Influence of spur dike on hydrodynamic exchange between channel and shoal of generalization estuary in physical model test

Widely applied in maintaining estuarial waterway depth, the spur dike has played an important role in currents and sediment exchange between channel and shoal and sediment back-silting in the channel. Through establishing a generalized physical model at a bifurcated estuary and conducting current tests under the joint action of runoff and tide, the influence of the spur dike length on current exchange between channel and shoal is analyzed. Results show that when the spur dike length reaches a certain value, the direction of the flow velocity shear front between the channel and shoal will change. The longer the spur dike, the larger the transverse fluctuating velocity at the peak of flood in the channel shoal exchange area, while the transport of the transverse hydrodynamics is obvious in the process of flood. There is an optimum length of spur dike when the shear stress in the channel and the longitudinal velocity in flood and ebb reach the maximum, and the flow velocity will decrease when the spur dike length is smaller or larger than the optimum. For a certain length of spur dike, the larger the channel shoal elevation difference, the larger the peak longitudinal flow velocity in the middle of the navigation channel in flood and ebb. However, the transverse flow velocity will first decrease and then increase. The transverse transportation is obvious when the channel shoal elevation difference increases.


Introduction
In 2010, the Yangtze Estuary Deep-Water Channel Regulation Project was completed. The water depth of the channel was increased from the maintaining water depth of 7 m before the project to the water depth of 8.5 m in the Phase-I Project, 10 m in the Phase-II Project, and 12.5 m in the Phase-III Project. The regulation project includes two leading jetties in the south and north with the length about 50 km, 19 spur dikes, diversion and dredging. With the operation of the 12.5-m channel, the back-silting quantity of the deep-water channel at the Yangtze Estuary is always very large. The annual average back-silting quantity is 8.2×10 7 m 3 from 2010 to 2016, among which the back-silting quantity in 2012 is as high as 1.0×10 8 m 3 including 80% of the back-silting quantity in the middle and lower reaches of the North Passage channel.
Some scholars have carried out many researches on high back-silting problem in the deep-water channel of the Yangzte Estuary. Liu et al. (2011) found there was water and sed-iment exchange in the south leading jetty through onsite overtopping flow and sediment observation. Tan (2009) concluded that sediment on the shoal suspended again under the action of wind waves to enter into the dredged channel resulting in the increase of sediment concentration. On the basis of onsite observation, Jin et al. (2013) detected that the near-bottom high-concentration suspended sediment is related to the settling characteristic of cohesive fine particle sediment in tidal currents. The influence of the sediment transport on back-silting in the channel is reflected as the channel-shoal sediment exchange. After the implementation of the Yangtze Estuary Deep-Water Channel Regulation Project, the riverbed was scoured locally and the area between spur dikes was silted in the North Passage, the shape of riverbed changed from "U" to "V", the cross section of the North Passage developed into the narrow-deep type, and the elevation ratio of the channel to the shoal increased. The scoured sediment and the deposited sediment in groin fields were very easily transported into the channel due to influence of wind waves. Since the elevation difference between the groin field and the channel increases, sediment more easily flows into the channel with the density current (Dou, 2015). With the increase of the elevation difference between the channel and the shoal, the density gradient of transverse current increases, and the transverse transport effect of current and sediment is obvious (Huijts, 2011). Many scholars (Hill et al., 2013;Marioti and Fagherazzi, 2011;Nowacki and Ogston, 2013) researched channel-shoal hydrodynamics for sediment exposed at low tide levels and submersed at high tide levels at estuaries and summarized that, when the ebb tide level is close to the shoal elevation, the crosswise flow velocity obviously increases; when the tide level just reaches the shoal elevation, the flow velocity will fluctuate. Besides, when the shoal water and the channel water have the relative movement at different flow velocities in the same flow direction or opposite flow direction, there is an obvious flow velocity shear phenomenon between the two waters, which is named the channel-shoal flow velocity shear front (Zhu, 1995). At present, there are a few experimental researches on channel-shoal hydrodynamics exchange under the influence of spur dike engineering. Through a physical modeling experiment of a generalized bifurcated estuary, the influences of different lengths of spur dikes and channel-shoal elevation difference on hydrodynamics are studied and the high-strength sediment back-silting mechanism in the channel is provided.

Research method
A physical model of a generalized bifurcated estuary for 50 m long and 30 m wide was set up regarding the Deep-Water Channel Regulation Project in bifurcation areas of the South Passage and the North Passage at the Yangtze Estuary as the prototype (Fig. 1a). The horizontal scale is 600 and the vertical scale is 150. A pair of leading jetties and spur dike group is built at one branch (named Branch I) and the distance between the leading jetties is 3 m. There is a channel with the bottom elevation of -10 cm between the leading jetties with the bottom width of 10 cm and the side slope of 1:10. The bottom elevation of shoal on both sides of the channel is -5 cm and the distances between the cen-ter lines of the channel to the south and north leading jetties are 1.0 m, respectively. There are separately four spur dikes in the south and north leading jetties to form four pairs of spur dike groups. The distance between the spur dikes on the same side is 3 m, the crest elevation of spur dikes is 0 cm, and the length of each spur dike is respectively 40 cm and 80 cm. The bottom elevation of riverbed is -10 cm from the upstream to the tributary. The bar shoal is located from the tributary to the offshore and the bottom elevation has a linear transition from -2 cm to -5 cm. The bottom elevation of open seas has a linear transition from -5 cm to -20 cm (Fig. 1b).
The upstream flow of the physical model is controlled by the reversible pump and the current flows into the model or reservoir through returning water galleries. The flood or ebb of tide level is controlled by the tail gate that is located at the corner of the downstream boundary of the model. The measure points of tide levels are laid in one branch between leading jetties (Fig. 1b) and three measure points for the current velocity are arranged accordingly in the channel center, the slope of the channel and the shoal of a transverse section of channel-shoal. Fig. 2a shows the plan sketch of measure points with the spur dike lengths of 40 cm  JIAO Zeng-xiang et al. China Ocean Eng., 2017, Vol. 31, No. 5, P. 624-630 625 and 80 cm. #1 is at the shoal, #2 at the slope area, and #3 at the channel center. Fig. 2b indicates the transverse section and measure points. A tracking-mode tidal gauge and a twodimensional electromagnetic-type current meter (ADS1016) are respectively adopted to measure experimental data. Fig.  2c depicts the control discharge and tidal level process at the upstream and downstream boundaries of the physical model.

Current velocity tests of different schemes
The velocities of three points at the shoal, slope area and channel center are measured in ebb tide. The measure points are 1 cm above the bed in the vertical direction and measure cycles are two processes including flood tide and ebb tide. The positive value of the longitudinal velocity is defined as the ebb direction (to the direction of open seas) and the negative value is the flood direction (to the direction of the upstream); the positive value of the transverse velocity is pointed to the channel and the negative value is pointed towards the shoal.
To research the influence of the spur dike length on the velocity between channel and shoal, three schemes including no spur dike and the spur dikes for 40 cm and 80 cm are adopted for test with the bottom elevation of the channel being -10 cm. To research the influence of the elevation differences on the peak velocities at the channel center in ebb and flood, three elevations of -6 cm, -8 cm and -10 cm respectively at the bottom of channels are adopted with the spur dike length of 40 cm and the bottom elevation of the shoal unchanged.

Influence of spur dike length on shear front
Current velocity (direction) shear front means that there are obvious differences occurring on the longitudinal velocity (direction) in water on both sides of the frontal surface within a small distance at the direction vertical to the flow movement direction. The velocity shear front exists in estuary, gulf and channel. The different occurring positions are affected by different hydrodynamics and topographic conditions. There are periodic shear front under the action of tides at the river mouth and there are generally obvious shear front four times. At the peak moments of ebb and flood, the velocity directions of channel and shoal are the same, the velocity at the channel center is larger than that at the shoal and the velocity shear front occurs. At the rest moments of ebb and flood, the velocity directions are opposite at the channel center and the shoal and the flow direction shear front occurs. It can be seen from Fig. 3 that when the ebb is at the rest, the velocity of ebb tide at the channel center is 0.24 cm/s without spur dike and the water is shallow in the shoal with the flood velocity of -12.49 cm/s, and there is a flow direction shear front between channel and shoal; at the peak moment of flood, the channel and the shoal are both flood tides and the velocity at the channel center increases to 5.45 cm/s with the shoal velocity of 2.88 cm/s and the ve-locity shear front occurs; at the rest moment of flood, the velocity of flood tide in the channel center is -1.76 cm/s and the velocity of ebb tide on the shoal is 0.43 cm/s. The flow direction shear front occurs between channel and shoal.
Under the condition that the length of spur dike is 40 cm, compared with no spur dikes, the velocity increases at the channel center and decreases on the shoal at the rest ebb moment. The hydrodynamics of the shoal is weakened by the spur dikes and the flow direction shear front is still between channel and shoal; at the peak flood moment, the velocity of the channel is larger than that on the shoal and there is a velocity shear front between channel and shoal; at the flood rest moment, the velocity of the channel is smaller than that on the shoal and there is a velocity shear front between channel and shoal; at the ebb peak moment, the velocity of the channel (5.59 cm/s) is larger than that on the shoal (1.65 cm/s) and a velocity difference between the channel and shoal is 3.94 cm/s and the velocity shear front occurs between channel and shoal.
Under the condition that the length of spur dike is 80 cm, at the ebb rest moment, there is a flow direction shear front between the channel and shoal; at the flood peak moment, the flood tide is in the channel and there is a flow direction shear front between the channel and shoal; at the flood rest moment, the velocity at the channel decreases and the velocity shear front weakens; at the ebb peak moment, there is a flow direction shear front between the channel and shoal.
It can be seen from comparisons of the velocity and its direction (see Table 1) with different lengths of spur dikes: at the ebb rest moment, there exists a flow direction shear front between the channel and the shoal; at the flood peak and ebb peak moments, for without spur dike and a spur dike of 40 cm, there are velocity shear fronts between the channel and the shoal, and for a spur dike of 80 cm, there is a flow direction shear front; at the flood rest moment, for without spur dike and a spur dike of 80 cm, there are flow direction shear fronts and for the spur dike of 40 cm, there is a velocity shear front. With different lengths of spur dike, the velocity at the channel center changes with the tidal level correspondingly, but the change of the velocity on the shoal is different. At the flood peak moment, the velocities without spur dike and with the 40-cm spur dike are in the flood tide direction, the velocity of the shoal decreases 92% with the 40-cm spur dike, while the velocity of the shoal is in the ebb tide direction with the 80-cm spur dike and the velocity increases about 51%. At the ebb peak moment, the velocity of the shoal decreases about 65% with the 40-cm spur dike, and the velocity of the shoal is in the direction of flood tide with the 80-cm spur dike and the hydrodynamics is weakened 4%. From Fig. 6, it can be seen that the main reason is that the longer the spur dike is, the stronger the action of circulation is, which has changed the velocity and its direction of the shoal.
3.2 Influence of spur dike length on the transverse velocity fluctuation From the change of transverse velocity within a tidal cycle in the slope area (Fig. 7), it can be seen that when the tidal level rises from the lowest level to the crest elevation (0 km) of the spur dike, the transverse velocities pointing to the shoal reach their maximum values with the 40-cm and 80-cm spur dikes and the velocity fluctuation occurs, and the velocity fluctuating intensity is related to the length of spur dike. When the tidal level is -0.26 cm, the transverse velocity with the 40-cm spur dike is -0.92 cm/s and with the 80-cm spur dike is -3.09 cm/s. This indicates that the longer the spur dike is, the larger the transverse velocity fluctuation is. With the rising of the tide level, the direction of the transverse velocity changes into the channel and the transverse velocities with the 40-cm and 80-cm spur dikes successively reach their maximum with basically same values. This is because that the constraining current action of spur dike is weakened after the spur dike is submerged. When the tidal level lowers, the velocity fluctuation is not obvious.
3.3 Influence of spur dike length on the shear stress in the middle of the channel The shear stress is an important factor of sediment incipient motion. The following research is for the shear stress of channel-shoal in consideration of the effect of the spur dike. The formula of the shear stress is: where ρ represents the density of water, k is the turbulence energy, and m is a coefficient. According to the relevant literature (Kim et al., 2000;Pacheco et al., 2009; Pope et al.,    (Svendsen, 1987).
u ′2 v ′2 where and respectively represent vertical and transverse turbulence energies.
In the experiment, 10 instantaneous velocities and the average of 10 velocities at a certain period (73 s, one-hour corresponding to the prototype) can be obtained by the electromagnetic current meter. The instantaneous velocity minus the average velocity is the fluctuating velocity. Fig. 8 shows the shear stress variation of the channel center with different spur dike lengths. It can be seen that at the ebb rest moment, the shear stress is 0.04 N/m 2 without spur dike, 0.06 N/m 2 with the 40-cm spur dike, and 0.08 N/m 2 with the 80-cm spur dike. At the flood peak moment, the shear stress is 0.07 N/m 2 without spur dike, 0.18 N/m 2 with the 40-cm spur dike, and 0.13 N/m 2 with the 80-cm spur dike. At the flood rest moment, the shear stress is 0.01 N/m 2 without spur dike, 0.06 N/m 2 with the 40-cm spur dike and 0.02 N/m 2 with the 80-cm spur dike. At the ebb peak moment, the shear stress is 0.07 N/m 2 without spur dike, 0.22 N/m 2 with the 40-cm spur dike, and 0.13 N/m 2 with the 80-cm spur dike. Generally, with the increase of the spur dike length, the shear stress in the channel center increases first and then decreases. When the spur dike is 40 cm long, it has the largest shear stress and the effect of the spur dike is the most significant.

Influence on the longitudinal velocity
For the longitudinal velocity in the channel center, at the flood peak moment, the velocity with 40-cm spur dike and 80-cm spur dike respectively increases by 60% and 0.5%, compared with no spur dike. At the ebb peak moment, the velocity with 40-cm spur dike and 80-cm spur dike respectively increases by 88.2% and 11.7%, compared with no spur dike. That means there is an optimum length of the spur dike. When the spur dike reaches this length, the velocities at flood peak and ebb peak in the channel center are the biggest ones and the effect of the spur dike is the most significant.
For the longitudinal velocity in the slope area, at the flood peak moment, the velocity with 40-cm spur dike and 80-cm spur dike respectively increases by 32.2% and 16.2% in comparison with no spur dike. At the ebb peak moment, the velocity with 40-cm spur dike increases about 32.5% but the velocity direction with 80-cm spur dike is opposite and the value is -6.23 cm/s. So from this, it can be concluded that when the spur dike is 40 cm long, the flood peak and ebb peak velocities in the slope area increase about 30%, and when the spur dike is 80 cm long, the slope area is mainly influenced by the circulation and the hydrodynamics weakens.
For the longitudinal velocity in the shoal, compared with no spur dike, at the flood peak moment, the shoal velocities with 40-cm spur dike and 80-cm spur dike respectively decrease by 24% and 83%. At the ebb peak moment, the velocities respectively decrease by 67% and 26%. It means that with the increase of the spur dike length, a circulation is formed in the shoal area and its velocity decreases.

Influence of spur dike length on the transverse velocity
Compared with the transverse velocity in the channel center without spur dike, at the flood peak moment, the ve-  locity increases 2.38 times with the 40-cm spur dike, and decreases to 63.2% with the 80-cm spur dike. At the ebb peak moment, with the increase of the spur dike length, the velocity gradually decreases. When the spur dike is 40 cm, the velocity decreases to 85%. When the spur dike is 80 cm, the velocity decreases to 42.1%. It can be seen that the transverse velocity in the channel center first increases and then decreases with the increase of the spur dike length. It also means that there is an optimum length of the spur dike.
Compared with the transverse velocity in the slope area without spur dike, at the flood peak moment, the velocity with the 40-cm spur dike increases 1.67 times, and the velocity with the 80-cm spur dike increases 5.61 times. At the ebb peak moment, the velocity with the 40-cm spur dike decreases to 57.1 % of that without spur dike, and the velocity decreases to 48.0% when the spur dike is 80 cm long. In the slope area, at the ebb peak moment, the transverse velocity direction points to the channel center from the shoal with the increase of the spur dike length.
Compared with the transverse velocities in the slope area without spur dike, at the flood peak moment, the transverse velocity largely increases and is 25.8 times that without spur dike when the spur dike is 40 cm, and the transverse hydrodynamics weakens and is 69.6% of that without spur dike when the spur dike is 80 cm long. At the ebb peak moment, influenced by the spur dike, the transverse velocity direction in the shoal points to the beach from the channel and the velocity increases 1.93 times with the 40-cm spur dike, and decreases to 35% of that without spur dike when the spur dike is 80 cm long. The transverse velocity variation in the shoal with the length of the spur dike shows that there also exists an optimum length of the spur dike.
3.5 Influence of the channel-shoal elevation difference on the velocity in the channel center Take the 40-cm spur dike as example, based on -5 cm bottom elevation of the shoal, the current tests with the bottom elevations of -6 cm, -8 cm and -10 cm were conducted and the influence of the elevation difference between the shoal and the channel (1 cm, 3 cm and 5 cm) were analyzed.
With the increase of the channel-shoal elevation difference, the longitudinal and transverse velocities in the channel center also increase. Compared with 1-cm channel-shoal elevation difference, the longitudinal velocity for the 5-cm channel-shoal elevation difference at the flood peak moment increases by 63.8% and the transverse velocity increases 2.34 times; the longitudinal velocity at ebb peak moment increases about 2.16 times and the transverse velocity increases by 91.2%. Compared with 1-cm channel-shoal elevation difference, the transverse velocity for the 3-cm channel-shoal elevation difference decreases by about 50% at the flood peak moment and 24% at the ebb peak moment. Thus, with the increase of the channel-shoal elevation difference, the longitudinal velocity in the channel center at the flood and ebb peak moments gradually increases and the transverse velocity first decreases and then increases.

Conclusions
This paper describes the influence of different spur dike lengths and channel-shoal elevation difference on hydro-  2.14 -4.14 -0.75 Fig. 9. Influence of different channel-shoal elevation differences on the velocity in the channel center.
dynamics characteristic indexes through the generalized physical model experiments at the bifurcated estuary, and main conclusions are as follows.
(1) At the peak moments of flood and ebb, there is a velocity shear front in the same direction between the channel and the shoal without spur dike or with the 40-cm spur dike. When the spur dike is 80 cm long, there is a velocity direction shear front between the channel and the shoal. Those mean that the spur dike at a certain length will change the velocity shear direction between the channel and the shoal. Additionally, the longer the spur dike is, the larger the transverse velocity fluctuation between the channel and the shoal is. When tide is flooding, the transverse hydrodynamics transportation is obvious, but when the tide is ebbing, there is no any velocity fluctuation.
(2) At the peak moments of flood and ebb, the shear stress in the channel center maximizes when the spur dike is 40 cm long. And with the increase of the spur dike length, the shear stress decreases. The shear stress in the channel center at the peak moment of ebb is larger than that at the peak moment of flood.
(3) From the change of the longitudinal and transverse velocities in the channel center, it can be concluded that there is an optimum length of the spur dike. When the spur dike reaches this length, the peak flood and ebb velocities in the channel center maximize and the effect of the spur dike is the most significant. When the spur dike is shorter or longer than this length, the velocities of flood and ebb in the channel center are small.
(4) For the spur dike with a certain length, when the elevation difference between the channel and the shoal increases, the longitudinal velocities at the peak moments of flood and ebb in the channel center also increase. At the same time, the current flows to the shoal at the peak moment of flood and the current flows to the channel center at the peak moment of ebb. The transverse transportation effect is obvious after the increase of the channel-shoal elevation difference. The channel-shoal elevation difference is a decisive factor of the transverse water and sediment transportation.