Effects of Channel Width Variations on Turbulent Flow Structures in the Presence of Three-Dimensional Pool-Riffle

Abstract

Changes in the width of channels or rivers that have three-dimensional pool-riffle can affect the key parameters of river engineering and flow resistance. Understanding the effect of width changes on flow structures helps to control erosion and sedimentation in coarse-bed rivers and better design ecological restoration projects. The present study investigates the effect of the sequential pool-riffle and its interaction with the bank narrowness on the turbulent flow characteristics. For this purpose, an experimental study was conducted in variable and fixed width flume with an aspect ratio greater than five. The results showed that when the flow decelerates (entrance of the pool), the negative and low longitudinal velocities expand as the flow depth increases. From both sides of the central axis, longitudinal velocities decreased when entering the middle part of the pool and reduced the flow width. The changes in the maximum turbulence intensity values, from the central axis towards the channel bank, in the variable and fixed width modes had an increasing trend. In all three longitudinal directions along the flume, the maximum turbulence intensity and the maximum Reynolds shear stress in the variable width mode were larger than those in fixed one. Knowledge of the flow pattern along a variable width stream and better understanding of velocity and Reynolds stress distribution will help engineers to better estimate the controlling parameters in river restoration and improve hydraulic models’ performance.

1. Introduction

The formation of irregular bed geometry and three-dimensional bedforms is inevitable in natural channels and rivers due to flow regime changes and channel width variations. The pool-riffle sequences are known as the main bedforms in coarse-bed rivers, defined as deeper and shallower parts of the bed, respectively. Many researchers discuss the presence of these forms in mountainous rivers [1,2]. Understanding the flow characteristics in river systems can help managers and engineers to better design hydraulic structures and stream restoration projects. Experimental simulation of river characteristics is a promising method to investigate the flow structure.

Various studies, including field studies [3,4,5,6], experimental studies [7,8,9,10,11], and numerical studies [12,13,14] investigate the effects of pool-riffle bedforms on flow characteristics. In the experimental study of [15], it was found that width contraction causes a local increase in the upstream water level gradient, the production of jet flow in the center of the pool, and the creation of vortices in the turbulent flow area in the downstream of the bed crest. The shear layer region between the vortex and the water jet is formed downstream of the bed crest. The width change in the narrowing areas controls the flow’s acceleration and deceleration, influencing the production of turbulence. Turbulence eddies are formed in the flow separation regions downstream of the crest and disappear during the movement downstream of the pool. MacWilliams et al. (2006) [16] investigated the reversal velocity hypothesis based on a field study with two- and three-dimensional numerical modeling. Their results show the occurrence of reversal velocity and average shear stress with increasing flow discharge. In addition, the secondary flows in the cross-section of the pool increase significantly with the increase in discharge. In addition, the narrowing of the channel causes the flow convergence and development of accelerating flow in the pool section, and the jet stream happening in width decreases downstream. Shear stress and velocity reach their maximum value in this region, and larger particles move in the pool region. Divergence in the pool’s tail and upstream riffle causes a decrease in the velocity, and, as a result, the deposit of sediment particles [16]. Yang et al. (2006) [17] and Dey and Lambert (2005) [18] determined the velocity and Reynolds distributions in non-uniform flows, showing that Reynolds stress has convex and concave shapes in decelerating and accelerating flows, respectively. In another study, it was indicated that the maximum and minimum shear stresses are phase-shifted over the bedform; the maximum shear stress occurs at the upstream and downstream of the riffle at high and low flow, respectively [19]. Soltani et al. (2020) [20] investigates turbulent flow on natural river bedforms and found that Reynolds stress and turbulence intensity follow a convex form in the main flow direction for accelerating and decelerating flows in central axis profiles. They conveyed more turbulence intensity at the entrance slope (pool part with decelerating flow) than at the exit slope (riffle part with accelerating flow) [20]. In another field study, researchers considered a reach of Babolroud river with width variation and found that the vertical components of the velocity near the pool bed are oriented downward, and upwards near the water surface, while in the riffle part, these components are oriented towards the bed in gravel-bed rivers, emphasizing the effect of width changes, flow non-uniformity, and changes in input sediments on the morphodynamics of the pool-riffle sequence [21]. Hassan et al. (2023) [22] determined the sediment mobility, step stability, and sediment storage in a step-pool reach in British Columbia in Canada. They revealed that sediment mobility is not dependent on the flow magnitude but is controlled by sediment supply [22]. Based on their research, the amount of width and wavelength change were known as significant factors affecting the sequence of pools and riffles. In the channel with a fixed width, doubling the input sediment rate led to a 30% increase in bed slope, while in the channel with variable width, the increase in slope was milder (about 7%). Moreover, at high flow rates, the reversal distribution of shear stress was observed in the bed’s pool [23]. In the experimental study of Najafabadi et al., 2018 [24] a two- and a three-dimensional model of a pool-riffle sequence was formed in a flume with a fixed width. They investigated and compared the hydraulic characteristics of the flow, including velocity, Reynolds stress, and the occurrence of flow separation. In the presence of two-dimensional pool and riffle, the results showed that the velocities in the direction of flow near the bed and on the upstream riffle bed are high, and that they decrease during the decelerating part of the flow. The trend of changes in velocity averaged in depth in the transverse direction shows that the velocities are higher near the central axis than those in the channel bank, indicating the flow’s convergence upon entering the pool part. Furthermore, the results indicate that the highest Reynolds shear stress occurs at the entrance slope of the pool, and the lowest turbulence intensity was observed in the middle of the pool [24].

Researchers have paid less attention to the impacts of three-dimensional pool and riffle bedforms along with the variation in width, based on the review of the above sources. In other words, studies have been widely conducted on two-dimensional bedforms, and most experiments have been conducted in channels with fixed widths. It should be noted that in some of the past works, the width variation in the laboratory channel was made only to check the morphology of the bed considering the rate of sediment input into the channel in the presence of bedforms, and the movement of sediment particles in the narrowing and opening of the channel plan [25,26,27]. In these studies, despite considering variations in the channel width, the flow structure and the effect of three-dimensional bedforms on the amount of flow turbulence has not been considered. The characteristics of turbulence and the estimation of critical parameters of river engineering are affected by the changes in flow width, which is one of the most important parameters that controls flow deceleration and acceleration [28]. The novelty and contribution of the present study is to investigate the effect of variations in the channel width in the presence of the three-dimensional pool and riffle on the turbulent flow structure in two cases of variable width and fixed width. This is done by a three-dimensional artificial pool-riffle with a variable width flume to simulate a natural environment in coarse-bed rivers.

2. Materials and Methods

2.1. Experimental Setup

In this study, a rectangular cross-section flume with 11.25 m length, 0.9 m width, and 0.7 m depth is used. The flume allows the observation and control of flow conditions through tempered glass banks. At the beginning of the flume, a stilling basin and a bar screen stabilizes the flow. A vertical gate controls the regulation of the flow depth at the end of the flume. Due to the horizontal installation, the flume cannot be adjusted for slope automatically, but it can be altered by modifying the gravel thickness along its path. The flow discharge is 30 $\frac{lit}{s}$. By using an ADV (acoustic doppler velocimeter, Vectrino+ made by Nortek, Norway), 3D velocity measurements can be made along the length and across the flume with a high accuracy. The schematic diagram of the experimental setup is illustrated in Figure 1.

This study uses gravel to build an artificial pool and riffle in the flume. The particle size is selected for the experiment to ensure there is no washing and moving in the bed. To create a pool and riffle bedform, gravel particles with a diameter of 10 mm were used. A geometric standard deviation ${\mathsf{\sigma }}_g$, granulation coefficient $G_r$, and average particle size $d_g$ were calculated based on the Equations (1)–(3) for the selected samples:

$$\sigma g={\left(\frac{d_{84}}{d_{16}}\right)}^{\frac{1}{2}}$$

(1)

$$G_r=\frac{1}{2}\left(\frac{d_{84}}{d_{50}}+\frac{d_{50}}{d_{16}}\right)$$

(2)

$$D_g={\left(d_{16}·d_{84}\right)}^{\frac{1}{2}}$$

(3)

where $d_{84}$, $d_{50 }$, and $d_{16}$ are the diameters of the bed particles, of which 84%, 50%, and 16% particles are smaller than given diameter, respectively in the grading curve. Particle uniformity leads to geometry standard deviation parameters $\sigma g$ and granulation coefficients $G_r$ near 1 [21]. These parameters are summarized in

Table 1. Characteristics of particles used in this research.

Dg (mm)	Gr	$\mathit{\sigma }\mathit{g}$	D84 (mm)	D50 (mm)	D16 (mm)	Type of Bed
12.37	1.39	1.39	13	10	6.73	Gravel

.

To perform this study, the entrance and exit slope angles of the pool and riffle were considered 15° and 17°, respectively. This selection is based on both the literature and the extensive experience of this study authors working in the area of river hydraulics to find dominant slopes of entrance and exit in pool and riffle in gravel-bed rivers. The literature review also confirms that the selected slopes in this study are within the observed range in rivers. A similar slope range has been used in other projects [8,24]. Accordingly, the artificial bedforms were constructed with these entrance and exit slopes by measuring the length and height of the bedforms precisely in rivers.

For the flume’s bed preparation, before starting the tests, the slope of the bed was 0%. A series of artificial pools and riffles were formed along the flume from 6.8 m to 8.85 m. After the last constructed bedform in the flume, 2.4 m of the flume length was covered with gravel that had a zero slope and a 0.2 m thickness. In addition, no sediment was transported into the three-dimensional pool-riffle bed when water flows through the flume at a steady discharge of 30 $\frac{Lit}{s}$.

To generate the variable width along the flume a structure made of PVC (Polyvinyl Chloride) material covered with a transparent fibrous sheet was installed along the vertical walls. Automatic CNC (Computer Numerical Control) machines were used to cut PVC into semi-ellipses with a large diameter of 1.2 m and a minor diameter of 0.22 m. The flume with variable width is shown in Figure 2 with a pool-riffle sequence. The 3D bed form used for this study has a trapezoidal shape.

A test was conducted in the flume under the following hydraulic conditions (

Table 2. A summary of hydraulic conditions and experiments.

Water Flow  $\left(\frac{\mathit{l}\mathit{i}\mathit{t}\mathit{r}}{\mathit{s}}\right)$	Depth of Water (cm)	Fr	$\mathbf{Re}\times$  ${10}^5$
30	14	0.33	0.31

). The banks’ effects on the velocity profiles were studied by taking 11 velocity profiles each along the central flume axis, at 0.12 m from the axis, and at 0.24 m from the axis (33 readings) during each series of tests. Because of the flume symmetry, all test series were only conducted on the right half.

A support base was designed to be installed perpendicularly to the channel bank in order to install the ADV in the required positions. The ADV and support base is shown in Figure 3.

This research uses an ADV with a measurement accuracy of 0.5%. The device’s audio frequency was 10 MHz with a distance from its center of sampling volume of 50 mm. All measurements were made at 200 Hz and 120 s with 24,000 measurements in each point. Owing to the ADV’s inherent limitation, velocity measurements along the vertical axis were limited to a range from 4 mm above the bed to about 50 mm below the water surface [29]. The ADV is affected by Doppler noise and spikes because of the shifting phase between the outgoing and incoming pulses [30]. In this work, the velocity data were filtered using WinADV32 (version 2.024) software. Spikes were removed using the phase–space threshold despiking filter [30], with a minimum acceptable correlation coefficient of 70% and signal-to-noise ratio of 15.

There is a minimum of 20 velocity measurement points in each velocity profile, and 50% of the measurement points are located in the inner layer (20% near the gravel bed) and 50% in the outer layer of the boundary layer (total depth of flow). The ADV was placed in 11 different positions (sections 1 to 11) with varying distances from the channel’s beginning in these experiments. The measurements were taken at depth of 14 cm from the bottom of three sections that were 10 cm, 20 cm, and 45 cm from the channel bank. Figure 4 shows where the ADV was deployed to collect 3D velocity data in this study.

2.2. Basics of Theory and Used Relationships

2.2.1. Calculation of Shear Stress

In this study, Reynolds shear stress $({\tau }_{xz}=\rho u_{\ast }{}^2)$ is calculated using boundary layer characteristics [31]. Calculations are performed using the entire velocity profile, which is based on boundary layer theory. Shear velocity is calculated using Equation (4) as follows [31]:

$${\mathrm{u}}_{\ast }=\frac{({\mathsf{\delta }}_{\ast }-\mathsf{\theta }){ \ast \mathrm{u}}_{\max }}{4.4{\mathsf{\delta }}_{\ast }}$$

(4)

A velocity profile is determined by $u_{max}$, which is the maximum point velocity, and $\theta$ and ${\mathsf{\delta }}_{*}$, which are the displacement thickness and momentum thickness, respectively, as determined by Equations (5) and (6):

$${\delta }_{\ast }={{\displaystyle \int }}_0^h\left(1-\frac{u}{u_{max}}\right)dy$$

(5)

$$\theta ={{\displaystyle \int }}_0^h\frac{u}{u_{max}}\left(1-\frac{u}{u_{max}}\right)dy$$

(6)

From the bed to the water surface, velocity values are used in the boundary layer method. The ADV is not capable of measuring velocity near the bed and water surface; hence, velocity values in these areas are extrapolated in this region.

2.2.2. Calculation of Turbulence Intensity

The normalized turbulence intensity is computed as below [32]:

$$NRMS=\frac{\sqrt{2k/3}}{u_{\ast }}$$

(7)

where k is the kinetic energy, calculated by Equation (8):

$$k=\frac{\overline{u^{\prime }{u}^{\prime }}+\overline{v^{\prime }{v}^{\prime }}+\overline{w^{\prime }{w}^{\prime }}}{2}$$

(8)

where $u^{\prime }$, $v^{\prime }$, $w^{\prime }$ are velocity fluctuations in flow direction, lateral and vertical directions, respectively.

3. Results and Discussion

3.1. Variable Width Mode

3.1.1. Flow Velocity

In Figure 5a–c, velocity contours in three directions are displayed along with longitudinal directions at 12 and 24 cm from the central axis of the flume. The figure shows that velocity values in the central axis are lower than in two other directions. In all directions, the middle areas of the entrance slope (decelerating flow) and the middle part of the bedform (deepest part) show flow separation, where the velocity values are negative. As indicated, negative velocities were observed near the channel bank. However, in the study of Fazel Najafabadi et al. [14], in a fixed-width flume with 3D bedforms, negative velocity and flow separation were not observed near the banks, and the length of the flow separation zone increased by moving away from the channel banks.

In addition, observed is the reduction in maximum velocities in the longitudinal direction located 24 cm from the central axis (the closest axis to the bank) compared to the other two longitudinal directions. Therefore, the maximum velocity occurred near the water surface in all three longitudinal directions and all parts of the bedform, confirming the results of Najafabadi et al. (2018) [24].

Figure 6a–c shows the lateral velocities (v) in three longitudinal directions. The lateral velocities are lower in the central axis direction than the other two longitudinal directions; however, a trend is also visible in the number of lateral velocity changes approaching the bank (from the central axis to 24 cm), so the values of lateral velocity in the direction of 24 cm from the central axis are at their maximum. On the entrance slope, which extends to the water level, a strong core of negative lateral velocities is observed in the central axis of the flume. At 12 cm from the central axis, moving towards the bank, a similar core can be seen in the second half of the bedform’s middle part, extending throughout its depth. Negative lateral velocities occupy most of the longitudinal profile closest to the channel bank (24 cm from the central axis), except for a small area in the middle part. Generally, negative lateral velocities occupy more surface area than positive ones in all three longitudinal axes.

In Figure 7a–c, the vertical velocity (w) contours in the three longitudinal directions indicate that negative velocities are often present in longitudinal profiles in the three directions around the central axis and 12 and 24 cm from it. The presence of obstacles results in the change in flume width along the channel banks. This change generates the vortices drifting opposite to the flow direction, resulting in more negative velocity near the banks than at the central axis. Despite that, the surfaces occupied by the lowest (most negative) vertical velocities are in the middle part of the pool. The reason for occurrence in middle of bedform is the presence of strong unfavorable pressure gradient in this region where the flow separation is developed, as revealed by negative velocity values. The results indicate that positive vertical velocities are often near the bed and on the exit slope (accelerating flow in riffle). Near the bed on the entrance slope, a small core of positive vertical velocities is observed at 24 cm from the central axis. Based on Najafabadi et al. (2018) [24], in non-variable width, the core has the highest vertical velocities at different distances from the bank in all longitudinal directions confirmed by the present study.

3.1.2. Turbulence Intensity

Figure 8a–c illustrates the turbulence intensities in the flow direction corresponding to three longitudinal directions. The results show that turbulence intensity increases from the central axis towards the bank, presenting the maximum turbulence intensity at 24 cm from the central axis, due to velocity gradients. High turbulence intensity covers the entire exit slope and riffle part downstream from the bed to the water surface in the central axis direction. In the upstream part of the entrance slope, exit, and riffle part of the upstream, high values of turbulence intensity appear in the longitudinal direction for 12 cm from the central axis. The maximum turbulence intensity values occur at the downstream riffle section or pool entrance extending to the deepest part of the pool. The main reason for this pattern is the presence of 3D bedform, which changes the classic distribution of turbulence intensity, showing a convex distribution for the turbulence intensity around the crest rather than a concave distribution. Near the bed, the turbulence intensity increases near the crest of bedform due to the significant effect of the pressure gradient. For this reason, in the beginning of pool the flow separation occurs due to riffle crest, a wake zone with a strong unfavorable pressure gradient, leading to the development of a high turbulence region.

3.1.3. Reynolds Shear Stress

Figure 9a–c shows the Reynolds shear stress $({\tau }_{xz})$ in the longitudinal directions of the central axis and 12 and 24 cm from the central axes, respectively. The results show that the negative values of Reynolds shear stress in all three directions are insignificant. In addition, the negative values of Reynolds shear stress are limited to small parts of the surfaces of the profiles presented in three directions, which are much less than the positive shear stress values. The occurrence of negative Reynolds shear stress values has also been reported in Najafabadi et al. (2018) [24] and MacVicar and Roy (2007) [33]. The cores of high values of Reynolds shear stress are often located near the bed decreasingly extending to the water surface. high Reynolds shear stress values are observed in all three axes of central and 12 and 24 cm from the central axis, in the deepest parts of the bedforms. This is because there is a direct relation between the flow depth and the Reynolds shear stress. The highest depth occurs in the middle of pool where the maximum Reynolds shear stress is observed. This is true for the flows with pressure gradient and uniform flows, as it is governed by equation τ = γhSf, where Sf is the energy slope.

3.2. Fixed Width Mode

3.2.1. Flow Velocity

Longitudinal velocity contours for the fixed width channel are displayed in Figure 10. The results show that negative velocities occur in all three directions. The magnitude of these values is equal in all three longitudinal directions, occurring in the entrance slope where the flow is decelerating near the bed. Due to the inertia of the flow, there are also negative values in the longitudinal direction of the central axis in the small part of the middle bedform. By comparing this section’s results with the variable width mode of a 14 cm depth, both modes display a similar pattern of negative velocities. However, the absolute value of the negative values of the longitudinal velocities in all three directions is more significant in the case of variable width than that of fixed width.

Further, the results show that maximum longitudinal velocities appear near the water surface and decrease toward the bed. In the upstream part of the riffle and the exit slope, the velocity near the bed is higher than in other parts. Such a result is reasonable for the velocity in the flow direction. On the other hand, the maximum velocity values in the two axes, 12 cm and 24 cm from the central axis are equal and lower than the central axis direction. A similar pattern of changes in the values of maximum velocities was observed in three longitudinal directions in the case of the 14 cm depth variable width. By comparing the values of the maximum longitudinal velocities in two cases of 14 cm depth with variable and fixed width, values in the case of variable width are higher than fixed width. The issue is due to the reduction of the flow cross-section area in the presence of the obstacle and the flow velocity’s relative increase.

Figure 11a–c shows the graphs of the lateral velocities (v) in the central axis’s longitudinal direction and two other longitudinal axes located at 12 and 24 cm from the central axis. Generally, when approaching the channel banks, the lateral velocities are influenced more by bank roughness, as a result showing higher lateral velocities than those in the central axis.

As indicated, most of the longitudinal profile surfaces in all three directions are occupied by minimum values of vertical velocities (Figure 12), and the cores of negative velocities are in the middle areas of the bedform and the entrance slope. High values of vertical velocities in all three longitudinal axes occurred in the accelerating flow on the exit slope near the bed. The results obtained in this section agree with Fazlollahi et al., (2015) [9]. A comparison with the variable width mode shows that the maximum vertical velocities occurred on the entrance slope in addition to the exit slope along the longitudinal central and 24 cm axes from the central. In the case of variable width, the maximum vertical velocities are more visible in the longitudinal central axis, and in the case of fixed width, in the longitudinal axis 12 cm from the central axis. Both fixed-width and variable-width modes display the lowest (most negative) vertical velocities in the longitudinal direction.

3.2.2. Turbulence Intensity

As indicated in Figure 13, high values of turbulence intensity in all three directions are spread in the upstream part of the bedform for the whole depth. In addition, in the longitudinal axis 24 cm from the central axis, the turbulence intensity is the maximum in the riffle part for the entire flow depth. Low values of turbulence intensity near-bed are often observed in the middle regions of the depressed bedform. The present results agree with the findings of Fazlollahi et al., (2015) [9] and Fazel Najafabadi et al. (2017) [14].

The maximum turbulence intensity values increase from the central axis to the closest longitudinal axis to the bank (24 cm from the central axis). In the longitudinal direction closest to the bank, the maximum turbulence intensity values are more than in the other two axes. When comparing these results to the variable width with the 14 cm depth mode, the maximum turbulence intensity values are observed on the riffle part upstream and downstream. In addition, the maximum turbulence intensity is higher in variable width than that of the fixed width.

3.2.3. Reynolds Shear Stress

The results of Reynolds shear stress $({\tau }_{xz})$ in the longitudinal direction show that negative shear stress values occur in all three directions (Figure 14a–c). Negative shear stresses occur in the pool and riffle parts in other studies [24,33]. The location of negative shear stresses is often near the water surface and in the middle of the bedform. In addition, these negative values are observed in the upstream part of riffle. Positive stresses occupy the major surface of the longitudinal profiles in all three longitudinal axes. The maximum Reynolds shear stress occurred near the bed and in the decelerating flow section. These results are similar to the findings of Fazel Najafabadi et al. (2017) in an experimental study on the 3D pool-riffle sequences [14]. In both studies, the Reynolds shear stress had convex distribution in the decelerating flow. It is notable that the maximum value in the variable-width stream occurs in the middle of pool.

The maximum shear stress values from the central axis towards the flume bank display an increasing trend. Comparing this section’s results with the variable width and the 14 cm depth mode show that in the variable width mode, the highest shear stress values were near bank. The location of maximum shear stresses in the longitudinal directions in the case of variable width are different from the fixed-width case; therefore, the values mentioned in the variable width case are often located at the end of the pool’s flat part. The results showed that the values of the maximum Reynolds shear stress in all three longitudinal axes are less in the case of constant width than in that in variable width.

4. Conclusions

This experimental study was conducted in a variable-width flume with 11.25 m length, 0.9 m width, and 0.7 m depth with artificial pool-riffle sequences in order to investigate turbulent flow characteristics. The main findings of this work are presented below:

• In the entrance of the pool, where the flow decelerates and flow depth increases, the longitudinal velocities display low and negative values. Upon entering the middle part of the pool and reducing the flow width, longitudinal velocities decreased on both sides of the central axis.
• In the case of variable width, the trend of changes in turbulence intensity from the central axis towards the bank increases, showing the maximum turbulence intensity in 24 cm from the central axis (the closest longitudinal direction to the bank). Turbulence intensity displays the highest value at exit slopes in downstream and upstream of riffles.
• Comparing the results of constant and variable widths (14 cm depth), a similar pattern of negative velocities is observed. However, the absolute value of the negative longitudinal velocities in all three axes is greater when the width is variable compared to fixed. Based on the numerical values of longitudinal velocities, the highest values of longitudinal velocities are observed in the central axis of the flume. Meanwhile, the maximum velocity values 12 cm and 24 cm from the central axis are equal and lower than in the other axes. The maximum transverse velocities in the middle region of the pool are higher in the variable width mode than in the fixed width mode.
• Comparison of the fixed and variable width modes shows higher maximum vertical velocities in most cross sections in the variable width mode. The maximum vertical velocities are also observed on the exit slope for both modes for riffles where the flow is accelerating.
• In regard to fixed width, the maximum turbulence intensity values tend to increase from the central axis towards the closest longitudinal axis to the bank (24 cm from the central axis). The minimum turbulence intensity near the bed in the variable width mode is often located in the pool. From the central axis toward the flume bank, the maximum turbulence intensity values increase in the variable width mode, and the maximum turbulence intensity in all three axes is higher in the variable width mode than in the fixed width mode.
• Based on a comparison of maximum shear stress values from different longitudinal axes, the highest value is near the bank in fixed width mode, and the maximum shear stress values decline from this axis to the central axis. In addition, the minimum (most negative) shear stress values happen along the central axis. For variable width, the highest shear stress values are near the bank. In the mode of variable width, maximum shear stresses are different than in the fixed width. This means that the mentioned values in fixed width are usually in the middle of the entrance and exit slopes. In all three longitudinal directions, the maximum Reynolds shear stress is higher with variable width than with fixed width.

There are some limitations of this study, including the inability of the ADV to measure data near the bed as well as the water surface. The application of PIV (Particle Image Velocimetry) for velocity measurements may address some of the limitations of ADV with the capability to collect data near the bed and the water surface. Another limitation is the uniformity of width variation. The flow depth is low (14 cm) without any change in the main direction. Some assumptions were also used in this study. No lateral flow exists and no vegetation in the banks and obstacles in the bed are prevalent in the cross section. Variations of sediment size are uniform, and no cobble and boulder exist in the flow direction. The entrance and exit slopes of the bedform remained constant during the data collection period and no sediment transport exists in the flume.

Future study will focus on gravel-bed rivers to investigate the effect of width variation in rivers. In future studies it is also important to investigate the velocity and turbulence for higher flow depths and coarse sediments. Vegetation is often prevalent on riverbanks, which can develop the secondary currents. Additional research is needed to understand riverbank vegetation’s effects on the estimation of key hydraulic parameters. At present, many hydraulic models assume uniform width, depth, and slope without considering the influence of width and bedform variation. This can result in inaccurate estimates of sediment transport and drag coefficient, impacting estimations of project cost. This is one of the main reasons to stop or to decelerate construction process in many river restorations projects.

The results of this research clearly show that the interaction of width variation and bedforms significantly impact Reynolds stress and turbulence intensity distributions. Estimation of key parameters of fluvial hydraulics depends on the knowledge of complex conditions in rivers including the variation of width and the presence of 3D bedforms. These complex conditions can significantly change flow resistance and sediment transport parameters including velocity distribution and shear velocity. Under- or overestimation of these parameters not only influences the prediction and performance of hydraulic models but also increases the cost of river restoration projects. The results of this experimental study can help the engineers to make better decisions for river engineering projects. Results can also help better estimate several important parameters in river engineering where width variation and pool-riffle sequences are prevalent. Knowledge of flow characteristics including velocity, turbulence intensity, and Reynolds stress can help design ecological restoration projects and determine the key features of fluvial hydraulics such as flow resistance and sediment transport. Width of streams is a key factor when designing stable channels. Knowledge of flow pattern along a variable width stream and application of the velocity and Reynolds stress results in 3D will help engineers estimate the controlling parameters in river restoration including the Shields parameter. The results of this study will help not only to better estimate the flow resistance, drag coefficient, and sediment transport, but also improve hydraulic model performance.