Flow Structures in Open Channels with Emergent Rigid Vegetation: A Review

Abstract

On the edges of rivers where the flow velocity is low, aquatic plants flourish, with emergent rigid herbs being the most common. Since the flow structures of vegetated flow are strongly influenced by vegetation distribution patterns, homogeneous and heterogeneous canopies are defined based on the characteristics of vegetation distribution. A review summarizing recent advances in flow structures under the influence of different types of canopy arrangements, including ribbon-like homogeneous canopies, ribbon-like heterogeneous canopies, and patched heterogeneous canopies, is needed. Their flow development process, shear layer properties, coherent structure features, and momentum exchange characteristics are summarized, and a future research agenda for an in-depth understanding of the interactions between vegetation and flow is also highlighted.

1. Introduction

Aquatic plants are widely distributed in natural and artificial rivers, lakes, and wetlands. In earlier studies, it was mostly believed that the presence of aquatic plants increased flow resistance and water depth and decreased channel conveyance during flood seasons [1,2]; thus, the removal of aquatic plants in rivers was suggested to accelerate the passage of flow [3,4]. However, with further research, it is gradually beginning to be recognized that aquatic plants play important roles in aquatic ecosystems, mainly in the following aspects: (1) purifying water quality, as aquatic plants can not only directly absorb pollutants, such as nitrogen, phosphorus, and heavy metals, but also promote the oxidative decomposition of pollutants and improve the self-purification ability of water by altering the microenvironmental dynamics [5,6,7]; (2) enriching biodiversity, as aquatic plants can provide oxygen, food, and habitats for aquatic organisms [8,9,10]; (3) enhancing bank stability, as aquatic plants can protect riverbanks and coastlines by slowing flow velocity, dissipating wave energy, improving sediment deposition, and resisting erosion, and can also mitigate the hazards of floods and tsunamis [11,12]; and (4) improving landscaping.

The presence of aquatic plants increases flow resistance, slows flow velocity, and affects sediment deposition and suspension on short time scales [11]. Especially within the canopy, stem-scale turbulence plays a significant role in sediment transport [13,14] and further affects the transport of organic materials. Over longer time scales, this may have important effects on the growth and expansion of local vegetation patches, as well as on river morphology [2,15,16]. In other words, when aquatic plants change flow structures, flow structures will in turn affect the growth and evolution of plants. Therefore, a comprehensive understanding of the interactions between vegetation and flow is of great significance for river ecological protection and restoration [17], which also makes the topic of vegetated flow more attractive for researchers.

In general, aquatic plants can be classified into rigid plants and flexible plants according to the bending deformation degree of stems under the action of water flow, and they can be further classified as emergent, floating, or submerged plants according to their forms, as shown in Figure 1. The presence or absence of vegetation and the distribution of vegetation species in river cross-sections are largely determined by the magnitude of flow velocity. For instance, in a main channel where the flow velocity is high, only mosses tend to grow, while, if the flow velocity is low in the main channel, submerged flexible plants and floating plants may dominate [18]. On the edges of rivers where the flow velocity is much lower, plants usually grow better, with rigid emergent herbs being the most common type [19].

The flow structures of vegetated flow are closely related to the distribution patterns of vegetation, and an investigation of the flow characteristics under different vegetation arrangements is crucial for an in-depth understanding of the interactions between vegetation and flow. Focusing on emergent rigid vegetation (e.g., reeds, calamus), which is widely distributed in natural rivers, the purpose of this review was to feature the research results and progress on flow structures under the influence of different vegetation distribution patterns, including the flow development process, shear layer properties, coherent structure characteristics, and sediment deposition characteristics, and to identify the prospect of the issues that need to be addressed in future research.

2. Generalization and Quantification of Rigid Vegetation

2.1. Rigid Vegetation and Its Modeling

It is a common method to model real plants as rigid circular cylinders with uniform diameters and heights in experimental and numerical studies [20,21,22,23], and this approach is realistic for plants with few branches and leaves that exhibit no deformation when subjected to water flow, e.g., sedges, reeds, and mangrove roots [24], but it is an oversimplification for flexible vegetation that may oscillate periodically in response to turbulent flow structures [25]. For an individual cylindrical plant, the diameter and height are usually denoted as d and h. When the ratio between water depth, H, and vegetation height, h, is lower than 1 (H/h < 1), it indicates that the vegetation is emergent.

Within the canopy, the distribution patterns of cylinder elements are often generalized as staggered, in-line, and random arrays [14,26,27,28,29], as depicted in Figure 2. For emergent rigid vegetation, the vegetation density can be described by the frontal facing area of plants per unit volume, i.e., $a=md$ (m refers to the number of plants per unit bed surface), and $\Phi =\pi a\mathrm{d}/4$, a nondimensional parameter that indicates the solid volume fractions of plants. More quantification parameters should be introduced in studies when more complex morphologies are considered [30], such as for Typha latifolia and Rotala indica, whose biomass varies vertically [27]. It is important to describe and quantify vegetation distribution properly, and the determination of quantitative parameters largely depends on the focus of the research itself [31], which has also been a major research topic [32,33].

2.2. Quantification of Drag

An obvious effect of the presence of aquatic plants in rivers is increased flow resistance. In early studies, vegetation resistance was often treated as the increase in riverbed roughness, and traditional resistance coefficients were used to quantify vegetation resistance, such as the Chezy coefficient, Darcy coefficient, and Manning coefficient [34]. However, Marjoribanks et al. [35] highlighted the limitations of these traditional treatments of vegetation resistance, i.e., (i) a strong dependence upon parameters with a poor physical basis that are usually determined empirically and (ii) a poor conceptual basis in which the changes in flow structures caused by vegetation cannot be reflected adequately, especially in high-dimensional numerical models. Thus, a more reasonable parameter, C_D, the drag coefficient of vegetation, was proposed to quantify the vegetation resistance.

The values of C_D are closely related to hydraulic conditions, vegetation distribution patterns, and vegetation morphologies [36,37,38]. The temporally and spatially averaged method was introduced in the statistical moments computation in vegetated flow to remove turbulent fluctuations and plant-scale heterogeneity, as defined by Raupach and Shaw [39]. The drag coefficient is usually defined as [40]

$$C_D=\frac{〈\overline{F_D}〉}{0.5\rho {〈\overline{u}〉}^2〈d〉},$$

(1)

where F_D is the drag force, ρ is the water density, and u is the flow velocity. Overbar and angular brackets indicate that the temporal average and spatial average are calculated, respectively. The hydraulic condition within canopies can be denoted by the stem Reynolds number, ${Re}_p=〈\overline{u}〉d/\upsilon$, where $\upsilon$ is the kinematic viscosity. For an isolated cylinder, C_D decreases initially with increasing ${Re}_p$, up to ${Re}_p$= O(10³). With a further increase in ${Re}_p$, $C_D$ tends to increase gradually and remains roughly constant when ${Re}_p$ is quite large, ${Re}_{p }$= O(10⁵) [41].

Studies have found that the C_D of vegetation elements within a canopy can be significantly different from that of isolated elements because of three mechanisms, namely, sheltering effects, delayed separation, and blockage effects [42]. Sheltering describes the condition in which some cylinders are located in the wake region of upstream cylinders [43], which results in a lower velocity and thus a lower drag force than upstream cylinders. This effect can be more significant with decreasing space between cylinders [44,45]. Delayed separation indicates that a larger mean separation angle than that of an isolated cylinder can be generated by turbulent fluctuations in the wakes of upstream cylinders and the accelerated flow between cylinders [1,46]. Both sheltering effects and delayed separation tend to decrease the drag coefficient when compared with the isolated cylinder, while blockage effects usually lead to an increase in the drag coefficient due to the enhanced velocity and wake pressure [46]. A detailed comparison between the drag coefficients of isolated cylinders, in-line arrays, and staggered arrays was conducted in the study by Melis et al. [47], and the results showed that, with an increasing Reynolds number, a switch from blockage to sheltering was observed in the cases of in-line and staggered arrays.

Furthermore, the drag coefficient of vegetation canopies is related to canopy density; at a given Reynolds number, the value of C_D increases initially and then decreases with increasing vegetation density [48]. It is noted that the in-line or staggered vegetation distribution pattern has a limited effect on drag force when the canopy density is high enough [49]. At larger scales, such as at the river scale, the canopy resistance no longer depends on the morphology of individual elements but is mainly determined by the width of the canopy relative to the river [50,51]. Based on indoor experiments and numerical calculations, supplemented by various data-driven methods, several models have been developed to predict vegetation drag coefficients under various conditions [22,23,42,52], and a detailed review of these models has been carried out by D’Ippolito et al. [53].

3. Flow Structures under the Effects of Different Canopy Layouts

In rivers completely covered with plants, the presence of vegetation mainly creates resistance to flow, slows the flow velocity, and reduces the cross-sectional area of the passage, and the overall flow field is relatively stable [14,48,54]. However, in natural rivers, emergent rigid plants rarely cover the entire river cross-section due to the high velocity in the main channel, and they are mostly distributed along the river banks and present a variety of layouts. A canopy can be classified into a homogeneous or heterogeneous layout based on its vegetation distribution characteristics. In this study, the homogeneous layout was defined as a canopy within which the plant morphology (including diameter, height, etc.) and its distribution pattern (including density, etc.) did not change with spatial variation (Figure 3a). As opposed to a homogeneous canopy, a heterogeneous canopy indicates that there are obvious differences in plant morphologies or densities within the canopy, and the differences are more prevalent in natural rivers. Along rivers, the shape of the canopy distribution is usually in the form of ribbons or patches, as shown in Figure 3.

3.1. Flow Structures under the Effects of a Ribbon-like Homogeneous Canopy

Plants with rigid stems tend to grow along riverbanks or in the middle of rivers, forming a ribbon shape. It was observed that a river initially obstructed with dense and chaotic shrubs would evolve into a well-organized system of ribbon-like canopies with time [55]. Under the effects of resistance, a diverging flow occurred upstream of the banded canopy; that is, most water was deflected into the main channel and accelerated, while only a small amount of water penetrated the canopy and further slowed until a fully developed region was reached [28,56]. The study by Rominger and Nepf [57] showed that the adjustment distance (L) needed to reach the fully developed region mainly depended on the canopy flow blockage, which can be described by $C_{D}ab$, where b is the half-width of the canopy without considering the wall effects. When the flow blockage is low ($C_{D}ab<2$), the adjustment distance is determined by the canopy drag length scale, ${{(C}_{D}a)}^{-1}$. When the flow blockage is high ($C_{D}ab\ge 2$), the adjustment distance is mainly determined by the half-width, b. For the conditions of Φ << 1, a simple relationship can be written as ${L~2/C}_{D}a$.

The velocity difference between the canopy and the main channel increases with distance downstream, which generates an inflection point in the lateral profile of mean velocity and creates an asymmetric shear layer of a two-layer structure [58]. Different from the free shear layer, the shear layer induced by canopy resistance will cease to develop once the fully developed region is reached [20], which indicates a balance between the production of shear-layer-scale turbulent kinetic energy and the dissipation within the canopy [59]. It is generally assumed that, in the fully developed region, the longitudinal gradient of the mean streamwise velocity remains zero [58,60], i.e., $\partial U/\partial x\approx 0$, and some researchers believe that the turbulent parameters should also remain uniform along the longitudinal direction [61].

Assuming that both the canopy and the main channel are wide enough to ignore the sidewall effects, a sketch of the flow structures in a channel covered with a ribbon-like canopy is presented in Figure 4. The laterally uniform velocity deep within the canopy is denoted as $U_1$, and the laterally uniform velocity in the main channel is denoted as $U_2$. Then, the shear layer between the canopy and the main channel can be characterized by the following parameters [56,62,63]: the differential velocity, $∆U=U_2-U_1$, the convection velocity, $\overline{U}=(U_1+U_2)/2$, and the velocity ratio, $\lambda =\frac{U_2-U_1}{U_1+U_2}$. The momentum thickness, $\theta ={\int }_{-\infty }^{+\infty }\left[\frac{1}{4}-\frac{U\left(y\right)-\overline{U}}{∆U}\right]$, is also a good characterization of the shear layer [56].

The asymmetric shear layer consists of the inner layer (δ_I) and the outer layer (δ_O), i.e., δ = δ_I + δ_O. Different quantitative determination methods of the shear layer width have been proposed in previous studies [64,65,66,67], as shown in

Table 1. Different quantitative determination methods of the width of the shear layer.

Studies	Shear Layer Definitions	Notes
Uijttewaal and Booij (2000) [64]	$\delta =\frac{U_c-U_f}{{(\partial U/\partial y)}_{\mathrm{m}\mathrm{a}\mathrm{x}}}$	$U_c$ and $U_f$ are the laterally uniform velocity in the floodplain and main channel, respectively.
Van Prooijen et al. (2005) [65]	$\delta ={2(y}_{75\%}-y_{25\%})$	$U\left(y_{x\%}\right)=U_f+x\mathrm{\%}(U_c-U_f)$; $y_{x\%}$ is the lateral position corresponding to the velocity, $U\left(y_{x\%}\right)$.
White and Nepf (2008) [66]	$\delta \approx \max \left(0.5{\left({\mathrm{C}}_{D}a\right)}^{-1},1.8d\right)+\frac{U_c-U_m}{{(\partial U/\partial y)}_{y_m}}$	$y_m$ and $U_m$ are the lateral position and the velocity corresponding to the matching point, respectively.
Truong and Uijttewaal (2019) [67]	$\delta =\left(y_0-y_{5\%}\right)+\left(y_{95\%}-y_0\right)$	$U_{5\mathrm{\%}}=(1+5\mathrm{\%})U_f$, $U_{95\mathrm{\%}}=(1-5\mathrm{\%})U_c$; $y_0$ is the lateral position corresponding to the inflection point.

. According to White and Nepf [58], the inner layer width is inversely proportional to the canopy drag length scale, which can be described as ${\delta }_I\approx \max (0.5{\left(C_{D}a\right)}^{-1},1.8d)$, while the outer shear layer width is determined by the water depth and bottom friction. In a channel covered with a submerged canopy, it was found that the vertical profile of the mean streamwise velocity agreed well with the hyperbolic tangent curve of the velocity distribution in the canonical mixing layer, suggesting the applicability of the mixing layer theory in vegetated flow [25,68]. However, Sukhodolova and Sukhodolov [69] pointed out that the mixing layer theory may be more applicable to conditions with dense canopies, while the shear layers generated by sparse canopies may be more suitable for the boundary layer theory. By assuming the canopy as a rough wall and setting the zero-plane displacement within the canopy to the distance of penetration width, Li et al. [61] found that the lateral profiles of the mean streamwise velocity in the outer shear layer followed logarithmic curves. An analogy can be drawn between the canopy flow with sufficient density and the turbulent rough-wall boundary layers, and the effect of increased canopy density on the flow corresponds well to the effect of decreased wall roughness [70].

The Kelvin–Helmholtz instability within the shear layer between the canopy and the main channel leads to strong turbulence and induces large horizontal coherent structures downstream [20,71]. It is difficult to define coherent structures precisely; they indicate the regions of space and time within which the flow field has a characteristic coherent pattern that is significantly larger than the turbulence scales [72]. Flow visualizations, conditional statistics of velocities, spectral analysis, and periodic characteristic recognition are common methods in coherent structure identification [58,64,72]. Coherent structures grow with distance downstream and reach a fixed scale in the fully developed region [25,59]. In addition, coherent structures penetrate part of the canopy, within which strong momentum exchange occurs. The penetration width can be determined as the distance from the canopy edge to the lateral position where the Reynolds stress decreases to 10% of its peak value [73]. This region indicates the decay of stress-driven flow [4], and its width is subject to the energy dissipation caused by canopy resistance [60].

Strong mass and momentum exchange is induced by a large velocity gradient within the shear layer, which is of great significance for river flooding capacity, bank stability, sediment transport, and biological and chemical exchange [66]. For the vegetated flow under high a Reynolds number conditions, the Reynolds stress is the dominant contributor to the total momentum exchange in the shear layer. Li et al. [61] further investigated the mechanisms of momentum exchange in vegetated flows and found that coherent structures were the dominant contributors to momentum exchange. Thus, on the basis of the hybrid eddy viscosity model proposed by Truong and Uijttewaal [67], a modified eddy viscosity model considering bottom turbulence, stem-scale turbulence, and turbulence induced by coherent structures can be given by

$$\begin{gathered} {\nu }_t= \\ \left\{\begin{array}{c}\lambda \sqrt{\frac{f}{8}}{U}_{d}H+\frac{1}{8}{C_t}^{-2}{C}_{D}d{U}_d+{\xi }^2{\delta }^2\left[{(\frac{U_d-U_1}{U_1})}^2+{(\frac{U_d-U_2}{U_2})}^2\right]\left|\frac{d{U}_d}{dy}\right|(inside canopy)\\ \lambda \sqrt{\frac{f}{8}}{U}_{d}H+{\xi }^2{\delta }^2\left[{(\frac{U_d-U_1}{U_1})}^2+{(\frac{U_d-U_2}{U_2})}^2\right]\left|\frac{d{U}_d}{dy}\right|(outside canopy)\end{array}\right.. \end{gathered}$$

(2)

where ${\nu }_t$ refers to the eddy viscosity, $\lambda$ is the dimensionless eddy viscosity, f is the friction factor, $U_d$ indicates the depth-averaged velocity, $C_t$ is a constant associated with the shape of the streamwise velocity profile, and $\xi$ is a proportionality coefficient. This modified model could be well applied to different experimental conditions by changing only one empirical coefficient. It was also noted that the empirical coefficient was inversely proportional to the canopy drag length scale [61].

Within the canopy, the stem elements decompose the large-scale vortices into small-scale vortices, especially those larger than the diameter of stems and the distance between stems. The presence of stem turbulence depends largely on the stem Reynolds number Re_p. In natural rivers, stem-scale turbulence can be observed only when Re_p > 200 [74]. In laboratory experiments, it has been proven that stem-scale vortices can be generated when Re_p > 120, and the wake flow becomes turbulent [75]. The wake flow provides additional turbulence that is no less than the bed shear turbulence, even for the case where the canopy is very sparse [76]. Therefore, the generation and dissipation of turbulent energy in vegetated flow cannot be estimated by bed shear stress but depends on vegetation resistance [77].

Upstream of the canopy, enhanced deposition can be observed due to decelerated velocity and decreased bed shear stress [60,69,78,79]. Sediment deposition increases more significantly with increasing canopy density [60,80]. The enhancement of deposition may occur only in the leading edge of the canopy, and the greater the blockage effect is or the smaller the stem diameter is, the shorter the length of the region with enhanced deposition is [29,60]. Inside the canopy, although the velocity is reduced by stem resistance, sediment deposition may be inhibited due to increased stem-scale turbulence [81,82]. The inhibition of sediment deposition and the enhancement of riverbed erosion within the canopy are closely related to stem-scale turbulence [80]. Follett and Nepf [83] found that net sediment erosion was positively correlated with stem-scale turbulence intensity. Notably, Takemura and Tanaka [84] proposed that stem-scale turbulence would be suppressed when the stem spacing was too small, i.e., in cases with a high canopy density (Φ > 0.44). In other studies, enhanced deposition was observed inside the canopy, which may have resulted from factors other than hydrodynamic conditions, such as microbiological factors [85,86].

The velocity distribution is one of the basic characteristics of vegetated flow, which is related to the flooding capacity, navigability, and transport and diffusion of pollutants in rivers. Liu and Shan [87] classified vegetated flow into four regions based on the velocity variation characteristics in the longitudinal direction, namely, the upstream region, upstream adjusted region, internal adjusted region, and fully developed region, and proposed corresponding analytical solutions for the longitudinal profiles of the depth-averaged mean streamwise velocity. Rameshwaran and Shiono [88] and Huai et al. [89] took the canopy drag force as an additional source term into the depth-averaged Navier–Stokes equation and obtained reasonable models of the lateral profiles of mean streamwise velocity in a fully developed region. Liu et al. [90] introduced a degree of submergence coefficient into the model to enable it to be applied both for submerged and emergent vegetated flows, and investigated the effects of secondary flow on the velocity distribution. White and Nepf [66] proposed an analytical method to model the velocity and Reynolds stress profiles in partially vegetated flow, based on the characteristics of the shear layer and coherent structures. In addition to the above analytical models, numerical solutions are common methods used to obtain the velocity profiles in vegetated flows, such as the singular perturbation method [91] and lattice Boltzmann method [92].

3.2. Flow Structures under the Effects of a Ribbon-like Heterogeneous Canopy

In most natural riverine environments, aquatic vegetation can vary considerably by species, leading to differences in distributional characteristics such as diameter, height, and density. The flow dynamics under heterogeneous canopies are significantly different from those under homogeneous canopies [70,93,94]. In particular, stem diameter and density are two important factors affecting the mean and turbulent parameters of emergent vegetated flows [95]. It is important to understand, quantify, and model the influences of heterogeneous canopies on flow structures and momentum exchange to obtain a comprehensive understanding of the interaction between vegetation and flow [31].

Experiments were conducted to investigate the flow characteristics in a channel planted with a natural heterogeneous canopy that alternatively consisted of different forms of submerged plants (grass, leafy, and cylindrical plants), in which spatial heterogeneity in velocity and turbulence fields was observed. The results showed that the mixed heterogeneous canopy increased velocity reduction and reduced turbulence at the canopy top [96]. Compared with a homogeneous canopy with uniform height, a heterogeneous height results in more intense mixing and stronger momentum exchange at the canopy top [97]. Bai et al. [93] investigated the flow under the action of a complex tree-like canopy, and found that fractal branches increased the flow dispersion and induced wake trails similar to the shape of the plants. The vertical variation in the plant biomass also significantly affected the flow structures. For example, for a canopy whose biomass increased with distance from the riverbed (e.g., Typha), the velocity, integral length scale, and turbulence all decreased with increasing distance from the riverbed. For canopies that presented a vertically uniform distribution, such as Rotala, the velocity, integral length scale, and turbulence were also vertically uniform [27].

The heterogeneity in canopy density affects the flow structures, generates heterogeneity in the flow field [98], and results in stronger dispersion [99]. The heterogeneity of the canopy also has a great influence on the water purification capacity of pollutants [7]. According to de Carvalho et al. [100], a heterogeneous canopy can improve the absorption effects of the heavy metal barium in flooded soil compared with a homogeneous canopy. In a canopy of heterogeneous density that consists of randomly distributed cylinders, turbulent kinetic energy mainly comes from the shedding of stem-scale vortices, while the generation and dissipation of turbulent kinetic energy are unable to reach a balance [95]. A detailed study of the flow structures under the effects of a canopy composed of alternating patches of sparse and dense vegetation was conducted by Li et al. [101]. The results showed that, compared with the homogeneous canopy with the same average density, the heterogeneous canopy caused greater resistance and momentum loss and needed a longer adjustment distance to reach the fully developed region. Furthermore, for vegetated flows with heterogeneous canopies, the shear layer width and momentum thickness fluctuated with variations in density, and the enhanced in-plane turbulent kinetic energy also showed a wavy shape.

3.3. Flow Structures under the Effects of a Patchy Heterogeneous Canopy

In addition to the canopy distributed in the form of continuous ribbons mentioned above, it is also common to see a canopy distributed in discontinuous patches. In particular, vegetation is always distributed in circular patches in its initial growth stage [102], and further grows and expands in the streamwise direction along the channel [103]. This is because the approaching flow usually diverges upstream of the canopy, a large amount of water bypasses both sides of the patch, and only a small amount of water bleeds into the canopy [81,83], as shown in Figure 5. Part of the water that bleeds into the canopy will continue to deflect laterally and flow out due to canopy resistance, and the remaining water flows downstream into the patch wake. The velocity around the patch is enhanced by deflected flow, which promotes the erosion of the riverbed at the edge of the patch and thus may further inhibit the lateral growth of the canopy [104,105].

Different from the flow structures around a solid cylinder with the same diameter as the canopy patch, a steady wake region forms downstream of a porous patch. The flow in the wake region is approximately laminar, and the flow velocity is low and remains constant, which enhances the sediment deposition therein and promotes canopy growth and expansion in the streamwise direction [11,106,107]. At the end of the wake region, the velocity begins to increase and will recover to the level of approaching flow velocity. Both the length of the wake region and the length of the velocity recovery region are closely related to the canopy density, and usually show a decreasing trend with increasing canopy density [108].

Two types of vortices of different scales can be observed downstream of the patch, as shown in Figure 5. One is the small-scale Karman vortex induced by single stems, and the other is the large-scale Karman vortex caused by the entire canopy patch [84]. Since some water bleeds through the canopy and flows directly downstream, its longitudinal momentum will inhibit the interaction of shear layers on both sides of the canopy. Therefore, the formation of patch-scale Karman vortices will be delayed compared with the case of a solid cylinder. Zong and Nepf [109] carried out experimental investigations based on circular patches of different sizes and densities, and found that, with decreasing canopy density, the length of the wake region increased and the intensity of patch-scale Karman vortices decreased.

In the study of Chen et al. [81], it was observed that there were two peaks in the turbulence intensity of flow downstream of the patch. The first peak was located at the ending edge of the canopy, which was related to the stem-scale turbulence within the canopy, and the location of the second peak depended on the formation of Karman vortices. With increasing canopy density, the intensity of the first peak decreased, while the intensity of the second peak increased, and the position of the second peak moved toward the canopy. The sediment deposition was inhibited due to the enhanced turbulence in the region where patch-scale Karman vortices occurred. Nicolle and Eames [108] defined three ranges of canopy density based on different flow patterns corresponding to different canopy densities. When Φ < 0.05, the stems inside the canopy acted as independent individuals on the flow, and only stem-scale vortices were observed. When 0.05 < Φ < 0.15, the canopy acted as a whole on the flow, and the shear layers that formed on both sides of the canopy developed downstream and interacted to generate wake vortices. When Φ > 0.15, the effects of the porous patch were roughly equivalent to those of a solid cylinder of the same size.

Studies have also been conducted to investigate the interactions between two neighboring canopies [102,110,111]. For two neighboring canopies distributed side-by-side in a channel, a wake region with low velocity will form downstream of each individual canopy, similar to flow patterns under the effects of a single patch, and this region is named the primary sedimentary region. As the flow develops downstream, the two wakes interact and result in a secondary sedimentary region, as shown in Figure 6. The formation of the secondary sedimentary region will promote the longitudinal extension of the region with enhanced deposition, thus further promoting the merging of the two adjacent canopies [16,111]. The lateral and longitudinal spacing between neighboring canopies also have important effects on flow patterns [110]. Vandenbruwaene et al. [102] simulated the growth and expansion of canopies by increasing the patch size (D) and decreasing the space between two side-by-side canopies ($\mathsf{\Delta }S$), and revealed the change in flow patterns under the effects of canopy growth. The results showed that the interaction between two adjacent canopies tended to increase initially and then decrease with the continuous increase in $D/\mathsf{\Delta }S$. When the value of $D/\mathsf{\Delta }S$ was greater than a certain threshold, the two adjacent canopies began to act on the flow as a whole. Based on these mechanisms, researchers have further explored the growth and succession process of aquatic vegetation using numerical simulations [16,112,113].

In addition to the lateral interactions between canopies, there are streamwise interactions. For example, riparian shrubs may act as an array of emergent canopy patches on the flow when overbank flow occurs during flood events [114]. Experiments were performed in a channel planted with one-line circular porous canopies [115], and an analogous mixing layer governed by local coherent structures was observed. Moreover, a velocity slowdown region and a velocity recovery region between two in-line adjacent vegetation patches were clearly observed. The existence of patch-scale Karman vortex streets was confirmed, indicating the limited effects of the in-line layout on the formation of Karman vortex streets. A separate study regarding the modeling of the velocity distributions demonstrated that the greater the canopy density was, the lower the frequency of Karman vortex shedding, the greater the turbulence intensity, and the less negligible the secondary flow within the vegetated region were [116].

The semicircular and square patches of the canopy have also been studied. Bennett et al. [117] found that the diversity of flow patterns and the sinuosity of flow increased significantly under the influences of semicircular patches staggered along both sides of the riverbank. Liu et al. [118] simulated the channel flow containing square canopies lined up along the bank by using three-dimensional large eddy simulation. The mean recirculation patterns inside the cavities and the large coherent structures were closely dependent on canopy density and cavity aspect ratio. The turbulence intensity at the interface between the cavities and the main channel was stronger than that in the solid case.

4. Summary and Prospects

This review summarized the generalization and quantification methods of emergent rigid plants in recent studies, and described the flow structures in the presence of different canopy layouts. Three types of common canopy arrangements were included, namely, a ribbon-like homogeneous canopy, a ribbon-like heterogeneous canopy, and a patched heterogeneous canopy. The interactions among aquatic vegetation, flow, and sediment are now drawing significant attention within the research community, given their importance in river ecological restoration. However, the topic of vegetated flow is of great complexity in that there are great differences between the flow structures under the effects of different vegetation forms and arrangements. More in-depth and comprehensive explorations through experiments and simulations are needed to develop a theory that is applicable for different conditions. The issues that need to be addressed in future research are highlighted below:

(1)

Rigid cylinders are reasonable models for some widely distributed herbs but are not good representations of leafy flexible plants. It was proven that there are large differences between the flow characteristics of rigid cylinders and plants of natural forms. Trying to make the plants as realistic as possible is the key to modeling the natural vegetated flow conditions accurately to provide reliable and scientific references for river restoration.

(2)

Aquatic vegetation alters flow patterns, while changes in flow structures will in turn affect the growth of vegetation. The distribution of vegetation may also change in response to seasonal or hydraulic conditions. Based on the understanding of the interaction mechanisms between vegetation, flow, and sediment, future research should consider strengthening the application of numerical simulation methods to investigate the whole process of vegetation growth, expansion, and succession better.

(3)

Vegetated flow is a multidisciplinary topic that involves not only sediment deposition and pollutant transport but also the movement of, predation by, and habitat of aquatic organisms. Therefore, it is necessary to seek reasonable arrangements of aquatic plants according to specific requirements to provide practical solutions for engineering problems and to create a healthy ecological environment.