Abstract

This study investigates the hydrodynamics and sediment transport processes around an isolated submerged non-uniform flexible vegetation (FV) element in an open-channel flow using FLOW-3D HYDRO. The observed reconfigured FV shape is represented using a hybrid solid–porous configuration with a height-varying frontal area and porosity. Numerical simulations incorporate the RNG k–ε turbulence model, the saturated Forchheimer porous-media formulation, and Nielsen’s bedload transport formulation, and are validated against laboratory measurements of velocity profiles and bed elevation changes. Results show that FV induces a distinct three-layer flow structure, with a velocity deficit within the canopy and an accelerated shear layer at the canopy–water interface. Flow vectors reveal wake formation and coherent vortices that promote sediment mobilization, while turbulent kinetic energy (TKE) peaks above the canopy due to shear-layer instabilities. A C-shaped scour hole develops at the FV base, followed by downstream deposition, consistent with experimental observations. Although computational fluid dynamics (CFD) slightly underpredicts the maximum scour and deposition magnitudes, it effectively reproduces the centerline bed-elevation trends (R² = 0.92) and key morphodynamic patterns with satisfactory agreement. The proposed robust and computationally efficient CFD framework demonstrates the capability of reproducing complex flow–vegetation–sediment interactions in vegetated channel systems and is applicable to river restoration, sediment management, and ecohydraulic design.

1 Introduction

Vegetation in open channel flows strongly influences hydraulic resistance, velocity structure, turbulence generation, and sediment transport processes. Submerged non-uniform flexible vegetation (FV) generates spatially heterogeneous flow fields through variable drag and flow-induced reconfiguration, thereby modifying local scour, deposition, and sediment redistribution. Understanding these coupled flow–vegetation–sediment interactions is important for river restoration, floodplain management, channel stability, and aquatic habitat sustainability.

Experimental studies have demonstrated that submerged vegetation substantially modifies flow structure, turbulence, and sediment transport processes. Submerged flexible vegetation generates layered flow with reduced in-canopy velocity, strong shear layers near the canopy top, and elevated turbulence intensity and turbulent kinetic energy (TKE) at the sheath–canopy and canopy–water interfaces, which influence momentum exchange, wake formation, sediment entrainment, and deposition (Ghisalberti and Nepf 2006; Gautam et al. 2019, 2025a). Flexible vegetation also alters the critical conditions for incipient sediment motion, while vegetation-generated turbulence lowers the threshold for sediment resuspension and regulates bedload transport, bedform evolution, scour, and downstream wake deposition (Wang et al. 2015; Zong and Nepf 2010; Tang et al. 2019; Yang and Nepf 2019). Recent studies further highlighted the importance of vegetation flexibility and morphology, showing that flexible canopies and non-uniform plant forms significantly affect turbulence generation, secondary circulation, and sediment redistribution patterns (Liu et al. 2024, 2025; Matsumoto et al. 2025). Additional flume investigations confirmed that vegetation spacing, type, and flexibility strongly modify turbulence structure, Reynolds stresses, and wake recovery in vegetated channels (John et al. 2023; Patra et al. 2023; Kumar et al. 2023). Nevertheless, most existing studies primarily consider vegetation patches, arrays, or simplified canopies rather than isolated non-uniform flexible vegetation. Moreover, detailed measurements around flexible vegetation remain experimentally challenging and spatially limited because of plant motion and evolving bed morphology.

Recent advances in computational fluid dynamics (CFD) have provided powerful tools for investigating detailed flow–vegetation interactions that are difficult to resolve experimentally. Early numerical studies primarily used distributed drag-force formulations to represent vegetation-induced momentum loss and successfully reproduced velocity attenuation, canopy shear layers, turbulence generation, and wake development in submerged vegetated flows (Li and Xie 2011; Boothroyd et al. 2016; Ghani et al. 2019; Dehrashid et al. 2023). More advanced numerical approaches, including immersed boundary methods (IBM), large eddy simulation (LES), and fully coupled fluid–structure interaction (FSI) models, were later developed to explicitly resolve vegetation deformation, vortex dynamics, and momentum exchange (Marjoribanks et al. 2014; Mattis et al. 2015; Familkhalili and Tahvildari 2022; Wang et al. 2022; Xu et al. 2022; Jin et al. 2024; Liu and Lin 2025). These studies demonstrated that vegetation flexibility substantially modifies drag distribution, Reynolds stresses, Kelvin–Helmholtz instabilities, canopy turbulence, and coherent wake structures (Liu et al. 2021; Alsina and Cherian 2024; Zhang et al. 2024; Chen and Li 2025; Chen et al. 2026). In parallel, CFD has increasingly been applied to sediment transport and morphodynamic processes in vegetated environments. Numerical investigations showed that vegetation can significantly influence local scour, suspended sediment deposition, and bed evolution patterns by altering near-bed velocity and turbulence structure (Kim et al. 2015; 2018; Ji et al. 2026). These studies also highlighted the importance of vegetation morphology, density, and frontal area distribution in controlling hydrodynamic response.

Nevertheless, most existing CFD studies primarily focus on hydrodynamics, rigid vegetation, idealized strip-like flexible elements, or vegetation patches and arrays under fixed-bed conditions. Realistic non-uniform flexible vegetation with height-dependent frontal area and experimentally observed reconfigured shape is rarely represented in morphodynamic simulations, while coupled flow–vegetation–sediment interactions around isolated submerged flexible vegetation remain largely unexplored. Although advanced IBM and FSI approaches can explicitly resolve vegetation motion and coherent turbulence structures, such models are computationally expensive and are often limited to hydrodynamic analysis without mobile-bed feedback. Consequently, the coupled interactions among flow modification, vegetation reconfiguration, and sediment redistribution around submerged flexible vegetation remain insufficiently understood. Moreover, while porous resistance concepts are widely applied in environmental flow modeling, their application to submerged non-uniform flexible vegetation interacting with a mobile sediment bed has received limited attention. Therefore, a computationally efficient and experimentally validated framework is needed to reproduce coupled flow–vegetation–sediment dynamics around isolated non-uniform flexible vegetation.

Accordingly, the present study develops a three-dimensional CFD model in FLOW-3D HYDRO to simulate coupled flow and sediment dynamics around isolated non-uniform flexible vegetation under clear-water conditions. The experimentally observed reconfigured vegetation shape is represented using a hybrid solid–porous configuration, in which the lower dense stem region is modeled as solid while the upper flexible canopy is represented as a porous zone with height-dependent resistance. The model is coupled with sediment transport formulations and validated against laboratory measurements of velocity profiles and bed elevation changes. The objectives of this study are to:

1. Investigate vegetation-induced modifications to flow structure and turbulence characteristics,
2. Examine local scour and downstream deposition patterns around submerged flexible vegetation, and
3. Evaluate the capability of an efficient CFD framework to reproduce coupled flow–vegetation–sediment interactions around non-uniform flexible vegetation.

2 Methodology

2.1 Governing equations

FLOW-3D can simulate complex fluid flows using various numerical methods and turbulence models. It employs the Volume of Fluid (VOF) method to track free surfaces by assigning each cell a water fraction (F), ranging from 0 (empty) to 1 (full), allowing partial fills at interfaces. To represent solid boundaries, it uses the FAVOR (Fractional Area/Volume Obstacle Representation) method, which defines geometry through fractional cell occupancy. FLOW-3D solves the three-dimensional Reynolds-averaged Navier-Stokes (RANS) equations using a finite volume approach on a structured rectangular grid, incorporating both VOF and FAVOR techniques for incompressible flows. The general continuity and RANS equations (Flow Science, Inc. 2025) for this set-up can be written as Equations 1 and 2:

(1)

(2)

Where:

i ∈ {x, y, z}	=	momentum/velocity component and corresponding coordinate direction,
j ∈ {x, y, z}	=	spatial coordinate direction of convection and differentiation,
vi	=	velocity component in coordinate direction i,
xi	=	spatial coordinate corresponding to direction i,
gi	=	local fluid acceleration in coordinate direction i,
ψi	=	Reynolds stress term in coordinate direction i requiring turbulence closure,
Π	=	hydrostatic pressure,
ΩF	=	fluid volume fraction per cell in the FAVOR method,
t	=	time,
Si	=	flow-accessible cross-sectional area associated with coordinate direction i,
ρ	=	fluid density, and
bi	=	flow losses within the porous media in coordinate direction i.

To estimate the turbulent Reynolds stress tensor, a turbulence closure model is required. The standard k-ϵ model is widely used, relying on a linear relationship to approximate shear stress. An alternative, the RNG k–ε model, uses the same fundamental equations but derives its constants explicitly rather than empirically. While it does not resolve turbulence structures in space or time, previous studies have found it effective for simulating flow in open channels. Thus, the RNG k–ε model is adopted in this study. The model involves two transport equations (Flow Science, Inc. 2025), (Equations 3 and 4):

(3)

(4)

Where:

k	=	turbulent kinetic energy,
Pk	=	production of turbulent kinetic energy due to mean velocity gradients,
u, v, and w	=	velocity components in the x, y, and z directions, respectively,
Bk	=	buoyancy-induced production of k,
ε	=	dissipation rate of k,
Dk and Dε	=	diffusion terms, and
λ1, λ2, and λ3	=	user-defined dimensionless parameters.

In the RNG k–ε model, default values for λ₁ and λ₃ are 1.42 and 1.6, respectively, while λ₂ is derived from k and P_k.

Vegetation is modeled as a porous region using the saturated Forchheimer model (Flow Science, Inc. 2025), which accounts for both viscous and inertial drag components. Porosity is represented in FLOW-3D HYDRO as the volume fraction Ω_F. Modeling the porous medium as a continuum and averaging over control volumes yields mass conservation equation (Equation 5):

(5)

Where:

Vm

=

microscopic flow velocity.

The momentum equation in porous media is based on Darcy's 1856 (Flow Science, Inc. 2025) observation that flow rate is proportional to the pressure gradient, expressed as Equation 6:

(6)

Where:

K	=	intrinsic permeability, and
μ	=	dynamic viscosity of the fluid.

A lower K indicates higher flow resistance, or drag, which is represented in the Navier-Stokes equations as a velocity-proportional drag term: b_i = F_DV_m,_žwhere F_D is the porous media drag coefficient. For media with large particles or fibers, significant microscopic velocity can cause inertial losses proportional to velocity squared, especially when the Reynolds number in porous media, R_eP > 10. Linear (Darcian) and quadratic (non-Darcian) losses combine into a single expression for the volumetric drag force per unit volume, F_D, in Equation 7:

(7)

Where:

α and β	=	linear and non-linear drag coefficients, respectively,
ϕ	=	porosity, and
D	=	average equivalent spherical diameter of the sand grains or fibers of the porous media.

When test data is unavailable, FLOW-3D HYDRO estimates α and β as: α = 180/D², β = 3/D.

In FLOW-3D, the sediment bed is represented as packed sediment for modeling bed-load transport. The packed sediment maintains a critical packing fraction, typically set at 0.64 by default but adjustable by the user. Bed-load movement occurs within a thin surface layer, a few grain diameters thick, where grains are mobilized through shear-induced entrainment and small-scale eddies at the sediment interface. In this study, the Nielsen (Flow Science, Inc. 2025) equation is employed to compute the volumetric sediment bed transport rate per unit bed width per time (q_b,r) (Equations 8 and 9).

(8)

(9)

Where:

r	=	sediment species index,
фr	=	dimensionless bed-load transport rate of sediment species r,
ρs,r	=	density of sediment species r,
ρ	=	fluid density,
dr	=	grain diameter of sediment species r,
gm	=	magnitude of gravitational acceleration,
θr	=	local Shields parameter for sediment species r,
θc,r	=	critical Shields parameter for sediment species r,
βN,r	=	constant for sediment species r, with a default value of 12.0, and
vb,r	=	volume fraction of sediment species r in the bed.

The local Shields parameter θ_r is calculated from the local bed shear stress τ (as per Equation 10), and the critical Shields parameter θ_c,r is obtained using the Soulsby–Whitehouse formulation (Flow Science, Inc. 2025) (Equations 11, 12).

(10)

(11)

(12)

Where:

τ	=	bed shear stress, computed using the law of the wall,
d*r	=	dimensionless grain diameter of sediment species r, and
μ	=	dynamic viscosity of the fluid.

The bed-load layer thickness δ_r for saltating sediment is estimated using van Rijn’s (1984) relation: δ_r = 0.3d_*r^0.7d_r(θ_r/θ_c,r-1)^0.5. For each sediment species ‘r’, the suspended sediment concentration is obtained by solving its respective transport equation.

(13)

(14)

Where:

Cs,r	=	suspended sediment mass concentration of sediment r,
Df	=	diffusivity,
cs,r	=	suspended sediment volume concentration of sediment r,
us,r	=	suspended sediment velocity vector of sediment species r,
usettling,r	=	sediment settling velocity of sediment species r, and
ν​	=	kinematic viscosity of the fluid (water).

The suspended sediment velocity calculated as: u_s,r = ū + u_settling,r*c_s,r. where ū is the velocity of the fluid–sediment mixture. The c_s,r is related to C_s,r by: c_s,r = C_s,r / ρ_s,r.

2.2 Experimental set-up

The numerical simulations in this study are based on experiments conducted at the Hydraulics Laboratory, Indian Institute of Technology Roorkee, as reported by Gautam et al. (2025b), and are briefly summarized here for completeness. A 28 m long, 1 m wide, rectangular recirculating flume with a 0.1% slope and fixed bed was used for the experiments. The test section, 5 m in length, featured a 25 cm thick layer of coarse sand (mean diameter d₅₀ = 2.36 mm) forming the sediment bed. A single FV model (representing sedge) was installed at the sediment bed center, 17.5 m from the inlet, as shown in Figure 1. The vegetation was 15 cm tall (hv) in in the undeformed state, a frontal width varying from 1 to 12 cm, reaching a maximum (Wv) of 12 cm (Figure 2a). It consisted of 35 flat leaves attached at the base, each with a mean frontal width of 5 mm. Although measuring plant flexibility is challenging (Nepf 2012), a flexible model with suitable material and density was chosen in this study to replicate sedge behaviour. Experiments and numerical simulations were conducted under two conditions: non-vegetated (plain bed, P) and vegetated bed (V), both under clear-water conditions (u∗/u∗c < 1, where u∗ is the approach shear velocity and u∗ c is the critical shear velocity of the bed material).

Figure 1 Experimental set-up.

Figure 2 (a) Flexible vegetation and the scouring and deposition locations, and (b) ADV measurement locations (L1 and L2).

Uniform flow was maintained using a tailgate for the plain bed tests. Experiments were performed at a flow rate of Q = 0.082 m³/s, yielding a uniform flow depth (Z) of 15 cm, a mean streamwise velocity (Um) of 0.55 m/s, a Reynolds number (R_e) of 50,235, a Froude number (F_r) of 0.50, and a shear velocity (u_∗) of 3.4 cm/s. During flow, the mean deflected height of the plant (Hv) was 8.75 cm. The flexible vegetation exhibited an average canopy porosity of 0.94, with a submergence ratio (Z/Hv) of 1.71. Three-dimensional instantaneous velocities were recorded using a Nortek micro-ADV (16 MHz) at a sampling frequency of 50 Hz for 60 seconds, resulting in 3000 data points per location (locations L1 and L2 are shown in Figure 2b).

Vertical spacing between measurement points was 0.5 cm within the canopy and 1 cm above, with over 20 points per profile. The ADV data was post-processed using the Phase-Space Thresholding (PST) method (Goring and Nikora 2002). Scour patterns were measured using a 5 MHz ultrasonic bed profiler operating with a 1-second sampling interval and collecting 1000 samples.

2.3 Numerical set-up

The numerical simulations of the experiments described in Section 2.2 were conducted using FLOW-3D HYDRO, a CFD software. The numerical formulation follows the governing equations introduced in Section 2.1, with the Cartesian coordinate directions x, y, and z corresponding to the directional indices used in Equations 1–4. For case P, simulations were run without FV, with only leveled sediment bed and solid aprons before and after the test section. For case V, FV was placed at the same location as in the experimental set-up and the numerical simulation was performed. The simulation units were set to the SI system. For case P, the simulation finish time was set to 400 s to achieve a steady and consistent solution. For case V, the finish time was extended to 3600 s to ensure steady flow and complete sediment transport. Water at 20°C, selected from the fluid database, was used as an incompressible single-phase fluid. Sharp-interface tracking was activated to distinguish the free surface, and gravity was set at -9.81 m/s² in the z-direction. Turbulence and viscosity were modeled using the RNG k–ε model. Although LES or detached eddy simulation (DES) can more explicitly resolve coherent vortex structures, they require substantially greater computational resources. Since coupled flow–vegetation–sediment simulations are themselves computationally challenging, the RNG k–ε model was selected because it has been widely applied in open-channel flows and provides computational efficiency, accurate prediction of mean flow characteristics, and lower numerical complexity. The open channel was divided into three sections in the FLOW-3D geometry module: an upstream solid apron (Bed-1, 0–15 m) and a downstream solid apron (Bed-3, 20–28 m), both made of cement mortar, and a middle sediment bed (Bed-2, 15–20 m). Based on experimental observations, a roughness height of 0.0019 m was assigned to Bed-1 and Bed-3 (corresponding to Manning’s n = 0.0137 (Yen 1992)), while a roughness height of 0.0059 m (2.5×d₅₀) was assigned to the sediment bed by the FLOW-3D solver (Flow Science, Inc. 2025). The modeled open channel with FV is shown in Figure 3.

Figure 3 Numerical domain showing solid aprons, sediment bed, and FV location.

Due to the complexity of FV modeling, explicitly simulating each leaf and its motion in FLOW-3D was not feasible. Experimental observations indicated that FV showed minimal fluctuations once deflected by the flow. Therefore, the reconfigured shape was traced, modeled in AutoCAD, and imported into FLOW-3D at the corresponding location. To simulate flow through gaps between leaves, a porous media approach was adopted: the upper part of the FV, characterized by large frontal gaps, was treated as a porous medium, while the lower part was modeled as solid due to the absence of frontal gaps, as shown in Figure 4. To simulate the drag induced by the porous portion of the FV, the saturated Forchheimer model was selected, which uses the porosity (φ) and equivalent drag diameter (D) of the porous medium, as described in Equations 5–7. A value of φ = 0.94 was specified, as obtained experimentally using the water-displacement method. The value of D was specified as 10 mm, corresponding to approximately twice the mean leaf frontal width, and was selected based on vegetation morphology together with preliminary comparative simulations, which showed improved agreement with the overall experimental velocity profiles, particularly near the bed and canopy interface. Further, the sediment transport model was activated, and the number of sediment species was set to 1 (r = 1), with a d₅₀ (d_r) of 2.36 mm, a sediment density ρ_s,r of 2650 kg/m³, and an angle of repose of 32 degrees. The Nielsen equation was used for the bed load transport rate, and the Soulsby–Whitehouse equation was used for defining the critical Shields number. The maximum packing fraction was 0.64, while the entrainment and bed load coefficients were 0.018 and 12, respectively. The interface between different geometries was defined using the FAVOR and VOF methods (Flow Science, Inc. 2025).

Figure 4 Reconfigured FV 3D model used in the numerical simulation.

In FLOW-3D, a structured mesh composed of hexahedral cells, also known as an orthogonal Cartesian mesh, was used. Previous studies have shown that this type of uniform mesh is ideal for complex-shaped objects and free surface flows, providing accurate and stable solutions (Gautam et al. 2022). In the present study, the entire numerical domain was discretized using a single mesh block. To determine the optimal cell size, a grid independence study was conducted by comparing percentage relative errors in volume flow rates between experimental and numerical results (Figure 5). A 5-mm mesh was found to provide accurate results with no significant improvement from further refinement. Although additional refinement could potentially improve resolution of localized flow gradients near the vegetation and scour region, FLOW-3D guidelines recommend that mesh size be well greater than the median sediment diameter (d₅₀ = 2.36 mm) to avoid numerical instability and non-physical sediment behavior. Refinement near or below d₅₀ is discouraged, especially in sediment transport modeling. Thus, the 5 mm mesh ensured stability, physical realism, and computational efficiency. Therefore, a 3D orthogonal mesh with a 5-mm cell size was constructed. This set-up was applied identically for both the P and V cases.

Accurate replication of any physical model in numerical simulations requires careful specification of boundary and initial conditions. FLOW-3D provides various boundary condition options to define the specific states of the model. In the coordinate system, the x-axis represents the longitudinal flow direction, the z-axis corresponds to the vertical direction, and the y-axis denotes the lateral direction relative to the origin. Since the flow domain is structured as a hexahedron within the Cartesian system, the primary mesh block consists of six distinct boundaries (Xmin, Xmax, Ymin, Ymax, Zmin, Zmax) (Flow Science, Inc. 2025).

Figure 5 Percentage relative error in volume flow rate vs cell sizes.

Since the mean velocity and flow depths were already defined in the experiments, the upstream boundary (Xmin) of the channel was set as the water inlet, with a specified velocity of 0.55 m/s and a fluid elevation of 15 cm, matching the experimental conditions. At the downstream boundary (Xmax), a pressure outflow condition with a fluid elevation of 15 cm was applied to maintain smooth flow continuity through the outlet. The free surface at the top boundary (Zmax) was defined by assigning a specified pressure condition and a fluid fraction of F = 0, ensuring atmospheric pressure. The bottom boundary (Zmin) and the side boundaries (Ymin and Ymax) were set as walls (W), imposing no-slip conditions at the bed and sidewalls.

The upper canopy region of the FV was modeled as a porous medium based on experimental observations indicating limited unsteady motion once reconfigured by the flow. Although this simplification does not explicitly resolve individual leaf dynamics or fine-scale fluid–structure interactions and may reduce accuracy in resolving fine-scale turbulence near the canopy interface, it effectively captured the bulk drag effects, flow stratification, wake development, and sediment redistribution patterns. The porous-media approach also ensured computational feasibility and numerical stability, which would be difficult to maintain with fully resolved fluid–structure interaction (FSI) or immersed boundary method (IBM) approaches, particularly for coupled morphodynamic simulations.

This study focused on a single flow condition corresponding to the validated experimental case. While boundary conditions such as turbulent inflow or varying water depths were not tested here, the experimental campaign included a broader range of scenarios. Future simulations will extend the model to multiple hydraulic conditions, including varying submergence ratios and flow depths, to assess the robustness and generalizability of the results. While the analysis is based on a single FV, the findings provide foundational insights into flow resistance, turbulence generation, and localized sediment transport. The modeling framework can be extended to simulate vegetation patches or arrays by adjusting plant density and spatial arrangement. Such extensions will help bridge the gap between controlled laboratory settings and complex field-scale ecohydraulic applications.

3 Results and Discussion

This study aims to simulate FV in an open channel using FLOW-3D and to compare and analyze the resulting flow hydrodynamics and local sediment dynamics. In this section, the numerical model is validated against experimental results by comparing streamwise velocity distributions at measurement locations L1 and L2, along with the centerline scour and deposition profiles. Additionally, velocity vectors and turbulence intensities in the xy, xz, and yz planes are plotted and compared for both the the plain (P) and vegetated (V) cases. Furthermore, sediment bed contours are plotted and analyzed.

3.1 Model validation

The numerical model was validated by comparing simulated streamwise velocity profiles with experimental data reported by Gautam et al. (2025b) at two centerline locations, L1 and L2, under both plain (P) and vegetated (V) conditions. The velocity profiles were normalized by the mean streamwise velocity (u/Um) and plotted against the relative vertical position (Z/Hv), as shown in Figures 6 and 7. For case P, Figure 6 (a–b) shows that the simulated velocity profiles agree well with experimental results at both L1 and L2. The profiles exhibit a typical logarithmic distribution, indicating fully developed open-channel flow with no obstructions. The high consistency between experimental and CFD data confirms the model's accuracy in replicating baseline hydraulic behaviour.

Figure 6 Comparison of streamwise velocity (u) from experimental and CFD results for the plain case (P) at (a) L1 and (b) L2.

In case V, the comparison is shown in Figure 7(a–b). At L1 (Figure 7a), located upstream of the vegetation, the flow remains largely unaffected, and the velocity distribution resembles that of the plain bed case. However, at L2 (Figure 7b), located just downstream of the vegetation, a distinct three-layer structure in the velocity profile is observed—typical of submerged vegetated flows. This layered structure results from the interaction between vegetation-induced drag, vertical momentum exchange, and canopy shear-layer development under subcritical flow conditions (F_r = 0.50).

Figure 7 Comparison of streamwise velocity (u) from experimental and CFD results for the vegetated case (V) at (a) L1, and (b) L2.

The CFD results effectively capture this behaviour: near the bed (Z/Hv < 0.4), velocity increases gradually due to lower drag. Within the vegetation canopy (0.4 < Z/Hv < 0.85), a velocity dip is evident, caused by increased resistance from the vegetation body. Around the canopy top (0.85 < Z/Hv < 1.2), a sharp velocity increase occurs as drag decreases in the more flexible upper part of the FV. In the free-stream region (Z/Hv > 1.2), the flow stabilizes and resumes a logarithmic profile. Although slight deviations are noted around the vegetation top (particularly at V-L2), the model reasonably replicates the complex flow behavior observed experimentally. For the vegetated downstream profile (V-L2), the Root Mean Square Error (RMSE) and R² values between the numerical and experimental results were 6.75 cm/s and 0.85, respectively, indicating good agreement. These discrepancies can be attributed to the simplification of FV as a porous medium and the limitations of capturing the dynamic behavior of flexible leaves. To further validate the model’s capability, the simulated centerline bed elevation change (ΔZ) was compared with experimental results for the vegetated case, as shown in Figure 8.

Figure 8 Comparison of centerline bed elevation change (ΔZ) from experimental and CFD results for the vegetated case (V).

The plot shows net scour and deposition along the centerline (x), with the vegetation located at x = 0 cm. The model captures both the extent and shape of the scour hole and deposition region with reasonable accuracy. The maximum scour depth observed was 2.48 cm, while the CFD simulation estimated it as 2.12 cm, corresponding to an underprediction of ~14.5%. Similarly, the maximum deposition height was 1.92 cm in the experiment and 1.54 cm in the simulation, corresponding to an underprediction of ~19.8%. Although the model slightly underestimates both scour depth and deposition height, the overall trends and spatial patterns are well represented. The RMSE and R² values for the centerline bed-elevation profile were 0.32 cm and 0.92, respectively, confirming strong agreement between the numerical and experimental results.

This underprediction is attributed not to simulation duration, as both numerical and experimental observations confirmed that sediment transport stabilized within 1 hour, but rather to model simplifications. Specifically, the representation of flexible vegetation as a porous medium does not capture unsteady leaf-scale motions and dynamic interactions that can locally enhance turbulence and bed shear stress. These simplifications are likely to contribute to the slight underestimation in sediment mobilization intensity. Unresolved leaf-scale motion and canopy-interface turbulence may influence localized sediment entrainment and vortex evolution near the vegetation boundary. Nevertheless, the model effectively replicates the key morphodynamic features and provides reliable insights into vegetation-induced sediment processes. Together, the close agreement between experimental and numerical results for both velocity and bed evolution confirms that the model effectively replicates key hydrodynamic and sediment transport processes around isolated submerged flexible vegetation.

3.2 Scouring and deposition

Figure 9 presents the contour plot of bed elevation change (ΔZ) obtained from numerical simulation for the vegetated case (V). The X-axis represents the streamwise direction, the Y-axis represents the lateral width of the flume, and the Z-axis indicates the net change in sediment bed elevation. The simulation results reveal distinct patterns of local scour and deposition induced by the presence of FV. A well-defined C-shaped scour hole forms around the base of the FV, consistent with flow separation and vortex formation around the stem structure. This is followed by a deposition zone downstream, resulting from deceleration of the flow and sediment settling.

Figure 9 Scour and deposition contour for the vegetated case (V).

The maximum scour depth of 2.12 cm occurs at the plant base along the centerline, matching the profile in Figure 8; similarly, the maximum deposition height of 1.54 cm is also consistent with the centerline results. The longitudinal extent of the deposition zone exceeds that of the scour hole, indicating a wider wake recovery region where sediment settles. In contrast, the lateral extent of both scour and deposition zones appears similar, suggesting symmetric flow disturbance and recovery across the channel width. The formation of the C-shaped scour zone can be attributed to horseshoe vortex systems and flow contraction around the vegetation stem. The increased drag and turbulence near the FV base enhance local shear stress, initiating sediment scouring. Under the present clear-water condition (u_*/u_∗c < 1), sediment entrainment was primarily governed by localized turbulence amplification and near-bed shear enhancement induced by vegetation-induced vortical structures. As the flow passes the vegetation and turbulence dissipates, the velocity gradient reduces, leading to sediment deposition in the downstream wake zone. The interaction between vegetation-induced drag and turbulence plays a central role in the spatial distribution of scour and deposition. The numerical model captures this interaction well, replicating both the extent and morphology of the erosion–deposition pattern experimentally observed.

3.3 Velocity and vectors

The streamwise velocity distribution and corresponding 2D velocity vectors were computed numerically and analyzed in three orthogonal planes: xy, xz, and yz, as shown in Figure 10. These plots reveal the spatial evolution of the velocity field and near-field hydrodynamics around the submerged FV, highlighting velocity gradients, wake formation, and flow recirculation.

Figure 10(a) shows the streamwise velocity (u) distribution in the horizontal (xy) plane at z = 8.75 cm, corresponding to the mean deflected height of the FV. As the flow approaches the vegetation, a distinct reduction in streamwise velocity is observed, forming a low-velocity zone centered at the FV location. The minimum velocity occurs directly at the FV position, where obstruction and drag are highest. Immediately downstream, a wake region with sustained low velocities persists, while the surrounding flow accelerates, resulting in the formation of a shear layer at the wake boundary. This shear layer facilitates lateral mixing between the slower core flow and the faster outer flow. The velocity vectors clearly illustrate this behaviour, with shortened vectors in the wake zone and elongated vectors on either side, confirming shear-induced momentum exchange.

Figure 10(b) presents the velocity field in the xz-plane at the channel centerline (y = 0.5 m), aligned with the FV center. Upstream of the FV, the velocity profile is logarithmic and consistent with fully developed open-channel flow. Upon encountering the FV, the velocity decreases sharply, especially beneath the canopy, due to drag imposed by FV. A localized velocity minimum forms immediately downstream of the FV. Above the canopy, streamwise velocity slightly increases due to flow acceleration over the obstruction. As the flow continues downstream, velocity begins to recover, though it remains lower than the undisturbed free-stream values. The vector field reveals upward flow motion immediately behind the FV, likely caused by the deflected canopy shape and turbulence-driven vertical mixing, which is important in mobilizing sediment and redistributing momentum vertically.

Figure 10(c) shows the flow in the yz-plane at x = 17.65 m, approximately 15 cm downstream of the FV base. The streamwise velocity is lowest near the center, consistent with the wake core, and increases laterally outward. Interestingly, the vertical structure of the velocity deficit mirrors the FV frontal area distribution: greater velocity reduction occurs near the canopy top (higher frontal width), while a smaller reduction is observed near the base (lower frontal width). Reduced velocities near the bed also result from wall shear stress. The velocity vectors exhibit a recirculating flow pattern, with clockwise and counterclockwise vortices forming on either side of the FV centerline. This symmetric vortex pair induces upward flow motion, contributing to sediment resuspension and transport. The presence of the deposition mound beneath this plane likely diverts the flow laterally, further reinforcing the formation of these coherent vortical structures. Overall, the simulations demonstrate the coupled influence of FV-induced wake turbulence and coherent vortices on momentum redistribution and sediment mobilization. The CFD model captures these dynamics well, validating its application in submerged vegetated flow simulations.

Figure 10 Distribution of streamwise velocity (u) in planes (a) xy, (b) xz, and (c) yz, along with respective 2D vectors for the vegetated case (V).

3.4 Turbulent energy

The distribution of turbulent kinetic energy (TKE) in the flow domain provides insights into the generation, evolution, and dissipation of turbulence induced by by submerged FV. Figure 11 presents TKE contours in three orthogonal planes; (a) xy at canopy height (z = 8.75 cm), (b) xz along the flume centerline (y = 0.5 m), and (c) yz across a vertical plane downstream of the FV (x ≈ 17.65 m). These plots illustrate spatial variations in turbulence intensity and its role in sediment mobilization and wake dynamics.

Figure 11 Distribution of turbulent kinetic energy (TKE) in planes (a) xy, (b) xz, and (c) yz for the vegetated case (V).

Figure 11(a) depicts the TKE field in the horizontal xy-plane at the deflected vegetation height (z = 8.75 cm). A distinct turbulent wake is observed downstream of the FV, characterized by a narrow, high-TKE core that expands laterally and dissipates further downstream. The highest TKE (~0.0032 J/kg) is concentrated just behind the FV, aligned with the zone of lowest streamwise velocity shown previously. This intense turbulence is associated with shear layer development at the vegetation–wake interface, where high velocity gradients occur between the obstructed core flow and accelerated outer flow. The gradual decay of TKE downstream reflects the transition from coherent vortex structures to more isotropic turbulence and eventual re-laminarization of the wake. The symmetric shape of the wake suggests balanced vortex shedding from both sides of the FV.

In Figure 11(b), the xz-plane along the flume centerline reveals vertical distribution of TKE as the flow interacts with FV. The highest turbulence (~0.0074 J/kg) occurs slightly above the canopy top, where flow separation and shear layers are strongest. This is consistent with the velocity inflection zone observed in Figure 10(b), which typically promotes Kelvin–Helmholtz instability and vortex roll-up. Moderate TKE is also seen in the lower canopy region and near the bed immediately behind the vegetation, indicating turbulence penetration downward that can enhance near-bed sediment resuspension. The overall vertical structure reveals a plume-like spreading of turbulent energy upward and downstream, confirming the presence of wake-induced mixing. Low TKE upstream of the FV confirms minimal upstream disturbance due to flow stagnation and shielding effects of the vegetation body.

Figure 11(c) shows the TKE distribution in the yz-plane, located 15 cm downstream of the FV center. The turbulence structure is symmetric mushroom-shaped, flanked by lower turbulence zones laterally. This pattern indicates the presence of a counter-rotating vortex pair in the wake region, commonly observed in flows past isolated bluff bodies. These vortices promote upward and outward momentum exchange, evident from the symmetric rise of TKE above the canopy and reduced values near the bed. Notably, elevated turbulence persists near the side boundaries, suggesting lateral expansion of the wake and possible interaction with sidewall shear layers. Near the bed, TKE remains low except under the FV base, where it rises slightly due to flow convergence and downward momentum transfer. These TKE fields confirm that FV enhances turbulence through canopy drag, wake shear, and vortex generation. The numerical model captures these dynamics effectively, validating its capability to resolve flow–vegetation–sediment interactions in submerged vegetated channels.

4 Conclusion

This study presents a comprehensive numerical investigation of flow and sediment dynamics around an isolated non-uniform submerged flexible vegetation (FV) using FLOW-3D HYDRO. The model incorporates height-varying frontal area, porosity-based drag representation, and sediment transport modeling, validated using detailed laboratory measurements. The simulation effectively reproduces the dominant flow–vegetation–sediment interactions, including velocity stratification, wake formation, turbulence generation, and associated scour–deposition patterns around the FV. CFD-predicted velocity and bed-elevation profiles showed good agreement with experimental data, supported by R² values of 0.85 and 0.92, respectively, validating the model’s fidelity. The results further indicate that vegetation-induced drag, momentum redistribution, and recirculating wake structures play an important role in turbulence modulation, sediment entrainment, and downstream deposition processes under submerged flow conditions. Slight underpredictions of scour and deposition magnitudes were attributed to the porous-media simplification of FV and unresolved leaf-scale flow interactions.

Overall, the study demonstrates that CFD, when calibrated with experimental observations, is a powerful and computationally efficient tool for investigating ecohydraulic and morphodynamic processes in vegetated channels. The proposed framework offers potential applications in river restoration, sediment management, vegetated floodplains, and nature-based engineering design. The modeling approach developed here can be extended to varying hydraulic conditions and more complex vegetation configurations, including vegetation patches with different plant densities and spatial arrangements. Future studies involving fully resolved vegetation-flow interactions coupled with mobile-bed morphodynamics may further improve prediction of canopy-scale turbulence and localized sediment processes.

Acknowledgments

The authors acknowledge IIT Roorkee for providing the facilities and support to conduct this research. The encouragement and constructive feedback from colleagues and mentors are also sincerely appreciated.

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