In recent years, the management and protection of river water resources have become increasingly important in the face of global climate change and increasing human activities (Rominger et al., 2010; Rowiński et al., 2018). The study of river flow characteristics can provide a scientific basis and technical support for solving related problems, enabling us to better predict floods and prevent water disasters. At the same time, proper regulation of river flow characteristics can help maintain the ecological balance of rivers, improve the efficiency of water resources utilization, and promote sustainable development (D'alpaos et al., 2016).
The flow characteristics of a river refer to the changing parameters such as water level, flow velocity, and flow rate depending on seasons, terrain, landforms, precipitation, climate, vegetation, and human activities. These patterns of change are the result of numerous factors that affect rivers. Historically, researchers mainly used methods such as experiments and prototype observations to study the flow characteristics of river water. For example, Tanino and Nepf, (2008) conducted laboratory experiments on the drag forces of randomly distributed rigid and protruding cylinders. Sun et al., (2009); Ozan, (2018) measured downstream flow velocity and boundary shear stress in a composite channel with a row of vegetation on the diffuse bank and showed the significant effects of vegetation on the distribution of flow velocity. Li et al., (2015) used ADV to investigate the flow velocity of water with and without vegetation in a curved open channel and found that there were significant velocity gradients in vegetated areas compared to non-vegetated areas. Shi et al., (2016) simulated sediment deposition around circular vegetation patches with rigid wood cylinders, analyzing the effects of sediment particle size, density, and water flow velocity. Caropi et al., (2019) measured average flow velocity and turbulent structures using an acoustic Doppler velocimeter and studied the dynamic movement of vegetation using video recordings. In another study, Chembolu et al., (2019) investigated the non-uniform flow and turbulent properties of water in laboratory experiments. They used different forms of natural vegetation (grass, multi-armed and cylindrical plants) arranged alternately. Their results showed distinct layered structures in the velocity profile for multi-armed and rigid vegetation. Velocity approached constant in the lower canopy and exhibited a logarithmic distribution in the upper canopy. The velocity of grass vegetation increased with depth due to the flexibility of its leaves. Li et al., (2019) studied the transverse and longitudinal distribution of flow velocity behind rigid submerged vegetation patches at different densities. They found that vegetation density affects depth-averaged flow velocity on both sides of vegetation patches, and increases with increasing vegetation density. Zhang et al., (2022) established a computational model for the hydraulic resistance of combined vegetation to clarify the effects of arboreal vegetation combinations and discretization on the hydraulic properties of slope flows. They considered the influences of stem diameter, Reynolds number, and slope.
With the development of computer technology and numerical simulation methods, domestic and foreign scholars have also begun to conduct flow simulation research based on software platforms such as Fluent, Flow-3D, CFX, etc., to simulate and analyze the characteristics of river flows (Patel and Gill, 2006; Rodriguez et al., 2004; Morvan et al., 2002). Zhang et al., (2013) used a deep average model to numerically simulate the water flow in curved channels and the water flow of emergent and submerged vegetation cover in curved channels. Meire et al., (2014) studied the interactions between adjacent vegetation patches and reported the mutual influences of adjacent surfaces during their development process. Zhao and Huai (2016) validated the Large Eddy Simulation model (LES) using channel experiments, and the obtained LES data agreed with the experimental data. The feasibility of using the LES model to simulate turbulent structures was verified by experiments, and the effects of non-continuous, rigid, submerged vegetation fields on water flow turbulence were investigated. Yang et al., (2019) simulated the water flow characteristics of a 180° curved channel with partially emergent rigid vegetation using the lattice Boltzmann method. Liu et al., (2021) investigated the drag characteristics of fully submerged circular vegetation patches in turbulent open channel flows by high-resolution numerical experiments. Jing et al., (2020) numerically modeled and simulated the interactions between the water flow and the non-submerged rigid vegetation using the Lattice Boltzmann Method (LBM). They verified the accuracy of the method by comparing experimental data and results from other computational methods. They also investigated the influence of vegetation with different densities, heights, and arrangement patterns on the velocity field, pressure field, and overall flow structure in the water current. Anjum and Tanaka (2020) performed numerical simulations for a water flow occupying half of the channel width with vertical two-layer vegetation, including one longitudinally discontinuous and two vertically arranged layers, using the tool CFD FLUENT. The results showed that the flow velocity in the gap was significantly lower than within the vegetation patches and that the local and discontinuous vegetation had a significant effect on the structure and resistance of water flow. Some researchers are concerned with the flow characteristics of water and the effects of vegetation in curved channels. Gorrick and Rodríguez (2014) conducted indoor experiments in a shallow arc of variable width with and without vegetation on the outer bank. The results showed that vegetation patches can greatly change the flow structure and force balance of the water. Li et al., (2015) analyzed the lateral and longitudinal dispersion coefficients of highly curved channels using a modified N-region model based on experimental data to determine the effects of vegetation on flow structure and dispersion. Mohammad et al., (2016) evaluated and analyzed the effects of streamlines, maximum velocity distribution, and secondary flow intensity on shear stress distribution in the bed of a 180° sharp bend. The results showed that the maximum secondary flow intensity occurs in the second half of the bend. Luo et al., (2018) found through numerical simulations that the circulation structure varies at different locations in a curved channel, with the intensity of circulation decreasing downstream at certain sections. Yuan et al., (2018) analyzed the flow and sediment transport characteristics at the junction of an open channel using experimental methods. The results showed that the structure of the flow field at the junction of an open channel has complex vortex and shear layer characteristics, and different inflow conditions and confluence angles significantly affect the properties of the flow field at the junction. Hamidifar et al., (2019) investigated the effects of rigid vegetation at river bends on bed topography and flow velocity fields in laboratory experiments and found that rigid vegetation significantly affects hydrodynamic processes in river catchments. Wang et al., (2020) used numerical simulation methods to investigate the effects of curvature ratio and vegetation density on flow in partially vegetated U-shaped channels. The results showed that the curvature ratio and vegetation density significantly affect the flow fields and sediment movement in the curved channels.
The above research mainly focuses on various aspects of vegetation in curved channels including types, coverage, combination patterns, and distribution. However, an equally important factor in affecting water flow characteristics is river morphology. The impact mechanism of changes in the bending angle of ecological vegetation on water flow characteristics is not yet clear. Therefore, conducting numerical simulation studies on water flow characteristics under changes in meander angle caused by ecological vegetation is of great practical significance to the study of the functioning mechanism of river ecosystems and the protection of aquatic environments in rivers. The first detailed theoretical and experimental studies of the flow in river bends are those of Rozovskii et al., (1957). The mathematical model of flow in curved channels by Rozovskii and his experimental work on a single 180º bend have provided valuable insights into the dynamics of fluid flow. However, several decades later, further research conducted by Blanckaert and his colleagues supplemented Rozovskii's work by investigating the effects of curved curvature and channel widening on flow dynamics. Blanckaert (2009) and his team focused on examining how the curved curvature and internal channel widening affect fluid flow behavior. Their research aimed to enhance our understanding of the complex flow patterns and characteristics occurring in these geometries. Through experimentation and the application of mathematical models, Blanckaert et al., (2004) were able to gather data on flow dynamics in curved channels with different curvatures and widths. Their work revealed important factors influencing flow behavior, such as secondary flows, pressure distribution, and flow separation phenomena. Overall, the research conducted by Blanckaert and his team expands upon Rozovskii's early work, extending our understanding of flow dynamics in curved channels. Compared with other studies on curves, the innovation of this work lies in the calculation and analysis of water flow characteristics from three aspects: Water flow velocity, turbulence kinetic energy, and distribution of meander circulation as the meander angle of the river changes. The study of water flow characteristics of curved channels is of great theoretical and practical importance. Theoretical significance lies in the fact that the water flow characteristics of curved channels are of a fundamental problem in the field of fluid mechanics research, providing insights into the laws of motion of fluids and hydrodynamic phenomena in complex waterway structures. From a practical application perspective, the water flow characteristics of curved channels are directly related to water resource utilization, environmental protection, and other issues. The study of its fluctuation law has important practical significance for the scientific and rational development and utilization of water resources, the protection of water ecological environment and the mitigation of water disasters. In addition, the role of ecological vegetation in influencing the flow characteristics of rivers is currently a focal point of research. Studying the response and regulation mechanism of ecological vegetation to the water flow characteristics of meandering rivers, as well as its relationship with energy dissipation of water flow and sediment transport, is of great significance for the maintenance and restoration of riverine ecological environments and the promotion of healthy aquatic ecosystems.