Experimental Assessment of the Turbulent Flow Field Due to Emergent Vegetation at a Sharply Curved Open Channel

Abstract

Emergent vegetation in river corridors influences both the flow structure and subsequent fluvial processes. This investigation aimed to analyze the impact of the bending and vegetation components in a sharply curved open channel on the flow field. Experiments were undertaken in a meandering flume (0.9 m wide, wavelength of 3.2 m, and a sinuosity of 1.05) with a 90-degree bend at the end of it, with and without vegetation, to achieve this goal. The individual vegetation elements arranged across the 90-degree bend of the flow channel were physically modelled using rigid plastic stems (of 5 mm and 10 mm diameters). Analysis of the findings from the flow velocimetry, taken at five cross-sections oriented at angles of 0°, 30°, 45°, 60°, and 90°, along the 90-degree bend indicates that as the plant density increases, the effect of centrifugal force from the channel’s bend on the cross-sectional flow patterns decreases. At the same time, the restricting influence of vegetation on lateral momentum transfer becomes more pronounced. Specifically, for increasing vegetation density: (a) higher transverse and vertical velocities are observed (increased by 4.35% and 9.68% for 5 mm and 10 mm reed vegetation, respectively, compared to the non-vegetated case); (b) greater turbulence intensity is seen in the transverse flow direction, along with increased turbulent kinetic energy (TKE); and (c) reduced near-bed Reynolds stresses are found. The average transverse flow velocity for the non-vegetated case is 18.19% of the longitudinal flow velocity and the average vertical velocity for the non-vegetated case and 5 mm and 10 mm reed vegetation is 3.24%, 3.6%, and 5.44% of the longitudinal flow velocity, respectively.

1. Introduction

The vegetation located in a curved segment of a channel can interact with the flow significantly, thereby contributing to the overall complexity of the flow structure. This interaction results in distinctive morphological consequences [1,2] in river corridors over long time scales. From this perspective, gaining a deeper perception of the flow dynamics in a curved part of a channel with vegetation may aid in developing effective strategies for sustainable river management [3].

When a bending section of a vegetated river cross-section is considered for a given channel and given flow conditions, the overall resistance generated against the flow can be classified into three major categories: surface roughness, which originates from the bed and banks; bending resistance; and vegetation-induced resistance. The present study aimed to assess the combined effects of the vegetated channel bend on the flow field, which also influences the hydraulic resistance of natural waterways. To this end, experiments were conducted in the same channel with and without vegetation. Different vegetation configurations were exposed to identical flow conditions to quantify the flow field.

The presence of centrifugal force in the bend of the channel gives rise to the formation of a spiral flow, also known as helical flow, along the curvature of the channel bend. The spiral pattern of the flow results in a variable velocity distribution [4,5] in the vicinity of the inner and outer walls, as well as diffusion [6] and sedimentation [7,8]. Typically, the velocity distribution in straight channels in natural waterways does not precisely follow a logarithmic pattern [9,10]. By investigating the flow velocity in a small bend with an aspect ratio of 3.6, De Vriend et al. [11] concluded that when the flow increases, the maximum velocity tends to move towards the inner bend. Additionally, it has been demonstrated that as the longitudinal pressure gradient increases, the maximum flow velocity tends to approach the inner wall [12,13]. The velocity pattern within the cross-section is subject to change, not only along the bend of the channel but also in the depth of the water. The specific characteristics of cross-circulation and the acceleration of the convective flow [14,15] are the determining factors in this regard. New methodologies have been developed to predict the average transverse velocity distribution for this type of curved channel [16,17]. The efficacy of the proposed method was evaluated through field tests conducted in five distinct riverine environments by Shan et al. [18]. The results demonstrated that the location of maximum velocity is independent of the relative submergence and curvature. Three-dimensional numerical simulations were developed to examine the effect of the hydraulic geometry of curved channels on velocity distribution. It was demonstrated that these tools can be effectively employed to predict the lateral distribution of average depth velocities within the cross-section of a curved channel [19,20].

The characteristics of flow turbulence in channel bends have been the subject of only a limited number of field studies. These studies also examined the structure of the velocity profile in the vicinity of channel walls. The investigation of river flows is typically conducted under fully developed turbulent flow conditions, as this is the most appropriate environment to study the primary responsible factor for the production of momentum in the flow domain, namely turbulent shear stress. Additionally, turbulence generated along the river channel plays a significant role in the transfer and dispersion of sediments, nutrients, and pollutants [21,22]. Most studies examining turbulence in bend channels are conducted along the central axis of the channel. Zeng et al. [23] investigated the occurrence of perturbated kinetic energy at different phases by illustrating the non-linear relationship between downstream velocity and crossflow circulation through the utilization of experimental and computational data collection [23]. Blanckaert and De Vriend [24] demonstrated that the flow adjacent to the outer wall of the bend in the channel exhibits reduced turbulence and wave-like movement compared to straight streams. This alteration in flow behavior is influenced by factors such as channel curvature, which can impact how water is mixed and transported within the channel. The experimental observations of Abad and Garcia [25] also showed that when the bends are oriented upstream of the valley, the secondary flow is not as well developed as when the bends are oriented downstream of the valley.

In natural rivers, vegetation exerts a certain degree of resistance to drag forces, depending on the plant architecture [26] and mechanical [27] properties. As a result of this phenomenon, the vegetative components experience compression, become more streamlined, and exhibit a swaying motion [28]. Compression and streamlining of the stems cause a decrease in the flow resistance in bends for small aspect ratios (width/flow depth) [29]. Vegetation reduces the centrifugal force at the entrance of the bend. However, it increases at the exit of the bend, leading to a decrease in the surface of the circulation cell due to the secondary current in the bend, which indicates a decrease in the flow velocity [30,31]. Nepf and Vivoni [32] showed that the intensity of turbulence in emergent vegetation is almost uniform along the flow depth. Vegetation causes the flow to become complex in the bend channels due to the presence of centrifugal force and the resistance of vegetation [33]. Shari et al. [34], in a laboratory flume with rigid and non-submerged vegetation and vegetation density, investigated different flow characteristics in terms of longitudinal velocity, transverse velocity, turbulence intensity, and TKE in relation to vegetation density, depth flow, and stem Reynolds number, and showed that the largest value of longitudinal turbulence and TKE reverses the boundary between the wake area and fast flow region. To determine the effect of turbulence structure on momentum transfer in the vegetation area, they used a rectangular channel with artificial emergent vegetation and compared it with experimental data. They found the generation of vortexes behind the vegetation [35]. Through experimentation, Wu et al. [36] identified that the flow characteristics in a vegetated channel comprised of glass rods (solid vegetation) of varying diameters and arrangements exhibited distinct patterns. Their findings indicated that the flow velocity is higher in the alignment mode than in the staggered mode [37,38]. Comparing vegetation physically modelled with emergent rigid stems to the case without vegetation in a rectangular cross-section channel at a 180° bend, they indicated that the effect of vegetation on the transverse turbulence dispersion factor is small. However, the longitudinal dispersion in the presence of vegetation can be much larger than the case without vegetation [39]. Liu et al. [40] found that vegetation substantially influences the longitudinal coefficient of variation by measuring the flow rate in the presence of emergent rigid vegetation in a channel bend. Kumar and Sharma [41] measured the flow velocity in a channel with emergent rigid vegetation (simulated with iron bars). They concluded that for each measurement position of the vertical velocity profile in the longitudinal direction of the flow, a gradual increase of the velocity goes towards the water surface. While near the bed surface, an increase in velocity is seen immediately in the vicinity of the vegetation element, which is probably caused by the vortices at the base of the vegetation elements [41]. Stoesser et al. [42] represented vegetation elements with rigid cylinders and found that flow turbulence is more affected by the density of the vegetation than the individual cylinders’ Reynolds numbers.

Most of these studies have been developed in a 180-degree curved channel, which is rarely observed in natural rivers. However, the existing studies have investigated velocity, Reynolds stress, turbulence intensity, and turbulent kinetic energy. Huang et al. [43] found that the longitudinal velocity is small in vegetation areas but large in the non-vegetation areas along a 180-degree sharply curved channel. Termini [44], Yang et al. [45], and Huang [43] showed that variation in velocity in the outer bank of the curve is considerably greater than that in the inner bank of the curve. In addition, the curve section enhances the turbulence intensity and turbulent kinetic energy (TKE), and minimum TKE occurs in the vegetation section. Sahoo and Sharma [46] found that the velocity generally increases in a zig-zag manner from the bed for sand bed sediment. Taye et al. [47] showed that longitudinal and lateral velocity profiles occur at the apex of a curved channel, and velocity in the vertical direction gives both negative and positive values with more randomness and reverse flow at the curved section. Sahoo and Sharma [46] and Taye et al. [47] considered negative values in Reynolds stress distribution due to narrow curved channels. Also, they showed that the Reynolds stress and turbulence intensity show an increasing trend from the bed up to y/h = 0.3 and, thereafter, a decrease. They reported scatter in data, especially for Reynolds stress distribution near the water surface. Jiang et al. [48] studied the flow in a 180-degree U-shaped flume using different sizes of circular cylinders. They found that a larger size produces greater streamwise velocity along the outer bank than the inner bank. Also, Reynolds stress values on the outer bank are all greater than those on the inner bank of the curved channel. Rismani et al. [49] showed that the Reynolds stress distribution presents a concave shape upstream of a 180-degree curved channel and a convex shape downstream of the curve.

Many laboratory and field studies have focused on the effect of the channel’s planar geometry (such as sharp bends) and riparian vegetation on the flow. However, more research is needed on the effect of the diameter of emergent vegetation (reeds with different rigid diameters in a regular arrangement) in bends by considering turbulence characteristics along the curved channel. Rigid emergent vegetation with different sizes and densities represents a part of the complex nature of fluvial studies. The differences in stem diameter and density generate various levels of heterogeneity in velocity and turbulence for emergent vegetation where vegetation height exceeds the flow depth.

The main objective of this study is to experimentally investigate the turbulent flow characteristics, including the velocity distribution, turbulence intensity, turbulent kinetic energy, and Reynolds shear stresses (RSS) in a coarse bed surface bend in the presence of rigid emergent reed vegetation with different diameters and regular arrangements. Also, comparing the results with those of a bare bed surface (without vegetation) will help determine the role of vegetation in bend channel restoration practices.

2. Materials and Methods

2.1. Flume Setup

All the experiments were conducted at the University of Science and Technology in Iran. The channel had rectangular cross-sections, with a width of 0.9 m throughout the meandering channel and was curved. The length of the arch was 8 m. As shown in Figure 1a, the wavelength of the curved channel was 3.2 m, with a sinusoid of 1.05. The angle of the outer wall of the bend was 136°, and the inner wall of the bend was 76°. Vegetation elements along the channel bend were arranged regularly at an angle of 90° in relation to the bend in section S1. This meandering was simulated based on a real bend in the Dariyuk River in Mazandaran province. The water level in the flume was regulated by the downstream tailgate of the channel, which was responsible for controlling the water flow. In all experiments, due to centrifugal force, the water depth at the outer wall was greater than at the inner wall. For all flow depths measured, an approximately 1 cm difference in the flow depth was prevalent between the inner and the outer walls; for example, at a 13 cm depth of flow in the channel bend, the flow depth at the outer wall was 14 cm and at the inner wall was 12 cm.

2.2. Characterization of Vegetated Zone

Cylinders made of plastic with a diameter of either 5 mm or 10 mm were used in the experimental vegetated zone. The vegetative elements were positioned at an angle of 90° with respect to the final bend in the channel. An elevated bed with a 2 cm thickness was employed to establish the vegetation of rigid stems with regular arrangement. The flume bed surface had a mild longitudinal slope of 0.002, which can be considered as a realistic value for a lowland meandering river. Figure 1b illustrates the arrangement of reed vegetation in a regular and emergent pattern at the bend. The variable of $\varnothing ={\displaystyle \frac{m\pi d^2}{4}}$ was used to identify the vegetation density. Herein, ‘d’ denotes the uniform diameter of elements, and ‘m’ denotes the vegetation density. The vegetation density values employed were Ø = 0.007 for the case where the vegetated area consisted of stems with a diameter of 5 mm and Ø = 0.028 for the situation where the vegetated area consisted of stems with a diameter of 1 cm. This configuration and density are consistent with those observed in the Dariyuk River, where the distance between reeds is typically 0.05 m. The channel had a recirculation system, where the water was transferred from the downstream end of the flume.

2.3. Measurement Techniques

The velocity and turbulence components were quantified utilizing a Vectrino acoustic Doppler Velocimeter (ADV, Nortek AS, Rud, Norway), which operated at a frequency of 200 Hz for a two-minute sampling duration. The velocimeter was mounted to a traverse system that is capable of movement in three directions. Data collection was carried out for three experimental arrangements: (a) a non-vegetated case, (b) a vegetation arrangement utilizing stems with a diameter of 5mm (as shown in Figure 2a), and (c) a vegetation arrangement using stems with a diameter of 10 mm (as shown in Figure 2b). Data collection was performed in five cross-sections oriented at different angles (S1 = 0°, S2 = 30°, S3 = 45°, S4 = 60°, S5 = 90°). In each cross-section, there were five vertical profiles. The distance between the measurement point and the bed surface in those vertical profiles was 4 cm. By configuration of the vertical placement of the ADV probe and adjustment of its orientation so that it always faced the mean approaching flow direction, measurements were taken consecutively up to a depth of 5 cm below the free water surface. The distance between two consecutive points in the vertical direction to measure velocity was considered a constant value of 2 mm near the bed, such as (5.4–5.6–5.8–6–6.2 to 9 mm). This study considered a constant distance of 5 mm (e.g., 95–100–105 mm) for the rest of the flow depth toward the water surface.

Sections S1 and S5 were situated at the most upstream and downstream points of the vegetated zone, respectively. The locations of the measurement sections of S2, S3, and S4 are illustrated in Figure 1b. In the time series of velocity/turbulence records, data of poor quality, defined as having a correlation coefficient below 0.7 and a signal-to-noise ratio lower than 15 dB, were removed. Subsequently, the method proposed by Nikora and Goring [50] was utilized to eliminate any contaminated values, thereby ensuring the integrity of the recorded data, while the velocimeter configuration was set carefully for the examined flows [51].

2.4. Experimental Conditions

Different reproducible flow conditions were repeated during the experiments in the vegetated flume for the various vegetated zone configurations. The water depth values were 9, 11, 13, 15, and 17 cm. The discharge values were 17, 20, 21, 23, and 25 L/s. All the experiments were conducted for the sub-critical flow conditions, which is reasonable because in lowland rivers that accommodate meandering plan-view profiles, subcritical flow conditions mostly prevail over a year due to the low bottom gradient profile. The experimental parameters of the channel along its centerline at different depths are summarized in

Table 1. Demonstration of the flow parameters for all flume experiments.

Flow Depth	Flow Discharge	Aspect Ratio	Position	No-Vegetation Case			Ø = 0.007 Solid Volume Fraction			Ø = 0.028 Solid Volume Fraction
H (cm)	Q (L/s)	$\raisebox{1ex}{$\mathit{W}$}\!\left/ \!\raisebox{-1ex}{$\mathit{H}$}\right.$ (-)	Section	${\mathit{U}}_{\mathit{a}\mathit{v}\mathit{e}}$ (cm/s)	Fr	Re ×104	${\mathit{U}}_{\mathit{a}\mathit{v}\mathit{e}}$ (cm/s)	Fr (-)	Re ×104	${\mathit{U}}_{\mathit{a}\mathit{v}\mathit{e}}$ (cm/s)	Fr	Re ×104
9	17	10.94	S1-3	8.2	0.087	0.74	10.9	0.116	0.98	9.79	0.104	0.88
9	17	10.81	S3-3	12.4	0.109	1.12	9.15	0.097	0.82	13.19	0.14	1.18
9	17	10.21	S5-3	15.2	0.162	1.37	7.96	0.084	0.71	12.89	0.13	1.16
11	20	8.954	S1-3	110.7	0.106	1.21	12.2	0.117	1.34	9.3	0.089	1.02
11	20	8.845	S3-3	13.75	0.132	1.51	9.7	0.093	1.06	9.5	0.092	1.05
11	20	8.354	S5-3	15.5	0.149	1.7	8.09	0.077	0.89	10.5	0.101	1.15
13	21	7.577	S1-3	13.2	0.117	1.72	10.6	0.094	1.38	12.5	0.11	1.62
13	21	7.485	S3-3	10.9	0.109	1.41	9.06	0.08	1.17	9.14	0.08	1.18
13	21	7.07	S5-3	16	0.14	2.08	11.5	0.102	1.5	10.4	0.092	1.35
15	23	6.566	S1-3	8.86	0.73	1.32	9.8	0.081	1.4	9.5	0.078	1.4
15	23	6.486	S3-3	9.4	0.078	1.4	7.4	0.061	1.11	8.2	0.068	1.2
15	23	6.126	S5-3	13.3	0.109	1.9	10.8	0.089	1.6	9.04	0.074	1.3
17	25	5.794	S1-3	8.2	0.063	1.3	7.2	0.055	1.2	8.08	0.062	1.3
17	25	5.723	S3-3	8.8	0.06	1.5	8.02	0.06	1.3	8.6	0.067	1.4
17	25	5.405	S5-3	11.8	0.09	2.01	5.8	0.04	0.9	6.4	0.05	1.09

. In total, 125 profiles were taken along the channel bend. Due to the high number of data, only information from the center of the channel was taken in the sections before vegetation, such as S1; the bend apex of the channel, or S3; and after vegetation, or S5, as shown in Table 1.

3. Analysis and Results

The flow velocities in the streamwise (u), vertical (w), and lateral (v) directions were decomposed into time-averaged ($\overline{u}$, $\overline{v}$, $\overline{w}$) and turbulent components (u′, v′, w′). Also, the velocity profiles near the bed surface follow the law of the wall for the case of a straight and unobstructed (not vegetated) wall-bounded flow, as shown in Equation (1)

$${\displaystyle \frac{{\overline{u}}_z}{u_{\mathrm{*}}}}={\displaystyle \frac{1}{\kappa }}\ln {\displaystyle \frac{z}{z_0}}$$

(1)

where u is the flow velocity in the streamwise flow direction (generally considered along the x× direction of a typical Cartesian coordinate system). u* is the shear velocity, and z₀ is the height of the bed surface (or hypothetical base level from the channel bed to the water surface). The depth of the velocity measurement point is set using the theoretical bed surface level, z₀, as a starting reference level. Also, κ is the Von Karman constant, which is considered to be 0.4 according to extensive field and laboratory studies [30]. One method for determining the bed level is using the log-law function, which can be solved by matching the measured data through trial and error. Attention is directed towards the roughness equivalent, z₀, corresponding to the d₅₀ of coarse bed material in a non-vegetated case, as well as the height of vegetation in the presence of vegetation inside the channel bed. The logarithmic law was validated by charting u versus n(z/z₀) and permitting a change in the breakpoint between segments within the range of z/h ≤ 0.2 [52,53].

The shear velocity is an effective variable for identifying/quantifying the drag and the average flow velocity [54]. Furthermore, current shear velocity studies tend to focus primarily on certain discharge levels rather than examining a larger range [55]. A methodology for calculating shear velocity in non-uniform flow has been established, namely boundary layer properties [56].

$$u*={\displaystyle \frac{{\left(\delta *-\theta \right)}^{u}max}{c\delta *}}$$

(2)

$$\delta *=\underset{0}{\overset{h}{\int }}\left(1-{\displaystyle \frac{u}{u_{max}}}\right)dy$$

(3)

$$\theta =\underset{0}{\overset{h}{\int }}{\displaystyle \frac{u}{u_{max}}}\left(1-{\displaystyle \frac{u}{u_{max}}}\right)dy$$

(4)

In this context, the delta is the displacement thickness of the boundary layer (m), and theta is the momentum thickness (the thickness of the boundary layer movement). Determining the constant value of c is one of the considerations for flows in the presence of coarse bed surfaces, which is generally 4.4 to 4.8. This study used the constant value c to measure the substrate stress. Firstly, the following equation was employed to determine the quantity of shear velocity within the resulting profile [57]

$$u*=\sqrt{{\displaystyle \frac{{\tau }_{Bed}}{\rho }}}=\sqrt{{\displaystyle \frac{-\rho (\overline{u^{\prime }{w}^{\prime }}+\mu \frac{\partial u}{\partial y})}{\rho }}}$$

(5)

where $u^{*}$ is equal to shear velocity, ${\tau }_{Bed}$ is equal to the sum of layered and turbulent stresses near the substrate, and $\rho$ is the specific gravity of the fluid and the viscosity of fluid dynamics. $u^{\prime }$ and $w^{\prime }$ are the deviations of the mean velocity. Due to the distinctive velocity distribution in the streamwise direction, the shear velocity may be determined using the boundary layer characteristics technique.

$$c={\displaystyle \frac{\frac{(\delta *-\theta )u_{max}}{\delta *}}{\sqrt{\frac{-\rho (\overline{u^{\prime }{w}^{\prime }}+\mu \frac{\partial u}{\partial y})}{\rho }}}}$$

(6)

Reynolds shear stress is a descriptive variable of turbulent flow mixing and aids in understanding the characteristics of turbulent fluctuations in open channels. It can be calculated using the following equations, where ρ is the density of water:

$$\mathsf{\tau }=-\mathsf{\rho }\overline{{\mathrm{u}}^{\prime }{\mathrm{w}}^{\prime }}$$

(7)

$$\overline{{\mathrm{u}}^{\prime }{\mathrm{w}}^{\prime }}={\displaystyle \frac{1}{\mathrm{N}}}\sum _{\mathrm{i}=1}^{\mathrm{N}}(\mathrm{u}-\overline{\mathrm{u}})(\mathrm{w}-\overline{\mathrm{w}})$$

(8)

To obtain the amount of turbulence intensity, the root mean square (RMS) of the streamwise, lateral, and vertical velocities have been used, which can be expressed with the following equations [58]

$$\sqrt{\overline{{{\mathrm{u}}^{\prime }}^2}}={\mathrm{u}}_{\mathrm{R}\mathrm{M}\mathrm{S}},\sqrt{\overline{{{\mathrm{v}}^{\prime }}^2}}={\mathrm{v}}_{\mathrm{R}\mathrm{M}\mathrm{S}},\sqrt{\overline{{{\mathrm{w}}^{\prime }}^2}}={\mathrm{w}}_{\mathrm{R}\mathrm{M}\mathrm{S}}$$

(9)

Turbulence decelerates flow by breaking the coherent structures into smaller forms. This fundamental process significantly influences the velocity profile within the cross-section. The magnitude of this effect is directly correlated with the transverse velocity component of flow. The degree of fluctuation-induced energy, which is a consequence of the flow fluctuations, is quantified by the variable of turbulent kinetic energy (TKE). It is written per unit mass and expressed as follows:

$$TKE=0.5\left(\overline{{u^{\prime }}^2}+\overline{{v^{\prime }}^2}+\overline{{w^{\prime }}^2}\right)$$

(10)

In the absence of vegetation inside a meandering canal, the presence of a streamwise pressure gradient and inertial force reduces depth and streamwise velocity at the inner wall [10,59]. Due to this well-established fact, secondary currents are generated within the meandering cross-section, with an outward flow near the water surface and an inward flow near the bottom. This leads to the phenomenon of lateral mass transfer. It is obvious that with the emergence of vegetation into the bending section, which is a common case in natural river corridors, vegetation-induced impact alters the velocity distribution within the cross-section [59,60]. The following subsections present an analysis of the impact of altered velocity distribution due to vegetation emergence on the flow field within the bending section.

3.1. Investigation of Longitudinal Streamwise Velocity Distribution

Figure 3 illustrates the dimensionless streamwise velocity profiles at various vertical sections for both vegetated and non-vegetated scenarios. It is known that velocity profiles in the straight open channels exhibit a logarithmic form. Upon examining Figure 3, it became evident that the velocity profile in the sharply meandering region was subject to alterations due to emergent vegetation, which is an expected outcome. In section S1, the velocity profiles resembled a logarithmic velocity profile for both vegetated and non-vegetated cases. This situation can be associated with the fact that in section S1, the flow in the meandering section is not fully developed within the meandering section yet. Also, in the vegetated cases, relatively higher velocity values were observed along the depth near the inner wall compared to the non-vegetated case. The larger the solid volume fraction of the plant community, the greater the velocity values near the inner wall. This suggests that as plant density rises during the growth process, the influence of centrifugal force due to meandering on the flow pattern within the cross-section diminishes, while the constraining impact of vegetation on lateral momentum transfer becomes more evident.

Figure 3 demonstrates that an increase in vegetation density results in an increase in velocity within the cross-section. Since all the experiments presented in the figures were conducted under identical discharge, this situation requires further explanation. This situation can be explained using insights from relevant literature. Yagci and Strom [61] experimentally showed that the influence of vegetation on stagnation and energy dissipation per unit channel length becomes increasingly significant with the densification of vegetation across the cross-section. In the wake region, each plant element acts as a turbulence generator, producing vortices that dissipate energy. Indeed, it is plausible to expect that these organized flow structures that occur in the wake region of vegetation elements would increase energy dissipation along the vegetated section. Consequently, vegetation growth inside the channel elevates the hydraulic gradient (i.e., an increased reduction in water depth per unit length of the channel in the streamwise direction), as conceptually shown in Figure 4, resulting in an augmentation in vertical velocity profiles in the streamwise direction.

Proceeding toward the centerline of the meandering section (i.e., from S3-3 to S3-5), the presence of vegetation results in the progressive emergence of maximum velocity in the lower layers. A comparison of the velocity profiles in the streamwise direction near the inner and outer walls indicated that the deviation from the logarithmic state is more pronounced on the inner wall. As the solid volume fraction of vegetation increases, the streamwise velocity profiles exhibit a uniform-like pattern near the inner wall (i.e., S5-1). This result aligns with Lopez’s [62] research, which demonstrated that the velocity distribution exhibits a uniform-like pattern vertically in the presence of emergent vegetation [62].

3.2. Investigation of Transverse Velocity Distribution

Figure 5 shows the dimensionless transverse velocity distribution within the vegetated zone, both for vegetated and non-vegetated configurations. The occurrence of both positive and negative transverse velocity values within a certain cross-section indicates the existence of secondary currents. It is a known fact that the existence of centrifugal force in the meandering section induces a lateral slope in the water surface, resulting in an elevation of the water level at the outer wall and a reduction at the inner wall. This induces a lateral hydrostatic pressure gradient within the cross-section, leading to a change in flow direction at the bed and the water surface. However, in the presence of vegetation, this recirculation pattern within the cross-section undergoes a certain degree of alteration due to the presence of the plant community. According to Figure 4, this effect becomes more evident near the end of the curving segment in the vegetated section. More specifically, vegetation’s presence diminishes the influence of centrifugal force, as previously discussed in greater detail in the above subsection.

According to Figure 5, in the absence of vegetation, the minimum transverse velocity values were recorded along the bed surface and towards the inner wall (positive transverse velocity values). Moreover, the maximum transverse velocity values were observed near the water surface, directed towards the outside wall (indicating negative transverse velocity values). For the non-vegetated case and sparsely vegetated case (i.e., lower solid volume fraction), as the flow progresses within the sharply meandering section (e.g., within section S5), the lateral mass-transfer-induced recirculation cell becomes increasingly pronounced and the negative values cover the significant portion of the vertical sections. In all experimental series in section S1, the trend of increasing flow velocity was positive. Hence, the lowest velocity is near the bed surface, and the highest is near the water surface (except for 10 mm of reed vegetation near the outer wall). The average transverse velocity of the flow in the direction of the depth of 13 cm of the channel for the non-vegetated case is equal to 18.19% of the longitudinal velocity of the flow, which shows the strength of transverse currents for this case.

Reed vegetation causes the maximum value of the transverse velocity of the flow from the inner wall to the outer wall near the water level and the lowest value of the transverse velocity near the bed surface in the first half of the bend (up to section S3) near the inner wall and the center of the channel. In the second half of the bend, for reed vegetation of 5 mm, the maximum transverse velocities near the inner wall and near the bed surface have positive values (flow direction from the outer wall to the inner wall).

The transverse velocity in the 10 mm reed vegetation in the second half of the bend causes a change in the velocity profile trend in all areas with positive values from near the bed surface to the water surface (the flow direction is from the outer wall to the inner wall).

The maximum transverse velocity values are near the inner wall, and the transverse flow velocity profile from the bed to the water surface in these areas is almost linear. As the diameter of the vegetation reed increases, the transverse velocity increases in the second half of the bend in the center and near the inner wall. The average transverse velocity of the flow in the direction of the depth of 13 cm of the channel for the case of reeds of 5 and 10 mm increases by 4.35% and 9.68% compared to the non-vegetated case, which shows the effect of increasing the diameter.

3.3. Investigation of Vertical Velocity Distribution

Figure 6 shows the dimensionless profiles of the vertical velocity for the cases with and without vegetation. In the non-vegetated case, the maximum vertical velocity along the channel bends near the water surface has negative values, which shows that water flows from the free water surface to the channel bed surface. Due to the presence of rotational cells caused by secondary flows, the vertical velocity values become positive near the outer wall at the beginning of the bend for section S1 (S1-5) and at the end of the bend of section S5 (S5-1), near the inner wall and the center of the channel. These rotational cells show that the flow rotation occurs from the channel bed towards the water surface.

In the cases with vegetation, the maximum velocities are observed in the range of the inner layer (Z/H ≤ 0.2). The average vertical velocity of the flow in the 13 cm channel for the case without vegetation and reed vegetation of 5 and 10 mm is equivalent to 3.24, 3.6, and 5.44% of the velocity in the longitudinal direction of the flow, respectively. Increasing the diameter of the reed vegetation $\left({\varnothing }_{vegreed}\right)$ causes an increase in the value of the vertical velocity of the flow.

3.4. Reynolds Shear Stresses

The cause of the secondary flow is the difference between the u′ and w′ values, which causes the production of secondary currents and affects the Reynolds stress distribution, u′w′. In turbulent flows, due to strong fluctuations in the velocity components, there is momentum transfer between different fluid layers, and these high-frequency fluctuations are the main cause of Reynolds stresses. The shear velocity can be obtained from the ADV-measured velocity fluctuations as follows [63]:

$$u_{\mathrm{*}}=\sqrt{\left|-u^{\prime }{w}^{\prime }\right|}$$

(11)

Figure 7 shows the dimensionless profiles of Reynolds shear stresses in the presence of vegetation compared to the non-vegetated case. Points with the highest shear stress are susceptible to erosion, whereas areas with lower shear stress are suitable for sedimentation. The areas with potential erosion can be identified by measuring and determining the shear stress in these areas. In the inner wall in the first half of the bend (between Sections S1(S1-1) and S3 (S3-1)), Reynolds shear stress values near the bed, without the presence of vegetation, are significantly higher than those in the outer wall. This indicates a risk for erosion of the inner wall. As the flow moves toward the second half of the bend, the maximum Reynolds shear stress is transferred to the outer wall, showing possible variability in erosion processes along a sharply curved channel.

The stress values in the second half of the bend in the outer wall are greater than the inner wall, which causes the erosion of the outer wall over time, and these results for the non-vegetated case are in agreement with the experimental study of Lee et al. [64], who researched a meandering channel of 90 degrees. They concluded that the highest stress values occur at the position of 70 degrees of the external wall in the meandering channel, and the highest stress value in the arch is about 3.5 times its lowest value.

The trend of Reynolds shear stresses changes in the longitudinal direction of the flow for the cases with and without vegetation near the bed surface, and the center of the channel bend includes positive and negative numbers, which indicate the presence of secondary flows, rotating cells, and vortices in the sections. The maximum values of the Reynolds shear stress in the longitudinal direction of the flow near the inner wall for reed vegetation are 10 and 5 mm along the bend of the channel near the bed, which are 2.8 and 3.2 times the Reynolds shear stresses near the outer wall, respectively, and, with the increase in flow depth, decreases from near the bed to the water surface. So, with the increase in the diameter of the vegetation $\left({\varnothing }_{vegreed}\right)$, Reynolds shear stresses decrease from near the bed to the water surface and become linear in the second half of the bend.

The investigation of transverse velocities in three-dimensional flows is important due to the existence of secondary flows. For this reason, the Reynolds shear stress distribution in the transverse direction $\mathsf{\tau }=-\mathsf{\rho }\overline{{\mathrm{v}}^{\prime }{\mathrm{w}}^{\prime }}$ is important (see Figure 8). In the non-vegetated case, in most of the measured points, especially the second half of the bend, the Reynolds shear stresses in the transverse direction are negative. The maximum stress is in the range of 0.2 < z/h < 0.4, except for the points near the inner wall at the beginning of the bend and near the outer wall at the end of the bend, which is due to the presence of vortices and rotating cells caused by the secondary flow. At these points, the maximum values of Reynolds shear stresses are different. In the vegetated cases, the maximum Reynolds shear stresses are near the bed surface, and the lowest is near the water surface. Figure 8 shows the Reynolds shear stresses in the transverse direction of the flow for the cases with and without vegetation.

For the case of reed vegetation of 10 mm in diameter, the maximum Reynolds shear stresses are in the transverse direction of the flow in the center of the channel, and they are 2 and 10 times higher than the lower Reynolds shear stresses found near the inner and outer walls, respectively. For reed vegetation of 5 mm, the maximum Reynolds shear stresses in the transverse direction of the flow are near the inner wall, which is 4.5 and 2 times higher than the Reynolds stress in the center of the channel and near the outer wall, respectively (Figure 8).

3.5. Turbulent Intensity

Fluctuation squared (RMS) scores were used to obtain the indices of disturbance fluctuations and their intensity. This design is defined as $\sqrt{\overline{{w^{\prime }}^2}},\sqrt{\overline{{v^{\prime }}^2}},and\sqrt{\overline{{u^{\prime }}^2}}$, and positive and negative fluctuations can be removed, as well as a clearer picture of the amount of velocity fluctuations. Turbulence has general effects on decelerating and decelerating the flow. The magnitude of this deceleration is a function of the velocity component and the initial measurements. Figure 9 shows the dimensionless distribution of turbulence intensity profiles for the cases with and without vegetation.

The distribution of turbulence intensity in the longitudinal and transverse directions for the case without vegetation is near the outer wall in the first half of the bend and near the inner wall in the second half of the bend due to the presence of rotating cells and the increase in the secondary flow, so that the maximum turbulence intensity outside is close to the water level. At other points of the bend, the turbulence intensity presents a decreasing trend, so its maximum is at the level of (Z/H ≤ 0.2)). The distribution of turbulence intensity among the vegetation in Sections S2, S3, and S4 has an increasing trend, so that the maximum turbulence intensity values are near the water surface. In section S1 (before vegetation), near the inner wall (longitudinal and transverse flow direction), the distribution of turbulence intensity due to the maximum gradient of negative pressure in this area causes the flow velocity to be maximized from the bed surface to near the water surface.

The moment the water flow hits the emergent rigid reed vegetation in its path along the meandering channel, it causes a decrease in the velocity behind the reeds of the vegetation, which causes the maximum intensity of the flow turbulence in these areas and the formation of horizontal (Von Karman) vortices, near the surface of the water. The maximum values of the turbulence intensity in the longitudinal and transverse directions of the flow for the case with the 10 mm reed vegetation are along the channel bend near the inner wall, which, in the second half of the bend, has an increasing and uniform trend from near the bed surface to the water level. Moreover, the maximum turbulence intensity values in the longitudinal and transverse directions of the flow for reed vegetation are 5 mm along the bend of the channel, respectively, in the center of the channel and the inner wall.

For the cases without vegetation, as well as for the cases with vegetation, the values of turbulence intensity are the highest in the transverse direction. Then, they are the highest in the longitudinal and vertical directions, respectively. So, with the increase in reed vegetation diameter (${\varnothing }_{vegreed})$, the turbulence intensity values in the transverse direction of the flow increase more than the turbulence intensity values in the longitudinal and vertical directions. The intensity of disturbance in the longitudinal and transverse directions in the channel arch is always higher than that of vertical disturbance [65,66].

3.6. Turbulent Kinetic Energy

From an energy perspective, the amount of kinetic energy carried by velocity fluctuations is called turbulent kinetic energy (TKE). Turbulent kinetic energy represents the average energy per unit mass related to turbulence eddies generated through the interaction between velocity and pressure fluctuations along the flow. It spreads and eventually dissipates through viscous forces. McLean et al. [67] stated that the kinetic energy spreads in the direction of the flow through the opposition between velocity and pressure fluctuations, and finally dissipates through viscous forces.

The dimensionless profiles of turbulent kinetic energy (TKE) for the cases with and without vegetation are compared in Figure 10. In the case of vegetated flows, turbulent kinetic energy increases in all cases, from the minimum levels near the bed surface to the maximum values near the water surface. Except in section S1 (before the vegetation) near the inner wall, the reason for the maximum turbulent kinetic energy near the water surface is that when the fluid passes through the reed vegetation, it slows down, and this velocity reduction creates a pressure gradient. The negative is behind the straws and near the surface of the water. This pressure gradient causes the fluid to move from the surrounding areas to these areas in the transverse direction, and this flow in the transverse direction creates horizontal Von Karman vortices.

While the maximum turbulent kinetic energy in the case without vegetation is near the bed surface, the changing trend is decreasing from the bed surface vicinity to the water level, except in the first half of the bend near the outer wall and in the second half of the bend near the inner wall, which is due to the existence of the centrifugal force in the bend of the channel and the difference in the water depth level on both sides of the channel wall causing a positive pressure gradient in these areas, which causes a decrease in velocity and the formation of a vertical vortex at these points. So, with the increase in the diameter of the reed vegetation $\left({\mathrm{\varnothing }}_{vegreed}\right)$, the amount of turbulent kinetic energy in the channel bend increases, near the outer wall.

4. Discussion

The present study is based on a simulation of a real meandering section of a gravel-bed river in northern Iran. The experiments simulated distinct conditions of the modelled meandering channel section, featuring a regular arrangement of rigid emergent vegetation positioned at the 90-degree coarse bed surface channel bend. The study examined both a case without vegetation and two types of reed vegetation: one with 5 mm diameter reeds and another with 10 mm diameter reeds. The experiments focused on assessing how the flow field was modified, including probing changes in the longitudinal, transverse, and vertical velocities, Reynolds shear stresses, turbulent intensities, and turbulent kinetic energy. The findings of this study reveal that the flow field in different directions, Reynolds stress, turbulence intensity, turbulent kinetic energy, sediment, and stem sizes change significantly along curved channels’ inner and outer banks.

Stem size played a significant role in turbulence in the curved channels, enhancing instability of the bed and river plan, confirming Jiang et al. [48] results. The 10 mm reed vegetation in the channel bend caused a wake (reversal) of the longitudinal flow velocity at the channel’s center, resulting in a linearized longitudinal velocity profile in the latter half of the bend. The maximum longitudinal velocity was observed near the inner wall along the bend. In contrast, the 5 mm vegetation produced maximum longitudinal velocity just beneath the water surface in the first half of the bend, near the inner wall, and in the second half of the bend, the maximum was at the channel’s center. Also, zig-zag velocity distribution from the bed toward the water surface shows some negative values, confirming the results of Sahoo and Sharma [46] and Taye et al. [47] in curved channels. The convex form of Reynolds stress distribution is not a general pattern along the curve, as it was reported by Sahoo and Sharma [46] and Taye et al. [47].

Vegetation led to a maximum transverse velocity in the first half of the bend, particularly near the water surface, directing flow from the inner wall toward the outer wall (positive value) in both the center and inner wall of the bend. In the second half of the bend, as the diameter of the vegetation increased, the transverse velocity profile became almost linear with positive values, enhancing the transverse velocity in the center and near the inner wall, thus contributing to the channel’s meandering.

As the diameter of the vegetation increased, the vertical velocity also increased along the channel bend. The maximum vertical velocity values were found within the range of Z/H ≤ 0.2, directed towards the channel bed surface, with maximum values occurring near the water surface. Also, vegetation density modified the velocity and turbulence distributions, showing a non-classic pattern due to the heterogeneity of vegetation patches, as reported for straight channels by Nepf [68] and Yang et al. [69].

Generally, with an increase in reed diameter, the Reynolds stress decreased throughout the channel bend, from near the bed surface to the water level. This caused a linearization of the Reynolds stress profile in the second half of the bend, with maximum Reynolds stress in the longitudinal direction observed near the inner wall. Maximum values of Reynolds stress, with negative values in the transverse direction, were noted in the non-vegetated bed surface within the range of 0.2 < Z/H < 0.4.

Vegetation led to maximized turbulence intensity along the reeds on the water surface. As the diameter of the vegetation increased, the intensity of the transverse flow disturbances rose compared to the intensity of the longitudinal and vertical turbulence, resulting in a linear progression of turbulence intensity changes. Interaction of turbulence and vegetation with different densities impacted the mean and turbulent flow field, showing different distributions from the bare straight (e.g., Stoesser et al. [42]) and the curved channels (e.g., Taye et al. [47]). Likewise, herein the presence of vegetation also resulted in the maximization of turbulent kinetic energy near the outer wall of the channel and along the reeds on the water surface, with these values increasing as the diameter of the reeds increased.

The findings from this study present a new scientific approach to flood control, water pollution management, and river restoration. By strategically arranging vegetation and selecting appropriate diameters along river bends, it is possible to influence stress and velocity distributions, subsequently reducing erosion of the channel walls. Additionally, reed vegetation can enhance the intensity and kinetic energy of turbulence in flowing water, aiding in the transfer of suspended or coarse particles. Altering the density and arrangement of vegetation in rivers can control the spread of pollutants, thereby improving water quality and environmental conditions. However, it is essential to consider the impacts of reed vegetation on water flow to mitigate potential issues and safeguard biological and ecological processes, which are crucial for effective river engineering management. Future research should consider using modern sensors to assess the geomorphic potential the modifications in the turbulent flow field have [70].

5. Conclusions

Experiments were conducted in a meandering channel with three different vegetation states: non-vegetated, 5 mm reed vegetation, and 10 mm reed vegetation, at five cross-sections (0°, 30°, 45°, 60°, and 90°) to analyze various hydraulic parameters, including longitudinal, transverse, and vertical velocities, Reynolds shear stress, turbulence intensity, and kinetic energy. The key findings are summarized as follows:

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With 10 mm reed vegetation, the longitudinal flow velocity in the channel center increases, linearizing the velocity profile in the second half of the bend, with the maximum velocity occurring near the inner wall. In contrast, with 5 mm reed vegetation, the maximum longitudinal velocity is observed just below the water surface in the first half of the bend, near the inner wall, and shifts to the channel center in the second half.

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Vegetation influences the maximum transverse velocity, which is highest near the water level in the first half of the bend, moving from the inner to the outer wall. Larger vegetation diameters lead to a more linear transverse velocity profile, with maximum values near the inner wall.

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Increased vegetation diameter enhances vertical velocity along the bend, with maximum values observed in the range of Z/H ≤ 0.2, both towards the channel bed surface and near the water surface.

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Larger reed diameters reduce Reynolds shear stresses throughout the bend, creating a linear stress profile in the second half and shifting the maximum stress position closer to the inner wall. The maximum Reynolds shear stresses in the transverse direction are negative in the Z/H range of 0.2 < Z/H < 0.4.

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Vegetation maximizes turbulence intensity near the water surface. Larger reed diameters enhance transverse turbulence intensity relative to longitudinal and vertical turbulence, resulting in a linear turbulence profile from the bed surface to the free water surface in the second half of the bend.

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Vegetation increases turbulent kinetic energy near the outer wall and along the water surface, with higher values associated with larger reed diameters.

These findings provide key insights for flood control, water pollution management, and river restoration. By arranging vegetation and selecting appropriate reed diameters, we can reduce channel wall erosion and improve water quality through increased turbulence that enhances particle transport. The effects of reed vegetation on water flow and ecology should be carefully considered to holistically improve the management of fluvial systems.