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This study explored the three-dimensional flow characteristics in a recirculation zone near a permeable buttress in curved channels with varying curvatures. Understanding these characteristics is crucial for managing natural river bends, as rivers often meander, with backwater zones formed behind obstructions, such as mountains in the riverbed. The direct comparison of the recirculation zones across different bend types revealed the correlation between the flow characteristics and bend curvature. However, previous studies have focused on flow velocities and turbulent kinetic energy without a probability density analysis. This analysis provided a more comprehensive understanding of the flow characteristics. Gaussian kernel density estimation was applied in this study to observe the distribution of the flow velocities, turbulent kinetic energy, and turbulent kinetic energy dissipation rate. The results indicated that the longitudinal time-averaged flow velocity in the recirculation zone typically ranged from −0.2 m/s to −0.8 m/s, with all the skewness coefficients exceeding 0. The horizontal time-averaged flow velocity in the recirculation zone fell between −0.175 m/s and −0.1 m/s. The skewness coefficients were negative at water depths of 16%, 33%, and 50% within the 90° and 180° bends, indicating a non-normal distribution. The probability density distribution of turbulent kinetic energy in the recirculation zone was skewed, ranging from 0 to 0.02 m2·s−2, with the skewness coefficient almost always greater than 0. The plot demonstrated multiple peaks, indicating a broad distribution of turbulent kinetic energy rather than a concentration within a specific interval. This distribution included both the high and low regions of turbulent kinetic energy. Although the overall rate of turbulent kinetic energy dissipation in the recirculation zone was relatively low, there were multiple peaks, suggesting the localized areas with higher dissipation rates alongside the regions with lower rates. These findings were significant for managing the meandering river channels, restoring the subaqueous ecosystems, understanding the pollutant diffusion mechanisms in backwater areas, the sedimentation of nutrient-laden sediments, and optimizing the parameters for spur dike design. [ABSTRACT FROM AUTHOR]

The long-term effects of the centrifugal force of water flow in a curved river channel result in the scouring of the concave bank and the silting of the convex bank. This phenomenon significantly impacts the stability of bank slopes and the surrounding ecological environment. A common hydraulic structure, the spur dike, is extensively employed in river training and bank protection. Focusing on a 180° bend flume as the research subject, this study examines the effects of spur dike placement on the concave bank side of the bend. To this end, a second-order accurate computational format in computational fluid dynamics (CFD) and the RNG k-ε turbulence model were employed. Specifically, the influence mechanism of the pick angle and the river-width-narrowing rate on the flow dynamics and eddy structures within the bend were investigated. The results indicated that both the river-width-narrowing rate and pick angle significantly influence the flow structure of the bend, with the pick angle being the more dominant factor. The vortex scale generated by a positive pick angle of the spur dike is the largest, while upward and downward pick angles produce smaller vortex scales. Both upward and positive pick angles have larger areas of influence, and the maximum value of turbulent kinetic energy occurs at the back of the secondary spur dike. In contrast, the downward pick angle has a smaller area of influence for turbulent kinetic energy, resulting in a smaller vortex at the back of the spur dike and leading to smoother water flow overall. In river-training and bank-protection projects, the selection of the spur dike angle is crucial for controlling scour risk. The findings provide valuable insights for engineering design and construction activities. [ABSTRACT FROM AUTHOR]