Optimization of Threshold Velocity Values for Sediment Transport at the Outer Bank of a 180-Degree Bend with Emergent Vegetation

Abstract

The interaction between curvature-induced flow and vegetation plays a crucial role in regulating threshold velocity, influencing sediment transport dynamics. This experimental study investigates the effects of flow velocity and turbulence, induced by both emergent vegetation and curvature-driven flow, on the threshold of sediment motion around a vegetated patch. Using an Acoustic Doppler Velocimeter (ADV), a total of 504 velocity profiles were collected under vegetated and non-vegetated conditions, considering a range of vegetation densities (φ = 0.001–0.0099) in both a straight channel and a 180-degree bend. The results indicate that vegetation modifies turbulent kinetic energy (TKE) and velocity gradients, thereby enhancing sediment mobility. Specifically, vegetation significantly reduces maximum velocity by up to 37%, shifting the flow core to the center and enhancing TKE by up to 30 times. This analysis shows that channel curvature contributes a maximum of 34% and 17% to turbulent kinetic energy in the first and second halves of a 180-degree bend, respectively. Turbulence from the bed and vegetation accounts for 50% in straight paths, while in curved paths, it reaches 37% and 32% in the first half and 48% and 42% in the second half of a 180-degree bend. This study proposes a model for turbulent kinetic energy (k_t) that incorporates velocity threshold constraints, validated through controlled laboratory experiments, highlighting the role of near-bed turbulence in modulating sediment transport. Furthermore, the findings demonstrate that sediment motion initiation is governed by both mean flow velocity and TKE, leading to the introduction of a novel criterion for assessing initial sediment transport conditions in curved and vegetated flows.

1. Introduction

Aquatic plants play a crucial role in providing valuable ecosystem services, contributing trillions of dollars to the global economy each year [1,2,3]. However, aquatic vegetation has been in decline, with over half of wetlands and numerous seagrass habitats lost in the U.S. in recent years [4]. Despite this decline, aquatic plants enhance ecosystem resilience by mitigating flood impacts, regulating the transport of substances, and improving overall ecological conditions. Meandering rivers are common in lowland areas, their curves supporting diverse ecosystems [5,6]. Meander migration results from erosion on the outer bank and deposition on the inner bank. Aquatic vegetation stabilizes channels by trapping sediment and strengthening banks; its removal significantly increases migration rates. Vegetation is vital for both long-term channel development and short-term sediment dispersion, yet research on its combined effects in curved channels is limited. Previous studies have thoroughly examined turbulent flow in unvegetated U-bend channels. This flow features a main current and secondary helical flows, including a primary circulation cell (driven by centrifugal force and pressure imbalances) and smaller cells near the outer bank (resulting from Reynolds stress). Vegetation significantly changes this flow pattern in curved channels [6,7,8,9,10,11]. While flow–vegetation–sediment interactions are well studied in straight channels, research on curved channels lags behind.

The interaction between water flow and sediment dynamics in the presence of aquatic vegetation is a key aspect of river mechanics, with significant implications for ecological management and environmental sustainability. Vegetation alters hydrodynamics by increasing flow resistance, which promotes sediment deposition and influences river morphology. Accurately predicting sediment transport rates is essential for various applications, including geoscience, channel design, environmental management, river restoration, flood risk mitigation, and understanding landscape evolution [12]. Despite its critical role, research on aquatic vegetation within the field of river mechanics remains limited, highlighting the need for further investigation into its effects on flow patterns and sediment dynamics. Field studies of sediment movement thresholds are extremely difficult because natural environments are complex and variable. Factors such as varied sediment composition, fluctuating water flow, and differing channel shapes make these studies challenging. Furthermore, a single sediment transport criterion for an entire river bend is impractical because each section experiences unique hydrodynamic forces and sediment interactions, influenced by local topography, vegetation, and river dynamics. Existing models for predicting sediment transport in vegetated regions often lack accuracy and effectiveness, underscoring the necessity for improved predictive frameworks [13].

1.1. Flow Dynamics in Curved Channels

Rivers seldom follow a straight course; instead, they typically adopt meandering or braided patterns, which have a profound impact on scour and sedimentation processes [14,15]. In these dynamic environments, hydrodynamic forces acting on sediment particles intensify as flow velocity increases. When these forces exceed the gravitational pull on bed sediments, sediment transport ensues [16], leading to variations in bed topography. The interaction between longitudinal and secondary flows in river bends, coupled with the development of helical flow patterns [17], further complicates flow dynamics. These factors contribute to higher sediment transport rates in bends compared to upstream straight sections [18]. Consequently, understanding sediment transport and the mechanisms governing incipient motion in curved channels requires more extensive investigation than in straight channels.

Parker et al. (1985) identified two primary directions of sediment transport in river bends: longitudinal transport, driven by the main flow, and lateral transport, influenced by the lateral velocity of the section. Their study also revealed that the initiation and movement of bedload are uneven across the cross-section [19].

Subsequent research has further expanded on these findings. Yen and Lee (1995) investigated bed topography variations in a 180-degree mild bend under unsteady flow, emphasizing the significant influence of secondary flow and velocity distribution at the outer bend [20]. Blanckaert and Graf (2001) demonstrated that cross-sectional velocity patterns in bends consist of two distinct circulation cells: a dominant classical helical cell in the central region and a weaker, counter-rotating corner cell, which is shaped by interactions between the outer bank and the water surface [21].

Xu and Bai (2013) conducted empirical studies on bed topography formation in meandering rivers with varying radii, examining how sinusoidal channel shapes impact flow variations and sediment morphology [22]. Vaghefi et al. (2016) performed experimental studies on flow patterns and shear stress in a 180-degree sharp open-channel bend, finding that secondary flow intensity peaks in the latter half of the bend. Their results also indicated that maximum shear stress occurs from the entrance of the bend to its apex, particularly along the inner wall [23].

Núñez-González et al. (2018) analyzed field data from a meandering river, demonstrating that grain size variations significantly affect incipient motion conditions. Their study established a correlation between boundary shear stress and bedload transport [24]. Moghaddassi et al. (2021) explored the relationship between average velocity-to-critical velocity ratios and their influence on sediment movement and scour depth in meandering channels, revealing that higher ratios intensify scour depth and trigger sediment transport at specific threshold values in different bends [18].

More recently, Rismani et al. (2024) examined how river meanders and channel curvature affect sediment motion, a crucial factor for effective river restoration. Their findings showed that velocity distribution is strongly influenced by threshold motion conditions due to curvature effects, producing a distinct convex velocity profile that varies within the bend. Notably, they found that the Critical Shields Parameter was 8–61% lower than the values predicted by the Shields diagram, decreasing from 0.042 at the bend’s entrance to 0.016 at its end [25].

Shafaei et al. (2025) examined the hydrodynamics of flow in a compound channel with a sinuosity of 1.3. They found that longitudinal velocity in inbank flows is 30% to 45% higher than in overbank flows. Furthermore, an increase in flow depth leads to a 60% reduction in transverse velocity, providing important insights for flood management and hydraulic structure design [26].

1.2. Incipient Motion of Sediment

Incipient motion refers to the moment when a sediment particle begins to move, a phenomenon extensively studied due to its critical role in sediment transport dynamics. Among the earliest and most influential contributions, Shields (1936) developed a practical method for assessing critical shear stress based on minimal bedload transport, a technique that remains widely utilized [27]. Over time, researchers have sought to refine and expand upon Shields’ work by incorporating additional factors that were initially overlooked, leading to the development of more precise equations and a revised Shields diagram for modeling sediment incipient motion in waterways.

Kramer (1935) investigated sediment particle motion under apparent flow conditions, laying the foundation for subsequent research on incipient motion [28]. Neill (1968) introduced the concept of critical velocity, defining it as the flow speed at which sediment particles begin to move along the channel bed [29]. Bagnold (1973) further advanced the understanding of incipient motion by describing it in terms of uplift forces, emphasizing the role of turbulence in mobilizing sediment [30]. Lavelle and Mofjeld (1987) explored the critical stress conditions necessary for incipient motion in turbulent flows, concluding that no single definition governs scouring processes due to the inherent variability in sediment transport timing and extent [31].

Dey and Debnath (2000) examined the influence of bed slope on sediment particle movement, determining that critical shear stress decreases as bed slope increases, based on both analytical and experimental investigations [32]. Similarly, Afzalimehr et al. (2007) analyzed the effects of decelerating flow on sediment movement thresholds in sand-bed channels, finding that the Shields critical parameter was lower under non-uniform slow flow compared to uniform flow conditions [33]. Motamedi et al. (2010) investigated sediment movement in gravel-bed rivers, calculating Shields stress based on observed bedload transport and comparing it to the Meyer–Peter Müller method. Their findings validated both approaches, demonstrating that critical Shields stress decreases as the ratio of median sediment size (d₅₀) to the size below which 90% of particles are finer (d₉₀) increases [34].

Bolhassani et al. (2015) explored the influence of riverbed slope and water depth relative to sediment size on the initiation of sediment movement in decelerating flows. Their experimental study, which examined sediment grains with median diameters of 0.95 mm, 1.8 mm, and 3.8 mm across riverbed slopes of 0.0075, 0.0125, and 0.015, demonstrated that sediment motion could occur even when the critical Shields stress fell below the Shields curve. This finding challenged the traditional applicability of the Shields diagram for decelerating flows [35]. More recently, Dodangeh and Afzalimehr (2022) investigated incipient motion under non-uniform flow conditions in both riverine and laboratory settings. Their study underscored the impact of bedforms, variations in river width, and flow non-uniformity on sediment transport, challenging the conventional application of the Shields diagram, which assumes uniform flow conditions. They highlighted the role of pressure gradients in non-uniform flows, revealing that the Shields diagram frequently underestimates particle motion in these environments. Their research also identified key distinctions in sediment movement between accelerating and decelerating flows, with greater motion observed under accelerating conditions [36].

1.3. Impact of Vegetation on Sediment Dynamics

Patches of both emergent and submerged vegetation are common features in many river systems. Along riverbanks, emergent vegetation typically forms extensive zones of defined width, often growing in a manner that stabilizes the shoreline [37]. An emergent canopy extends throughout the full depth of the water column and frequently breaks the surface [38]. The influence of vegetation on river dynamics can be analyzed from two primary perspectives. First, vegetation serves a crucial role in mitigating erosion by increasing flow resistance and hydraulic roughness. This added resistance stabilizes the riverbed and banks through the reinforcement provided by plant roots, which in turn reduces flow velocity and elevates water levels during flood events [39,40]. However, while vegetation generally reduces flow velocity, it can also generate localized turbulence near the riverbed. This intensified turbulence may enhance sediment transport processes, potentially contributing to bed erosion [13,41,42,43]. Thus, the interaction between vegetation and river dynamics exhibits both protective and erosive effects.

Several studies have investigated bedload transport in vegetated areas, with notable contributions from Jordanova and James (2003), Kothyari et al. (2009), and Yager and Schmeeckle (2013) [44,45,46]. Hongwu et al. (2013) and Wang et al. (2015) simulated the effects of vegetation on sediment incipient motion using artificial cylinders arranged in aligned patterns to represent rigid emergent and flexible submerged vegetation. Their findings demonstrated that incipient motion is initiated by continuous scouring around vegetation, significantly increasing sediment transport. Notably, they observed that the flow velocity required for incipient motion is lower in riverbeds with submerged or emergent vegetation compared to non-vegetated conditions [47,48]. Wang et al. (2015) further noted that the velocity threshold for incipient motion increases in the presence of flexible vegetation due to energy loss in the flow caused by plant swaying [48].

In a controlled laboratory study, Shahmohammadi et al. (2018) examined the effects of submerged vegetation patches on sediment incipient motion within a straight flume. Their results indicated that the average threshold velocity for sediment movement was reduced by 20% in the presence of vegetation, attributing this to an increase in turbulence intensity, which facilitates sediment transport. Moreover, they found that the Shields parameter was 1.5 times higher with vegetation on the bed than in its absence within a straight flume setting [43]. More recently, Hadian et al. (2023) investigated turbulent flow characteristics in channels with vegetated banks of varying widths. Their study highlighted the influence of channel shape, vegetation density, and slope on bed material movement and velocity distributions. They observed that vegetation produced a Z-shaped pattern in Reynolds shear stress distributions. Furthermore, they concluded that the Shields method was ineffective for evaluating incipient motion under these channel configurations [49].

Biological methods for erosion control and stream habitat restoration have gained prominence as cost-effective and ecologically sustainable alternatives to traditional hard engineering solutions such as dikes, levees, and concrete barriers [39,46,50,51,52]. The effectiveness of vegetation in reinforcing riverbeds depends on several factors, including plant size, density, submergence level, spatial arrangement, and growth stage [53,54,55]. These attributes directly influence flow dynamics, sediment transport, and overall channel morphology.

Keshavarzi et al. (2016) found that the presence of vegetation significantly altered flow energy distribution, with cross-sectional kinetic energy increasing from 0.05% in fixed-bed tests to 4.30% with double rows of vegetation. Additionally, vegetation reduced Reynolds shear stress along the test section, indicating its stabilizing effect on the flow structure [56]. Hamidifar et al. (2020) observed that sediment particles tend to accumulate in regions with higher turbulent kinetic energy (TKE). Their findings demonstrated that both single and double rows of tree models effectively reduced bed erosion in sharp bends, with scoured bed volume decreasing by up to 70.4%. Notably, a single row of trees was found to be particularly effective in minimizing maximum erosion depth [57]. Wang et al. (2024) employed CFD-DPM to study particle transport in partially vegetated and non-vegetated U-bend channels. Their findings revealed that vegetation near inner channel walls weakens secondary circulation and alters particle distribution, creating wavy patterns due to dynamic eddies. The Probability Density Function (PDF) showed that particle distribution is affected by secondary flow in non-vegetated channels, while vegetation generates a complex mixing layer that complicates this distribution. Sediment heterogeneity was higher in vegetated areas, and vertical profiles indicated that secondary flow enhances sediment transport in non-vegetated channels, whereas vegetation hinders it, illustrating the complex interactions between vegetation, flow dynamics, and sediment transport [58].

Further expanding on these insights, Rismani et al. (2024) examined the influence of rigid emergent vegetation on sediment dynamics in a 180° river bend, specifically focusing on the outer bank. Their results indicated that vegetation significantly enhances turbulent kinetic energy, with the highest levels observed at a 150-degree angle—18 times greater than in non-vegetated areas. Interestingly, the impact of vegetation on flow and sediment transport was found to be more pronounced on the outer bend than on the inner side, highlighting its role in modifying channel hydraulics [59]. Similarly, Raeisifar et al. (2025) studied the effects of emergent vegetation on flow dynamics in meandering channels. Their research revealed that increasing plant density alters flow patterns, intensifying turbulence and turbulent kinetic energy while simultaneously reducing near-bed Reynolds stresses. These findings underscore the significant role of vegetation in shaping flow structures and sediment transport processes in curved channels [60]. Galia and Poledniková (2025) investigated the influences of woody vegetation on the dynamics of meandering rivers, focusing on the relationship between meander morphology and vegetative cover. Their research elucidated the effects of vegetation on erosional processes and meander stability within fluvial systems. The findings offer important insights into the interplay between ecological factors and river geomorphology, enhancing the understanding of meander dynamics [61].

While significant research has been conducted on incipient motion in straight channels, experimental studies examining sediment transport in curved channels, particularly in the presence of vegetation, remain limited. The complex interplay between channel curvature and vegetation-induced flow resistance introduces additional challenges in predicting sediment movement. This study aims to experimentally investigate sediment incipient motion in a 180-degree bend channel, focusing on how curvature influences sediment dynamics. Furthermore, the research seeks to optimize vegetation density at various locations within the bend to enhance understanding of its role in sediment transport processes. By systematically analyzing vegetation placement and density, this study will provide valuable insights into the hydrodynamic and morphological effects of vegetation in meandering channels, contributing to improved river management and erosion control strategies.

2. Materials and Methods

2.1. Physical Model Setup

The experiments were conducted in a glass-walled flume that features a bend (Figure 1). The flume measures 0.6 m in both width and depth. At the upstream, there is a 90° bend, followed by a straight section that is 4.33 m long, and a downstream 180° bend. This bend is classified as mild, with a curvature-to-width ratio of R_C/B = 4.23 [62]. The flow discharge (Q) was supplied by a centrifugal pump, which has a maximum capacity of 90 L/s for circulating the water. The entire experimental area was covered with 31 cm of sediment, consisting of 10 cm of coarse gravel (mean size of 20 mm, which remained stationary) at the bottom, and 21 cm of uniform sand with a median grain size of d₅₀ = 1.3 mm at the top.

Before each experiment, the bed surface was leveled, and the pump was activated to fill the flume. Initially, to avoid disturbing the sediment bed, the flow discharge was kept very low, with the gate closed during this phase. Once the water level reached a certain height, the gate at the end of the flume was gradually opened to establish stable flow at the desired water depths of 13, 15, and 17 cm. After reaching the specified depth, the flow discharge was increased until sediment movement was observed, indicating that the threshold condition had been met. After establishing the threshold for sediment movement, data collection began. A down-looking Acoustic Doppler Velocimeter (ADV) was used to collect 3D velocity data at a sampling frequency of 25 Hz for a total duration of 4 min. Approximately 6000 velocity data points were recorded at each measurement location. To reduce noise interference, two criteria were applied: a signal-to-noise ratio (SNR) greater than 15 and a correlation coefficient exceeding 70%.

2.2. Experiments Framework

Experiments were conducted in two distinct groups: (1) a straight section of the flume measuring 4.33 m in length and (2) a 180-degree bend with an external length of 8.88 m and an internal length of 6.96 m. The experiments included various runs, both with varying solid volume fractions ($\varphi$) of vegetation and without vegetation in the bend, as well as on the straight path with either a fixed or mobile bed. Open channel flow with submerged vegetation differs significantly from that with emergent vegetation regarding sediment erosion and deposition. Vegetation substantially alters mean velocity and turbulent kinetic energy (TKE), reducing both compared to bare beds in emergent conditions. Submerged vegetation also shows similar reductions, but a velocity gradient develops at the vegetation’s top. Stem density, species, and morphology influence these flow patterns; larger frontal areas lead to greater velocity and TKE reductions [37,38,54,63]. During floods, erosion occurs in unvegetated and sparsely vegetated areas, while sedimentation occurs in densely vegetated areas [64]. Most studies model vegetation canopies as arrays of rigid, cylindrical elements, assuming a uniform frontal area and turbulence length scale. However, Xu and Nepf (2020) studied two species with different morphologies. Typha, with its basal leaf clusters, showed decreasing velocity, length scale, and TKE with distance from the bed. Rotala, with uniformly distributed leaves, exhibited uniform velocity, length scale, and TKE. In both canopies, TKE exceeded that of bare-bed conditions at the same velocity [65]. Given the vegetation present in the surveyed rivers, reed vegetation was selected for this research. Efforts were made to use reeds with approximately the same diameter for the initial tests. However, finding a large quantity of reeds with the same diameter proved to be nearly impossible. Therefore, this study used cylindrical wooden sticks with a circular cross-section, similar to reeds. Rigid circular cylinders with a diameter of 0.005 m and a height of 0.6 m were used instead. These cylinders were arranged in different patterns on PVC boards to simulate emergent vegetation. The solid volume fraction (ϕ) is calculated using the formula ϕ = (nd²π/4), where n represents the number of dowels per unit area, ranging from 0 to 507 stems per square meter, and d is the stem diameter. As a result, the solid volume fraction varied from 0 to 0.0099. Four different densities of emergent vegetation were applied to the outer sidewall of the flume, as shown in Figure 2. Also, the method for installing vegetation on PVC is demonstrated in Figure 3.

Additionally, three flow depths, of 13 cm, 15 cm, and 17 cm were examined. A total of 504 velocity profiles were collected during 126 tests conducted in this study (as detailed in

Table 1. Summary of experimental runs.

Test No.	Channel Curvature (Degree)	Water Depth (m)	Solid Volume Fraction (ϕ)
Mobile bed (d50 = 1.3 mm)—without emergent vegetation
1–3	0	0.13, 0.15, 0.17	0
4–6	30	0.13, 0.15, 0.17	0
7–9	60	0.13, 0.15, 0.17	0
10–12	90	0.13, 0.15, 0.17	0
13–15	120	0.13, 0.15, 0.17	0
16–18	150	0.13, 0.15, 0.17	0
19–21	180	0.13, 0.15, 0.17	0
Mobile bed (d50 = 1.3 mm)—with emergent vegetation
22–33	0	0.13, 0.15, 0.17	0.001, 0.003, 0.005, 0.0099
34–45	30	0.13, 0.15, 0.17	0.001, 0.003, 0.005, 0.0099
46–57	60	0.13, 0.15, 0.17	0.001, 0.003, 0.005, 0.0099
58–69	90	0.13, 0.15, 0.17	0.001, 0.003, 0.005, 0.0099
70–81	120	0.13, 0.15, 0.17	0.001, 0.003, 0.005, 0.0099
82–93	150	0.13, 0.15, 0.17	0.001, 0.003, 0.005, 0.0099
94–105	180	0.13, 0.15, 0.17	0.001, 0.003, 0.005, 0.0099
Fixed bed—without emergent vegetation
106–108	0	0.13, 0.15, 0.17	0
109–111	30	0.13, 0.15, 0.17	0
112–114	60	0.13, 0.15, 0.17	0
115–117	90	0.13, 0.15, 0.17	0
118–120	120	0.13, 0.15, 0.17	0
121–123	150	0.13, 0.15, 0.17	0
124–126	180	0.13, 0.15, 0.17	0

). In each velocity profile, the distance between collected points within the lowest 20% of the flow depth was 0.3 cm, while for the remaining 80%, it was 1 cm. Depending on the water depth, between 16 and 20 points were collected for each profile.

Given the absence of a universally accepted definition for incipient sediment motion, it is crucial to establish a clear standard for identifying the onset of sediment movement in this study. In experiments conducted without vegetation, Kramer’s average transport criterion is used to determine the threshold at which sediment begins to move. This threshold is typically identified by the noticeable displacement of medium-sized sediment particles within the bed material [28]. While this method is primarily qualitative, it effectively captures the initial stages of sediment transport, providing a reliable indicator of when sediment begins to shift.

In flows with vegetation, sediment transport occurs in two distinct phases. The first phase involves local scouring around vegetation stems, which does not result in net downstream sediment transport. The second phase includes bed scouring and the noticeable movement of sediment beyond localized scour holes [66]. Since local scouring does not contribute to the downstream transfer of sediment, it is not considered a valid criterion for movement thresholds in this study. Instead, the criteria for incipient sediment motion in vegetated areas are based on the methodologies established by Hongwu et al. (2013), Shahmohammadi et al. (2018), and Wang et al. (2021) [43,47,66]. According to Kramer’s criterion, sediment motion in vegetated flows begins when transport becomes visibly evident outside of scour holes and at the downstream edge of the vegetation zone [28].

Wang et al. (2021) further demonstrated that in river bends, the onset of sediment motion is influenced by both longitudinal and lateral flow components due to secondary flow effects. They observed that the longitudinal velocity required for sediment movement is lower in bends compared to straight sections. Additionally, they found that transversal sediment transport in meanders is often uneven, and bends do not always contribute to net downstream sediment movement [66].

In summary, this study defines significant longitudinal sediment transport as occurring outside of scouring regions and vegetated zones, aligning with Kramer’s criterion [28]. Given that sediment motion thresholds rely on visual identification, direct observation of incipient motion across an entire 180° bend presents practical challenges due to the uneven distribution of secondary flows. To address this, sediment movement thresholds were assessed separately in six sections, each covering a 30° central angle and spanning an outer bend length of 148 cm. This segmented approach ensures a more precise evaluation of sediment dynamics across the bend, accounting for localized variations in flow structure and transport behavior.

2.3. Theory

In a bare channel without vegetation, the critical velocity for incipient sediment motion, U_c, is usually connected to the time-mean bed shear stress ($\tau$). However, recent studies show that turbulence also contributes to initiating sediment motion by influencing particle movement [13,59,67]. In a bare channel, turbulence’s role is reflected in the Shields diagram, as turbulent kinetic energy and bed shear stress are linearly related [68]. In a vegetated channel, however, the turbulence is predominantly generated by the vegetation [69], so that $\tau$ is no longer used as a substitute for near-bed turbulence. This may explain why bed shear stress models from open channel studies fail in vegetated channels [41,46,47]. Turbulence generated by vegetation has been found to enhance sediment resuspension and bedload transport, resulting in sediment mobilization at lower velocities compared to what is typically observed on bare beds [41,42,46,47,48]. Eddies around sediment particles are essential for sediment transport, as they generate forces that can lift and move these particles. Turbulence in the water column creates pressure fluctuations, which apply a lift force on the particles. Understanding this process is crucial for comprehending sediment dynamics in aquatic environments. Research by Tinoco and Coco (2014, 2018) and Yang et al. (2016) highlights the significance of these mechanisms in sediment movement, demonstrating how turbulence initiates sediment transport [13,41,42]. The lift force in turbulent flow primarily arises from pressure fluctuations generated by turbulence around sediment particles. These pressure fluctuations are proportional to the square of the velocity fluctuations [70,71,72].The kinetic energy of turbulence is represented as $k_t=(\overline{u^{\prime 2}}+\overline{v^{\prime 2}}+\overline{w^{\prime 2}})/2$, where $u^{\prime }$, $v^{\prime }$ and $w^{\prime }$ denote turbulent velocity fluctuations in the streamwise, lateral, and vertical directions, respectively. Consequently, it is anticipated that pressure fluctuations are proportional to turbulent kinetic energy, which implies that the lift force driving sediment movement also correlates with the turbulent kinetic energy.

In a bare channel, the near-bed k_t is proportional to $\tau$ [68], which is itself proportional to the time-averaged, depth-averaged velocity squared U² [73,74]. This relationship can be expressed as k_tb = C_bU², where k_tb is bed-generated turbulence and C_b is a coefficient that depends on bed roughness [13,74]. Yang et al. (2016) noted that in a vegetated channel, both bed-generated turbulence and vegetation-generated turbulence contribute to the near-bed turbulent kinetic energy (k_t). For simplicity, they assume that the total near-bed k_t is the sum of these two components, without considering any mutual interactions. It is proposed that the total near-bed k_t can be estimated as follows [13]:

$$k_t=k_{\mathit{tb}}+k_{\mathit{tv}}$$

(1)

Here, k_tb represents the turbulence generated by the bed, while k_tv denotes the turbulence produced by the vegetation. For a sparse emergent canopy, specifically when d/s_n < 0.56, where d denotes the stem diameter and s_n refers to the average surface-to-surface distance to the nearest neighboring stem, stem-scale eddies can develop throughout the canopy. Consequently, the turbulence generated by the vegetation can be expressed using Equation (2) [69]:

$$k_{\mathit{tv}}=1.2{\left[C_D{\displaystyle \frac{\varphi }{(1-\varphi )\pi /2}}\right]}^{2/3}{U}^2.$$

(2)

Here, C_D represents the stem drag coefficient, and ϕ refers to the solid volume fraction within the canopy. For Equation (2) to be applicable, the stem Reynolds number (R_ed = Ud/ν) must exceed 120 to generate stem wake turbulence (in this study, R_ed > 120) [54].

In channels with bends, turbulence is not only generated by the bed; it can also result from transversal momentum exchange by the cross-sectional flow that differs from straight paths. As a result, relying on existing models based on shear stress may lead to inaccuracies. Therefore, it is crucial to develop an appropriate turbulence-based model for predicting the threshold of sediment movement. In a vegetated channel with curvature, the turbulence generated is influenced by the bed, vegetation, and the curvature of the flow. This study assumes that the total near-bed k_t is determined by the combined effects of these three factors, without addressing their interactions, as Equation (3):

$$k_t=k_{\mathit{tb}}+k_{\mathit{tv}}+k_{\mathit{tc}}$$

(3)

k_tb is the turbulent kinetic energy generated from the bed, k_tv is the turbulent kinetic energy generated from the vegetation, and k_tc is the turbulent kinetic energy resulting from the curvature of the flow path. Therefore, Equation (4) can be used to calculate the turbulent kinetic energy when all three factors mentioned above are present:

$$k_t=C_b{U}^2+C_v{U}^2+C_c{U}^2$$

(4)

C_b, C_v, and C_c are the coefficients related to the roughness of the bed, vegetation, and channel curvature, respectively. To calculate each of these coefficients, it is sufficient to eliminate the effects of the other two, and with the known average flow velocity and the measured turbulent kinetic energy, C_α = k_t/U² can be determined.

3. Results and Discussion

3.1. Distribution of the Downstream Velocity

The distribution of the downstream velocity component for incipient sediment motion (U) along a straight path and at angles of 30, 90, and 120 degrees, both with and without emergent vegetation, is presented in Figure 4. Figure 4 compares several observed vertical profiles at different vegetation densities. The profiles shown are from the outer bank region (10 cm from the outer bank), the central region (30 cm from both the outer and inner banks), and the inner bank region (10 cm from the inner bank). The profiles observed in these three regions are rather similar in the absence of vegetation, but they differ significantly from the logarithmic profile except along the straight path, and the shift of the maximum velocity toward the outer bank as the flow progresses through the bend is notable. This results in a downward shift of the maximum velocity ($\mathrm{Z}/\mathrm{h}\approx 0.3)$, both of which are typical of bend flow. This has been investigated numerically by Cheng et al. (1976), de Vriend (1981), and Winters (1987), and experimentally by Hille et al. (1985) and Blanckaert and Graf (2004) [75,76,77,78,79]. They reported that in cases of weak curvature, the core of maximum downstream velocity shifts outward, eventually positioning itself near the outer bank [75,76,77,78,79]. This behavior is consistent with our experimental observations.

In the presence of vegetation, the profiles observed in the outer bank region change slightly compared to those in the center and inner bank regions. In the bend, the velocity profile on the outer bend is convex, and as it approaches the inner bend, the shape of the profile takes on an S shape. The presence of vegetation in the outer bend reduces velocity, especially in the outer bend, and shifts the core of maximum velocity toward the center of the channel. Additionally, vegetation leads to a velocity reduction of up to 37% in the outer bend and 62% in the straight path compared to conditions without vegetation. Shahmohammadi et al. (2018) stated that in the presence of submerged vegetation across the channel width at a straight path, the average threshold velocity is 20% lower than in the absence of vegetation [43]. This lateral gradient of longitudinal velocity between the vegetated region and the channel center facilitates momentum transfer through secondary flow, accelerating sediment movement in the vegetated region [80]. In addition to flow curvature, the presence of vegetation at the position of maximum velocity has a significant influence, particularly along the outer bend. For instance, in the upper part of the water column, the velocity can be up to 35% smaller than that in the lower part, where the core of maximum velocity is located close to the bed. Keshavarzi et al. (2016) stated that in the presence of vegetation on the inner bank, the velocity increases uniformly from the bed to the free surface along the inner bank and the central line. However, on the outer bank, the velocity increases from the channel bed, reaching its maximum value near the bed before decreasing toward the water surface [56]. Hamidifar et al. (2020) demonstrated that in the absence of cylindrical rods, the maximum velocity at the entrance to the flume bend occurs near the inner bank. While the centerline shows the least variation in velocity, the peak velocity shifts toward the outer bank as the flow progresses past the curve vertex. They also found that both models of cylindrical rods caused the maximum velocity to be deflected downstream of the bend apex toward the inner bank [57]. The results of this study indicate that secondary flow effects (dip phenomenon) arise from the interaction between flow curvature, centrifugal force, longitudinal channel flow, and vegetation. Furthermore, the velocity distribution in the vegetated region and the maximum velocity position reveal that the influence of vegetation is more significant than that of flow curvature in generating secondary flow and altering the position of maximum velocity.

Across all three locations, critical velocity decreases as the vegetation solid volume fraction (ϕ) increases, with a relative increase in critical velocity observed at the maximum vegetation solid volume fraction. Hongwu et al. (2013) and Yang et al. (2016) estimated similar U_crit values based on stem density for grain sizes of 0.54–0.8 mm and 0.6–0.85 mm, and for 1.7–2 mm, respectively. For example, Yang’s data show that the critical velocity values for d = 1.7–2 mm, with ϕ = 0–0.049, range from 0.17 to 0.39 m/s [13,47].

3.2. Distribution of the Turbulent Kinetic Energy (k_t)

The distribution of turbulent kinetic energy (k_t) at the sediment motion threshold (U = U_crit) for different solid volume fractions of vegetation and various bend angles is shown in Figure 5. In the absence of vegetation, k_t reaches its maximum value near the channel bed. This occurs because vortices are created by friction with the bed, and this generates greater velocity fluctuations. At the water surface, k_t reaches its minimum value. As the flow reaches the apex and its second half of the bend, the shape of the distribution of turbulent kinetic energy shifts from linear to concave. This change indicates an increase in k_t at both the surface and the bed of the flow, while showing a gradual decrease in k_t in the mid-depth. The results of this study are consistent with the distribution of turbulent kinetic energy presented in the research by Blanckaert and Graf (2001) [21]. The trend of turbulent kinetic energy reflects the exchange of energy between flow layers, which in the absence of vegetation can be related to secondary flow and the helical structures of flow in curved paths.

Moreover, investigations in the absence of vegetation show that k_t is greater in the inner bend compared to the outer bend. This could be due to specific flow conditions in the inner bend that lead to increased turbulence. Blanckaert and Graf (2001) observed in their experimental study of a 120-degree bend that the level of turbulent kinetic energy in the inner bend is higher than that in the outer bend, noting that the pattern of cross-sectional velocities contains two circulation cells. One cell, located in the center region, is the classical helical cell, while a weaker counter-rotating cell is found in the corner formed by the outer bank and the water surface. Both the outer bank cell and the reduced turbulent activity help protect the outer bank and the adjacent bottom. The outer bank cell keeps the area of maximum velocity away from the bank, while the decreased turbulence leads to lower shear stress on the outer bank. Therefore, the morphological evolution of bends relies not only on the mean flow but also on the turbulence [21]. However, the growth of the outer bank cell was only observed in high-curvature bends, which are not included in the case of the present study. Taye and Kumar (2022) observed in a sinuous channel that the location of maximum turbulence differs between the bend upstream, bend downstream, and the bend apex [81].

In the presence of vegetation, the profiles of k_t observed in the outer bank region change completely compared to non-vegetation, transitioning from concave to convex; as the flow approaches the water’s surface, energy values increase, while the lowest values are found near the bed. In contrast, when there is no vegetation, this trend reverses. The presence of vegetation alters the location of maximum turbulent kinetic energy within the channel’s depth. In the inner bank region and center, the shape of the profile remains unchanged.

The turbulent kinetic energy was significantly enhanced by the vegetation in the outer bank region. The channel-averaged turbulence intensity in the outer bank region along the straight path was 8 times greater than the value measured for a bare bed throughout the flow depth, and it decreased near the bed. As the flow entered the bend, k_t in the outer bank region increased to approximately 30 times throughout the flow depth, and was 6 times greater near the bed compared to the bare-bed condition. This increase was more pronounced in the second half of the bend. Moreover, investigations show that k_t was greater in the outer bend compared to the inner bend. The turbulent kinetic energy at the bed in the outer bend was 3.5 times greater than the inner bend and center during the first half of the bend. In the second half of the bend, this amount decreased to 2.5 times. However, the results of this study do not align with the findings of Hamidifar et al. (2020), who showed that high values of normalized turbulent kinetic energy were measured near the outside bank from the vertex to the exit of the bend. Both configurations of the cylindrical rods were found to reduce turbulent kinetic energy at the outer bank [57].

The turbulent kinetic energy (k_t) increased with increasing φ up to 0.003 on the outer bend because the increased stem density provided more opportunities for generating stem wake turbulence [13]. However, after reaching a certain threshold, k_t began to decrease. This indicates that beyond a specific density, the impact of vegetation on turbulent kinetic energy diminishes. Nepf (2012) demonstrated that in a channel with a long patch of emergent vegetation along the right bank, when φ C_D > 0.5 (C_D is the drag coefficient), turbulent stress does not penetrate to the centerline of the patch. In this case, the velocity within the patch is determined by the balance between the potential gradient (due to the bed and/or water surface slope) and vegetation drag. Conversely, when φ C_D < 0.5, turbulent stress can reach the patch centerline, and the velocity within the patch is governed by the balance of turbulent stress and vegetation drag [82]. These findings explain the reduction in turbulent kinetic energy at high densities of vegetation. Additionally, the presence of vegetation in the outer bend leads to a reduction in turbulent kinetic energy in the center and inner bend compared to conditions without vegetation.

3.3. Assessing the Effects of Various Parameters on Turbulent Kinetic Energy (k_t)

To assess the effects of various parameters on turbulent kinetic energy (k_t), we need to explore several key factors that influence its generation and dissipation. The assessment of the effects of the bed, vegetation, and channel curvature on the turbulent kinetic energy (k_t) is presented in Figure 6, detailing how each parameter is calculated and its impact on turbulent kinetic energy. As mentioned in the introduction, the kinetic energy of turbulance is $k_t=(\overline{u^{\prime 2}}+\overline{v^{\prime 2}}+\overline{w^{\prime 2}})/2$, where $u^{\prime }$, $v^{\prime }$, $w^{\prime }$ denote the turbulent velocity fluctuations in the streamwise, lateral, and vertical directions, respectively, which are collected in the laboratory using ADV. Over a bare bed (without vegetation), the near-bed $k_t$, denoted as $k_{tb}$, is the bed-generated turbulence and proportional to the mean velocity and dependent on bed roughness. The value of $k_{tb}$ was estimated measured $k_t$ from experiments conducted without vegetation on the straight path. In a straight path with vegetation with a fixed bed, the near-bed $k_t$ is denoted as $k_{tv}$. The turbulence generated in the stem wakes depends on the solid volume fraction. Since, in the conducted experiments, only the state of vegetation with a movable bed was considered, $k_{tv}$ alone cannot be measured, and $k_t$ is the sum of the two, sediment particles and vegetation. Both bed-generated and vegetation-generated turbulence contribute to the near-bed $k_t$, expressed as ${k_t=k}_{tb}+k_{tv}$, neglecting any mutual influence. The value of ${k_t=k}_{tb}+k_{tv}$ was estimated measured $k_t$ from experiments conducted with vegetation on the straight path with a mobile bed. Ultimately, $k_{tv}$ is determined based on the value of $k_t-k_{tb}$. In a curved channel without vegetation with a fixed bed, the near-bed $k_t$ is denoted as $k_{tc}$. The turbulence produced in a 180° bend depends on the particle’s location—whether on the inner or outer wall—across different bending angles (highlighting a need for further research by other investigators). In a curved channel with mobile-bed conditions, both bed-generated and curved channel-generated turbulence contribute to the near-bed $k_t$, expressed as ${k_t=k}_{tb}+k_{tc}$, neglecting any mutual influence. The value of ${k_t=k}_{tb}+k_{tc}$ was estimated measured $k_t$ from experiments conducted with a curved channel and mobile bed. It is important to note that in this study, $k_{tc}$ can be calculated independently, as tests were also conducted in the curved channel with a fixed bed. Thus, in this scenario, only channel-generated turbulence contributes to the near-bed turbulent kinetic energy, resulting in $k_t=k_{tc}$. These values are useful for validating data from other tests and estimating $k_{tb}$. The values of $k_t$ at densities φ = 0.001 and 0.0099 were calculated from experiments conducted in a curved channel with vegetation and a mobile bed. In this context, all three parameters contribute to turbulence generation, expressed as ${k_t=k}_{tb}+k_{tv}+k_{tc}$, neglecting any mutual influence.

After measuring turbulent kinetic energy (k_t) in each experiment as described above, Figure 6 illustrates that the overall effect of different channel curvature angles on turbulent kinetic energy for the initial sediment movement is less significant compared to the scenario where vegetation is present on the outer bend. The highest turbulence production due to curvature occurs in the first and second halves of the 180-degree bend, accounting for maximums of 34% and 17% of the total turbulent energy, respectively, while its contribution drops to a minimum of 10% in the second half of the bend. Furthermore, the contribution of turbulence generated by the bed and vegetation—related to the bed conditions, flow dynamics, density, and type of vegetation—consistently accounts for 50% each in a straight path, while in the curved path, it reaches maximums of 37% and 32% in the first half of the bend and 48% and 42% in the second half. Figure 6 also indicates that at lower densities, vegetation is associated with higher turbulent kinetic energy. The minimum total turbulent kinetic energy under sediment movement conditions occurs in the straight section and within a curvature angle of 90 to 120 degrees, even though the energy produced by each parameter within this angle is notably high. This suggests that in this region, the interaction of the examined parameters has a negative effect, leading to mutual attenuation.

3.4. Prediction of Turbulent Kinetic Energy (k_t) in Vegetation Regions of Channel Curvature

To further support the turbulence model, the near-bed turbulence was estimated using Equation (4). The bed turbulence coefficient, $C_b$, was calculated from the measured bare-bed values of $k_t=19.15 ({\mathrm{c}\mathrm{m}}^2/{\mathrm{s}}^2)$ and $U_{cr}=43(\mathrm{c}\mathrm{m}/\mathrm{s})$; specifically, $C_b=k_t/{U_{cr}}^2=0.01$. In the study by Yang and Nepf (2016), the value of $C_b$ was considered to be 0.025 for h ≈ 0.2 m and d_s = 0.6–0.85 mm [13]. To calculate the channel curvature turbulence coefficient C_c, data from experiments on a fixed bed and curved path were utilized, with values varying along the 180-degree bend from 0.007 to 0.01 at the center of the flume, from 0.002 to 0.01 on the outer bend, and from 0.009 to 0.014 on the inner bend. For calculating vegetation turbulence coefficient $C_v$, data from experiments on a straight path with vegetation were used, with values ranging from 0 to 0.003 at the center of the flume, from 0 to 0.05 on the vegetated outer bank, and from 0 to 0.001 on the inner bank. To calculate $C_v$ from Equation (2), the value for C_D was approximated as 1 for our experimental conditions [73]; $C_v$ = 0.0089–0.041 was estimated for φ = 0.001–0.0099, which is consistent with our results [13]. The predicted $k_t=C_b{U}^2+C_v{U}^2+C_c{U}^2$ (Equation (4)) agreed with the measured $k_t$, which both validated Equation (4), as shown in Figure 7, and supported the hypothesis that the critical velocity was set by a threshold in near-bed $k_t$.

The average turbulent kinetic energy (k_t) under varying conditions, comparing a straight path to a 180-degree bend, both with and without vegetation, is illustrated in Figure 8. The time-averaged k_t differed between the straight path and the 180-degree bend, regardless of vegetation presence. Notably, the average k_t in the 180-degree bend without vegetation was significantly lower, approximately half of that observed on the straight path without vegetation. Moreover, the straight path without vegetation demonstrated a greater range of k_t variation compared to the 180-degree bend. With the presence of vegetation, turbulent kinetic energy (k_t) reached its maximum in the 180-degree bend, with values in vegetated conditions being nearly 7 times greater than those in non-vegetated areas. However, the range of k_t variation was significantly broader when vegetation was included. In a straight path with vegetation, k_t was approximately twice that observed in the absence of vegetation. These results indicate that the combined effects of vegetation and channel curvature have the most substantial influence on the production of turbulent kinetic energy.

The average velocity at incipient motion under varying conditions, comparing a straight path to a 180-degree bend, in both the presence and absence of vegetation, is illustrated in Figure 9. As observed, the average velocity at incipient motion on a straight path with vegetation is at its minimum, meaning that the bed particles begin to move more quickly under these conditions. The average velocity at incipient motion on a curved path with vegetation is nearly similar to that of a straight path with vegetation. On the other hand, the maximum values for the threshold velocity are observed on a straight path without vegetation. In fact, the presence of vegetation reduces the threshold velocity on both straight and curved paths to about half of the values found in the presence of vegetation.

The comparison of the results in Figure 8 and Figure 9 indicates that while vegetation increases turbulent kinetic energy and ultimately facilitates sediment movement, as according to the results of Yang et al. (2016) and Shahmohammadi et al. (2018) [13,43], as well as this study, relying solely on turbulent kinetic energy results in curved paths is insufficient.

Assuming that each particle requires a specific threshold velocity to initiate movement, which consists of two components—the average channel velocity for movement initiation (U_crit) and the necessary velocity fluctuations to start movement (u′, v′, w′)—we can interpret the discrepancies between results of turbulent kinetic energy and critical velocity as follows: With a constant channel velocity, an increase in turbulence leads to higher instantaneous velocities, causing sediment to begin moving sooner (at lower critical velocities). Specifically, as turbulence rises, the velocity fluctuations required to initiate movement also increase, thus reducing the average critical velocity needed for a particle to start moving. In this context, the role of turbulent kinetic energy in initiating sediment movement becomes clearer. Vegetation produces greater velocity fluctuations compared to the non-vegetated area, indicating that a lower average velocity is sufficient for initiating particle movement. Consequently, in these situations, fluctuations in flow velocity or turbulent kinetic energy are critical for sediment transport. When the channel lacks vegetation, the turbulent kinetic energy at the outer bank is at its lowest (Figure 8), while the critical velocity is at its highest (Figure 9). This means that the average flow velocity is vital in the sediment transport process. Experimental observations demonstrate that vegetation enables sediment particles to move more quickly along the outer bank. Overall, a concurrent examination of turbulent kinetic energy and average critical flow velocity is essential for understanding the threshold conditions for sediment movement. Here, a new criterion (u_ck) is proposed for channels with curvature and vegetation to describe the maximum velocity required for the initiation of sediment movement. If we assume that u_ck = U_cr + u′_k, where u′_k represents the additional velocity fluctuations in the flow direction necessary for sediment transport, this can be quantified using turbulent kinetic energy $\alpha \sqrt{k_t}$ (as elaborated in Section 2.3, where k_t = CU²). The value $\alpha =1/\sqrt{C}$ serves as an appropriate coefficient. Therefore, we can express it as $u_{ck}=U_{cr}+\alpha \sqrt{k_t}$. To estimate the coefficient $\alpha$, it is sufficient to calculate the coefficient C separately for different groups according to Section 3.4. The values of $\alpha$ for different groups at the outer bend and inner bend are presented in

Table 2. The values of $\alpha$ for different groups.

Category	$\mathit{\alpha }$max-Outer Bend	$\mathit{\alpha }$max-Inner Bend
Straight path without vegetation	10	10
180-degree bend without vegetation	4.1	10
Straight Path with vegetation	7.1	6.5
180-degree bend with vegetation	3.8	6.3

.

The new threshold criterion of sediment movement is illustrated in Figure 10 for a channel with curvature and vegetation. This criterion remains relatively constant across all vegetation densities and angles of a 180-degree bend. The dashed line indicates the average value of u_ck, which is 0.5 in the outer bend and 0.58 in the inner bend. At a flow velocity of 0.58 (m/s), we observe sediment movement across all vegetation densities and throughout the entire 180-degree bend.

Although it is crucial not to overly emphasize the selection of a universal value for the sediment movement, as highlighted by Buffington and Montgomery (1997), it is equally important to focus on identifying credible values for the Shields parameter or other criteria that are tailored to specific applications, taking into account the flow structure [83]. In channels defined by curvature and vegetation, the application of the proposed criterion (u_ck), irrespective of vegetation density and bend angle, appears to be more practical. While progress has been made in understanding how vegetation, water flow, and sediment interact, key research gaps persist. Improved methods are needed to study the effects of vegetation density and channel curvature on sediment transport. It is suggested that the effects of various vegetation densities be studied to determine the optimal vegetation for controlling sediment transport in channel bends. Further research should explore different vegetation types and their impacts across various bend configurations, using a combination of field studies and computer modeling.

4. Conclusions

This study aimed to elucidate the combined effects of vegetation and channel curvature on sediment movement thresholds by analyzing their influence on turbulent kinetic energy (k_t) and flow velocity. The findings demonstrate that, in the absence of vegetation, maximum velocity shifts toward the outer bank as flow moves through bends, while higher turbulent kinetic energy is observed in the inner bend compared to the outer bend. However, the presence of vegetation significantly alters both turbulent kinetic energy and velocity profiles, particularly in the outer bend regions. Vegetation reduces maximum velocity by up to 37%, shifting the velocity core toward the channel center. Moreover, vegetation enhances k_t in the outer bank region, with increases reaching up to 30 times greater than in non-vegetated conditions.

The analysis further indicates that while channel curvature influences turbulent kinetic energy, its effect is considerably less pronounced than that of vegetation in the outer bend. In curved channels, the primary source of turbulence originates from flow separation and helical flow structures, which generate eddies. In contrast, in vegetated channels, turbulence arises through two dominant mechanisms: wakes generated by individual plant elements, which exert greater influence than bed shear, and shear stress induced by variations in plant frontal area.

To better characterize these effects, this study developed a turbulent kinetic energy model using a velocity threshold, validated through laboratory experiments. The results confirm that turbulent kinetic energy is lower in a 180-degree bend without vegetation compared to a straight channel but increases dramatically in the presence of vegetation, underscoring the substantial impact of both vegetation and curvature on k_t production.

The findings of this study emphasize that the onset of sediment motion is governed not only by mean flow velocity but also by turbulent kinetic energy. A new criterion for determining the initial conditions for sediment transport has been introduced, applicable to flow conditions influenced by both curvature and vegetation. However, further detailed observations are necessary to refine the coefficients involved in this criterion and improve its predictive accuracy. In general, this study suggests using low-density vegetation in the first half of the bend and higher-density vegetation on the outer bend in the second half to reduce sediment transport.