*4.2. Horizontal Circulation of Water Flux*

The history of the flow rate at cross-sections is integrated over the floodtide and the ebbtide periods to produce the cross-sectional water fluxes (CSWF), as listed in Table 2. According to the simulation results, the reasons for the spillover of water from the North to the South Branches are analyzed in two terms.


**Table 2.** Cross-sectional water fluxes (*CSWF*) at tide stations (unit: ×10<sup>8</sup> m<sup>3</sup>/day).

1 Note: In the table, a negative value means the direction of the flux is landward, while a positive value means the direction of the flux is seaward. Arrangements of the cross-sections are shown in Figure 3.

First, the tail reach of the North Branch is trumpet-shaped with a wide mouth, in favor of accommodating a grea<sup>t</sup> deal of landward tidal flows during floodtide durations. At the same time, the valid river width of the North Branch decreases from the downstream to the upstream, which is accordingly 5–8 km (tail reach), 3–5 km (lower reach), 1–3 km (middle reach), and 1 km (upper reach). Although the *CSWF* at QLG is only 22.4–26.0% of that at STG during floodtide durations, the huge landward floodtide discharge at the mouth of the North Branch and the fast shrinking river width together determine that strong flow intensity can be kept in all the lower, middle, and upper reaches. The velocities in the upper, middle, and lower reaches of North Branch are, respectively, observed to be as large as 2.4, 3.0, and 2.5 m/s, during a floodtide period. The landward floodtide tidal flow moves along the North Branch, while the strong flow intensity is maintained. Finally, some pioneer floodtide flows continue to go through the upper reach of North Branch and arrive at the bifurcation, forming the spillover of water. After a short spillover time, the transition between the floodtide and the ebbtide comes, and the spillover of water is ended.

Second, the upper reach of the North Branch is narrow and almost orthogonal to the South Branch (see Figure 3), which prevents upstream inflows from entering during ebbtide durations. As a result, in upper reach of the North Branch, the seaward ebbtide *CSWF* is smaller than the landward floodtide *CSWF*. At the same time, in the upper reach of the North Branch, the flow intensity during ebbtide durations (maximum velocity, 1.5 m/s) is sharply decreased relative to that during floodtide durations (maximum velocity, 2.4 m/s). The *CSWF* difference between the floodtide and the ebbtide durations at QLG of the North Branch is 0.6–0.47 × 10<sup>8</sup> m<sup>3</sup>/day, accounting for 24.2–28.8% of the landward floodtide *CSWF*. The *CSWF* difference of the North Branch runs downstream along South Branch during ebbtide durations, and a horizontal anticlockwise circulation of water flux is formed.

### *4.3. Sediment Spillover from North to South Branches*

The simulated history of the sediment transport rate at cross-sections is integrated over the floodtide and the ebbtide periods to produce the cross-sectional sediment fluxes (*CSSF*), as listed in Table 3. According to the simulation results, sediment transport of the North Branch, related closely to its hydrodynamics, is analyzed to clarify the mechanics of the sediment spillover from the North to the South Branches.

First, the source of the sediment, which spills over from the North to the South Branches, is recognized. The *CSSF* results show that there exists a critical position of zero sediment flux (ZSF) in the lower reach of North Branch, where the seaward ebbtide *CSSF* just counteracts the landward

floodtide *CSSF* in a 1-day runoff-tide process. The ZSF critical position locates about 4 km upstream of STG. Riverbeds in the middle and lower reaches upstream of the ZSF critical position in the North Branch experiences erosions during floodtide durations, corresponding to strong flow intensities there. Sediment concentration of the landward tidal flow is essentially increased during its journey through the erosion reaches of the North Branch. This results in high sediment concentrations of 6–8 kg/m<sup>3</sup> in the reach between QLG and SHG of during floodtide duration in field data. The landward floodtide high-concentration flow, going through cross-section QLG, provides sediment input for the upper reach of North Branch, some of which spillovers from the North to the South Branches.


**Table 3.** Cross-sectional sediment fluxes (*CSSF*) at tide stations (unit: × 10<sup>4</sup> t/day).

1 Note: In the table, a negative value means the direction of the flux is landward, while a positive value means the direction of the flux is seaward. Arrangements of the cross-sections are shown in Figure 3.

Second, the kinetic energy of flow, used to advance the spillover of sediment in the Yangtze Estuary, is analyzed. During a floodtide period, the landward flow still maintains considerate intensity (flow velocity) in the upper reach of the North Branch, and at the same time, provides enough kinetic energy for carrying and transporting sediment. The landward floodtide sediment-carrying flow goes through the upper reach of the North Branch and towards the bifurcation. In the journey of the landward flow, partial sediment in the flow deposits on the riverbed along the upper reach of the North Branch, due to the gradually reduced flow intensity. The left part of the sediment in the landward flow arrives at the bifurcation and then spills over to the South Branch.

The process of the sediment spillover in the Yangtze Estuary experiences the following stages. After the floodtide period begins, it takes about 5 h to form the high-concentration floodtide flows in the middle North Branch. The high-concentration floodtide flow arrives at QLG at about 6 h after the floodtide, and begins to spill over to the South Branch at about 7 h. After that, the sediment spillover lasts about 3 h. Then, the transition between the flood and the ebbtides comes, and the sediment spillover gradually disappears.

Third, in the upper reach of the North Branch, the *CSWF* and the flow intensity during ebbtide durations are both sharply reduced relative to those during floodtide durations. The seaward ebbtide *CSSF* is also much smaller than the landward floodtide *CSSF* in the upper reach of the North Branch. The *CSSF* difference between the floodtide and the ebbtide durations at Station QLG is 43.85–11.26 × 10<sup>4</sup> t/day, accounting for 37.5–34.9% of the landward floodtide *CSSF*. The *CSSF* difference of the North Branch is caused by the sediment which spills over from the North to the South Branches. The sediment, arising from the spillover, runs downstream toward the coast along with the ebbtide flow of the South Branch, and a horizontal anticlockwise circulation of sediment flux is formed.

Mechanics of sediment spillover in the Yangtze Estuary can be summarized as a successive process comprising the source, transport, and drainage of the sediment of the spillover.
