Impacts of emergent rigid vegetation patches on flow characteristics of open channels

Natural river environments, characterized by fluctuating inundation levels during flood and drought cycles, lead to the formation of diverse river channels and floodplains. These ecosystems support a variety of vegetation, including trees, shrubs, and grasses (Li et al. 2019; Ren et al. 2020; Aydogdu 2023). Aquatic vegetation, either fully submerged or partially exposed, plays a pivotal role in altering flow structures, affecting sediment deposition and resuspension, and shaping riverbed morphology. This contributes to the stability and resilience of aquatic ecosystems (Szabo-Meszaros et al. 2018; Wu et al. 2020; Zhang et al. 2020). By retaining, intercepting, and absorbing water flow through its roots, leaves, and stems, aquatic vegetation effectively reduces flow velocity, rate, and kinetic energy. This can mitigate scouring and erosion of riverbanks and beds, foster the growth of riparian vegetation, and decelerate water and soil loss (Tal & Paola 2007; Cornacchia et al. 2022). Moreover, it significantly influences the transport of pollutants, sediments, microorganisms, and other entities, both biotic and abiotic (Li et al. 2023; Wu et al. 2023; Zhan et al. 2024). Thus, understanding the impacts of aquatic vegetation on flow characteristics is essential for effective water ecological management.

Aquatic vegetation often forms non-uniformly distributed patches in natural and artificial river landscapes (Zhao & Huai 2016; Schoelynck et al. 2018; Li et al. 2019). The complex boundary shapes of these patches lead to intricate flow structures and turbulent characteristics around them (Follett & Nepf 2012; Li et al. 2022). The flow adjustments made by these patches alter local flow conditions in the river channel, affecting shear stress profiles and turbulent characteristics near the vegetation communities and bed area. This plays a decisive role in local bed morphology (Luhar et al. 2008; Le Bouteiller & Venditti 2015). Moreover, reduced flow velocity within the wake region behind these patches can encourage local deposition (Gurnell et al. 2012; Yamasaki et al. 2021). During flood periods, water inundates floodplains, resulting in shallow depths and low-flow velocity structures. When vegetation patches are too dense, they impede the flow significantly, leading to sediment deposition within the patches and hindering flood discharge. Conversely, sparse vegetation patches can trigger bed erosion under certain conditions, causing instability in the riverbank slopes.

The majority of relevant experimental studies mainly focused on the wake structure of flows around patches (Zong & Nepf 2016; Hu et al. 2018), which have multiple limitations. For example, due to the presence of dense cylinders in a patch, it is difficult to obtain clear measurement results by particle image velocimetry. The local flow field directly behind a cylinder is confined to a space that is often too small and tortuous for traditional probes to pass through (Zhang et al. 2019). In contrast, numerical simulations offer detailed insights into flow patterns throughout the entire domain.

Modern computer technology has enabled various mathematical models based on Navier–Stokes equations to effectively simulate turbulence structures of flows, aligning well with flume experimental data (Keramaris et al. 2017; Kim et al. 2018; Sonnenwald et al. 2019). Researchers have explored the pros and cons of different computational models. Kološ et al. (2020) conducted numerical simulations of the flow around a cylinder with a high Reynolds number. They calculated the wake drag coefficient, lift coefficient, pressure coefficient, and wake velocity field, and then compared shear stress transport k–ω model, large eddy simulation (LES) model, scale adaptive simulation model, and detached eddy simulation model. Finally, the best evaluation results were obtained from the LES model. The LES model yielded the best results, proving its efficiency despite the high computational costs.

Although numerical simulation methods have shown potential in studying flows under vegetation, research has mainly focused on turbulent kinetic energy and turbulent intensity distribution. Comprehensively and accurately analyzing energy changes in vegetation patches remains challenging. Detailed analyses of turbulence structures in vegetation patches are currently insufficient (Sonnenwald et al. 2017; Truong & Uijttewaal 2019; Li et al. 2020). More effective implementation of river ecological restoration by artificial approaches calls for a better understanding of how vegetation distribution impacts turbulence structures in river channels (Nikora et al. 2008; Huai et al. 2021).

The current study was conducted to explore the effects of emergent vegetation patches on open-channel flows. LES was performed to thoroughly analyze the flow velocity, turbulent kinetic energy, and vorticity profiles under single-vegetation patches with various densities. Power spectral density and quadrant analyses were used to elaborate the rules of flow energy change and the trends of material transport after water obstruction by the patches from a further perspective. The results of this study could provide a new angle for unraveling the changes in complex turbulence structures in the patch areas of emergent vegetation, in order to contribute meaningfully to future ecological restoration and redevelopment efforts, it is imperative to undertake a comprehensive investigation into the impact of vegetation distribution characteristics on water flow.

Equation (6) consists of an unknown quantity ⁠, which is associated with small-scale fluctuations filtered after application of the filter function. represents the filtered value of momentum flux per unit mass of fluid in turbulent motion. Because numerical simulation cannot acquire flow information across all scales, is unknown and a model for should be developed to close the LES equations. Then, by substituting it into Equation (6), the simplified filtered equation can be obtained.

This study referenced previous studies, setting the value of the constant of the wall-adapting local eddy-viscosity model to ⁠, aiming to achieve more accurate results within a wide range of flow rates (Kim et al. 2019).

Simulation calculation was carried out for two groups of circular emergent vegetation patch. To simulate the vegetation patch, rigid cylinders (diameter d = 0.5 cm, height h = 20 cm) were neatly arranged in a circular range (diameter D = 10 cm). At this time, the blockage ratio of the cross-section where the patch was located was β = D/B = 0.2, where B is the width of the flume. This ratio ensures a minimal impact of flume sidewall vortices on the study area's vortex shedding, according to Sahin & Owens (2004) and Kumar & Mittal (2006).

In this study, the LES turbulence model, wall-adapting local eddy-viscosity subgrid-scale turbulence model, and finite volume method were used to discretely solve Navier–Stokes equations. In the numerical calculation, the smallest grid is located at the position of the vegetation patch stem, with a scale of 0.005 m. The velocity in the vicinity is ∼0.05 m/s, resulting in a ratio of 0.02 s. To ensure computational accuracy and convergence, the time step should be less than or equal to one-fifth of the ratio between the smallest grid size and the surrounding flow velocity. Therefore, a time step of 0.01 s is set in this study. Additionally, considering that in previous studies, the minimum residual value for iterations is typically set to 1 × 10⁻⁴ to achieve strict accuracy, the minimum residual for each equation is set to 1 × 10⁻⁴ in this study (Xiang et al. 2020). Furthermore, the computational model was configured to perform a maximum of 60 iterations per time step. Iterations were designed to cease when the equation's convergence criteria, defined as the residual falling below the aforementioned minimum threshold, were satisfied. This process then progressed to the subsequent time step for further iterations. The boundary conditions were set as follows: velocity inlet boundary at the inlet, pressure outlet boundary at the downstream outlet, free water surface boundary at the top water surface, and no-slip wall boundary at the bottom and sides, including vegetation surface.

For the LES calculations, precise mesh generation was imperative. Adhering to the boundary layer requirement of y⁺ ≤ 1, all-hexahedral meshes with specialized refinement in the vegetation patch area were generated. This approach included dividing the walls of individual cylinders within the patch into five distinct layers of boundary mesh to ensure detailed and accurate LES simulations. In this calculation, the inlet velocity is V = 0.5 m/s, and the model length is 3.6 m. The total calculation time is 40 s, which corresponds to the water flowing through five model lengths to ensure stability in the computational model. The computed data are then sampled, and for subsequent flow field calculations and analyses, physical quantities such as flow velocity are averaged over 1-min sampling intervals.

Based on the research content of the simulation, the mean velocity at the inlet was set to U₀ = 0.2 m/s as a verification example. The model verification experiment was carried out in the Multiphase Flow and Flow Visualization Laboratory of Xi'an University of Technology (Xi'an, Shanxi Province, China). The experiments were conducted in a rectangular flume of dimensions 7.50 m × 0.30 m × 0.45 m (length × width × height), manufactured by Armfield (MODEL S6-MKII), with the sidewalls made of glass and a fixed bed slope of 0.1%. Polymethyl methacrylate (PMMA) plates, forming a stable base, were installed across the flume's bottom for rigid vegetation simulation, using PMMA rods. Two types of vegetation patches with different densities (dense patch: ϕ = 0.17, sparse patch: ϕ = 0.05) were arranged, with the diameter of the patches adjusted to achieve a blockage ratio (β) of 0.2 relative to the width of the cross-section. The inflow rate was set to 9.15 L/s, with an average flow velocity (U₀) of 0.2 m/s at the cross-section. Flow velocities were measured using an acoustic Doppler velocimeter.

Analysis of the acquired data revealed that the relative errors between the numerical simulations and experimental results were below 5%, demonstrating a high degree of concordance in velocity profiles. This alignment suggests the appropriateness of the turbulence model and calculation parameters employed in the numerical study for accurately simulating open-channel flows with vegetation patches. It was noted, however, that the numerical simulation results were marginally higher than the experimental outcomes. This discrepancy can be attributed to the use of plexiglass for vegetation simulation in the experiments, contrasting with the no-slip solid wall boundary condition applied to the vegetation surface in the simulations. Despite employing the wall-function method for near-wall region corrections, slight variances from the experimental results persisted.

Zong & Nepf (2016) defined the region downstream of a patch, where longitudinal mean velocity continues to decrease along the streamwise direction as the ‘steady wake region’. In this region, both the mean velocity and turbulence intensity are significantly reduced. The flow in the steady wake region mainly originates from the longitudinal outflow through the patch. The formation of the steady wake region is additionally tied to the horizontal shear layers formed at the outer edges on both sides of the patch. These two shear layers act as barriers for the wake region. They separate the high-velocity flow past both sides of the vegetation patch from the low-velocity flow in the core zone of the wake, allowing the wake region to maintain low momentum levels within certain longitudinal distances. The above results indicate that no steady wake region is formed downstream of the sparse patch, whereas a ∼0.1-m-long steady wake region exists in the dense patch. Similar to the results of Chang & Constantinescu (2015), we also observed a patch-scale steady wake region downstream of the dense patch, indicating pronounced cylinder–wake interactions within this area.

The velocity in the non-vegetated area increases slightly as a consequence of the flow around the patch and lateral outflow through the patch. This region is defined as the ‘uniform region in the non-vegetated area’ by Li et al. (2020). With low patch density, the highest velocity in the non-vegetated area emerges at the exit of the patch, and the maximum acceleration rate is ∼6.5% of the inflow velocity. After passing through the patch, the velocity slowly decreases within a distance of 0.3 m and then levels off. With a high patch density, the highest flow velocity is found at the exit of the patch, with a maximum acceleration rate of ∼14.0%. After passing through the patch, the velocity slowly recovers at low rates over a long distance. Consistent with the findings of Zong & Nepf (2016), the velocity continues to decelerate after entering the patch, with the velocity at the patch exit being lower than that at the patch entrance. In principle, the wake flow cannot fully recover as the momentum loss due to cylinder drag remains constant downstream of the patch.

When the flow passes a single cylinder, it would generate flows on both sides of the cylinder, accompanied by boundary layer separation on both sides (if the Reynolds number is high enough). Then, the Kelvin–Helmholtz instability due to shear begins to develop, which causes periodic vortex shedding downstream of the cylinder, resulting in a Karman vortex street. Generally, when the cylinder has a slenderness ratio h/D < 2, it is thought that the periodic vortex shedding behavior downstream of the cylinder would be significantly suppressed (Lee et al. 2007). Considering the overall slenderness ratio of the circular vegetation patch simulated in this study (h/D = 2), patch-scale Karman vortex street can be observed downstream of the vegetation patch.

Overall, when the patch density is relatively low, the energy carried by water with low-frequency bands decreases linearly under the log–log coordinate system. In contrast, the decrease in the energy carried by water with low-frequency bands slows down under relatively high patch density. This provides evidence that the water is subjected to greater resistance under relatively high patch density. The underlying reason is that under low vegetation density, the gaps between vegetation allow the vortices generated by disturbances to fully develop. Due to drastic momentum exchange and energy dissipation, the high energy carried by large vortices is rapidly transferred to small vortices, or they are decomposed into high-frequency small vortices. The mutual transfer and conversion processes of energy are accompanied by considerable energy consumption. In particular, a large amount of energy is consumed by the separation of boundary layers and the diffusion of wake vortex at the downstream exit of the patch. With a high density of vegetation patch, the turbulence of water is limited and the energy dissipation occurs slowly, so that the momentum exchange between water does not reach a very high level.

At the central position of the patch (Figure 14(b), monitoring point #3), the large difference in patch density between the two conditions results in remarkable variation in the major quadrants contributing to momentum exchange. In the sparse patch, the dominant flow pattern is outward interactions, whereas in the dense patch, ejections are predominant with a contribution ratio of ∼57%, in agreement with the observations of Poggi et al. (2004). At the junction of the patch exit and the flow (Figure 14(c), monitoring point #4), in contrast to the sparse patch dominated by outward interactions, intensive momentum exchange occurs in the flow in the dense patch, and the greatest contribution comes from ejections. Sweeps also affect the generation of shear stress, with a contribution ratio of 12%. In the downstream area of the patch (Figure 14(d), monitoring point #5), the flow field starts to recover gradually and its momentum exchange is primarily contributed by outward interactions and sweeps. Moreover, sweeps play a more prominent role under the condition of high patch density.

The study enhances the understanding of how emergent vegetation affects flow in open channels. It is important to note that in the natural world, aquatic vegetation, due to its diverse modes of existence such as submerged, emergent, and floating forms, and its morphological attributes such as stems, stalks, and leaves, typically exhibits a range of distinct external morphologies and structural resilience, accurately characterizing real vegetation presents significant challenges. The scope of this study is confined to emergent rigid vegetation in shallow, low-velocity channels. A reasonable approach is to represent vegetation as idealized cylinders. With this simplification, this study is confined to idealized vegetation elements, characterized solely by their diameter and height, without considering additional structural complexities. While the artificial vegetation patches employed in this study do not exhibit the intricate characteristics of natural vegetation, this methodological approach provides a controlled experimental setting that enables the differentiation of the effects of diverse vegetation parameters on hydrodynamic processes. The findings of this study provide foundational insights into the general principles of flow–vegetation interactions, aiding in a broader understanding of plant effects on fluid dynamics and laying the groundwork for more detailed investigations in the real world.

This study demonstrates the impacts of emergent vegetation patches on velocity, turbulence, and energy exchange characteristics of open-channel flows using the numerical method of LES. The major conclusions are as follows:

• 1. Impact on flow velocity: The study demonstrates that vegetation patches markedly influence the flow field's velocity profiles. Specifically, a substantial decrease in flow velocity within vegetated areas was observed, with the dense patch showing a maximum deceleration rate of ∼42.0% at 0.1 m downstream. This starkly contrasts with the sparse patch, where the maximum deceleration rate is ∼21% at the patch's exit, signifying the profound impact of vegetation density on flow behavior.

• 2. Turbulence and vorticity: The presence of vegetation notably intensifies the vorticity field, leading to coherent structure formation behind the patch. This effect varies between sparse and dense patches, with the former facilitating large-scale vortex shedding and the latter inhibiting it. The study's detailed analysis reveals a significant increase in Reynolds stress in the patch area, especially under dense vegetation, highlighting the intricate relationship between vegetation density and turbulence.

• 3. Dominant flow patterns and Reynolds stress: The analysis identifies ejections and inward interactions as the predominant flow patterns at the patch site, contributing to about 80% of the total Reynolds stress. Interestingly, in the dense patch, the interior Reynolds stress is mainly due to ejections (∼57%), while in the downstream development region, outward interactions and sweeps are more prominent.

In the future, it will be of great significance to study how flow characteristics vary with changes in patch shape. Relevant research results could have practical implications for determining appropriate vegetation arrangement methods (e.g., patch size, density, interior shape) in ecological restoration and river channel management.

This research was supported by the National Key Technologies R&D Program of China (No. 2022YFF1300803), the National Natural Science Foundation of China (No. U2243201), and the Joint Open Research Fund Program of State Key Laboratory of Hydro-science and Engineering and Tsinghua – Ningxia Yinchuan Joint Institute of Internet of Waters on Digital Water Governance (sklhse-2023-Iow06).

All relevant data are included in the paper or its Supplementary Information.

The authors declare there is no conflict.