The three-dimensional free surface characteristics of flow around two equal diameter cylinders in a side-by-side arrangement were studied numerically. The flow fields were simulated with a three-dimensional finite volume method based on the RNG k-ɛ model for Reynolds number Re = 1.0 × 10⁴. The volume-of-fluid method was applied to track air–water interfaces. Computations were performed for gap ratios of 1.25, 1.5, and 1.75 to examine the influence of the gap between two cylinders, and for distance to diameter ratios of 8.0 and 1.0 to study the wall proximity effects. The model was verified by comparing it with the other numerical and experimental results. The results indicated that the evolution of the free surface was periodic in time scale. A weak hydraulic jump occurs in the wake flow. Moreover, a significant difference between upstream and downstream free surface elevations exists in the vicinity of the cylinder. A runup in front of the cylinder and a ‘depression’ around the side edge were also observed. Computational results showed that the flow near the two cylinders was pushed outwards, and the flow between the cylinder and the wall was deflected inwards by the wall. The vortex structures on and near the free surface were closely correlated with the free surface. The shedding vortex far from the free surface was not affected.

Steps effectively dissipate the energy of water along a path and reduce the size of the stilling basin but are rarely used in curved spillways. The shore spillway of a reservoir, which is restricted by topography, must be arranged in a curved shape. At high flow velocity and low water depth, some areas of the base plate of the curved spillway were not covered by the water. The water flow into the stilling basin did not form a submerged hydraulic jump. It was proposed that a step with bottom non-uniform heights be placed in the smooth base plate of the curved spillway to improve these undesirable hydraulic phenomena. A physical model experiment with a length scale of 1:40 verified the feasibility of the curved stepped spillway in engineering. Based on the k-ε model and volume-of-fluid (VOF) method, a three-dimensional numerical model was established, and the reliability of the numerical model was verified by measured data. The main flow region, velocity field, cavitation on a step, and the energy loss rate of steps were discussed. The comparison between a curved spillway with and without steps shows that the steps balance the partial centrifugal force in the curved section, making the water depth of the cross-section evenly distributed, and the base plate was no longer covered by water. The flow pattern on the steps was skimming flow, and the velocity of the flow into the stilling basin was greatly reduced. The elevation of the concave bank of the base plate was raised, resulting in the formation of transverse flow, which in turn constituted a three-dimensional energy dissipation pattern with the longitudinal flow. The energy loss was significantly higher than that of the smooth curved spillway. However, the triangular region near to the concave bank on the base plate experienced negative pressure, and an aeration device in front of the steps was needed.

The water velocity undergoes a significant increase during the initial stage of floods. The present study focuses on investigating the scours and silting occurring in an S-shaped gravel-bed river. The primary objective is to analyze the impact of 10-year flood events on both the riverbed and bank stability. This river is located in the Sai-jiang River reach, Fujian Province, China. A numerical model of riverbed scours and silting is herein tested. The research results indicate that the morphological evolution of the whole river section is affected in the early stage of flood evolution; however, in the later stage, some key places such as the bridge and the river land are still greatly affected. The apex of the river bend is in close proximity to the downstream river island, resulting in scour at the head of the river island that deviates from conventional patterns of head scour and tail siting. Furthermore, the presence of artificial structures like bridges exacerbates the scour and silting processes in river beds during flood events. For this case, the riverbed adjacent to the Banzhong Bridge pier experienced a widening of approximately 50 m and downstream extension of around 300 m, with a maximum vertical scouring depth of 2.87 m.

During floods, debris accumulates around the pier in the channel. The depth of debris accumulation beneath the water surface significantly influences on local scouring around the pier, and affecting its flood-fighting capacity. Flume experiments were carried out to investigate local scour around the pier when debris accumulations occurred at three distinct levels: on the water surface (Ha/H = 0), in the middle of the water body (Ha/H = 0.5), and near the riverbed (Ha/H = 0.8). Through numerical simulation verified by experiments, the flow characteristics were obtained, and the impact of the subaqueous debris position on the flow field was analyzed. The results show that the debris accumulations significantly aggravate the local scouring around the piers. Longitudinal and transverse maximum scour depths around the pier increase progressively as the debris accumulates from the water surface toward the riverbed. The maximum scour depth is directly proportional to the extent of debris penetration beneath the water surface. Specifically, when the debris is near the riverbed (Ha/H = 0.8), the scour depth reaches its maximum. Compared to without debris, the maximum longitudinal scour depth increases by 28.3%, while the maximum transverse scour depth increases by 53.8%.