Keywords

1 Introduction

Most of the existing studies on numerical simulation of tidal rivers are carried out on a large spatial scale, and thus most of these models are 2-dimensional (2D) which can be used to investigate depth-averaged velocity distribution or the topographic evolution of rivers (Xie et al. 2018). These 2D models can estimate large-scale sediment erosion and deposition, but can hardly reproduce complex local flow structures. During the routine maintenance of waterways, local scouring and deposition are of concern to waterway management departments. In order to study the local sediment transport and topographic changes, detailed 3D numerical simulations are needed (Bever and MacWilliams 2016).

Hu et al. (2009) carried out a numerical simulation near the estuary of the Yangtse river using a coarse grid with the minimum grid spacing inside the estuary being about 300 m, and the average grid spacing reaching 2,000 m. A later study carried out by Ding (2011) used a much finer grid in comparison to the former with a grid spacing around 30 m in the tidal reach of the Yangtse river. Because this study used a mixing length model to calculate the eddy viscosity in the Reynolds equations, the applicability of this simple model based on the mixing length concept is limited by the need to prescribe mixing-length variations for different flow conditions (Pourahmadi and Humphrey 1983). In addition, in spite of a finer grid being used in Ding et al. (2011), the grid is still too coarse to reveal 3D flow structures for a river reach characterized by complicated topography, e.g., bifurcation sections in a tidal river.

The KW is a typical bifurcation section in the downstream Yangtze River. Sedimentation frequently occurs at the entrance of the KW, which reduced the navigation depth of the waterway. Previous studies have found that the flow velocity tends to decrease in the center of the channel and thus causes sediment deposition (Cao et al. 2011, Chen et al. 2012, Wang 2016). However, the mechanism that causes the decreased flow velocity is unclear. As a consequence, this study aims at studying the detailed flow characteristics in the KW using a fine-grid 3D turbulence model to simulate flow processes and explains the observed sedimentation issue in the waterway.

2 Numerical Model

The 3D model in this study is built based on the Delft3D by employing multiple vertical layers. In the Delft3D-FLOW module, four turbulent stress closure models can be used, and the widely used k - ϵ model is selected. Previous studies have demonstrated that the k - ϵ model can well simulate the flow characteristics in most cases in river simulations (Fischer-Antze et al. 2008). The upstream boundary of the model was located far from the entrance of the KW (10 km upstream) in order to accurately simulate the inlet flow conditions considering the complex topography upstream of the KW. A curved orthogonal grid was generated with the number of cells being around 800,000. The grid size of the planar grid ranges from 10 m to 50 m. By comparing the simulation results of models with 5, 10, 15, and 20 vertical layers, the secondary flow structures can be well reproduced when the number of layers reaches 10. Therefore, the 10-layer model was chosen for the subsequent simulation.

Fig. 1.
figure 1

The computational grid of the KW

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The boundary conditions of the 3D model are provided by another large 2D model. The upstream and downstream boundaries of the 2D model are located at the Datong and the Xuliujing, respectively, and these two stations have long-term measured flow and water level data. The 2D model is calibrated and validated, and then provides the boundary conditions for the current 3D model, i.e., the flow discharge and water level temporal processes at the upstream and the downstream, respectively. To compare the flow characteristics under different hydrological conditions, the flow processes during flood tides in flood and dry seasons are simulated.

The initial value of the model roughness (the Manning coefficient) was 0.025, which was adjusted during the calibration process according to the measured flow processes and the calibrated roughness coefficient ranges from 0.02 to 0.03. The turbulent eddy viscosity is calculated based on the zero-equation turbulent flow model, Ut = αu∗h, where u∗ is the frictional flow velocity and α is a constant value of 1. The calculation time step is taken as ∆t = 6 s.

Fig. 2.
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Validation results of the 3D model

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The 3D model was validated using the data measured during flood tides from February 20 to February 21, 2019, and data of ebb tides from February 15 to February 16, 2019. Due to a large number of measurement points, several locations shown in Fig. 1 are selected for validation. The validation results are shown in Fig. 2, in which only the magnitude and orientation of the surface velocities were displayed. This figure shows the simulated velocity magnitude, flow direction, and water level during the flood tide compared with the measured data. The model well reproduced the water level process at the validation positions and the tidal level error is less than 0.10 m. The flow velocity and direction are in good agreement with the measured results as well.

3 Results

The planar large-scale flow characteristics in the KW are studied based on the depth-averaged velocity field and vortex distribution. The secondary flow structures are analyzed by extracting typical cross-sections from the 3D velocity field, and four cross-sections are extracted for each experimental run, including CX1, CX2, CX3, and CX4 as shown in Fig. 3. The vertical coordinates of all cross-sections were stretched (magnified by 30 times) for a clearer view of the cross-sectional flow structures.

Fig. 3.
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The locations of the four typical cross-sections in the KW

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3.1 Flow Characteristics During the Flood Season

Figure 4(a) shows the distribution of the depth-averaged flow field, from which significant large-scale flow structure can be readily observed. Firstly, at the entrance of the KW, the strong recirculation structures on both sides of the channel occur due to the upstream narrowing topography and sequential secondary circulations develop. In addition to the circulations at the entrance of the KW. Because of the flow separation of the mainstream near the entrance, circulation structures of different sizes are distributed on the left side of the river channel from the entrance to the vicinity of the Sanyiqiao sidebar, specifically, the biggest circulation being developed covering the sidebar. The large-scale structures indicate that this area is prone to slow flow velocity where sediment is easily deposited during the flood season, which explains the development of the sidebar near the Sanyiqiao.

Figure 4(b) shows the vorticity distribution at the KW, from which the development and shedding of large-scale vortices near the entrance of the KW can be observed. The chaotic flow pattern at the entrance contrasts with the flow pattern downstream, and the turbulent flow explains the origin of the high shear stress and high turbulent kinetic energy at the entrance. The formation of these large and small vortices is influenced by two factors, one is the strong turbulence flow caused by the upstream topography, and the strong contraction at the entrance of the KW. A strong wake area developed downstream the entrance of the KW where vortices are continuously generated, grew, and shed. The dislodged vortex can be transported to the middle area of the Sanyiqiao sidebar.

Figure 5(a) and (b) show the velocity distribution, streamline, and turbulent kinetic energy (TKE) distribution at the CX1 cross-section. The most evident feature of this section is a strong and narrow vortex on the right side of the river. To the left of this vortex is the core of the main flow characterized by high velocities, in contrast to the low velocities on the right side of the vortex. Such a flow distribution is due to the fact that this region is located downstream of a topographic constricted section, and a planar circulation flow is formed behind this contraction. Thus, a strong secondary flow structure is formed at the intersection of this circulation and the main flow, similar to the cross-sectional flow near a groin field.

On the left side of this vortex, the flow consists of two large vortices. The right vertex is a typical secondary flow structure observed in bend flow. However, this vortex is limited to the center of the river compressed by vortices on two sides. The maximum flow velocity of the CX1 occurs on the left side of the river instead of the deepest portion, which is different from normal bend flow. This is attributed to the presence of a strong lateral vortex on the right side, which squeezes the mainstream and makes the core of the main flow to the left.

Fig. 4.
figure 4

Depth-averaged flow velocity and vorticity distribution in the KW during the flood season

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As the maximum flow velocity in CX1 shifts to the left, the maximum gradient of flow velocity moves to the left accordingly, which leads to the maximum TKE near the bed being located on the left side of CX1. Such a distribution has a substantial impact on downstream sediment transport. The bedload transportation is often consistent with the bed shear stress distribution, and the TKE is usually positively correlated to bed shear stress. Thus, the largest sediment transport zone in this section should be located on the left side of the river. As a consequence, sediment advances along the left bank and deposits when flow velocity reduces, which represents a major sediment source for the sedimentation on the downstream sidebar.

Fig. 5.
figure 5

The velocity distribution (left column) and the TKE (right column) of the four cross-sections during the flood season

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On the right side of the channel, due to the presence of a strong lateral vortex, a strong turbulence region is formed near the vortex. The intensity of the TKE in this region exceeds that of the bed. This intense turbulence contributes to the suspension of the sediment and the transported sediment may deposit downstream where flow velocities decrease.

3.2 Flow Characteristics During the Dry Season

Figure 6(a) shows the depth-averaged flow velocity and vorticity distribution in the KW during the dry season. The main difference from the flood season is the disappearance of the large-scale circulation structures near the Sanyiqiao. In Fig. 6, streamlines pass smoothly through the Sanyiqiao sidebar. This phenomenon means that the Sanyiqiao sidebar is prone to sedimentation during the flood season, whereas scouring occurs in the dry season.

In addition, the flow near the entrance of the KW changed significantly. Due to the reduced flow discharge, the separation of streamlines is not as evident as in the flood season, and the resulting horizontal circulations on both sides shrink accordingly. There is a single circulation structure on each side, in contrast to a series of secondary circulation structures in the flood season.

Fig. 6.
figure 6

Depth-averaged flow velocity and vorticity distribution in the KW during the dry season

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Figure 6(b) shows the distribution of vorticity during the flood tide of the dry season, from which it can be seen that the development of vortices is significantly reduced compared to that during the flood season. Especially at the entrance of the KW, the magnitude and coverage of vortices are significantly reduced compared with that during the flood season, and no large-scale vortices mixing phenomenon occurs. However, the topographic contraction on the right side of the channel still causes small-scale vortices, and the shedding vortices move downstream along the right bank.

Figure 7 shows the flow velocity, streamlines, and the TKE distribution of the cross-sections. In the CX1 cross-section, the secondary flow structure caused by the topographic contraction at the right bank is obvious, thus forming a low flow velocity area on the right side. Due to the existence of the secondary flow structure which squeezes the high-velocity flow to the left side of the river. The flow velocity distribution is thus similar to that during the flood season, with the large velocity gradient being located on the left bank. As a result, the greatest TKE occurs on the left bank of the riverbed. The high TKE at the junction between the slow flow on the right and the main flow can be observed, but it is much weaker compared to the TKE on the left side of the riverbed. The high TKE indicates that intense sediment transport is located on the left bank, rather than the deepest area.

The flow velocity in the CX2 cross-section is much lower compared to that during the flood season. The flow separation is greatly reduced, as shown by the shrinking low flow velocity area on both sides compared with that during the flood season. The circulation is significantly weakened and the maximum velocity occurs at the deepest area, and the maximum velocity area shifts to the left to a certain extent in comparison to the flood season. Similar changes occur in the cross-sectional variation of the TKE. In addition, due to the lack of strong mixing during the flood, the TKE gradually decreases with increasing distance from the bed. Intense turbulence still exists in the center of the riverbed.

The flow at the cross-section CX3 can be divided into three secondary flow structures, whereas there no such structures can be observed during the flood season. On the left side, due to the disappearance of large-scale circulation on the Sanyiqiao sidebar, no slow flow area is found on the left side. The distribution of the TKE is consistent with that of the flow velocity gradient, which is similar to the distribution during the flood season but with reduced intensity.

Due to the enlarged area at the CX4 cross-section and the vanish of the large circulation at the Sanyiqiao, the lateral flow structure at this cross-section was well adapted to the local topographic features, showing two large secondary flow structures on the left and right sides corresponding to the inlet of the downstream left and right branches. The maximum TKE of the cross-section is located at the deepest area, which means that the intensive sediment transport zone is located near this area and readily enters the downstream left branch.

Fig. 7.
figure 7

The velocity distribution (left column) and the TKE (right column) of the four cross-sections during the dry season

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4 Conclusions

In this study, flow characteristics of the tidal reach, the KW which is a typical bifurcation reach in the lower Yangtze River, were studied based on a 3D numerical model. With the help of the simulation results, this study demonstrated the existence of large-scale flow structures in both planar and vertical directions and these structures vary from the flood season to the dry season. In the flood season, the flow at the entrance of the KW is characterized by intense turbulence due to the upstream complex topography and the topographic constraint at the entrance. Due to the suddenly increased width of flow downstream the constraint, large-scale circulation structures are developed on the Sanyiqiao sidebar. In addition, the intense turbulent flow at the inlet increases the sediment transport rate, which makes this circulation area highly susceptible to sedimentation. Therefore, in the flood season, sediment accumulation is likely to occur at the Sanyiqiao sidebar, which causes the decreased depth of the waterway and often channel dredging is usually required. In the dry season, the above two factors are greatly weakened, and the circulation structure at the Sanyiqiao sidebar is disappeared. The combination of the influence of the above factors causes sediment erosion during the dry season, and the navigation conditions of the channel improve accordingly.