entrance of the North Branch. The varying riverbed evolution at the entrance of the North Branch and the varying water/sediment fluxes, under different designs of regulations, are related and analyzed. An essential improvement for the weird horizontal shape of the North Branch by an engineering method is shown to be possible, while the regulation mechanism of the engineering method and the response of estuarine riverbed evolution to the regulation are clarified. This study provides a new insight for improving estuarine branches with weird horizontal shapes, by reshaping the tidal processes and the accompanying sediment transports in a branching estuary.

1. Introduction

The Yangtze Estuary has three-level bifurcations (the North and the South Branches, the North and the South Channels, and the North and the South Passages) and four outlets into the sea (Figure 1). The North Branch and the South Branch of the Yangtze Estuary are, respectively, written as N-Branch and S-Branch for short. The Yangtze Estuary has a complex tidal flow, sediment transport, and morphological dynamics [1,2,3,4], and the horizontal shape of the N-Branch is weird. The N-Branch has a narrow upper reach (almost orthogonal to the S-Branch) and a trumpet-shaped lower reach with a wide outlet. The special horizontal shape brings a significant flood risk to cities along the N-Branch, in rainy seasons or periods of storm surges. Moreover, because of the weird horizontal shape of the N-Branch, the flood-tide flow of the N-Branch, carrying a lot of sediment, is often found in field observations to spill over to the S-Branch [5,6]. Currently, the sediment spilling causes the riverbed deposition and the shrinkage of the entrance of the N-Branch, which further deteriorates the situation of flood defense for cities along the N-Branch.

An engineering regulation, which is launched at the Guyuan Sand (GYS) just outside the exit of the N-Branch (Figure 1), is proposed to narrow the outlet to the sea and decrease the flood risk to the cities along the N-Branch in a direct way. The GYS regulation is to form an improved layout for the outlet of the N-Branch mainly by building dikes (e.g., encircled and separation dikes). At the same time, the possibility of reversing the shrinkage evolution of the entrance of the N-Branch by regulation is also studied and expected. In fact, to ensure and facilitate the development of the economics of the cities surrounding the Yangtze Estuary, in former times anthropogenic activities such as the reclamations and river regulations [7], reservoirs [8], navigation engineering [9], and others [10] have been widely launched. In contrast with these common projects, the GYS regulation locates specially at one outlet of the Yangtze Estuary, in which the bidirectional flow inside the outlet evolves into the rotational flow in offshore areas. It means that the GYS regulation will produce much more extensive influences. The challenges for studying the effects of the GYS regulation and its influences on the estuarine riverbed evolution are analyzed as follows.

The spilling of mass from the N-Branch to the S-Branch leads to a horizontal flow/sediment circulation in the Yangtze Estuary. The tidal flow and its adjoint process (e.g., sediment transport and riverbed evolution) of the Yangtze Estuary are complicated and the response rules of the riverbed evolution to the GYS regulation are also complex, due to special morphologies, runoff–tide interactions, and horizontal flow/sediment circulations. Against this background, the influences of the GYS regulation are summarized. First, when a regulation locates outside just one outlet (a special location) of an estuary, it will lead to a widespread and complex influence on the estuary [11]. The rotational flow near the shore and the bidirectional flow of the tidal reaches inside the outlet will both be reshaped by the new outlet. Second, the disturbances of the regulation to tidal flow and its adjoint process will be dynamic, because of the periodically unsteady property of the estuarine tidal flows. Third, variation in the routing of the tidal flows in the N-Branch brought by the regulation will be special, because of the weird horizontal shape of the branch. This variation will decrease/increase the exchange of mass between the branches of the Yangtze Estuary. It means that the GYS regulation will lead to complex disturbances in the processes of the estuarine tidal flows, sediment transports, and riverbed evolutions in the branching Yangtze Estuary.

The forthcoming GYS regulation for the Yangtze River is studied using a two-dimensional (2D) numerical model in this paper. The effects and influences of different designs of the GYS regulation are compared and studied and discussed, while the response mechanics of the riverbed evolution of the branching estuary to the anthropogenic activity are focused on.

2. Numerical Model for Yangtze Estuary

2.1. Summarization of Hydrodynamics and Sediment Transport Models

2.1.1. Numerical Formulation

Numerical models are usually adopted to conduct studies on estuarine tidal flows and sediment transports. A 2D numerical model on unstructured grids is built for the domain of the entire Yangtze Estuary, to conduct the current study. The model uses a staggered grid of variable arrangement [12], on which the vertically averaged 2D shallow water equations (SWEs) are solved [13]. Numerical methods, such as the finite-volume method (FVM) and the finite-difference method (FDM), are combined. A θ semi-implicit method [14] and a multistep Eulerian–Lagrangian method (ELM) [15] are adopted to solve the free-surface gradients and the advections in momentum equations, respectively, within the framework of the operator-splitting technique. The continuity equation is solved using the FVM, to ensure mass conservation. The resulting model for tidal flows is not only mass-conservative but also quite stable (it can use large time steps).

In terms of sediment load, because the annual bed-load quantity in the Yangtze Estuary accounts for only 1–2% of the total load [16], only the transport of suspended load is considered in the present model. The non-uniform suspended sediment is dealt with using a fractional method, in which it is divided into four fractions. The vertically averaged transport equation, with sediment exchange between the flow and the riverbed as a source term, is used as the governing equation of the non-uniform suspended transport:

$${\displaystyle \frac{\partial \left(h{C}_k\right)}{\partial t}}+{\displaystyle \frac{\partial \left(uh{C}_k\right)}{\partial x}}+{\displaystyle \frac{\partial \left(vh{C}_k\right)}{\partial y}}={\displaystyle \frac{{\upsilon }_t}{{\sigma }_c}}\left[{\displaystyle \frac{{\partial }^2\left(h{C}_k\right)}{\partial x^2}}+{\displaystyle \frac{{\partial }^2\left(h{C}_k\right)}{\partial y^2}}\right]+\alpha w_{sk}\left(S_{*k}-C_k\right)$$

(1)

where k is the fraction indices of the non-uniform sediment, k = 1, 2, …, N_s (N_s is the number of fractions); C_k and S_*k = the sediment concentration and the sediment-carrying capacity of flows for the k_th fraction of the non-uniform sediment, respectively, kg/m³; w_sk = the settling velocity of the k_th fraction of the sediment, m/s; α = the coefficient for recoverying saturation, which is set to 1.0 and 0.25, respectively, in case of scouring and depositing [17]. The FVELM [18] is adopted to solve the advection term of the transport equation. It conserves mass both locally and globally.

Significant computational load will be caused by a large number of the fractions of the non-uniform sediment for a fully unsteady 2D numerical model for the tidal flows and sediment transport in a huge computational domain, such as the entire Yangtze Estuary. A numerical model must satisfy the requirement of efficiency for real applications. Hence, the non-uniform sediment, whose transport is simulated in the model, is divided into 4 fractions, with the particle size of the suspended load and their different physical/chemical property in Yangtze Estuary being fully considered. The 4 fractions have the size ranges of 0–0.031, 0.031–0.125, 0.125–0.5, and >0.5 mm, sequentially. Moreover, the w_s of the fine sediment (Fraction 1) is determined per field data in the Yangtze estuary (the method can include the influence of the sediment flocculation), while those of other fractions are directly calculated by classic formulas of settling velocity.

Zhang’s formula [19] is adopted to calculate the flow’s sediment-carrying capacity, which is written as follows

$$S_{*}=K{\left[U^3/\left(gh{w}_s\right)\right]}^m$$

(2)

where U is the vertically averaged velocity ($U=\sqrt{u^2+v^2}$) of the flow; m is an exponent and set to 0.92 in the sediment transport model; K is the sediment-carrying coefficient and calibrated by numerical experiments with field data.

Almost all the formulas for calculating the flow’s sediment-carrying capacity are derived from the uniform sediment experiments or related theories and cannot be directly applied to non-uniform sediment. Zhang’s formula [17] and Wei’s method [20] are combined to calculate the fractional sediment transport capacities of the flow for the non-uniform sediment. It is assumed that the distribution of the sediment-carrying capacity of non-uniform sediment is related to the sediment composition of both the upstream inflow and the surface layer of the riverbed. The sediment transport model calculates the sediment-carrying capacity of the non-uniform sediment first, based on which the model assigns the total sediment-carrying capacity.

Before the application of Zhang’s formula to non-uniform sediment, we first need to determine the settling velocity of the k_th fraction of sediment (w_sk), based on which a test formula is constructed for a temporal calculation. The test formula for calculating the temporal sediment transport capacity for the k_th fraction of sediment is

$$S_{*k}^{*}=K{\left[U^3/\left(gh{w}_{sk}\right)\right]}^m$$

(3)

Then, the following steps are taken to calculate the fractional sediment transport capacities of the flow for the non-uniform sediment.

① Assuming that the upstream inflow is clean water (with the sediment concentration being zero) temporarily, we use Equation (3) to calculate the temporal transport capacity of the k_th fraction of the sediment ($S_{*k}^{*}$). The $S_{*k}^{*}$ is then multiplied by the weight percentage of the k_th fraction of the sediment in the surface layer of the riverbed, to obtain the contribution from the k_th fraction of the riverbed materials.

② For a given location, the contributions of each fraction of the riverbed sediment (“Contribution 1”) and the contributions of each fraction of the inflow sediment concentration (“Contribution 2“) are combined to calculate the comprehensive weights of each fraction of sediment, which are regarded as the gradation (P_k) of the sediment transport capacity of the non-uniform sediment. The weighting formula for calculating P_k is

$$P_k=(P_{\mathrm{u},k}{S}_{*,k}^{*}+C_k)/{\displaystyle \sum _{k=1}^{N_s}(P_{\mathrm{u},k}{S}_{*,k}^{*}+C_k)}$$

(4)

where, P_k is the weight percentage of the k_th fraction of sediment in the surface layer of the riverbed.

③ Using the calculated gradation of the sediment-carrying capacity for the non-uniform sediment and the representative particle size of each fraction, the weighted average is used to calculate the average particle size of the non-uniform sand

$${\overline{w}}_s={\displaystyle \sum _{k=1}^{N_{\mathrm{s}}}{P}_k{w}_{sk}}$$

(5)

④ Using ${\overline{w}}_s$, we calculate the total sediment-carrying capacity of the non-uniform sand:

$$S_{*}=K{\left[U^3/\left(gh{\overline{w}}_s\right)\right]}^m$$

(6)

⑤ Using the gradation of the sediment transport capacity of the non-uniform sediment (P_k), the total sediment-carrying capacity is divided for each fraction as follows:

$$S_{*k}=P_k{S}_{*}$$

(7)

Corresponding to Equation (1), riverbed deformation caused by the transport of the k_th fraction of the sediment is described by

$${\rho }^{\prime }{\displaystyle \frac{\partial z_{bk}}{\partial t}}=\alpha w_{sk}\left(C_k-S_{*k}\right)$$

(8)

where z_bk = the riverbed deformation caused by the k_th fraction of the sediment, m; ρ߰ = the dry density of the bed materials, kg/m³. The gradation of the bed materials is also updated using the method of [20].

2.1.2. Computational Domain and Grid

The tidal reach and the estuary of the Yangtze River and the neighboring sea area are included in one model, as shown in Figure 1, to ensure a sufficient description of the coupling of the river, the coast, and the ocean. Datong, which is 620 km upstream of the coastline and the tidal limit of the Yangtze estuary, is chosen as the upstream boundary of the 2D model. The computational domains of the sea are extended to deep-water (>50 m) regions, whose boundaries are considered as seaward open boundaries. The eastern open boundary of the sea areas is near 124° E, and the southern and northern boundaries of the sea areas are, respectively, near 28.7° N and 33.9° N.

Because of a number of islands and shoals with different scales, the river regime of the Yangtze Estuary is complex [21]. Grids of 200 × 80 m² and 400 × 200 m² are, respectively, used in the regions of the tidal reach and the N-Branch/S-Branch, while the grid scale is gradually increased to 500–2000 m² and 2000–5000 m², respectively, in coastal areas and the sea. The resulting grid has 199,310 quad cells.

The topographic data, measured from 2006 to 2011, are used to interpolate the terrain of the grid of the model. The topographic data of 1/10,000, measured in June 2006, were used in the reach of the Yangtze River, from Datong to Jiangyin. The topographic data of 1/10,000, measured in November 2011, were used in the reach of the Yangtze River, from Jiangyin to Xuliujing. In the N-Branch of the Yangtze Estuary, the topographic data of 1/10,000, measured in December 2011, were used. In the GYS area outside the North Branch of the Yangtze Estuary, the topographic data of 1/10,000, measured in 2012, were used. In the S-Branch of the Yangtze Estuary, the topographic data of 1/25,000, measured in November 2011, are used. Open-access satellite geodetic topographic data of scatter points are used in the coastal regions and the sea areas.

2.1.3. Boundary Conditions

For the upstream inflows, field data (river discharge and sediment concentration) at the Datong hydrological station (Station Datong, as shown in Figure 1) are used as the basic data input for the boundary conditions of the upstream runoff.

The tidal pattern in coastal shallow-water areas is irregular. For this reason, the seaward open boundaries of the current model are defined in the deep-water regions far from the coast, where the tide pattern is basically restored to regular astronomical tides and the sediment concentration of the flow is almost equal to 0. Hence, the time series of the tidal levels of the seaward open boundaries can be predicted by the Global Tide Model [22]. At the same time, a Dirichlet-type boundary condition of C_k = 0 (k = 1, 2, …, N_s) can be directly applied to the seaward open boundaries.

Moreover, the tidal levels at the open boundary of the sea areas is not uniform, so the model’s seaward open boundaries are divided into 48 segments, as shown in Figure 1. The tidal harmonic constants of tides at the midpoints of the 48 segments at the seaward open boundary are obtained, respectively, by interpolation based on a constituent database of a full global grid. And then the tidal level processes of the 48 segments are calculated by the Global Tide Model. The time interval of the tidal level data, outputted by the Global Tide Model, is regulated to 1 h. Taking the process from 14 to 16 December 2012, in the Yangtze Estuary as an example, the 2-day tidal levels of the 48 segments at the seaward open boundaries, calculated by GTM, are shown in Figure 2.

2.1.4. Initial Conditions

The initial conditions have an important influence on the simulation of estuarine tidal flow and sediment transport. Generally, it is necessary to provide a reasonable field of tidal current and sediment concentration as the initial conditions for the computational domain, before conducting a short-term or a long-term estuary simulation. In our studies, the initial conditions can be determined by a pre-simulation method. The duration of the basic tidal flow process at the open boundary of the sea areas, used in the pre-simulation, should ensure at least two rises and two falls, to satisfy the requirement of tidal flow closure. We regulate that the duration of the pre-simulation is 2 days. The tidal-level process at sea boundaries, within the first two days of the period of the formal simulations (e.g., Figure 2), is used as the open boundary condition of a pre-simulation. Then, the pre-simulation takes the following steps.

Step 1: The physical fields at the initial time are set. The initial water levels of the tidal reaches between the inflow and the coastlines are interpolated or evaluated based on the field data. The initial water levels of the coastal and sea areas are set to zero. The initial flow velocity and sediment concentration in the whole computational domain are set to 0. In such a way, rough initial physical fields are formed.

Step 2: The boundary conditions are set. The basic 2-day tidal flow process at the seaward boundary, which has been chosen for pre-simulation, is circulated to generate a long time series of boundary conditions. At the same time, the average river discharge and sediment concentration of the first two days of the period of the formal simulations are used as the open boundary conditions for the upstream inflow.

Step 3: Using the initial condition (in Step 1) and the boundary conditions (in Step 2), a simulation (namely the preliminary simulation) runs until the periodic variations in the simulated processes of tidal levels and sediment concentration are minor. The result of the preliminary simulation is saved as a hot-start file which provides the initial condition for the tests of calibration, validation, and other formal simulations.

2.2. Calibration/Validation of the Numercial Model

The Manning’s roughness (n_m) and the coefficient of the flow’s sediment-carrying capacity (K) are calibrated by tests against the field data. An estuary includes tidal reaches, coastal, and offshore areas, which are different in river bed conditions, and flow and sediment transport characteristics, leading to different model parameters in each region. According to the range of various regions, the Yangtze Estuary is divided into 58 zones (Figure 3) to set independent model parameters for each zone.

We choose the field data of spring/neap tides during 6–16 December 2012 to calibrate the parameters of the model and then validate the accuracy of the model. The hydrological survey measured the histories of water levels at 14 fixed gauges from 6 December (the 340th day of 2012) to 16 December. At the same time, the histories of flow velocity and sediment concentration in two groups (A and B) of survey points were observed from 8 December at 12:00 to 9 December at 21:00 for neap tides and from 14 December at 7:00 to 15 December at 13:00 for spring tides. Arrangements of the cross-sections and the survey points in the hydrological survey are shown in Figure 4. The cross-sections and the survey points are observed synchronously, and the records of the histories of flow velocity and sediment concentration meet the requirements of two continuous rises and falls, which made the tidal flow close. During the hydrological survey, the daily average river discharge at Station Datong (the upstream boundary) gradually reduced from 22,000 (6 December) to 18,700 m³/s (16 December).

In all the numerical experiments, the model uses a computational time step (Δt) of 90 s to carry out the computation of hydrodynamic and sediment transport.

2.2.1. Numerical Experiments of Tidal Flows

The parameter, n_m, of the hydrodynamic model is calibrated using the spring-tide process from 0:00 on 14 December to 0:00 on 16 December. The discharge at the upstream open boundary is 19,000 m³/s. The n_m of each zone is adjusted, until the tide-level histories, produced by the model, agree with the measured data in the hydrological survey. After that, n_m is optimized, so that the velocity histories, calculated by the model, also agree with the field data. The value of n_m was finally determined to be 0.022–0.021 from Datong to Jiangyin (JY), 0.021–0.015 from Jiangyin to Xuliujing (XLJ), and 0.014–0.011 for the N-Branch and the S-Branch. The values of n_m in the N-Branch and the S-Branch approach those reported by other researchers [23,24]. Using this distribution of n_m, the histories of the tidal levels and the depth-averaged velocities, calculated by the model, are shown to fit the field data well. The velocity fields of the Yangtze Estuary at selected times of calibration testing are shown in Figure 5.

The validation experiment for the hydrodynamic model is conducted, using the spring/neap tide process of the Yangtze estuary from 6 December to 16 December in 2012. The results of the validation experiment are shown in Figure 6 and Figure 7. The mean absolute error (MSE) in the water level is generally less than 0.15 m, compared with the data from the hydrological survey. The mean absolute relative error (MSRE) in depth-averaged velocity in two groups of survey points is less than 10%. The hydrodynamic model is shown to achieve a satisfactory accuracy.

2.2.2. Numerical Experiments of Sediment Transport

The parameter, K, of the sediment transport model is also calibrated using the spring-tide process from 0:00 on 14 December to 0:00 on 16 December. The discharge at the upstream open boundary (Datong) is 19,000 m³/s, while the sediment concentration is 0.112 kg/m³. After a trial-and-error process using the numerical model, the parameters (K) of the zones are finally calibrated to be 0.11–0.08 from Datong to Jiangyin, 0.07–0.04 from Jiangyin to Xuliujing, and 0.05–0.02 for the N-Branch and the S-Branch. The obtained parameters, K, in the coastal zones and sea zones of the Yangtze Estuary are found to be 0.07–0.02, which are smaller than those of inland rivers (0.1–0.2) but approach the values (about 0.07) reported by other researchers [24]. Using this distribution of K, the sediment transport model produces histories of the sediment concentration which fit the field data well. The sediment concentration fields of the Yangtze Estuary at selected times of the calibration test are shown in Figure 8.

The validation experiment for the sediment transport model is conducted, using the spring/neap tide process of the Yangtze estuary from 6 December to 16 December in 2012. The results of the validation experiment are shown in Figure 9. The histories of the sediment concentration calculated by the model are generally observed to agree with the field data, where only minor errors in the amplitude are observed. The MSRE in the simulated sediment concentrations is generally less than 20%. The reasons for some remarkable errors in certain periods are analyzed as follows.

First, the formula adopted to calculate the sediment-carrying capacity in the model does not include a term describing the influences of sediment incipiency, but at the same time contains a third power of the velocity. As a result, the sediment-carrying capacity, calculated by the formula, is sensitive to the velocity. Hence, the history of the sediment concentration, calculated by the model, changes closely with the flood and the ebb of the tidal flow, as shown in Figure 9. Second, the hydrological survey includes the neap-tide and spring-tide periods. During the neap-tide periods, the sediment accumulates at the bottom layers of the flow, while the vertical distribution of the sediment concentration is remarkably non-uniform. Because the instrument used to measure the sediment concentration has the limitations of sensitivity and vertical positioning accuracy, it is difficult to accurately catch the sediment concentration of the bottom layers of the flow during the neap-tide periods. This may lead to a large error in calculating the average sediment concentration over the water depth. During the spring-tide periods, the distribution of the sediment concentration in the vertical line is relatively uniform, and it is easy for the instrument to conduct an accurate measurement for the average sediment concentration over the water depth. These two aspects are the possible reasons for the larger error in the simulation of the neap-tide periods (Day 343) and the better fit in the simulation of the spring-tide periods (Day 349) in Figure 9.

2.2.3. Numerical Experiments of Riverbed Evolution

The ability of the model in simulating the riverbed evolution of the Yangtze Estuary is verified using the topographies of December 2011 and November 2013, where a 2-year simulation of fully unsteady tidal flow, sediment transport, and riverbed deformation between 1 December 2011 and 30 November 2013 in the Yangtze Estuary is conducted. We choose the field data of spring/neap tides during 6–16 December 2012 to calibrate the parameters of the model and then validate the accuracy of the model. In the chosen period, the total runoff is 17947 × 10⁸ m³ and the total inflow suspended load is 2.854 × 10⁸ tons from Datong (the upstream open boundary), where the daily-averaged discharge and sediment concentration are imposed. At the seaward open boundaries, the time series of tide levels with an interval of one hour are used. The topography measured in December 2011 is used as the initial topography. The elevations of the grid in regions of reclamations/regulations are set using the value of the engineering design, while the cells in these regions are made non-erodible. Then, the numerical model is run step by step, from 1 December 2011 to 30 November 2013, to obtain the final topography.

Based on the final topography obtained by the model, the topography profiles of the cross-sections at the branches of the Yangtze Estuary are interpolated. The cross-sectional profiles obtained by the model are compared with the field data (measured in November 2013) at several selected cross-sections of the N-Branch, as shown in Figure 10. It is found that the simulated profiles at most cross-sections agree with the field data. Typically, some reach of the N-Branch is narrowed by projects during 2011–2013, e.g., the Xincun Sand reach. In such reaches, the flow is more centralized and has a stronger ability of scouring than that in the original wider channel. As a result of the intensive erosion, the shoals are removed in these reaches during the simulation period, which can be observed at the cross-section CS5. It must be pointed that some midterm projects of reclamations and regulations during 2011–2013 are not considered in the simulation. Moreover, the current model does not have the ability to calculate bank failures. These two aspects result in, at some cross-sections, the deviation of the simulated riverbed profiles from the measured profiles. The N-Branch is shown to experience a mild erosion during December 2012 and November 2013 in the simulation, and it is consistent with the field. The erosion quantity of sediment is 4617.65 × 10⁴ tons according to the field data, and the simulation is shown to have a relative error of +11.1%.

3. Morphological Dynamics of North Branch under the Regulation

The high-resolution 2D numerical model is used to conduct a study of the morphological dynamics of the Yangtze Estuary under the GYS regulation in this section.

3.1. Computational Conditions of Prediction Simulation

The prediction is first run without the GYS regulation (Figure 11a). Second, three simulations are run, respectively, under Designs 1–3 (Figure 11b–d). The current outlet of the N-Branch (without the regulation) is denoted by “Design 0,” and these three designs for the regulation are denoted by Design 1−3 and introduced as follows. The summation of the channel widths at the head of the GYS is used to represent the width of the outlet. Design 1 uses two unjammed outlet channels, whose total width is about 11 km. Design 2 uses a southward channel which is 6.5 km wide, with the northward channel being blocked off. Design 3 uses a northward channel which is 4.5 km wide, with the southward channel being blocked off. In the 2D model, the grid is locally refined to describe the structures (e.g., the new dikes in Figure 12). For different designs of the GYS regulation, the cells in the area of regulation are set to be non-erodible in the simulations.

Because the forecast simulation is conducted after the impoundment of the Three Gorges Reservoir (TGR), the impact of the operation of the TGR should be considered in the inflow conditions (including the processes of discharge and sediment concentration) of the 2D model at the upstream boundary. Moreover, the representativeness of the inflow process should be considered at the same time. Because of these aspects, it is not simple to determine a proper inflow condition for forecast simulation. Hence, the leading institute of the research project (Changjiang Institute of Survey, Planning, Design, and Research, China) proposed the sub-topic of “inflow boundary conditions” in research, through which a proper inflow condition is studied and determined. The research of the sub-topic is independent of the current research reported in this paper, while the content and result of the former can be found in [25]. A detailed presentation of the studies of [25] may be beyond the scope of this study. Therefore, in the following, only the key points and the main results of the studies in [25] are summarized.

The aim of the sub-topic research [25] is to found a “compositive” 1-year flow-sediment process, which includes the operation of the TGR and can fully represent the wet, middle, and dry hydrological years of the lower Yangtze River. In this study, such a “compositive year” is colloquially called the “typical year”. According to [25], the flow-sediment process of the typical year is generated in the following method.

First, a one-dimensional (1D) numerical model is developed for the flow and sediment transport in the TGR. A 20-year simulation of the flow, sediment transport, and riverbed evolution of the TGR is conducted, using the hydrological process from 1991 to 2000 (the process is circulated twice to make a 20-year hydrological series), to generate the flow-sediment process of the outflow of the TGR.

Second, a 1D model is developed for the middle and lower Yangtze River (including large lakes along the river). A 20-year simulation of the flow, sediment transport, and riverbed evolution of the middle and lower Yangtze River is conducted, using the results of the first step as the inflow conditions at the entrance of the middle Yangtze River. As a result, a 20-year flow-sediment process of Datong is calculated.

Third, based on the 20-year flow-sediment process of Datong, the discharge and the sediment concentration are ranked according to the magnitude, then a frequency analysis is conducted to generate the flow-sediment process of a compositive year.

After the team of the sub-topic research finished their study, they output a 1-year hydrological process (including the daily-averaged discharge and sediment concentration at Datong), which is provided as the inflow conditions of the 2D model in this paper. Our study uses a mandatory hydrological condition in the 2D forecast simulations. Because the hydrological series of 1991–2000 cover fully the wet, middle, and dry hydrological years, the hydrological condition of the resulting typical year is representative.

Forecast simulations of the riverbed evolution of the Yangtze Estuary are conducted, using the above 1-year typical (compositive) hydrological process as the inflow conditions of the 2D model. At the same time, the tide levels of 1999 with one-hour intervals are used to set seaward boundaries. At Datong, the total runoff in this year is 9687.92 × 10⁸ m³ and the total sediment quantity is 1.23 × 10⁸ tons. The diurnally-averaged discharge and sediment concentration (at Datong) of the typical year are imposed at the inflow boundary. Three kinds of designs are proposed for the GYS regulation at the outlet of the N-Branch, where three new outlets have different widths and directions (Figure 11). For each case with or without the GYS regulation, a simulation of a 365-day unsteady process of flow and sediment transport is run.

3.2. Predicted Riverbed Evolution

3.2.1. Regional Quantities of Riverbed Deformation

Based on the results of the 365-day simulation, the amounts of riverbed deformation in different regions of the Yangtze Estuary with/without the GYS regulation are listed in

Table 1. Riverbed deformation of the estuarine area under the GYS regulation.

Region	No Regulation (×104 m3)	Variation Rates of Deformation (%)
		Design 1	Design 2	Design 3
XLJ	660.8	0.7	2.0	4.6
N-Branch	3885.7	2.6	−1.6	−48.0
S-Branch	6561.1	−0.9	−8.4	17.4
Total	11,107.5	0.4	−5.4	−6.2

(domain divisions are shown in Figure 13).

In the absence of the regulation, the Xuliujing (XLJ) region and the N-Branch and S-Branch overall experience an erosion of riverbed in the typical year process of tidal flow and sediment, with a total riverbed deformation of 11107.5 × 10⁴ m³. ① The riverbed erosion of the XLJ region (R1) is 660.8 × 10⁴ m³. ② The riverbed erosion of the N-Branch (R2-R6) is 3885.7 × 10⁴ m³. The upper reach (R2) of the N-Branch is in a state of deposition, the middle and lower reaches (R3-R5) are in a state of erosion, and the outlet reach (R6) is in a state of micro erosion. ③ The riverbed erosion of the S-Branch (R7–R12) is 6561.1 × 10⁴ m³. Using a calculation based on the areas of the regions, the R1, R2–R6, and R7–R12 experience a riverbed deformation of −10.9 cm, −10.6 cm, and −5.5 cm, respectively (negative values indicate erosion) under Design 0 (without regulation).

The distributions of riverbed deformation in the Yangtze Estuary after the typical-year flow-sediment process of selected cases are provided in Figure 14. Overall, the GYS regulation does not change the basic rules of riverbed evolution in the Yangtze Estuary but affects the amplitude of riverbed deformation in certain regions. ① The change in riverbed deformation in the XLJ region is minor under the GYS regulation, and the variation rates under Design 1–3 are 0.7%, 2.0%, and 4.6%, respectively, compared with that without regulation. ② In the N-Branch, the thickness of riverbed deformation is −10.9 cm, −10.4 cm, and −5.5 cm, respectively, under Design 1–3. The variation rates are 2.6%, −1.0%, and −48.0%, respectively, compared with that without regulation. ③ In the S-Branch, the thickness of riverbed deformation is −5.5 cm, −5.0 cm, and −6.5 cm, respectively, under Design 1–3. The variation rates are −0.9%, −8.4%, and 17.4%, respectively, compared with that without regulation. The influences of Design 2 and 3 on estuarine riverbed evolution are quite different, and the latter has the greatest influence on the riverbed evolution of the N-Branch.

3.2.2. Local Deformation at the Outlet of the N-Branch

The local riverbed evolution at the outlet of the N-Branch is directly influenced by the GYS regulation, as shown in Figure 15. Under Design 0, at the outlet of the N-Branch, the channel (including the south and the north parts) has a total width of 11 km. After the action of the process of the typical annual process of tidal flow and sediment, the outlet area only experiences a minor erosion of the riverbed, with the amplitude of riverbed deformation being −0.2–0.2 m.

In Design 1, the GYS (mainly the part which has high terrain and limited conveyance capacity of flow) is excluded by an encircled dike, while narrowing of the outlet of the N-Branch to the sea is not obvious. Therefore, the influence of the regulation on riverbed deformation at the outlet of the N-Branch is direct but minor. After the action of the process of the typical annual estuarine process, the amplitude of riverbed deformation in the outlet region of the N-Branch remains at −0.2–0.2 m, as shown in Figure 15b. In contrast, the influence of Design 2 and 3 on riverbed deformation at the outlet of the N-Branch is significant.

In Design 2 (with a southward outlet), the width of the outlet of the N-Branch is decreased from 11 km to 6.5 km, and the flow becomes concentrated. More intensive erosion of the riverbed is observed at the outlet of the N-Branch after the 1-year estuarine process, with riverbed deformation being −1.5 m–0.5 m (Figure 15c). In Design 3 (with a northward outlet), the width of the outlet of the N-Branch is further decreased to 4.5 km, and the flow becomes more concentrated than that of Design 2. The most intensive erosion of the riverbed is observed at the outlet of the N-Branch after the 1-year tidal process, with the riverbed deformation being −2.0 m–0.5 m (Figure 15d).

It can be concluded that the riverbed deformation at the outlet of the N-Branch after the 1-year estuarine process is directly determined by the width of the new outlet channel. In addition, in the middle and the lower reaches of the N-Branch, compared with the riverbed deformation without the GYS regulation (22.8 cm), the deformations under Design 1 and 2 (23.3.5 cm and 23.8 cm, respectively) change little, while the value decreases by about 10 cm under Design 3.

3.2.3. Local Deformation at the Entrance of N-Branch

Riverbed evolution at the entrance of the N-Branch is closely related to the reshaped the tidal process and the accompanying sediment transport of the N-Branch, which may be considered as an indirect but significant influence of the GYS regulation. During the flood-tide period, the landward flow of the N-Branch, which carries a large quantity of sediment, goes upstream along the upper reach of the N-Branch and spills over into the S-Branch. In this process, some sediment carried by the flood-tide flow will deposit on the riverbed along its journey, because of the decreased flow intensity and the stagnation of the spillover flow at the bifurcation. As a result, continuous sedimentation happens in the upper reach, from Chongtou (CT) to Qinglonggang (QLG), and then the entrance of the N-Branch. The GYS regulation is shown to affect the riverbed evolution of the N-Branch by reshaping the tidal process along the N-Branch, which is particularly obvious near the entrance of the N-Branch (see Figure 16).

The upper reach of the N-Branch, from the bifurcation (CT) to QLG, is characterized by a compound cross-section of floodplain and channel. During the flood-tide period, most of the landward tidal flows goes upstream in the channel and a large flow intensity is kept there, while the flow intensity is low in the widespread floodplains on both sides of the channel. In the channel with large flow velocities, it is difficult for sediment to deposit, and the riverbed is even observed to be locally eroded. At the same time, a low flow intensity means a low sediment transport capacity, so sediment deposits extensively on the floodplains.

Figure 16a shows the distribution of riverbed deformation at the bifurcation after the 1-year flow-sediment process and without the GYS regulation. Overall, the entrance region of the N-Branch shows sediment deposition and channel shrinkage, and the average thickness of silt was 14.4 cm, after the 1-year flow-sediment process. Sediment deposition is shown to extensively happen on the floodplains with a maximum silt thickness of about 1.1 m, while local erosion and little deposition are observed in the channel. The GYS regulation does not change the basic rules of the erosion and deposition at the entrance of the N-Branch, but affects the amplitude of riverbed deformation to some degree, as shown in Figure 16b–d. Under Design 1, the riverbed deformation at the entrance of the N-Branch changes little (see Figure 16b). Under Design 2, the average silt thickness at the entrance of the N-Branch is reduced by 9.3 cm, with the maximum deposition being about 0.90 m. Under Design 3, the average silt thickness is reduced by 9.0 cm, with the maximum deposition being about 0.75 m. Relative to those in Design 2, the deposition of the floodplain and the erosion of channel in Design 3 are both remarkably reduced.

Moreover, the riverbed deformation in the middle and lower reaches of the N-Branch has the following properties. Under Design 0, the middle and lower reaches experience an erosion of 22.8 cm. Under Design 1 and 2, the average thickness of riverbed erosion becomes, respectively, 23.5 cm and 23.8 cm, which are found to change little. However, the average erosion thickness is found to be reduced remarkably to 10.0 cm under Design 3.

In this section, the morphological dynamic of the N-Branch under the GYS regulation has been clarified by simulations. In the following, variation in the tidal process and the accompanying sediment transport under the regulation will be studied, to clarify the response of riverbed evolution at the entrance of the N-Branch to the regulation. Meanwhile, the possibility of reversing the shrinkage evolution of the entrance of the N-Branch by regulation is also discussed.

4. Response Mechanics of Riverbed Evolution to the Regulation

Through reshaping the process of the tidal process and the accompanying sediment transport of the N-Branch (especially changing the spilling of mass from the N-Branch to the S-Branch), the GYS regulation affects the riverbed deformation of the N-Branch. The response mechanics of the riverbed evolution of the N-Branch to the GYS regulation are quantitatively studied by simulating the processes of typical spring/neap tides in this section. Because the responses of riverbed evolution at the exit reach of the N-Branch are straightforward, the entrance reach is focused on.

4.1. Simulation Conditions

The used conditions of spring/neap tides are as follows. For the inflow boundary, the flow rate and sediment concentration are, respectively, 19,000 m³/s and 0.112 kg/m³. At Datong, the diurnal fluxes of water and sediment are, respectively, 16.41 × 10⁸ m³ and 18.39 × 10⁴ tons. The tide histories of a spring/neap tide are, respectively, used at the seaward boundaries, leading to two kinds of 1-day simulation. The simulations were run without regulation and with the GYS regulation (Designs 1–3). The results of the simulations under Designs 1–3 are compared with those under Designs 0.

The regulation reshapes the estuarine tidal process and the accompanying sediment transport, resulting in new histories of discharges (Q_W) and sediment transport rates (Q_S) at the cross-sections of estuarine reaches. The histories of Q_W and Q_S are recorded at seven hydrological cross-sections (Figure 13), respectively. For each of the cross-sections, the history of Q_W is integrated, respectively, over the periods of the flood tide and the ebb tide, to obtain the cross-sectional water flux (CSWF) of the corresponding time. Similarly, the simulated history of Q_S is also integrated over the periods of the flood tide and the ebb tide, to obtain the cross-sectional sediment fluxes (CSSF).

Based on these calculations, the effects of the regulation on the tidal process and the accompanying sediment transport are found to be confined to the regions downstream of XLJ. The GYS regulation reshapes the tidal process and the accompanying sediment transport in the N-Branch directly and has little influence on those of the S-Branch. Under the regulation, the changes in Q_W, CSWF, Q_S, and CSSF in the N-Branch are shown to be much bigger than those in the S-Branch. Therefore, the changes in the Q_S and CSSF of the N-Branch are focused on in the following.

For the sake of convenience, we use the following divisions for the N-Branch in the coming analysis: the upper reach is from the bifurcation of the N-Branch and S-Branch to Qinglonggang (QLG); the middle reach is from QLG to Shanhegang (SHG); the lower reach is from SHG to Shantiaogang (STG); and the tail reach is from STG to Lianxingang (LXG). The channel widths of the upper, middle, lower, and tail reaches of the N-Branch are shown to be sequentially 1, 1–3, 3–5, and 5–8 km.

4.2. Reasons for Deposition at the Entrance of N-Branch

The tidal process and the accompanying sediment transport in simulations without regulation is analyzed to clarify the reasons for riverbed evolution at the entrance of the N-Branch.

In the flood-tide period, because of a huge landward flood-tide discharge at the outlet and a fast shrinkage of river width, strong flows are still kept in the lower, middle, and upper reaches of the N-Branch, where the velocity is shown to be as big as 2.4, 3.0, and 2.5 m/s, respectively. Some flood-tide pioneer flow continues to go through the upper reach of the N-Branch and then arrives at the bifurcation, leading to the spillover of water. The water, which spills over from the N-Branch, runs downstream along the S-Branch in the ebb-tide duration.

Sediment transport along the N-Branch happens simultaneously with the aforementioned tidal process. As a result, the middle and lower reaches of the N-Branch experience considerable erosions of riverbed during a flood-tide duration, corresponding to the strong flows there. During the journey of the flow through the eroding reaches of the N-Branch, the landward tidal flow’s sediment concentration remarkably increases. Large sediment concentrations of 6–8 kg/m³ are often observed in field data in the reach between QLG and SHG in the flood-tide period. In short, the weird morphology of the N-Branch facilitates the form of an erosion region in its middle and lower reaches, which provides a sediment source input for its upper reach.

In a flood-tide time, the tidal flow in the upper reach of the N-Branch, which maintains considerate intensity (large velocity), provides energy for the transport of sediment. The flood-tide flow (which carries a lot of sediment) goes through the upper N-Branch and towards the bifurcation. In the journey of the landward tidal flow, some sediment is separated out from the flow and deposits on the riverbed in the upper reach of the N-Branch, because of the gradually decreased flow intensity or the stagnation of flow. The remaining landward flood-tide flow, after this journey, goes through the bifurcation and spills over from the N-Branch to the S-Branch.

The reason for riverbed deposition, which happens at the entrance of the N-Branch, is summarized as follows. The eroded middle and lower reaches of the N-Branch provide sediment input for the entrance reach of the N-Branch, and some of the sediment deposits on the landward journey of the tidal flow, leading to a shrinkage of the entrance of the N-Branch. It details why sediment deposition happens at the entrance of the N-Branch in the former simulations (Figure 16a).

In the following sections, disturbances of the GYS regulation in the tidal processes of the N-Branch are first summarized. Second, variations in the sediment transport process of the N-Branch under the regulation are clarified. Finally, based on simulation results, the cross-sectional water/sediment fluxes along the branches of the Yangtze Estuary, with and without engineering, are analyzed. The response mechanics of the riverbed evolution at the entrance reach of the N-Branch of the Yangtze Estuary to the GYS regulation are explored.

4.3. Responses of Tidal Flow to GYS Regulation

By building encircled and separation dikes to form new flow boundaries, the regulation brings complex disturbances to adjacent clockwise rotational flows, reshaping the tidal process in the branching Yangtze Estuary. Due to the weird morphology, the propagation of the tidal wave and its deformation along the N-Branch are complex under regulation. In addition to a common narrowing effect, a so-called “guiding effect” is found for the design of a southward outlet, against the background of a clockwise rotational tidal flow. The effects are here explained.

First, narrowing of the outlet leads to a “narrowing effect” and will reshape the tidal process along the N-Branch. For a given channel, the flow conveyance capacity generally scales with respect to the width of the channel. The width of the outlet is reduced to 6.5 and 4.5 km under the regulation of Design 2 and 3, respectively, from the initial width of 11 km. Simulation results show that the peaks of the Q_W histories along the N-Branch in flood-tide and ebb-tide periods are both decreased and delayed, with the histories of Q_W becoming flatter. Meanwhile, because of the reduced flow conveyance capacity at the outlet of the N-Branch, some of the seaward ebb-tide water flux which is originally drained by the N-Branch is diverted into the S-Branch.

Second, the southward and the northward new outlets are found to have different effects on the tidal flows along the N-Branch, against the background of a clockwise rotational flow around the regulation. During the flood-ebb transition period, the northward coastal current is guided by the southward channel (Design 2) into the outlet channel of the N-Branch (Figure 17c), which is called the “guiding effect”. The direction of the new outlet of Design 3 and the near-shore coastal current are towards the same direction, so the guiding effect will not happen (Figure 17d). The “guiding current” caused by the guiding effect, leads to extra landward flow and further reshapes the tidal process of the N-Branch. It increases the landward discharge, the water flux, and the duration of large discharges in the flood-tide period and results in a “guiding storage” of water along the N-Branch. In ebb-tide periods, the guiding storage transforms to a seaward flow which goes together with the ebb-tide flow and increases the seaward discharge along the N-Branch.

Third, because of the overlapping influence of the narrowing and guiding effects, the variation in the tidal processes along the N-Branch under Design 2 varies (Figure 18). The narrowing effect exists through the tidal process, while the guiding effect mainly has an action in the second half of the flood-tide time and the first half of the following ebb-tide time (namely, the flood-ebb transition period). The two effects enhance each other, but at other times or locations counteract each other. Moreover, variation in the tidal process along the N-Branch under the regulation is also influenced by the detailed design (e.g., width, direction, and others of the new outlet) and the environment-related factors (e.g., the trumpet-shaped morphology and the irregularity of estuarine rotational flows around the GYS). Therefore, the compositive response of the tidal processes to the GYS regulation is very complex at the cross-sections along the N-Branch.

4.4. Sediment Transport Process under GYS Regulation

The regulation reshapes the tidal processes of branches, further influencing sediment circulation. The histories of the flow rate (Q_W) and the sediment transport rate (Q_S) of Design 1–3 are compared with those of Design 0 in Figure 18 (simulation result from a successive 24 h tidal process). Variations in the Q_W and the Q_S process under different designs of the GYS regulation are here described quantitatively by the change in the peaking Q_W (denoted by Q_{W, peak}) and the peaking Q_S (denoted by Q_{S, peak}). The variations in Q_{S, peak} under the GYS regulation are listed in

Table 2. Variation in the peaking sediment transport rate (Q_{S, peak}) after GYS regulation.

Region	Cross Section	QS, peak (Spring)	Spring Tide (%)			QS, peak (Neap)	Neap Tide (%)
			D. 1	D. 2	D. 3		D. 1	D. 2	D. 3
River	XLJ	3.26	−0.11	−0.19	−0.26	0.88	−0.11	−0.19	−0.26
North Branch	QLG	8.37	−0.22	−5.78	−50.06	1.75	−1.90	−13.27	−34.09
	SHG	15.94	−1.39	−16.41	−30.37	3.35	−2.02	−17.31	−27.15
	STG	12.19	−0.19	−15.42	−24.01	2.59	−2.17	−13.05	−17.07
South Branch	NM	7.89	1.50	3.60	2.43	1.62	0.28	2.97	7.14
	North C.	6.73	1.97	1.35	2.99	1.13	0.34	0.85	4.29
	South C.	4.35	0.80	0.64	2.56	0.77	0.25	0.11	4.22

Note: Q_{S, peak} (unit: ×10⁴ kg/s) represents the peaking cross-sectional sediment transport rate (without regulation), respectively, in the flood-tide period and the ebb-tide period.

. According to Section 4.2, the morphological dynamic at the entrance region of the N-Branch is mainly related to the flood-tide period, so only this process of sediment transport under the regulation is analyzed in the following (where the simulation results of spring tide is taken as an example).

Under Design 1, the encircled dikes around GYS produce little disturbance to the surrounding tidal flows, because the partial region of the GYS, which is excluded from the flow area, is characterized by high elevation and low flow conveyance. Under Designs 2 and 3, the flood-tide flow is confined, respectively, within the south and the north channels beside the GYS. The outlet width of Design 3 is 4.5 km, while that of Design 2 is 6.5 km. Design 3 has a narrower and more tortuous flow path, which makes it more difficult for the flood-tide flow to go upstream into the N-Branch. As a result, Design 3 produces a much stronger narrowing effect than Design 2.

During the flood-ebb transition period, the velocity fields around the GYS are shown in Figure 17 for different designs. The northward near-shore flow in Design 1 is divided into two parts, and they bypass the GYS, respectively, and then continue to go northward. Parts of the lagged water outside the outlet (by the narrowing effect during the first-half flood-tide period) in Designs 2 and 3 go upstream through the outlet. Compared to Design 3, Design 2 has a southward outlet and leads to a guiding effect, which will help to guide the coastal current into the N-Branch.

During a spring-tide period, the weak narrowing effect in Design 1 only leads to a minor reduction of 0.2–1.6% in Q_{W, peak} and 0.2–1.4% in Q_{S, peak} at cross-sections along the N-Branch. Among the three designs, Design 3 has the strongest narrowing effect. As a result, under Design 3, the histories of the flood-tide Q_W are shown to have the most shrinkage along the N-Branch. Design 3 is shown to lead to a significant reduction of 18.3–23.2% in Q_{W, peak}. Corresponding to reduced flood-tide flow intensity, the histories of the flood-tide Q_S along the N-Branch are also shown to shrink sharply. According to the simulation result, Design 3 leads to a significant reduction of 24.0–50.1% in Q_{S, peak} along the N-Branch.

Under Design 2, the narrowing effect reduces the flood-tide Q_W along the N-Branch, while the landward guiding current increases the flood-tide Q_W. For the N-Branch, the guiding current become weaker from lower to upper reaches, and the overlapping results of the narrowing effect and the guiding current also change along the N-Branch. In the middle and lower reaches of the N-Branch, a moderate reduction of 4.2−6.9% in Q_{W, peak} is observed. Following the reduced flood-tide flow intensity, the Q_{S, peak} in the middle and lower reaches is reduced by 16.4−15.4%, with the histories of Q_S remarkably shrinking. In the upper reach, the guiding current enlarges the flood-tide Q_W, which counteracts most of the influences of the narrowing effect. Because of the guiding current and its deformation along the N-Branch, the Q_{W, peak} is not reduced obviously at QLG under Design 2. Under the overlapped narrowing effect and guiding current, the duration of the large flood-tide Q_W at QLG is lagged but well kept. Correspondingly, only a minor change happens for the sediment transport in the upper reach, where the history of the flood-tide Q_S at QLG is lagged, with the Q_{S, peak} being reduced by 5.78%. In the upper N-Branch, the reduction in Q_{S, peak} under Design 2 is an order of magnitude smaller than that under Design 3, because of the influence of the guiding current under a southward outlet.

4.5. Cross-Sectional Sediment Fluxes under GYS Regulation

In Figure 18, the simulated histories of Q_W and Q_S under the GYS regulation are shown to shrink remarkably under Design 2 and 3, resulting in reductions in the cross-sectional water flux (CSWF) and sediment flux (CSSF). The variations in CSSF during the flood-tide period are listed in

Table 3. Variations in cross-sectional sediment flux (CSSF) after GYS regulation.

Region	Cross Section	CSSF (Spring)	Spring Tide (%)			CSSF (Neap)	Neap Tide (%)
			D. 1	D. 2	D. 3		D. 1	D. 2	D. 3
River	XLJ	55.76	−0.02	−0.05	−0.05	15.28	−0.02	−0.05	−0.05
North Branch	QLG	116.73	−0.83	−14.89	−55.62	32.28	−0.62	−18.98	−33.74
	SHG	244.80	−0.64	−13.07	−25.38	56.09	−1.17	−11.04	−18.84
	STG	190.93	−0.39	6.45	−3.28	42.65	−0.58	−7.60	−6.42
South Branch	NM	157.33	1.31	3.61	−3.82	31.61	0.61	1.07	3.78
	North C.	130.29	1.41	2.35	0.71	20.87	0.69	0.77	3.49
	South C.	82.05	0.56	0.79	3.67	13.83	0.48	0.67	3.03

Note: CSSF (unit: ×10⁴ t/day) represents the cross-sectional sediment fluxes (without regulation), in the flood-tide and the ebb-tide durations.

, respectively. For similar reasons as Section 4.4, only variations in the flood-tide CSWF and CSSF brought about by the regulation are focused on (using the simulation results of the spring tide).

During the spring-tide period, the weak narrowing effect of Design 1 only produces a minor reduction of 0.2–0.9% in CSWF and 0.4–0.8% in CSSF along the N-Branch. Design 3 has the strongest narrowing effect, where the histories of the flood-tide Q_W and Q_S along the N-Branch both shrink sharply. As a result, Design 3 leads to a significant reduction of 3.6–30.2% in CSWF and a significant reduction of 3.3–55.6% in CSSF.

Under Design 2, the guiding current and the outlet narrowing produce opposite actions, and the overlapping result of the two effects varies along the N-Branch. Correspondingly, the CSWF and CSSF will be affected differently along the N-Branch. In the middle and lower reaches, despite the reduction in Q_{W, peak} and Q_{S, peak}, the flood-tide CSWF at SHG and STG still have an increment of 1.23% and 4.95%, respectively, due to the increased duration of the large flood-tide Q_W. In particular, the landward flood-tide CSSF is increased by 6.45% in the lower reach, corresponding to the remarkably increased CSWF. However, the increment of the flood-tide CSWF at SHG is quite limited, after the sediment transport capacity is reduced in the middle reach because of the flattened history of the Q_W. The CSSF in the middle reach (at SHG) is shown to be reduced by 13.1%. In the upper reach of the N-Branch, the guiding current increases the flood-tide Q_W, which has counteracted most of the influence of the narrowing effect. Under the overlapped narrowing effect and guiding effect, the duration of the large flood-tide Q_W at QLG is lagged but well kept. As a result, the CSWF at QLG is shown to be almost unchanged. Because of the flattened histories of Q_W, the sediment transport capacity is also reduced in the upper reach of the N-Branch, leading to a reduction of 14.9% at QLG.

4.6. Relation between Riverbed Evolution and Fluxes of Water and Sediment

Based on the results of the aforementioned two aspects of the studies (the prediction of typical annual riverbed evolution, and the calculation and analysis of the water/sediment fluxes at the cross-sections in the scope of the Yangtze Estuary during a spring/neap tide), the riverbed erosion and estuarine water/sediment fluxes are related and analyzed in the following. Then, the response mechanism of the riverbed evolution of the weird branch (the N-Branch) of the Yangtze Estuary to the engineering regulation is discussed and clarified.

Under Design 1 (with two outlets), the regulation causes little influence on the water/sediment fluxes along the N-Branch, and so the amplitude of riverbed deformation at the entrance region of the N-Branch is almost the same as that without regulation. Design 3 (with a northward outlet) produces the strongest influence on the ability to accept flow at the outlet of the N-Branch, and it leads to a remarkable shrinkage of discharge and the sediment transport rate in the upper reach of the N-Branch. The flood-tide CSWF and CSSF will experience, respectively, a decrease of 30.2% and 55.6% in the upper reach of the N-Branch. Corresponding to the sharp decrease in the water/sediment fluxes, the amplitudes of floodplain deposition and channel erosion are both remarkably reduced at the entrance region of the N-Branch (Figure 16d).

Unlike Design 3, the outlet channel of Design 2 (using a southward outlet) receives an additional landward guiding flow during the flood-tide period, which counteracts most of the influence of the narrowing effect on tidal flow and the accompanying sediment transport in the upper N-Branch. Under Design 2, the CSWF and CSSF along the upper N-Branch are only reduced by 0.1% and 14.9%, respectively. Hence, the resulting influence of Design 2 on the sediment transport and the riverbed evolution of the entrance of the N-Branch is minor (Figure 16c).

In the GYS regulation for the outlet of the N-Branch, the three designs cause a regulation of different degrees for the water/sediment fluxes along the upper reach of the N-Branch and therefore lead to different influences on the riverbed evolution of the entrance region of the N-Branch. This is the mechanism of the engineering regulation, and it explains the variation in the riverbed evolution of the entrance region of the N-Branch after the conduction of the GYS regulation.

5. Discussion

Local clog and stagnation of flows often happen in large branching estuaries with branches of weird horizontal shapes, resulting in significant flood risks and environment-related problems. For such problematic branches, when an essential improvement of the weird horizontal shape of the branch has not been found, people often increase the conveyance ability of the branch by dredging (to provide a provisional foundation for current requirements of flood-defense, navigation, environment-related issues, and so on). However, dredging is usually an expedient, and the problems are not radically solved. A dredged reach is often found to be deposited by sediment in a short time after the activity, and additional subsequent dredges are needed.

This study proposes a new insight for improving the estuarine branches with weird horizontal shapes, by reshaping the flow/sediment processes in a large branching estuary. Namely, through regulating the estuarine water/sediment fluxes, people change the rules and the tendency of the riverbed evolution of the weird estuarine branches. As a result, the horizontal shape of the weird branches is improved, and real problems are finally solved.

For the N-Branch of the Yangtze Estuary (which is in this study chosen as an example of the regulation of the weird branches of a branching estuary), the detailed findings are as follows.

First, the reasons for riverbed deposition at the entrance region of the N-Branch are studied by simulating the riverbed evolution of a typical year and by simulating a spring/neap tide. The trumpet-shaped horizontal shape facilitates the erosion of the middle and lower reaches of the N-Branch, which provides the sediment input for the entrance reach. When the flood-tide flow goes through the upper reach of the N-Branch, some of the sediment deposits on the landward journey of the tidal flow, leading to a shrinkage of the entrance of the N-Branch. This conclusion is consistent with field observations and the results of former qualitative studies [26,27,28,29].

Second, the response mechanics of riverbed evolution at the entrance of the N-Branch to the GYS regulation are clarified by relating the varying riverbed evolution at the entrance region of the N-Branch and the varying water/sediment fluxes along the branches under different designs of new outlets. Design 3 (with a northward outlet) produces the strongest influence on the ability to accept flow at the outlet of the N-Branch and leads to a remarkable shrinkage of the discharge and the sediment transport rate in the upper N-Branch. As a result, the deposition at the floodplain and the erosion in the channel are both remarkably reduced at the entrance of the N-Branch. Design 2 (using a southward outlet) is characterized by an additional landward guiding flow during the flood-tide period, and only leads to a mild influence on the water/sediment fluxes and riverbed evolution at the entrance of the N-Branch. Riverbed evolution at the entrance of the N-Branch is found to be related to the tidal and sediment transport process of the N-Branch.

Third, the findings of the studies imply that the shrinkage of the entrance of the N-Branch can be controlled or even reversed and that an essential improvement for the weird horizontal shape in a branching estuary by engineering methods is possible.

6. Conclusions

The regulation of the N-Branch (with a weird horizontal shape) of the three-level branching Yangtze Estuary is taken as an example to study the response mechanics of riverbed evolution of a branching estuary to an anthropogenic activity. A 2D numerical model, on a high-resolution unstructured grid of about 200,000 cells, is used. The regulation mechanism of an engineering method and the response of estuarine riverbed evolution to the regulation are focused on.

The morphological dynamics of the Yangtze Estuary in a typical hydrological year are simulated. The reasons for the riverbed deposition at the entrance region of the N-Branch are analyzed. The local riverbed evolution at the outlet region of the N-Branch is influenced directly by the regulation. When the width of the outlet of the N-Branch is narrowed, the riverbed at the outlet experiences obvious erosion. At the same time, the regulation is shown to have significant indirect influences on the riverbed evolution of the entrance region of the N-Branch.

The response mechanics of riverbed evolution at the entrance of the N-Branch to the regulation are studied by simulating a spring/neap tidal process. Water/sediment fluxes at the cross-sections along the branches in the estuary during the spring/neap tides are quantitatively calculated and analyzed. The varying riverbed evolution at the entrance region of the N-Branch and the varying water/sediment fluxes under different designs of regulations are related and analyzed. It is found that the regulation changes the rotational flows around the GYS and further reshapes the estuarine circulations of mass inside the outlets, especially the exchanges of mass between different branches. Design 3 (with a northward outlet) has the strongest influence on the ability of accepting flow at the outlet of the N-Branch, and it leads to a remarkable shrinkage of discharge and the sediment transport rate in the upper N-Branch and remarkably reduces the riverbed deformation at the entrance region of the N-Branch. In Design 2 (using a southward outlet), the landward guiding flow will counteract most of the narrowing effect, and finally riverbed deformation at the entrance region of the N-Branch is only mildly experienced. Riverbed evolution at the entrance region of the N-Branch is closely related to the tidal and sediment transport process of the N-Branch.

The findings of the study also imply that the shrinkage of the entrance of the N-Branch can be controlled or even reversed and that an essential improvement for the weird horizontal shape of the N-Branch by engineering methods is possible. This study provides a new insight for improving estuarine branches with weird horizontal shapes by reshaping the processes of the tidal flow and the accompanying sediment transport in a branching estuary.