Numerical Modeling of Vegetation Influence on Tsunami-Induced Scour Mechanisms

Abstract

Tsunami-induced scour around coastal embankments and nearshore structures is a primary cause of structural instability and failure. However, the hydrodynamic mechanisms by which coastal vegetation mitigates this scour remain insufficiently understood. This study employs three-dimensional numerical simulations to investigate the influence of rigid and flexible vegetation on overflow-induced scour downstream of embankments and local scour around structures under tsunami-like inundation. The simulations were conducted using Ansys Fluent 2021R2, utilizing the Volume of Fluid (VOF) method to capture the free surface and the RNG k − ε turbulence model within the Reynolds-averaged Navier–Stokes (RANS) framework. Computational geometries were reconstructed from laboratory experiments, and the model’s reliability was validated against measured water surface profiles. The results demonstrated that vegetation significantly alters flow dynamics, velocity distributions, vortex structures, and both the magnitude and patterns of bed shear stress within scour holes. Specifically, in overflow-induced scour, vegetation suppresses scour intensity by inducing backwater effects, enhancing momentum diffusion, attenuating flow impingement on the bed, and reducing peak bed shear stress. Conversely, for local scour around structures, vegetation increases upstream water depth while intensifying downstream wake vortices, leading to scour hole elongation—particularly under dense and tall vegetation. These findings offer novel insights into the hydrodynamics of vegetation-induced scour mitigation and provide guidelines for optimizing vegetation configurations to enhance the tsunami resilience of coastal infrastructure.

1. Introduction

Tsunamis, characterized by extremely long wavelengths and periods, are typically generated by submarine earthquakes, volcanic eruptions, and other seafloor disturbances [1]. They carry immense hydrodynamic forces capable of causing direct damage to coastal structures. However, extensive post-tsunami field investigations have revealed that scour around structures during tsunami inundation is also a critical factor contributing to structural damage or collapse [2,3]. Tonkin et al. [4] highlighted that two primary scour mechanisms are significantly correlated with tsunami intensity parameters (e.g., flow depth and velocity): overflow-induced scour, resulting from high-energy jets impinging on the landward toe of levees, and local scour, driven by shear flows around nearshore buildings. These two types of scouring primarily affect coastal levees and nearshore buildings, respectively, and are key mechanisms leading to structural instability [2,3]. Therefore, the development of effective mitigation strategies targeting overflow and local scour is essential to improving the resilience and safety of coastal levees and buildings against tsunami hazards.

Given the vulnerability of coastal levees to scouring damage caused by tsunami overtopping, existing studies have demonstrated that installing geotechnical structures—such as concrete foundations [5] and geogrids [6]—at the landward toe of levees can effectively resist the direct impact of tsunamis, slow down the scouring process, or shift the scour downstream [7], thereby protecting levee structures. However, when the scour pit is displaced downstream, various downstream buildings may be put at risk [8]. Moreover, the construction of concrete blocks and geogrids can be technically challenging. Considering that many existing levees were built without such anti-scour facilities, the cost of reinforcing these structures is prohibitively high [9]. In recent years, the energy-dissipating capability of coastal vegetation has garnered increasing attention. Natural or planted vegetation is frequently present behind coastal levees or surrounding nearshore buildings. Post-tsunami field surveys and laboratory experiments have indicated that such vegetation acts as a natural defense, not only shielding inland structures during tsunami events but also reducing overtopping-induced scour at the landward toe of levees [10,11].

Vegetation has been recognized as an effective protective measure for mitigating overflow-induced scour downstream of dikes during extreme tsunami or storm surge events [12]. Vegetation attenuates impact forces and reduces flow velocities by dissipating the energy of large storm waves and tsunamis [13]. Field surveys from the 2004 Indian Ocean Tsunami (IOT) and 2011 Great East Japan Tsunami (GEJT) showed that areas with coastal forests suffered less damage in comparison to those lacking such forests during the tsunami events [10,14]. Recent studies focus on the effects of vegetation on diminishing scour depth by dissipating flow energy. Matsuba et al. [11] showed that vegetation significantly reduces overtopping pressure on the dike surface through laboratory experiments. Rahman et al. [9] found that the maximum scour depth at the dike toe was reduced by approximately 29–37%, and the scour length decreased by about 28–34% by installing double-layer rigid vegetation downstream of the dike. Rahman and Tanaka [8] placed low rigid submerged vegetation together with taller rigid emergent vegetation downstream of the dike at fixed intervals. They observed reductions of 30.2–58.6% in the maximum overflow scour depth and 21.9–41.9% in scour length at the dike toe. In addition, they demonstrated that tsunami-borne driftwood could be intercepted by emergent vegetation that further mitigated local scour. Lin et al. [15] quantified the effects of vegetation density, height, and rigidity on scour dynamics under varying overtopping flow intensities. Since complex flow structures around vegetation are difficult to capture using experimental or analytical approaches [16,17,18], computational tools such as computational fluid dynamics (CFD) have been increasingly adopted to investigate these complex hydrodynamic processes. Numerous numerical studies have examined the effectiveness of coastal forests in mitigating incoming tsunamis under various vegetation configurations [19,20,21]. However, the combined effects of flexible vegetation and the development of scour holes, which are closely linked to flow characteristics, remain insufficiently understood. Therefore, obtaining three-dimensional flow field information within both overflow-induced scour holes and local scour holes in the presence of rigid and flexible vegetation is essential.

This study extends the work of Lin et al. [15]. In that study, the effects of rigid and flexible vegetation on the reduction in tsunami-induced scour were investigated experimentally; however, detailed flow structures were not resolved, which may have limited a comprehensive understanding of the underlying physical mechanisms. In the present study, we employed numerical simulations to examine the influence of vegetation on overflow-induced scour downstream of tsunami dikes and on local scour around structures. The findings are expected to provide guidance for nearshore vegetation configuration for tsunami protection and to contribute to improved disaster prevention, mitigation, and sustainable development in coastal regions. The remainder of this paper is organized as follows: Section 2 describes the implementation of the numerical model; Section 3 validates the numerical results; Section 4 presents and discusses the simulation outcomes; and Section 5 summarizes the main conclusions.

2. Numerical Setup

2.1. Governing Equation and Turbulence Model

The computational fluid dynamics software Ansys Fluent 2021R2is used to perform numerical simulations. To model open channel flow, the Volume of Fluid (VOF) model is used to track the water–air interface. The core of the VOF model is the volume fraction equation, which describes the phase volume fraction within each grid cell. Time-varied and three-dimensional governing equations are given in tensor notation by:

(1)

Continuity equation:

$${\displaystyle \frac{\partial \rho }{\partial t}}+{\displaystyle \frac{\partial }{\partial x_i}}·(\rho u_i)=0,$$

(1)

where $\rho$ is the fluid density, $t$ is time, and $u_i$ are the Cartesian components of the filtered velocity field, where the index $i$ = 1, 2, and 3 indicates the $x$ (streamwise), $y$ (spanwise), and $z$ (vertical) directions, respectively.

(2)

Navier–Stokes equations:

$${\displaystyle \frac{\partial }{\partial t}}\left(\rho u_i \right)+{\displaystyle \frac{\partial }{\partial x_i}}·\left(\rho u_i{u}_j\right)=-{\displaystyle \frac{\partial p_s}{\partial x_i}}+{\displaystyle \frac{\partial }{\partial x_j}}·\left[\mu \left({\displaystyle \frac{\partial u_i}{\partial x_j}}+{\displaystyle \frac{\partial u_j}{\partial x_i}}\right)\right]+\rho f_i,$$

(2)

where $p_s$ is the fluid pressure, $\mu$ is the dynamic viscosity of fluid, and $f$ is the volume force.

(3)

Volume fraction equation:

$${\displaystyle \frac{1}{{\rho }_q}}\left[{\displaystyle \frac{\partial }{\partial t}}({\alpha }_q{\rho }_q)+{\displaystyle \frac{\partial }{\partial x_i}}\left({{\alpha }_q\rho }_q{u}_{qi}\right)\right]=\sum _{p=1}^n({\dot{m}}_{pq}-{\dot{m}}_{qp}),$$

(3)

where this represents the volume fraction of the phase, where $0<{\alpha }_q<1$, ${\sum }_q{\alpha }_q=1$; ${ \rho }_q$ and ${ \mu }_q$ are the density and dynamic viscosity of phase $q$, respectively, ${\dot{m}}_{qp}$ is the mass transfer from phase $q$ to phase $p$, and ${\dot{m}}_{pq}$ is the mass transfer from phase $p$ to phase $q$. The VOF model dynamically averages the physical properties of the fluid based on the volume fraction of each phase. Therefore, in Equations (1) and (2), the density $\rho ={\sum }_q{\alpha }_q{ \rho }_q$ and the viscosity $\mu ={\sum }_q{\alpha }_q{ \mu }_q$, where air is the first phase with ${ \rho }_{air}=$1.225 kg/m³, ${ \mu }_{air}={1.79\times 10}^{-5} \mathrm{k}\mathrm{g}/(\mathrm{m}·\mathrm{s})$, and water is the second phase with ${ \rho }_{water}= 998.2 \mathrm{k}\mathrm{g}/{\mathrm{m}}^3$, ${ \mu }_{air}={1\times 10}^{-3} \mathrm{k}\mathrm{g}/(\mathrm{m}·\mathrm{s})$. For turbulence closure, the Renormalization-Group (RNG) $k-\epsilon$ turbulence model, known to describe low-intensity turbulence flows and flows with strong shear regions more accurately, was selected. The RNG $k-\epsilon$ model systematically removes all small scales of motion from the governing equations by considering their effects in terms of larger-scale motion and a modified viscosity [22].

2.2. Computational Domain, Study Parameters, and Mesh Generation

The computational domain is based on the laboratory experiments carried out in [15]. The experimental flume was a 16 m long ($L_w$), 0.5 m wide ($W_w$), and 0.5 m high ($H_w$) recirculating flume located at the Coastal Engineering Laboratory of Zhejiang University, China. Three physical models were also designed following the scale similarity principle of $L_r=1/100$: an embankment model (EM), vegetation model (VM), and building model (BM), as shown in Figure 1. To realistically reproduce tsunami overtopping conditions, the tailgate was completely opened so that the downstream water level remained below the sediment bed, thereby eliminating tailwater effects on both the overtopping-induced scour behind the embankment and the local scour around the building model. Further details of the experiments can be found in [15].

Based upon the work in [15], eight cases varying in vegetation configuration were simulated (

Table 1. Summary of simulation cases.

No.	Case	Vegetation Parameters			Vegetation Type	Number of Grids (Millions)
		Rigidity	${\mathit{H}}_{\mathit{V}\mathit{M}}$ (cm)	$\mathit{D}$ (%)
1	N ($h_{e0}^{\prime }$= 0.41)	/	/	/	/	2.27
2	N ($h_{e0}^{\prime }$= 0.58)	/	/	/	/	2.35
3	FS13 ($h_{e0}^{\prime }$= 0.58)	Flexible	13	1.38	Submerged	3.61
4	FD13 ($h_{e0}^{\prime }$= 0.58)	Flexible	13	5.40	Submerged	4.44
5	RS5 $(h_{e0}^{\prime }$= 0.58)	Rigid	5	1.38	Submerged	2.94
6	RS13$(h_{e0}^{\prime }$= 0.58)	Rigid	13	1.38	Emergent	4.67
7	RM13$(h_{e0}^{\prime }$= 0.58)	Rigid	13	2.32	Emergent	5.77
8	RD13$(h_{e0}^{\prime }$= 0.58)	Rigid	13	5.40	Emergent	8.36

). Each simulation case nomenclature integrated three identifiers: the first letter indicated the vegetation type (F for flexible, R for rigid, and N for no vegetation); the middle letter denoted the vegetation density (S for sparse at 1.38%, M for medium at 2.32%, and D for dense at 5.40%, where the density is quantified as the fractional area of the bed occupied by vegetation stems [18]); and a numeric suffix specified the $H_{vm}$ (either 5 cm or 13 cm). All cases with flexible configuration remained submerged, whereas rigid ones with $H_{vm}$= 13 cm transitioned to emergent conditions. Two flow rates $Q$ were selected: 0.0097 and 0.0168 ${\mathrm{m}}^3/\mathrm{s}$, corresponding to dimensionless overtopping flow depth $h_{e0}^{\prime }(={\displaystyle \frac{h_{e1}+h_{e2}}{2H_{em}}})$, which represents the initial tsunami flow intensities of 0.41 and 0.58 [15].

To reduce computational costs, the following simplifications were adopted. (1) Since the flow velocity is relatively high (with a depth-averaged overtopping velocity of approximately 0.6 m/s) and the flow is in a supercritical regime, the flexible vegetation primarily deflects in the direction of the flow with minimal oscillatory motion, resulting in less disturbance to the surrounding water. Therefore, the oscillatory motion of flexible vegetation was neglected, and its deflection angle, as measured in [15], was assumed to be constant. In this model, the flexible vegetation is treated as lean but rigid. (2) The bottom boundary was fixed using the final eroded bed geometry obtained from [15], a treatment that has been commonly adopted in previous studies [22,23].

According to [15], the test section between the two $YZ$ cross-sections located at $X$ = −5.4 m and $X$ = 5.2 m in the physical model experiment was taken as the computational domain. Software such as SolidWorks, COMSOL Multiphysics, and Ansys Workbench Meshing (Ansys 2021 R2) was used to perform 1:1 geometric modeling, on the basis of which mesh generation was carried out.

During the geometric modeling stage, the flume, dike, and building models were identical across all simulated conditions and could, therefore, be modeled directly. However, the vegetation and bed-surface profiles varied among different flow conditions, requiring separate modeling for each case. For the vegetation groups, the models corresponding to the numerical simulation conditions adopted in this study are shown in Figure 2 (the rectangular base beneath the vegetation is enclosed by the bed surface during modeling and does not affect the final geometry). Rigid vegetation was modeled directly, whereas flexible vegetation was modeled according to its bending angle in water. In this study, the flume, dike, building, and vegetation group models were all constructed in SolidWorks.

The bed-surface profile ($X$ = 0–3.7 m) was modeled using dense 3D point-cloud data. In the region $X$ = 0–0.8 m, the laterally uniform bed surface [8,9] was extrapolated from a 2D profile recorded by a digital camera [15]. In the region $X$ = 0.8–1.45 m, where the bed surface near the building is more complex, dense 3D point-cloud data were generated using binocular-vision measurement technology [15]. Due to occlusion in the $Y$ = 0–0.06 m range, missing data were reconstructed by interpolating the 2D bed profiles. In the region $X$ = 1.45–3.7 m, where the bed surface is relatively smooth, 3D point-cloud data were interpolated from upstream and downstream measurements. The surface was exported to SolidWorks (Figure 3a). Finally, the embankment, building, vegetation, and bed models were combined in SolidWorks to form the complete computational domain (Figure 3b).

During the meshing process, meshes were generated separately for each case, following the same design principles. To balance accuracy and efficiency, the computational domain was divided into two modules, as shown in Figure 3c. Domain ① ($X$ = −0.5 to 1.55 m, $Y$ = 0 to 0.5 m, $Z$ = 0 to 0.4 m) included the vegetation, building, and scour models, with a mesh size of 12 mm, and local refinements near key surfaces. Domain ②, the non-primary area, used a mesh size of 28 mm. Due to the complex bed surface, domain ① used tetrahedral meshes, while domain ② was mainly hexahedral, with a small portion of tetrahedral meshes. The meshing was done using Workbench Meshing software (Ansys 2021R2), and the front and rear views of domain ① are shown in Figure 3d,e.

It should be noted that this study does not involve the analysis of flow around individual vegetation plants or within vegetation plants, but primarily focuses on the impact of vegetation as a whole on the internal flow field structure of upstream dam-backflow scour pits and downstream localized scour pits near buildings. Therefore, a refined mesh with a resolution of 2 mm on the surface of the vegetation plants (equivalent to 1/4 of the minimum vegetation gap, $c_{vm}$ = 8 mm) is sufficient to meet the research accuracy requirements of this study. Additionally, the RNG $k-\epsilon$ model is a high-Reynolds-number turbulence model that assumes fully developed turbulence. However, due to the presence of the boundary layer near the wall, turbulence is not fully developed in this region. In this case, the turbulence model is not applicable, and special treatment methods, such as wall functions, must be used to address the flow issues near the wall. According to the Ansys Fluent User Manual [24], when using wall functions, it is generally required that the dimensionless wall distance $y^{+}$ be between 30 and 300. With the selected mesh size, after solving in Ansys Fluent, the $y^{+}$ values on the surfaces of the vegetation model, building model, bed surface, and flume wall in the computational domain (①) are all around 80 to 180, which satisfies the requirements for solving the near-wall region and further demonstrates the rationality of the above mesh division.

2.3. Boundary and Initial Conditions and Computational Algorithms

Boundary and initial conditions have a significant impact on the simulation results. The boundary and initial conditions for this study are as follows:

(1)

Inlet Boundary Condition: The model’s inlet is set as a velocity inlet, with varying inlet velocities depending on the operating conditions. The average inlet velocity is calculated based on the water depth and flow rate at the inlet, as well as the inlet water depth.

(2)

Outlet Boundary Condition: The model’s outlet is set as a pressure outlet, with the pressure set to atmospheric pressure and the outlet water depth varying according to the operating conditions.

(3)

Wall Boundary Conditions: The top boundary of the model is set as air and defined as a pressure outlet with atmospheric pressure. The surfaces of the tank walls, quartz sand bed, vegetation clusters, and building surfaces are all set as no-slip walls. In numerical simulations, the roughness of the walls must be specified according to their physical properties. The roughness height for the smooth walls on the sides and bottom of the tank is set to 0.0001 m. The roughness height of the quartz sand bed is typically set to the median particle diameter, which is 0.0028 m. The roughness of the surfaces of the vegetation clusters and building models is higher than that of the tank walls and is set to 0.0005 m [25].

(4)

Initial Condition: The inlet boundary conditions are used to initialize the entire computational domain, facilitating faster convergence.

For computational algorithms, pressure–velocity coupling is performed using the Coupled Model to ensure convergence and stability. For spatial discretization, the gradient is calculated using the Least Square Cell-Based format, the pressure is solved using the PRESTO! algorithm, and both turbulence kinetic energy and turbulence dissipation rate are computed using a second-order upwind scheme to improve computational accuracy. Ansys Fluent allows the selection of either steady-state or transient methods during computation. The steady-state method is only applicable when the physical quantities are in steady state, while the transient method can be used for both steady-state and transient conditions, providing more reliable results. Therefore, this study employs a transient calculation method with a time step of 0.01 s to ensure compliance with the Courant–Friedrichs–Lewy (CFL) condition. Convergence is considered to be achieved when the residuals of all computed variables are less than ${10}^{-3}$.

The simulations were conducted on a High-Performance Computing workstation equipped with Intel Xeon Platinum 8173M processors (2.0 GHz) and 96 GB of RAM. Each simulation case was parallelized across 56 physical cores using MPI (Message Passing Interface). For Case RD13 (8.36 million cells), the average wall-clock time required to reach a statistically stationary state was approximately 60 h.

3. Model Validation

In this study, Cases N and RS13 are selected to validate the numerical models. The experimental free surface elevation profiles in [15] were extracted from side-view images captured by a camera, while the numerical data was based on spanwise-averaged free surface elevations. To determine the mesh resolution for the simulations, a mesh-size independence study was first performed. To conduct the validation, computational meshes with different levels of refinement were used. The refinement level of the numerical model was adjusted by changing the overall mesh size of the computational domain ① and locally refining the mesh around the structure models and bed surface within domain ①. The mesh size of the less critical computational domain ② remained constant at 28 mm. The details of the selected mesh parameters are shown in

Table 2. Grid independence verification parameters for Case N.

Grid Resolution	Grid Size of the Computational Domain ① (mm)	Local Refined Grid Size (mm)	Grid Size of the Computational Domain ② (mm)	Total Number of Grids (Million)	M.A.E. (mm)
Course	18	6	28	1.08	3.07
Median	12	4	28	2.35	2.58
Fine	10	2	28	7.38	2.57

and

Table 3. Grid independence verification parameters for Case RS13.

Grid Resolution	Grid Size of the Computational Domain ① (mm)	Local Refined Grid Size (mm)	Grid Size of Vegetation Surface (mm)	Grid Size of the Computational Domain ② (mm)	Total Number of Grids (Million)	M.A.E. (mm)
Course	12	4	3	28	2.85	4.67
Median	12	4	2	28	4.67	1.89
Fine	12	4	1	28	10.11	1.74

, and the validation results are illustrated in Figure 4.

It can be observed that all mesh refinement levels defined in Table 2 and Table 3 show good agreement with the experimental data. The mean absolute error (M.A.E), defined as ${\displaystyle \frac{{\sum }_{i=1}^n\left|X_i-X_i^{\prime }\right|}{n}}$, where $X_i$ are the measurement values, $X_i^{\prime }$ are the simulated values, and $n$ is the total number of data points, is used to evaluate the performance of numerical models. The M.A.Es between the numerical and experimental water surface profiles for Case N ($h_{e0}^{\prime }$ = 0.58; Figure 4a) are 3.07 mm, 2.58 mm, and 2.57 mm for coarse, medium, and fine meshes, respectively. These small and closely matched errors demonstrate both the accuracy of the numerical model and the mesh independence of the results. Two possible sources of deviation are identified: (1) millimeter-scale fluctuations of the free surface in the physical model tests due to undular hydraulic jumps and (2) the exclusion of weak seepage flow within the sediment bed in the numerical model. Given the small discrepancies between simulation and experimental data, the numerical model is considered feasible. Taking into account both computational efficiency and simulation accuracy, the mesh size for domain ① is set to 12 mm, and the locally refined mesh size around structure models and the bed surface is set to 4 mm.

Due to the relatively small diameter and spacing of the vegetation elements in the vegetation-group model, the vegetation surfaces require a more refined mesh than that used for the building models and the bed surface. Based on the numerical model validation under the non-vegetated conditions, Case RS13 ($h_{e0}^{\prime }$ = 0.58, vegetation case; Figure 4b) was selected for further numerical verification. The detailed mesh parameters are listed in Table 3, and the validation results are shown in Figure 4b. The results indicate that, for the coarse, medium, and fine meshes, the numerical simulations show good agreement with the experimental data. The M.A.Es between the simulated and measured water surface profiles for Case RS13 are 4.67 mm, 1.89 mm, and 1.74 mm, respectively. Although the coarse mesh exhibits relatively larger errors, the errors associated with the medium and fine meshes are small and very close to each other. This demonstrates that the resistance effects induced by the vegetation-group model can be well resolved when the mesh size on the vegetation surfaces is less than or equal to 2 mm, satisfying the requirements of numerical accuracy and grid independence. Considering both computational efficiency and simulation accuracy, a vegetation surface mesh size of 2 mm was, therefore, adopted.

4. Results and Discussions

4.1. Overflow-Induced Scour

4.1.1. Velocity Distribution

When investigating the flow characteristics during the local overflow-induced scour process, velocity distribution is a key parameter, as it directly governs the intensity and spatial extent of scour. Figure 5a,b illustrate the velocity field at the vertical central section of the overflow scour hole under non-vegetated conditions, where the velocity $U$ represents the resultant velocity composed of the $X$-, $Y$-, and $Z$-direction components. It can be observed that the overflow velocity reaches its maximum along the embankment slope and decays rapidly toward both sides. These velocity patterns indicate that the overflow is jointly influenced by gravity and inertia on the slope, resulting in a concentrated and energetic flow.

The overflow enters the stilling basin in the upper part of the embankment slope; however, the main body of the overflow remains relatively independent within the ambient fluid, exhibiting a velocity distribution distinctly different from that of the surrounding water above. After detaching from the slope, the overflow continues to move in its original direction due to inertia, with potential energy continuously converting into kinetic energy. Once the flow leaves the slope boundary, strong shear interactions with the ambient water in the stilling basin develop, accompanied by vertical spreading, leading to an expansion of the relatively low-velocity shear zones on both sides of the slope. At this stage, since the overflow and the ambient fluid have the same density, momentum exchange between them occurs primarily through turbulent diffusion, resulting in a continuous decrease in the mean velocity [26].

At the location where maximum scour occurs, the overflow impinges obliquely onto the bed surface, causing a change in flow direction. The flow then moves upward along the adverse bed slope at the downstream edge of the scour hole. Due to significant energy loss during the impact, the overflow velocity reaches its minimum at this stage. During the subsequent ascent along the adverse slope, potential energy is converted back into kinetic energy, but the reduction in the flow cross-sectional area leads to a secondary increase in velocity. The results reveal that the adverse slope at the downstream edge of the scour hole undergoes the greatest bed deformation during the later stages of the experiment, where high-velocity flow transports sediment toward the downstream region of the scour hole. Upon entering the relatively flat bed downstream of the scour hole, the overflow continues to move upward due to inertia, while the near-bed flow velocity decreases, causing part of the transported sediment to gradually deposit and form a depositional sand dune.

To examine the effects of vegetation on the velocity field, Figure 5c–h show the velocity distributions on the vertical central sections of the overflow-induced scour hole under vegetated conditions. Vegetation induces a backwater effect in the stilling basin, causing the overflow to enter the basin earlier. Compared with non-vegetated cases at the same discharge, shear and entrainment between the overflow and the ambient fluid are enhanced. With increasing vegetation density $D$, height $H_{vm}$, and stiffness, momentum diffusion intensifies, leading to reduced lateral velocity decay, a wider overflow core region (defined as $U>0.4$ m/s within the scour hole), and more rapid streamwise velocity attenuation along the centerline of the section. This indicates that under the influence of vegetation, the energy transfer between the overflow and the surrounding fluid becomes more pronounced. The distribution of kinetic energy in the overflow becomes more dispersed. As a result, the kinetic energy carried by the overflow when it reaches the bed decreases, thereby reducing the scouring rate of the overflow.

For RD13 ($h_{e0}^{\prime }$ = 0.58, Figure 5h), dense rigid emergent vegetation significantly raises water level at the stilling basin, causing strong mixing and an upward shift of the overflow core, which detaches from the slope and enters the scour hole at a smaller inclination angle. This reduces the efficiency of potential-to-kinetic energy conversion and further suppresses scour. Overall, vegetation transforms overflow energy from a concentrated impact mode to a distributed dissipation mode by extending the energy dissipation pathway. Low-velocity wake zones form downstream of individual vegetation elements; however, their spatial extent is limited to the order of the vegetation diameter.

4.1.2. Streamline Patterns

Streamlines provide an intuitive representation of flow paths and vortex structures within the scour hole and, therefore, constitute an important tool for investigating scour processes. Figure 6a,b show the streamline patterns of the overflow-induced scour hole at the vertical central section under non-vegetated conditions. Distinct recirculating vortex structures are observed in the section. From the free surface downward, a large positive vortex (counter-clockwise) and a smaller negative vortex (clockwise) are present.

This vortex system forms because, after entering the stilling basin, the vertical domain expands abruptly. Driven by gravity and inertia, the overflow continues to move along the slope direction but cannot occupy the entire basin, leading to momentum exchange with the ambient fluid and inducing flow motion and vortex generation. The main body of the overflow is located between the two vortices, with streamlines connecting the dam crest and the depositional dune downstream of the scour hole.

As discharge increases (Figure 6a,b), the sizes of both the positive and negative vortices increase, and both vortices are located in low-speed regions within the scour hole. Although the negative vortex is close to the bed, its velocity is relatively low, so it is not the primary scouring area. The streamlines of the main flow bend sharply as they approach the scour hole, and this intense scouring shapes the lowest point of the hole.

To examine the effects of vegetation on flow structures, Figure 6c–h show the streamline patterns at the vertical central section under vegetated conditions. Vegetation-induced backwater causes the overflow to enter the stilling basin earlier and impinge on the scour hole at a smaller inclination angle. Consequently, the curvature of the main overflow streamlines within the scour hole decreases, and the impact location on the downstream adverse slope shifts upward, thereby reducing the peak impact pressure. Furthermore, the upward-shifting main overflow increasingly compresses the space of the positive vortex.

Numerical results show that increasing vegetation density $D$, height $H_{vm}$, and stiffness progressively reduce the size of the positive vortex, indicating diminished energy dissipation, consistent with the observed reduction in the energy loss along the overtopping scour section in [15]. The negative vortex shifts closer to the deepest point of the scour hole; however, due to its low velocity, it tends to inhibit scouring. In Case RD13 ($h_{e0}^{\prime }$ = 0.58, Figure 6h), dense rigid emergent vegetation raises the water level in the stilling basin sufficiently to eliminate the positive vortex. This occurs because the overflow enters the basin earlier, and the streamlines are confined to the surface layer, leaving no space for vortex development.

4.1.3. Distribution of Bed Shear Stress

Regarding scour studies, bed shear stress ($\tau$) serves as a fundamental physical quantity for describing the interaction between the flow and the bed. The calculation of τ is represented as follows:

$${\tau }_x=\left(\mu +{\mu }_t\right){\left.{\displaystyle \frac{\partial u}{\partial z}}\right|}_{z=0},{\tau }_y=\left(\mu +{\mu }_t\right){\left.{\displaystyle \frac{\partial v}{\partial z}}\right|}_{z=0},$$

(4)

$$\tau =\sqrt{{\tau }_x^2+{\tau }_y^2}.$$

(5)

Based on the grain size of bottom sediments, the corresponding critical shear stress ${\tau }_{cr}$ is 2.03 Pa. Figure 7a,b provide the distribution of bed shear stress $\tau$ within the overflow scour hole under the non-vegetated condition. It can be observed that the shear stress on the upstream positive slope of the scour hole is generally lower than ${\tau }_{cr}$. Moreover, the peak values of $\tau$ over the surface of the scour hole significantly deviate from the scour-hole bottom and instead are concentrated in the transition zone between the downstream adverse slope of the scour hole and the depositional sand dune. This presents a highly spatially oriented band-like distribution, indicating that during the quasi-steady scour stage, the dominant scouring region is located on the downstream adverse slope rather than at the bottom of the scour hole. As tsunami intensity $h_{e0}^{\prime }$ increases, the banded region of peak shear stress ($\tau$ > 4.5 Pa) expands, accompanied by an increase in the maximum shear stress within this region. This mechanism explains why the scour rate for Case N ($h_{e0}^{\prime }=0.58$) exceeds that for Case N ($h_{e0}^{\prime }$ = 0.41), as reported in [15].

To examine the effect of vegetation on bed shear stress $\tau$, Figure 7c–h show the distributions of $\tau$ within the overflow scour hole for vegetated cases along $X$ = 0–700 mm. The results reveal that vegetation significantly modifies the shear stress distribution by reducing peak $\tau$ values [26], narrowing the peak region, and shifting it downstream toward the depositional sand dune. These effects intensify with increasing vegetation density ($D$), height ($H_{vm}$), and stiffness. This behavior is associated with the vegetation-induced upward shift and straightening of the main overflow core, which transfers high-speed flow from the scour-hole bed toward the surface. As ${\tau }_x$ and ${\tau }_y$ are governed by the vertical velocity gradients $\partial u/\partial z$ and $\partial v/\partial z$, the reduced near-bed gradients lead to pronounced attenuation of peak shear stress. Moreover, the bed shear stress $\tau$ over the depositional dune within the vegetation patch is markedly lower than that in non-vegetated cases, indicating a substantial reduction in near-bed shear on the fixed bed. This decrease reflects the redistribution of flow momentum and enhanced energy dissipation induced by vegetation. For rigid vegetation with $H_{vm}$ = 13 cm, increasing vegetation density leads to a progressive weakening and eventual disappearance of the banded high-shear region ($\tau$ > 4.5 Pa), demonstrating a pronounced modification of the near-bed shear-stress field. In addition, the area where $\tau$ exceeds the critical shear stress ${\tau }_{cr}$(=2.03 Pa) is significantly reduced. These hydrodynamic features are consistent with the reduced scour and enhanced deposition observed in the corresponding physical experiments, although the present simulations are conducted on a fixed bed.

4.2. Local Scour Around Structures

4.2.1. Velocity Distribution

The three-dimensional flow characteristics around the local scour hole near the structure are significant; therefore, data from multiple cross-sections are required to comprehensively analyze the surrounding flow field. Figure 8 presents a schematic of three vertical sections (Section 1, Section 2 and Section 3) around the structure, with the coordinates of the start and end points of each section projected onto the $XY$ plane. The velocity fields along these three vertical sections are analyzed in the following.

Figure 9(a1–b3) show the velocity field distributions along the vertical sections of the local scour hole under non-vegetated conditions. Section 1, located inside the scour hole, exhibits high water levels and deep scour due to upstream impoundment, with high-velocity zones distributed obliquely along the curved bed and a localized near-bed velocity maximum. Section 2, at the structure corner, is characterized by flow bypassing, with a near-wall low-velocity zone ($Y$ = 380 mm) and an extensive high-velocity region near the free surface caused by flow contraction and momentum concentration. Section 3, downstream of the structure and adjacent to a depositional mound, shows shallow flow with low surface velocities and a localized high-velocity zone over the mound bed.

To investigate the effects of vegetation on the velocity field distributions along various vertical sections of the local scour hole, Figure 9(c1–h3) present the velocity fields under vegetated conditions. In all vegetated cases, the water surface elevations in Section 1 and Section 2 are higher than those in the non-vegetated case. This is primarily because the upstream vegetation increases flow resistance and energy loss, leading to reduced flow velocity and increased water depth. In contrast, the water surface elevation in Section 3 is comparable to that of the non-vegetated case.

In Case FD13 ($h_{e0}^{\prime }$ = 0.58; Figure 9(d1–d3)), dense submerged flexible vegetation markedly increases the downstream velocity gradient, resulting in higher velocities in the upper layer and lower velocities near the bed. Consequently, a pronounced velocity difference develops upstream of the local scour hole in Section 1, with the high-velocity region exhibiting a strongly curved pattern due to inertia. In Case RD13 ($h_{e0}^{\prime }$ = 0.58; Figure 9(h1–h3)), dense emergent rigid vegetation disturbs the flow throughout the entire water depth, reducing downstream velocity gradients. As a result, the velocity difference in Section 1 becomes weak, and the low-velocity zone is confined to the near-bed region within the scour hole.

4.2.2. Streamline Patterns

To further illustrate the flow pathways and vortex structures along the three sections, Figure 10(a1–b3) present the streamline patterns of the vertical sections of the local scour hole under non-vegetated conditions. In Section 1, a distinct negative vortex is observed near the scour-hole surface. According to previous studies [24], this vortex corresponds to a horseshoe vortex. The presence of the horseshoe vortex induces sweep and ejection events through its interaction with the bed, leading to intermittent sediment transport [24]. In Section 2, another pronounced negative vortex appears near the structure model, which is a wake vortex generated by flow separation at the structure corner. On the right side of the wake vortex, a smaller horseshoe vortex is also observed when $h_{e0}^{\prime }$ = 0.58, which may represent the downstream tail of the U-shaped horseshoe vortex identified in Section 1. The low-pressure region of the horseshoe vortex entrains sediment particles and ejects them into the wake region, where deposition occurs downstream of the structure, forming an elliptical depositional mound. In Section 3, small vortex clusters are observed near the free surface adjacent to the structure, likely caused by boundary-layer separation induced by an adverse pressure gradient associated with the abrupt velocity reduction downstream of the structure. As ${ h}_{e0}^{\prime }$ increases, the sizes of the horseshoe vortex in Section 1, the wake vortex in Section 2, and the near-surface vortex clusters in Section 3 all increase, leading to greater scour depth.

To examine the influence of vegetation on the streamline patterns of the vertical sections, Figure 10(c1–h3) show the corresponding results under vegetated conditions. In Section 1, comparison between Cases FD13 ($h_{e0}^{\prime }$ = 0.58; Figure 10(d1–d3)) and RD13 ($h_{e0}^{\prime }$ = 0.58; Figure 10(h1–h3)) with the same vegetation height ($H_{vm}=$13 cm) indicates that curved flexible vegetation and emergent rigid vegetation exert contrasting effects on the horseshoe vortex near the scour-hole bed. As discussed earlier, these two vegetation types, respectively, increase and decrease the downstream vertical velocity gradient, resulting in enlargement and attenuation of the horseshoe vortex, respectively (Figure 10(d1–d3),(h1–h3)). In Section 2, the wake vortex gradually enlarges with increasing vegetation density ($D$), height ($H_{vm}$), and stiffness, explaining the experimental observation [15] that dense and tall vegetation under strong inflow conditions ($h_{e0}^{\prime }$) promotes pronounced downstream extension of the scour-hole tail. In Section 3, under flexible vegetation conditions, the small near-surface vortex clusters adjacent to the structure increase in size, which is associated with increased water depth due to the reduced height of the elliptical depositional mound.

4.2.3. Distribution of Bed Shear Stress

To identify the primary scour regions within the local scour hole, the distribution of bed shear stress $\tau$ was analyzed. As reported in [15], distinct morphological features, including triangular mounds and an inclined sediment belt, are formed around the local scour hole (Figure 10(a1–a3)). The spatial distributions of $\tau$ under non-vegetated conditions are illustrated in Figure 10(a1–a3),(b1–b3). Analysis of the bed shear stress within the scour hole shows that $\tau$ on the upstream bed increases initially and then decreases with increasing scour depth, forming a distinct high-shear-stress band at the mid-portion of the upstream bed. The shear stress within this band exceeds the critical shear stress ${\tau }_{cr}$(=2.03 Pa), indicating that it represents the dominant region of scour development within the local scour hole.

Irregular regions of peak shear stress also occur at the downstream part of the scour hole near the structure corner, connected to the upstream high-shear band. These shear stress distributions indicate that scour rates are relatively low in the deeper upstream portion of the scour hole, and the scour hole is in a downstream expansion stage. With increasing tsunami intensity $h_{e0}^{\prime }$, both the peak shear stress and the scour rate increase.

Compared to the overflow scour hole, the bed shear stress $\tau$ on the surface of the local scour hole is relatively larger, with the peak value increasing from 6.5 Pa to 8.5 Pa. However, the overflow scour volume is approximately ten times that of the local scour volume, as [15] reported. This phenomenon is attributed not only to the significant scale differences between the embankment and structure models, but also to the fundamental differences in the dynamic mechanisms of overflow and local scouring. According to Figure 6a,b and Figure 7a,b, the flow direction within the high bed shear stress zone at the rear edge of the overflow scour hole is unidirectional; thus, entrained sediment can be rapidly transported out of the hole. In contrast, as shown in Figure 10(a1–a3),(b1–b3) and Figure 11a,b, vortices exist within the high-shear regions of the local scour hole, causing sediment to undergo repeated suspension and deposition, which significantly reduces the sediment transport efficiency.

To investigate the influence of vegetation on the bed shear stress $\tau$ distributions along the vertical sections of the local scour hole, Figure 10(c1–h3) present $\tau$ distributions for vegetated cases over the range $X$ = 700–1500 mm. Under the influence of upstream vegetation in the overflow scour hole, the irregular regions of peak shear stress at the downstream part of the scour hole expand and exhibit increased $\tau$ values. These effects become more pronounced with increasing vegetation density ($D$), height ($H_{vm}$), and stiffness. This indicates that vegetation enhances the strength of wake vortices, thereby increasing bed shear stress and promoting downstream development of the scour hole, which explains the experimental observation that dense and tall vegetation under strong inflow conditions ($h_{e0}^{\prime }$) leads to significant downstream elongation of the local scour hole.

It should be noted that for flexible vegetation with $H_{vm}$ = 13 cm (Cases FS13 and FD13), the flow field downstream of the vegetation exhibits pronounced vertical velocity stratification, with substantially higher velocities in the upper layer than in the near-bed region, as shown in the velocity distributions along vertical Section 1 (Figure 9(c1,d1)). In contrast, for rigid vegetation with the same height (Cases RS13, RM13, and RD13), the velocity difference between the upper and lower layers is considerably reduced (Figure 9(f1,g1,h1)), indicating enhanced vertical momentum exchange. Consistent with these flow characteristics, the near-bed shear stress τ over the triangular mound located upstream of the scour hole is lower in Cases FS13 ($h_{e0}^{\prime }$ = 0.58; Figure 11c) and FD13 ($h_{e0}^{\prime }$ = 0.58; Figure 11d) than in the rigid-vegetation cases, particularly Case RD13 ($h_{e0}^{\prime }$ = 0.58; Figure 11h). This reduction in $\tau$ reflects the redistribution of flow momentum associated with vegetation flexibility, while the implications for sediment transport and morphological evolution are inferred from corresponding experimental observations rather than directly resolved by the fixed-bed simulations.

5. Conclusions

Tsunami-induced scour around coastal embankments and nearshore structures is a major contributor to structural instability and failure. To investigate the hydrodynamic mechanisms through which coastal vegetation influences scour-related processes, this study employs the RNG $k-\epsilon$ turbulence model in ANSYS Fluent to simulate flow characteristics over fixed, final scoured beds, based on representative physical model experiments. The simulated water-surface profiles agree well with laboratory measurements, indicating that the numerical model reliably captures the key flow features.

For overflow conditions downstream of embankments, the overflow core attains its maximum velocity along the slope-parallel centerline and gradually decays downstream. After detachment from the slope, shear-induced vortical structures govern flow impingement on the bed, forming a concentrated band of elevated near-bed shear stress that is closely associated with the locations of intense scour observed in the experiments. The introduction of vegetation produces a backwater effect that elevates the overflow trajectory, enhances momentum diffusion, and redistributes flow energy away from the near-bed region, leading to a reduction in near-bed shear stress on the fixed bed.

For local flow around nearshore structures, the hydrodynamic field is dominated by the interaction between upstream horseshoe vortices and downstream wake vortices. Peak bed shear stress occurs downstream of the structure, which corresponds to the experimentally observed tendency for longitudinal scour development. Vegetation increases overall flow resistance and energy dissipation, reducing the incident flow velocity approaching the structure. However, it also modifies wake dynamics by intensifying downstream vortical structures and locally increasing bed shear stress in the wake region. This hydrodynamic response provides a plausible explanation for the elongated scour holes observed in physical experiments under dense and tall vegetation conditions, even though the numerical simulations are conducted on a fixed bed.

However, it should be noted that the RNG $k-\epsilon$ model adopted in this study is based on the Reynolds-averaged Navier–Stokes (RANS) framework and provides only time-averaged turbulence information, without resolving transient turbulent features such as vortex shedding or the energy cascade of turbulent kinetic energy. Future studies, supported by high-performance computing resources, may adopt more advanced approaches such as the $k-\omega$ SST model, Large Eddy Simulation (LES), or Direct Numerical Simulation (DNS) to achieve higher temporal and spatial resolution of turbulent flow structures, secondary currents and three-dimensional flow separation near vegetation edges. Additionally, the effect of the elastic modulus of vegetation on flow dynamics—particularly regarding the extent of vegetation deformation and its interaction with the flow—requires further investigation. Finally, combining numerical simulations with real-time observations of scour evolution would enable a more comprehensive study of turbulence characteristics during various stages of downstream embankment scour and local scour development around hydraulic structures.