https://orcid.org/0000-0002-5145-6185
Abstract
The present paper aims to evaluate the effect of emergent rigid vegetation density on the flow's turbulence structure and hydraulic parameters at the non-prismatic floodplains. The experiments were performed using the physical model of the asymmetric non-prismatic compound channel. The results show that the velocity distribution in the vegetation flow is more influenced by the drag force caused by the vegetation than by the bed shear stress and does not follow the law of logarithmic velocity distribution throughout the non-prismatic section. The intense velocity gradient at the interface of the main channel and the floodplain leads to the development of strong secondary currents, increased Reynolds shear stresses, apparent shear stresses and momentum exchange in this region. Vegetation also decreases mean kinetic energy in the floodplain and increases it in the main channel. The mean turbulence exchange coefficient for the non-prismatic compound channels without vegetation was 0.23 and for the divergent and convergent compound channels was 0.035 and 0.020, respectively. The comparison of the local drag coefficient results shows that the fluctuations of this parameter are greater in the divergent section than in the convergent section due to the strong secondary currents in the interface.
HIGHLIGHTS
This paper is the result of original research in the field of river engineering.
Its innovation is in the field of compound open channel and flow turbulence structure.
The Acoustic Doppler Velocimeter (ADV) profiler has been used with high accuracy to understand the flow structure.
Vegetation on flood plains and its effects on flow hydraulic is novel.
Comparison has been made between the effects of divergence and convergence on flow hydraulics.
INTRODUCTION
Natural rivers usually have the main channel to transmit the perennial flow and vegetated floodplains to transfer excess flow during extreme events. Vegetation in floodplains changes not only the flow capacity in the compound channel but also the ecological system of rivers and affects flow characteristics such as velocity distribution, turbulence structure, and vortices, as well as mass and momentum exchange between vegetated and non-vegetated areas (Nezu & Sanjou 2008; Uotani et al. 2014). Due to the presence of vegetation, a strong velocity gradient and significant secondary currents occur at the interface between the main channel and the floodplain. As a result, a shear layer forms between the main channel and the floodplain, causing Kelvin–Helmholtz instability (Bousmar 2002). Due to Kelvin–Helmholtz instability, large horizontal coherent flow structures (LHCS) with horizontal longitudinal scales are formed, which are the main factor in controlling the structure of turbulent flows (Bousmar 2002; White & Nepf 2008; Adrian & Marusic 2012). Coherent vortices at the interface of the main channel and floodplain result in increased mass and momentum exchange between vegetated and non-vegetated areas, complicating hydraulic perception of flow (White & Nepf 2008; Anjum & Tanaka 2020). Many researchers, such as Weber et al. (2016), Zhang et al. (2017), and Koftis & Prinos (2018), have used numerical simulations to study the structure of turbulent flow fields in vegetated channels.
is the turbulent shear stress.Zhao et al. (2019) and Yan et al. (2019) experimentally studied turbulent flow structure in the presence of submerged vegetation in open channels; Yu et al. (2019) studied wake structure in the presence of non-submerged vegetation. The effect of vegetation density on the stage-discharge rating curve has been studied experimentally by several researchers for various single-row vegetation configurations on floodplains (Barbosa 2014; Ahmad et al. 2020). Many researchers also studied the effect of vegetation density on the drag coefficient of flow through a set of rigid cylindrical elements (Nepf 1999; Tanino & Nepf 2008; Kothyari et al. 2009; Stoesser et al. 2010; Mulahasan et al. 2017; Sonnenwald et al. 2019). As can be seen, most studies of vegetated floodplains have focused on straight compound channels, whereas non-prismatic compound channels with vegetation on converging and diverging floodplains are missing in the literatures. Natural riverine channels usually have a non-prismatic section, and tree vegetation is located on the floodplain. In natural rivers, flow conditions change from uniform to non-uniform due to changes in the cross-section of the river. Under such conditions, hydraulic analysis is much more complex than uniform flow (Yonesi et al. 2013). Previous studies show that many aspects and gaps related to vegetated floodplains have not explored the non-prismatic vegetated compound channels. In this study, the flow field in a non-prismatic compound channel with vegetated floodplains was focused on understanding the physic of flow for different converging and diverging floodplains.
Furthermore, this paper aims to evaluate the role and effects of the density of non-submerged vegetation on turbulent flow structure, including the distribution of flow velocity, turbulence characteristics, and mass and momentum exchange, and compare these parameters at different convergence and divergence angles. Investigating the effects of vegetation on floodplains in a non-prismatic compound channel on the flow turbulence structure is a strategic idea that can contribute to a better understanding of the hydrodynamics of flow.
MATERIALS AND METHODS
Experimental model
. Three angles of 3.8, 5.7, and 11.3 degrees were used to create divergent and convergent floodplains (refer to Figure 1(a) and 1(b)). In the following Figure 1(a) and 1(b), yf is the flow depth in the floodplain. The rigid cylindrical plastic rods with 10 mm diameter (D) were used to model the vegetation in the floodplain. Vegetation arrangement in the divergent and convergent floodplain was performed in a similar and row manner, and the rods were placed in a row with three different densities. The space between rows (
) was fixed and equal to 75 mm, and the space between elements (
) was chosen to be 50, 75, and 100 mm, respectively (refer to Figure 1), based on the experiments of Yang et al. (2007). Thus, the spacing ratio (Sr = ly/D) for the three vegetation densities will be equal to 5, 7.5, and 10, respectively, which is within the range recommended by Terrier et al. (2010). The flow depth and the discharge were measured using a point gauge and electromagnetic flowmeter with an accuracy of 0.01 L/s, respectively. Electromagnetic flowmeters were mounted to the flow inlet pipe of the flume. 
Schematic of flume and arrangement of vegetation elements: (a) divergent floodplain and (b) convergent floodplain.
Schematic of flume and arrangement of vegetation elements: (a) divergent floodplain and (b) convergent floodplain.
Due to the formation of non-uniform flow in non-prismatic sections, the relative depths (Dr = yf /H) in the middle of the divergence and convergence regions were adjusted by the tailgate (Table 1). In the present study, a total of 96 experiments were performed. The parameters tested are summarized in Table 1.
Experimental tests parameters
| Exp. Series | Spacing ratio (Sr) | Qexp.(l/s) | Dr | Floodplain angle (θ°) | Reynolds number 105 (Re) | Froude number (Fr) | Number of tests |
|---|---|---|---|---|---|---|---|
| P–Sr–Dr | 5, 7.5, 10 | 25–35 | 0.15, 0.25, 0.35, 0.45 | – | 1.059–1.773 | 0.148–0.411 | 12 |
| D–θ–Dr | – | 25.5–34 | 0.15, 0.25, 0.35, 0.45 | 3.8, 5.7, 11.3 | 1.081–1.797 | 0.160–0.413 | 12 |
| D–θ–Sr–Dr | 5, 7.5, 10 | 25.25–34.7 | 0.15, 0.25, 0.35, 0.45 | 3.8, 5.7, 11.3 | 1.066–1.768 | 0.152–0.408 | 36 |
| C–θ–Sr–Dr | 5, 7.5, 10 | 25.25–34.7 | 0.15, 0.25, 0.35, 0.45 | 3.8, 5.7, 11.3 | 1.062–1.777 | 0.150–0.410 | 36 |
| Exp. Series | Spacing ratio (Sr) | Qexp.(l/s) | Dr | Floodplain angle (θ°) | Reynolds number105 (Re) | Froude number (Fr) | Number of tests |
|---|---|---|---|---|---|---|---|
| P–Sr–Dr | 5, 7.5, 10 | 25–35 | 0.15, 0.25, 0.35, 0.45 | – | 1.059–1.773 | 0.148–0.411 | 12 |
| D–θ–Dr | – | 25.5–34 | 0.15, 0.25, 0.35, 0.45 | 3.8, 5.7, 11.3 | 1.081–1.797 | 0.160–0.413 | 12 |
| D–θ–Sr–Dr | 5, 7.5, 10 | 25.25–34.7 | 0.15, 0.25, 0.35, 0.45 | 3.8, 5.7, 11.3 | 1.066–1.768 | 0.152–0.408 | 36 |
| C–θ–Sr–Dr | 5, 7.5, 10 | 25.25–34.7 | 0.15, 0.25, 0.35, 0.45 | 3.8, 5.7, 11.3 | 1.062–1.777 | 0.150–0.410 | 36 |
P, prismatic channel; D, divergent floodplain; C, convergent floodplain; Sr, the ratio of vegetation space; θ, angle of divergence or convergence; Dr, the relative flow depth.
Flow velocity measurement sections.
Drag coefficient (CD)
. Due to the interaction between the rods, the flow structure is very different from the behavior of a single rod. Therefore, this aspect should be considered in calculating the CD of a set of elements on the floodplain (Zdravkovich 1987). Sonnenwald et al. (2019) and Kothyari et al. (2009) presented the drag coefficient of vegetation in a uniform flow in Equations (3) and (4), respectively:
is the obstruction volume fraction. In this study, the average number of rods per unit area (Nv) is 260, 185, and 145 per square meter, respectively, depending on the type of vegetation arrangement.Friction factor
Comparison of the modified Keulegan Equation (1938) and the equation of Rameshwaran & Shiono (2007).
Comparison of the modified Keulegan Equation (1938) and the equation of Rameshwaran & Shiono (2007).
Variations of the global Manning's roughness coefficient versus the flow depth for a prismatic compound channel with and without vegetation on the floodplain.
Variations of the global Manning's roughness coefficient versus the flow depth for a prismatic compound channel with and without vegetation on the floodplain.
RESULTS AND DISCUSSION
Flow velocity distribution
Transverse distribution of the longitudinal component of flow velocity at different vegetation densities in the floodplain at Dr = 0.35, θ = 5.7o, right: converging cross-section, left: diverging cross-section.
Transverse distribution of the longitudinal component of flow velocity at different vegetation densities in the floodplain at Dr = 0.35, θ = 5.7o, right: converging cross-section, left: diverging cross-section.
The V-shaped velocity distribution behind the vegetation elements is due to the change in linear momentum around the vegetation stem and the formation of a shear layer on both sides of the vegetation element, which is consistent with the results of Sanjou et al. (2010), Mulahasan et al. (2017) and Ahmad et al. (2020). The formation of the Von Karman vortex section behind the vegetation elements leads to a transverse exchange of mass and momentum between the vegetated and non-vegetated regions within the floodplain. This results in a higher flow velocity in the non-vegetated area than in the vegetated area of the floodplain, which is readily observed in the Sr = 7.5 spacing ratio. In the case of dense vegetation (Sr = 5), the flow separation is slower, and the area of the rotation behind the rod is much smaller. In this case, the vortices created behind the elements overlap due to reducing the space between the elements and weakening the flow velocity's prolific motion.
In addition, due to the reduction of the flow cross-section and the small number of vegetation elements involved in the flow pattern, the flow velocity in the middle region of the divergence is higher than at the end and follows the same pattern. In the middle of the convergence section, the cross-sectional region of the stream decreases, but due to the increase in flow resistance, the flow velocity in the floodplain in this area is almost as high as at the entrance. This leads to the fact that in the convergent section, unlike in the divergent section, the sine wave amplitude of the flow velocity remains constant as one moves from the interface to the floodplain wall.
is the shear velocity of the flow . The value of ks can be calculated from Equation (10) (Ackers 1991):
Comparison of the vertical velocity distribution with the logarithmic distribution law at Dr = 0.35, Sr = 5, θ = 5.7o, (a and c) middle and end of the divergent section, respectively, (b and d) middle and the entrance of the convergent section, respectively. Please refer to the online version of this paper to see this figure in colour: https://dx.doi.org/10.2166/aqua.2023.043.
Comparison of the vertical velocity distribution with the logarithmic distribution law at Dr = 0.35, Sr = 5, θ = 5.7o, (a and c) middle and end of the divergent section, respectively, (b and d) middle and the entrance of the convergent section, respectively. Please refer to the online version of this paper to see this figure in colour: https://dx.doi.org/10.2166/aqua.2023.043.
In vegetated floodplains, flow velocity profiles moving from the wall to the interface almost follow an S-shaped profile, consistent with the results by Yang et al. (2007). The S-shaped distribution divides the vertical flow profile into three regions: uniform section in front of the solid cylinder, point of inflection at the top of the dowel, and region of acceleration above dowel till free surface. The following vertical velocity profile is dependent on the flow depth, the position of the profile on the floodplain, divergence and convergence angle, and the vegetation density. In addition, the velocity distribution is affected by two boundary layers, one at the channel bed and the other at the surfaces of the vegetation elements. Moreover, in the main channel, due to the strong secondary currents, the maximum flow velocity is not observed at the water level but in the floodplain at the water level, which confirms the results of the previous section.
Vertical distribution of velocity component in flow direction in different vegetation densities.
Vertical distribution of velocity component in flow direction in different vegetation densities.
Secondary currents
Streamwise and secondary current vectors in the divergent compound channel with and without vegetation.
Streamwise and secondary current vectors in the divergent compound channel with and without vegetation.
Streamwise and secondary current vectors in the convergent compound channel with and without vegetation.
Streamwise and secondary current vectors in the convergent compound channel with and without vegetation.
Moreover, the mixing layer development at the interface between the main channel and the floodplain also plays an important role in inducing strong vortices. The intensity of the secondary current is lower in the convergent section than the divergent section because of a reduction in the transverse gradient of the flow velocity at the interface. In the divergence region, the direction of secondary vectors on the floodplain has two completely different patterns, so that in the region near the interface, the directions for the vectors are toward the main channel, and in the more distant region, the secondary current vectors move toward the floodplain wall (refer to Figure 8).
In the divergent section, the floodplain geometry enhances the Kelvin–Helmholtz instability effect. In the convergent section, on the other hand, the direction of the secondary vectors is always observed from the floodplain to the main channel, which weakens the Kelvin–Helmholtz instability effect and reduces the intensity of the secondary currents. In the presence of vegetation, the direction of secondary currents within the main channel is always counterclockwise (see Figure 9(c) and 9(d)). Regardless of the vegetation density, the drag force and transverse shear stress increase with increasing flow depth. An increase in drag induces anisotropy of the channel's turbulence and the generation of stronger secondary flows at higher relative depths.
Flow turbulence
) has often used Equation (12):
Vertical variations of turbulence intensity in flow direction, transverse and vertical directions for different vegetation densities in different positions, Dr = 0.45, θ = 5.7o, (a, b, c) divergent compound channel, (d, e, f) convergent compound channel.
Vertical variations of turbulence intensity in flow direction, transverse and vertical directions for different vegetation densities in different positions, Dr = 0.45, θ = 5.7o, (a, b, c) divergent compound channel, (d, e, f) convergent compound channel.
Because of the velocity gradient at the interface, the turbulence intensity is greater in the divergent section than in the convergent section. The floodplain vegetation reduces the fluctuations of the longitudinal component of the flow velocity and increases the fluctuations of the transverse and vertical components of the flow velocity.
) in the divergent and convergent sections with and without vegetation at Dr = 0.45, θ = 5.7°. In the presence of vegetation, the turbulence intensity increased in the presence of strong vortices in the main channel bed and near the interface of the main channel to the floodplain compared to the non-vegetated floodplain. Also, over the floodplain region, the propagation of vortices and the intermittent transverse movement of flow behind each element has resulted in the negative magnitude of turbulence in the vegetated floodplain compared to the non-vegetated condition. An increase in vegetation density due to the reduction in flow velocity reduces the severity of turbulence in the floodplain. Since the flow is accelerated in the convergent section, the turbulence values are higher than in the divergent section. In addition, turbulence intensity is greater in the middle of the divergent section than at the end and greater in the middle of the convergent section than at the entrance. 
Flow turbulence intensity distribution (u′/u*) for different vegetation densities at Dr = 0.45, θ = 5.7o, (a, b) without vegetation, (c, d, g, h) divergent section, (e, f, i, j) convergent section.
Flow turbulence intensity distribution (u′/u*) for different vegetation densities at Dr = 0.45, θ = 5.7o, (a, b) without vegetation, (c, d, g, h) divergent section, (e, f, i, j) convergent section.
Transverse distribution of depth-averaged turbulence kinetic energy for different vegetation densities at Dr = 0.45, θ = 5.7o, (a, b) middle and entrance of convergence, (c, d) middle and end of divergence, respectively.
Transverse distribution of depth-averaged turbulence kinetic energy for different vegetation densities at Dr = 0.45, θ = 5.7o, (a, b) middle and entrance of convergence, (c, d) middle and end of divergence, respectively.
The turbulence kinetic energy increased at the interface between the main channel and the floodplain in the vegetated floodplain (see Figure 12(a)–12(d)). However, the TKE value in the floodplain of the divergent section is lower than that in the non-vegetated condition since the increase in flow resistance induces the formation of weak secondary currents in this region. On the other hand, in the convergent section, the kinetic energy of turbulence increased compared to the non-vegetated condition. An increase in vegetation density increases the kinetic energy at the interface but decreases the momentum exchange between vegetation elements in the floodplain.
Distribution kinetic energy distribution normalized at different vegetation densities at Dr = 0.45, θ = 5.7o, (a, b) without vegetation, (c, d, g, h) divergent section, (e, f, i, j) convergent section.
Distribution kinetic energy distribution normalized at different vegetation densities at Dr = 0.45, θ = 5.7o, (a, b) without vegetation, (c, d, g, h) divergent section, (e, f, i, j) convergent section.
MKE variations in the non-prismatic compound channel, right: end of divergence and entrance of convergence, left: middle of divergence and convergence.
MKE variations in the non-prismatic compound channel, right: end of divergence and entrance of convergence, left: middle of divergence and convergence.
CONCLUSIONS
In this research, the effect of vegetation density and floodplain angle on hydraulic parameters and flow patterns in the non-prismatic compound channel was investigated, although in order to find out the real effects of vegetation, flexible vegetation should be used in submerged and emerged conditions, however the following results can be inferred:
The presence of the vegetated floodplain in the non-prismatic compound channel increases factors such as friction, turbulence disturbance, and drag forces and significantly reduces flow rate in this region, and significantly increases the velocity gradient between the vegetated area and the free zone. The S-shaped distribution of flow velocity in the floodplain divides the flow into three zones, the size of which depends on flow depth, measurement position, and vegetation density. In addition, the distribution of flow velocity is influenced by two boundary layers, one in the bed and the other in the surfaces of the floodplain vegetation elements. The depth-averaged flow velocity in the floodplain is reduced by 64.5 and 60.6% in the presence of vegetation in the divergent and convergent compound channel, respectively. In natural rivers, the roughness of the vegetation is more predominant than the roughness of the riverbed, so that the distribution of flow velocity is more influenced by the drag force caused by the vegetation. Drag force due to the presence of vegetated floodplain causes that at relatively high depths of the flow, the difference in flow velocity between the main channel and the floodplain is significant, while the behavior of the compound channel in the non-vegetated floodplain approaches that of the straight channel. Vegetation in the floodplain has resulted in a change in the pattern and direction of secondary vectors. The size and intensity of secondary currents have increased in the main channel and decreased in the floodplain of the non-prismatic sections with vegetation compared to non-vegetated conditions. Turbulence intrusion is evident at the interface between the main channel and the floodplain with vegetation. Turbulence heterogeneity and Reynolds’ shear stress increase due to intensified momentum exchange in this region. Floodplain vegetation reduces the MKE of the flow in the floodplain. In the interfacial region between the main channel and the floodplain, the formation of large-scale horizontal coherent vortices leads to the generation of maximum apparent shear stress in this region, which is greater in the divergent section than in the convergent section. All these changes in the divergence and convergence area will be due to the change in the stage-discharge curve of the rivers and the amount of sediment transport. These cases should be further investigated in the future.
DATA AVAILABILITY STATEMENT
All relevant data are included in the paper or its Supplementary Information.
CONFLICT OF INTEREST
The authors declare there is no conflict.
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