Effects of a diversion dyke on river flow: a case study

Bagua Island is located in the lower reach of the Yangtze River, situated in the north of Nanjing City in China. The Yangtze River in this reach can be classified as an anastomosed river, and the Bagua Island splits the river course into two branches. The right branch is the main watercourse nowadays; it is about 10·4 km long, around 1070 m wide and 19·0 m deep. As this right branch is wider and much straighter than the left branch, the incoming flow can easily run into it, so the right branch discharges approximately 87% of the total flow rate of the Yangtze River. However, the left branch is approximately 21·6 km long, which is over twice the length of the right one. In the dry season, the left branch watercourse is narrow, at about 606 m wide and 9·0 m deep (Ji, 2002; Li and Liu, 2002; Zhang and Zang, 2003). The direction of the flow into the left branch is nearly 90° from the streamwise direction of the upstream Yangtze River, which makes it even more difficult for to enter the left branch.

In fact, the left branch was the main watercourse with broad and deep cross-sections as early as 1865, and the inflow angle was also small. The relative strength of the left and right branches did not switch until the 1940s. The riverbed of the Bagua anastomosed river has been undergoing a natural evolution process. Owing to frequent flooding, sediment erosion and deposition, the waterline of the Bagua Island has changed greatly since the 1950s, and the head of the Bagua Island has kept moving downstream. The left branch of the Bagua reach has declined consistently, while the right branch has gradually become the mainstream. As shown in Figure 1, the talweg of the upstream river was inclined to the right bank in 1952. Then, it shifted to the left bank from 1954 to 1965. After 1965, the talweg of the channel swayed a little to the right bank before moving back to the left bank again from 1979 to 1989. Meanwhile, the diversion point moved downstream by about 2230 m from 1952 to 1985, and it moved closer to the left bank by about 460 m. The 0 m contour line shows that the island head moved downstream by 1400 m from 1952 to 1985 (Xiao and Tang, 2012). As the bank protection work has been built in front of the Bagua Island in 1985, the evolution of the Bagua reach has been slowed down. However, the left branch is undergoing a decline over these years. At present, it only discharges about 13% of the total river flow rate in the dry season, which is significantly less than the figure in 1957 of around 22% (Ji, 2002).

Despite the decrease in the flow, the left branch of the Bagua reach of the Yangtze always plays an important role in regional economy and shipping. The total industrial output along the left branch accounts for about 40% of the whole of Nanjing's industrial output. The broad river surface offers a good environment for the shipping industry. In order to stabilise the flow rate and reduce the sediment accumulation in the left branch, a lot of river regulation works have been constructed from 1956 to 1993 (Chen and Liu, 1999; Sun et al., 1995; Zang, 2002; Zhang and Zang, 2003). In 1956, bank protection works were built along the Nanhua bend in the left branch, after which time similar works were widely used to repair the collapsed banks. In particular, bank protection works were introduced at the head of the Bagua Island in 1985, while putting the recession of the island head under control. Although river regulation works have effectively protected the river banks and the head of the island, they still seem to be unable to maintain the current situation, as the left branch is still slowly declining. Dredging slightly increases the flow through the left branch, but it is costly. An effective measure to avoid the eventual decline of the left branch is yet to be confirmed.

More recently, some numerical model results (Hou et al., 2011; Yan et al., 2010) have shown that the extension of the bar head further upstream can effectively stabilise the partition of the discharge. Chen and Yu (2012) revealed that the main reason for the flow through the left branch decreasing remarkably is the construction of wharves there. Little information is known about the effect of building a diversion dyke in front of Bagua Island. The aim of this paper is to study the impact of a diversion dyke on water level, flow regime and discharge partition based on a fully dynamic shallow water model. To represent the complex and irregular topography of the natural river, the numerical simulation adopts arbitrary curvilinear grids. First a computational model is set up for the Bagua anastomosed river; this is then calibrated and validated by comparing the numerical predictions with field observations and physical model tests. It is a two-dimensional model, and solves the water depth and depth-averaged velocity components. Subsequently, this model is employed to simulate how the length and angle of the diversion dyke impact on the water level, flow regime and the partition of the incoming flow between the two branches. The results are useful for channel management and regulation. In the meantime, considering the financial and technical constraints on the building of such a dyke, recommendations are provided at the end of the study regarding the shape of the diversion dyke and its effectiveness.

Shallow water equations are widely used in analysing the flows in natural rivers, shallow lakes and floodplain. It is assumed that the horizontal scale of the flow is much larger than the vertical scale. In Cartesian coordinates, these depth-integrated equations can be written as

where t is time; ζ is the water surface level above datum; q_x and q_y are the volumetric discharges per unit width in the x and y directions, respectively; g is the acceleration due to gravity; H is the total water depth; and C is the Chezy coefficient.

With the help of boundary-fitted coordinate transformation, these governing equations are reformulated, so that the curvilinear mesh in the physical domain is mapped onto the uniform rectangular mesh in the computational domain, which simplifies the finite-difference discretisation. Operator-splitting technique and total variation diminishing (TVD)–MacCormack scheme are employed in constructing the solution method. To enhance the accuracy and stability of the model, the maximum time step is confined as a predetermined value which is restricted by the well-known Courant–Friedrich–Lewy (CFL) condition. Second-order accuracy is achieved in both time and space. An empirical wetting/drying treatment has been developed to track the moving interface between the dry ground and the water-occupied area. All these numerical algorithms have been extensively tested to be valid in past studies. Readers are referred to Liang et al. (2007a, 2007b, 2010) for details.

In this study, the focus is placed on the impact of a diversion dyke on the flow in the left and right branches of Bagua River reach. As shown in Figure 2, the model domain stretched from Sihao Wharf to Gangchi, which was approximately 21 km long according to the streamwise distance of the right branch. The entire length of the two branches around Bagua Island was included inside the computational domain. The upstream boundary was about 6·7 km from the head of the Bagua Island, which was long enough to ignore the influence of the diversion dykes on the flow at the upstream end. The downstream boundary was also sufficiently far away from the tail of Bagua Island, so that the river confluence does not affect the flow at the downstream end. In Figure 3, five velocity measurement cross-sections and seven water level gauging stations (the black dots) were labelled out, which will be used in the model verification in the next section. There are also four monitoring points (the squares) in Figure 3 to monitor the water level in Section 5.

The computational mesh was superimposed over the map of the region in Figure 2, and it contained 762 × 84 cells in total. Only every 16th grid point was plotted in Figure 2 in order to achieve a good visual effect. In drawing the mesh, 29 grid points were placed within each river cross-section in the left branch and 55 grid points were placed in the right branch, so that the flow structure in the channel was sufficiently resolved. The natural topographies were inherently complex and irregular, especially at the upper part where the Bagua river reach splits into the left branch and right branch. As shown in Figure 2, the computational mesh generally followed the shape of the domain, so the resolution corresponded well with the width of the water body. Moreover, most of the quadrilateral cells had sides of similar lengths and the four corner angles in a cell were close to 90°. Figure 3 shows the locations of some gauging stations and cross-sections, where the predicted results will be compared with the measurements.

The bed elevations of the river were interpolated from cross-sectional profiles surveyed in July 2011. The consequent bed levels over the whole computational domain were demonstrated in Figure 4, from which it can be seen that the left branch was shallow and meandering. The flow at the upstream and downstream junction points deviated severely from the main channel. There were two deep grooves located near the head and the end of the Bagua Island, with the deepest bed levels of about −35 m and −50 m, respectively.

The model was first verified against the observations made by Nanjing water conservancy bureau and the physical model experiments obtained by Xiao and Tang (2012). During the simulation, the flow rate at the upstream boundary (Sihao Wharf) was specified at 15 290 m³/s, which was the flow rate in the dry season. There were experimental data at this flow rate, which will be used for the model verification. Corresponding to the flow rate, the water level at the downstream boundary (Gangchi) was set to 1·616 m. The initial velocities were set to zero inside the domain. The initial water levels were either 1·616 m at wet cells or the same as the bed elevations at the dry cells. The computation used a time step of 0·3 s. In order to obtain the steady-state solution, the simulation was run for 172 800·0 s, which was found to be long enough for the solution to be independent of time.

In the numerical model, the bed resistance was a very important hydrodynamic parameter and needed to be calibrated. It is obvious that this parameter may vary from point to point in reality, but acceptable results may be achieved by using a fixed value across the domain. Desirable solutions were attained with Manning's roughness value set at n = 0·033.

The locations of the calibration and validation sites have been labelled in Figure 3. Comparisons among the model predictions, field measurements and the physical model experiment data were made at all of the observation sites. Figure 5 shows that there is generally a good match among them, in terms of both the water levels and velocity profiles, which demonstrates that the current simulation is quite acceptable.

The diversion ratio of the left branch was observed to be 12·4% in May 2011 during the dry season. The model prediction of this ratio is 12·12%, which is quite close to the field measurement. In the physical model experiment, a 550 m long diversion dyke with a 35° angle to the left of the minus y axis and a 750 m long diversion dyke with a 45° angle to the left of the minus y axis were separately added to the flow, as shown in Figure 6. The data obtained from the experiment show that the diversion ratio increases by 2·72% and 2·45%, respectively, with the addition of the two dykes. With these dykes, the model prediction gives the increases to be 2·46% and 2·24%, respectively. Again, the accuracy of the model is verified in these more complex situations.

Therefore, the accuracy of the model was deemed satisfactory and suitable for simulating the diversion dyke in such a large domain.

After verifying the reliability of the established hydrodynamic model, parametric studies were undertaken to investigate the influences of the diversion dyke of the Bagua River reach. Given the assumption that the dyke is straight and is never overtopped, then the length and the angle of the diversion dyke are the only two parameters that play the important roles in deciding the diversion ratio. The diversion dyke starts at the head of the Bagua Island. Its elevation level was set to 5 m, which is higher than the possible maximum water levels throughout the simulations. As shown in Figure 6, the angle is defined as between the diversion dyke and the minus y axis, and the following values were tested: 5°, 15°, 25°, 35°, 45°, 55°, 65°, 75° and 85°. The following five lengths of diversion dyke were tested: 350 m, 550 m, 750 m, 950 m and 1150 m. A boundary-fitted curvilinear mesh of high resolution was generated in the model. The grid size was very small compared to the river width, so the bed elevation was simply changed at the location of the dyke to block the flow between adjacent cells. In this way, it is assumed that the width of the dyke is equal to the grid size. In this parametric study of the diversion dyke, the computational condition is identical to that used in the model verification.

The water levels along the river are important to flood risk and river navigation. In order to monitor the impact of the diversion dyke on the water levels, four monitoring points are chosen. They are the squares in Figure 3. One point, Huangjiawei, is set at the upstream direction of the diversion dyke to observe the impact on the upstream water level, while the Yanziji monitoring point is used to explain the impact on the downstream water level. The other two points represent the left side and the right side of the dyke, respectively.

The model predictions of the water level dependence on the angle and length of the dyke are shown in Figure 7. This indicates that the water levels both in the upstream branch and in the left branch are significantly affected by the diversion dyke. However, the water level in the right branch is only slightly affected by the diversion dyke, regardless of the angle and the length of the diversion dyke.

In Figure 7(a), water level in the upstream monitoring point of Huangjiawei is increased by the dyke if the angle of diversion dyke is between 5° and about 65°. A small angle means the dyke is pointing more to the right branch, which forces more water to flow through the left branch by raising the water level on the left side of the upstream sections. Naturally, the water level rise upstream of the dyke gets larger when the length of the dyke is bigger, with the highest water level of 2·22 m for the 1150 m long and 5° angled dyke, which is much larger than the water level 1·71 m without the diversion dyke. However, the water level remains fixed at about 1·74 m, when the dyke points to the left branch (the angle is from 65° to 85°). Because the right branch is the main channel, partially blocking the left branch does not much affect the water level in the upstream locations. Figure 7(b) shows the same trend as Figure 7(a) when the angle of diversion dyke is between 5° and about 65°, with the highest water level of 2·2 m when the dyke is 1150 m long and 5° angled. When the angle is between 65° and 85°, with the flow being blocked in the left branch, the water level drops correspondingly. Since the 1150 m long diversion dyke almost blocks the left branch entirely, the water level on the left monitoring point falls significantly to only 1·62 m. In contrast, the curves shown in Figures 7(c) and 7(d) indicate that the water levels at the two monitoring points in the right branch are hardly affected by the construction of the dyke. The water level drops only slightly, when the angle is between 5° and 45°. The reason may be that the right branch is so wide that it can hardly be affected by the introduction of a short dyke in the middle of the river and the flow rate change in the left branch.

Figure 8 indicates the flow field without any diversion dyke, that with a dyke of 5° angle, 350 m long, and that with a dyke of 55° angle, 550 m long. Figure 8(a) shows that the incoming flow splits into two branches at the head of Bagua Island. Because of the high resistance in the left branch, the velocities in the left branch are much smaller than those in the right branch, and most of the incoming water turns to the right branch. The flow direction of the left part of the upstream sections, which is going to enter the right branch, is about 70° with respect to the minus y axis. The measured direction of this part of the upstream river is also about 70°. Figures 8(b) and 8(c) show how the streamlines near the front of the island are modified by the diversion dyke. When the angle is small, the splitting streamline between the flows in the left and right branches moves to the right bank of the river, which is achieved by creating a water level gradient in the upstream cross-sections. The incoming flow has a higher level near the left bank, which drives the flow through the left branch. When the angle of the dyke is large, for example, 85°, the left branch is almost blocked, so the flow can hardly go into the left branch.

It can be seen from Figures 9(a) and 9(b) that the diversion ratio of the incoming flow to the left branch varies greatly with the length and angle of the diversion dyke.

As shown in Figure 9(a), when the length of the diversion dyke is fixed, the larger the angle, the smaller the diversion ratio. For example, at the larger length of 1150 m, it varies dramatically from 45·03% to 0·4% while the angle changes from 5° to 85°. At the shorter length of 330 m, the drop of the diversion ratio is much more moderate, that is, from 14·81% to 11·67%. When the angle is fixed, as shown in Figure 9(b), the diversion ratio gets larger for greater length with any angle between 5°and 65°. In these cases, the dyke contributes to the blocking of the right branch. The diversion ratio fluctuates moderately when the angle is from 65° to 75°. It varies from 11·91% to 12·68% with the 65° angle and from 11·81% to 10·09% with the 75° angle. However, the diversion ratio drops as the length of the dyke is getting larger with any angle from 75° to 85°. Figure 9(a) shows that when the angle is approximately 70°, the length of the diversion dyke is no longer an influencing factor for the diversion ratio, which can be explained from the velocity fields. As shown in Figure 8(a), the angle between the left part of river mainstream direction and the minus y axis is about 70°. Therefore, if the angle of the dyke is set to 70°, the mainstream flow will just flow as it did without the dyke. No matter how long the dyke is, the flow fields are nearly unaffected.

It is widely recognised that the left branch will be sustainable as long as the diversion ratio of the left branch is about 20% (Yan et al., 2010). In order to achieve the target, the angle between 5° and about 37° and the length from 550 m to 1150 m should be considered according to Figures 9(a) and 9(b). As shown in Figure 4, the natural topographies around the head of the Bagua Island were complex, with a deep groove at the entrance to the right branch. Considering the financial and technical constraints on the building of such a dyke, a 550 m long and 5° angled diversion dyke is a practical and feasible option, with a rise of almost 19·32% of the incoming flow to the left branch.

A shallow-water model was set up for the flow around the Bagua Island, which is located in the Nanjing reach of the Yangtze River. A high-quality curvilinear mesh was generated to cover the domain, which started at Sihao Wharf and ended at Gangchi. It was first verified to be an efficient and suitable model for this study by comparing the simulated water level, velocities and diversion ratios with the field measurements and the physical model experiments. A diversion dyke can modify the water levels, flow fields and the flow rates to the left branch of the river. It was found that the dyke mainly affects the water levels on the left side of the upstream channel and in the left branch, but does not much change the water levels in the right branch. By changing the flow field, the left branch's diversion ratio varies greatly when the length and the angle of the diversion dyke changes. An exception is when the angle of the diversion dyke is about 70°, where the diversion ratio barely changes with the length of the dyke, because the dyke is almost parallel to the left side of incoming flow. A 550 m long and 5° angled diversion dyke can make the left branch get about 19·32% of the incoming flow.

What the authors have achieved in this paper is a useful piece of testing work. The paper only focuses on the options of the diversion dyke through a hydrodynamic study. More studies are needed to consider a wider range of options and long-term sediment transport effects. To increase the flow through the left branch to ensure the continuing development of the area, a number of methods, such as widening and dredging the left branch, can also be considered. In the meantime, all the river regulation works that are building in the Bagua reach should be premised on the navigation requirements.

This work was supported by the State Key Program of National Natural Science of China (No. 51239003), the National Science Foundation for Distinguished Young Scholars of China (No. 51125034), the National Natural Science Foundation of China (No. 51450110079) and the National Basic Research Program of China (973 Program) (No. 2011CB403303).