A semi–implicit numerical model with a linear solver is proposed for the free-surface and pressurized mixed flows in hydraulic systems. It solves the two flow regimes within a unified formulation, and is much simpler than existing similar models for mixed flows. Using a local linearization and an Eulerian–Lagrangian method, the new model only needs to solve a tridiagonal linear system (arising from velocity-pressure coupling) and is free of iterations. The model is tested using various types of mixed flows, where the simulation results agree with analytical solutions, experiment data and the results reported by former researchers. Sensitivity studies of grid scales and time steps are both performed, where a common grid scale provides grid-independent results and a common time step provides time-step-independent results. Moreover, the model is revealed to achieve stable and accurate simulations at large time steps for which the CFL is greater than 1. In simulations of a challenging case (mixed flows characterized by frequent flow-regime conversions and a closed pipe with wide-top cross-sections), an artificial slot (A-slot) technique is proposed to cope with possible instabilities related to the discontinuous main-diagonal coefficients of the linear system. In this test, a slot-width sensitivity study is also performed, and the suitable slot-width ratio (ε) for the linear solver is suggested to be 0.05–0.1.

Because of special morphologies and complex runoff–tide interactions, the landward floodtide flows in Yangtze Estuary are observed to spill over from the North to the South Branches, carrying a lot of sediment. To quantitatively clarify the spillover problem, a two-dimensional numerical model using a high-resolution channel-refined unstructured grid is developed for the entire Yangtze Estuary from Datong to river mouths (620 km) and part of the East Sea. The developed model ensures a good description of the river-coast-ocean coupling, the irregular boundaries, and local river regimes in the Yangtze Estuary. In tests, the simulated histories of the tidal level, depth-averaged velocity, and sediment concentration agree well with field data. The spillover of sediment in the Yangtze Estuary is studied using the condition of a spring and a neap tide in dry seasons. For a representative cross-section in the upper reach of the North Branch (QLG), the difference of the cross-sectional sediment flux (CSSF) between floodtide and ebbtide durations is 43.85–11.26 × 10⁴ t/day, accounting for 37.5–34.9% of the landward floodtide CSSF. The mechanics of sediment spillover in Yangtze Estuary are clarified in terms of a successive process comprising the source, transport, and drainage of the spillover sediment.

Responses of irregular rotational tidal flows to an outlet regulation (the Guyuan Sand (GYS) regulation) in the three-level branching Yangtze Estuary are studied by a high-resolution numerical model and theoretical analysis. The project is launched around GYS at the outlet of the North Branch of the Yangtze Estuary. The tidal flows around GYS are rotational and become irregular under the influences of the runoff-tide interactions, rapidly varying topographies and complex solid boundaries in coastal areas. Three designs of GYS regulation were studied, including various diversion dikes and new outlets of different widths. The regulation disturbs the irregular rotational flows around GYS, and further changes the estuarine tidal processes and the water exchange between different branches of the branching Yangtze Estuary. It was interesting to find that additional current and additional storage are formed along the North Branch when a southward outlet and the clockwise rotational flow met around GYS. This special phenomenon is named “guide effect” in this study. The guide effect, together with common resist effect (arising from the narrowed outlet channel), reshapes the estuarine tidal processes. Based on the simulation result and a theoretical analysis, response mechanics of irregular rotational tidal flows to the outlet regulation in complex branching estuaries are quantitatively studied.

The impacts of backwater due to large dam construction on flow may lead to navigation or flood control problems in curved rivers. This study conducted flume experiments to investigate the effects of backwater on the velocity distribution characteristics of a 90-degree bend. The experimental results show that the backwater degree (η, defined as the ratio of flow depth under backwater to that under non-backwater conditions) has significant impacts on the three-dimensional velocity distribution in the bend. The depth-averaged velocities decrease with increasing backwater degree, and the deflection degrees of depth-averaged velocities are found to be highly related to the backwater degree and cross-sectional position. In this experimental setup, the mean cross-sectional velocity decreases by 67.2% as η increases from 1.00 to 3.64 for Q = 35 L/s; 63.7% as η increases from 1.00 to 3.26 for Q = 52 L/s; and 60.1% as η increases from 1.00 to 2.80 for Q = 52 L/s. The maximum values of transversal and vertical velocities near the riverbed gradually shift to the inner bank as the backwater degree increases at the 45° cross section. The center of the high transversal velocity area shifts about 0.1 m toward the inner bank as the backwater degree increases from 1.00 to 3.26 for Q = 52 L/s, which can reduce the erosion of the riverbed near the outer bank. In the current study, we also demonstrate that the growth and decay processes of secondary flow cells under backwater conditions are similar to those under non-backwater conditions. However, the scales and positions of the secondary flow cells change continuously with different backwater degrees. From the entrance to the exit of the bend, the secondary flow intensity first increases, and then decreases, with its maximum values occurring at the 45° cross section. The findings detailed in this manuscript provide insights for navigation channel design in reservoir backwater zones.

Riverbed topography in natural rivers commonly features sand dunes, whose morphological variations can alter the turbulent flow structure near the bed and thereby affect processes of channel scour, deposition, and sediment transport. In this study, a series of flume experiments was conducted using an acoustic Doppler velocimeter (ADV) to simulate fixed bedforms of different dune scales (ratio of wavelength to flow depth, λ/h) in a laboratory flume. Velocity measurements were taken along the water depth at the dune crest and trough for each test case. The near-bed distributions of mean flow velocity, Reynolds stress, turbulent kinetic energy (TKE), and turbulence intensity were obtained at the crest and trough under three flow conditions, allowing analysis of the vertical decay of turbulence intensity at different locations on the dune. The results show that the dune steepness (Ψ, defined as dune height over wavelength) is a key parameter controlling the near-bed flow structure. As Ψ increases, the near-bed velocity gradient, Reynolds stress, TKE, and peak turbulence intensity all increase significantly, with the peak positions shifting closer to the bed. The trough region, due to flow separation and vortex shedding, exhibits substantially higher values of all turbulence-related parameters than the crest, making it the primary zone of energy dissipation and turbulence production. This study provides experimental evidence and theoretical reference for understanding the mechanism by which sand dune morphology influences flow structure, and it offers insight for predicting riverbed evolution.

High-speed water flow conditions can cause erosion of the bedrock in engineering areas. Due to the lack of accurate evaluation of bedrock scour and erosion rates, there has been a consumption of manpower and resources without achieving satisfactory engineering outcomes. Therefore, studying the scouring and erosion effects of water flow on bedrock is of significant importance for maintaining the sustainable development and safety of engineering projects. Using the bedrock prototype from the Xiaonanhai site in the upper reaches of the Yangtze River, a model test device was developed to conduct anti-scour tests on the bedrock. The study quantitatively examined the basic physical properties, incipient erosion velocity, and erosion rates of different types of bedrock. The study found that the prototype bedrock under natural exposure, submerged immersion, and alternating wet and dry conditions showed a trend of decreased tensile strength, with the alternating wet and dry conditions being the most detrimental to maintaining the physical properties of the rock mass. The anti-scour velocity of silty claystone and clayey siltstone samples increased with the increase in tensile strength, and the erosion rate increased with the increase in shear stress. If the shear stress is kept constant, the erosion rate decreases with the increase in tensile strength. The erosion rate is inversely proportional to the ratio of the bedrock’s tensile strength to the riverbed shear stress, with the fitting relationship showing a piecewise linear distribution. The research results can provide guidance for the safe production of engineering involving bedrock erosion in engineering reservoir areas that are conducive to sustainable development.