Flow Dynamics and Local Scour Around Seabed-Mounted Artificial Reefs: A Case Study from Torbay, UK

Abstract

This study investigates the flow dynamics and local scour around a Reef Cube^® artificial reef deployed in Torbay, UK, using computational fluid dynamics. The flow is modelled using Reynolds-Averaged Navier–Stokes (RANS) equations with a k-ω SST turbulence model. A novel hydro-morphodynamic model employing the generalized internal boundary method in HELYX (OpenFOAM-based) is used to simulate scour development. Model performance was validated against experimental data for flow fields, bed shear stress, and local scour. Flow simulations across various scenarios demonstrated that parameters such as the orientation angle and arrangement of Reef Cubes significantly influence flow patterns, bed shear stress, and habitat suitability. The hydro-morphodynamic model was used to simulate scouring around a reef cube in the Torbay marine environment. Results indicate that typical tidal flow velocity flow in the region is barely sufficient to initiate sediment motion, whereas extreme flow events, represented by doubling the mean flow velocity, significantly accelerate scour development, producing holes up to ten times deeper. These findings underscore the importance of considering extreme flow conditions in scour analyses due to their potential impact on the stability and failure risk of AR projects.

1. Introduction

Historical records reveal that human activities have detrimentally affected millions of acres of coral reefs and depleted various fish populations worldwide due to overexploitation, habitat degradation, pollution, and global warming [1,2,3,4]. Artificial reefs (ARs), which are human-made structures designed to mimic natural reef characteristics, have emerged as a crucial strategy to mitigate these impacts by enhancing fishery resources, improving coastal ecological conditions, and providing habitats for marine organisms [5,6,7,8].

The relationship between flow dynamics and AR performance is well-documented in the literature, particularly in terms of upwelling (which brings nutrients) and the wake regions (which affect the settlement of organisms). Upwelling occurs when deep, nutrient-rich water rises toward the surface near the AR, enhancing nutrient transport, the food chain, and fish settlement [9,10]. In contrast, in the wake region downstream of the AR, water flow is disrupted by the reef structure, which promotes biomass production by facilitating sediment and nutrient deposition. This area supports the AR’s role as a shelter, spawning ground, and feeding area, attracting marine species [9,11,12].

Jiang et al. [13] and Jiang et al. [14] showed good agreement between experimental and numerical data on cubic and trapezoidal ARs, supporting computational fluid dynamics (CFD) for AR performance monitoring. Ahmed et al. [1] found that streamlined helmet AR designs improve flow velocity compared to hollow cube ARs, potentially increasing nutrient supply to organisms inside the reef. Jiao et al. [7] examined the flow field around tube-shaped ARs arranged in triangular tube stack configurations, revealing that upwelling and back vortex intensities increase with for larger stack. Wang et al. [3] concluded that the number and size of openings in cubic ARs significantly impact upwelling. Rahman et al. [15] used CFD to analyze a decommissioned oil platform’s performance as an AR, indicated the influence of changing the angles of incident flow on upwelling and wake eddy effects. Wang et al. [16] noted the positive impacts of increasing the complexity of available habitat on reef fish abundance, species diversity, and richness using cubic and triangular ARs constructed applying fractal theory. Jiang et al. [17] revealed that the roughness of the reef surface significantly affects turbulence intensity and bottom shear stress. Kong et al. [18] showed that porous ARs made from recycled oyster shells improved biological attachment and ecosystem stability. Barros et al. [19] modelled cubic ARs with varying numbers of open cylindrical, showing that specific hole configurations ensure nutrient renewal through effective circulation. Guo et al. [20] found that macrobenthic communities were more abundant and diverse downstream of ARs, while microbial diversity increased upstream. Maslov et al. [9] compared circular and droplet-shaped multi-functional ARs, and found droplet-shaped ARs perform better for biodiversity and shoreline protection compared to circular ones on two key variables: upwelling velocity and wake region.

While these studies offer valuable insights into the functionality of ARs, the anticipated decades-long lifespan of ARs necessitates a shift in focus toward a more comprehensive understanding of their long-term performance in dynamic marine environments. Pan et al. [21] highlighted the need for considering factors such as stability against slipping, overturning, and seabed erosion. Baine [22] found that over 50% of AR programmes fail due to poor site selection and insufficient planning, with seabed material properties playing a critical role in the success of AR projects. Poor site selection, particularly in locations susceptible to seabed sedimentation and erosion, has been recognized as the leading cause of AR programme failures, proven to be even more critical to the project’s success than the reef design characteristics for flow functionality [23,24,25,26].

Research on local scour around ARs is scarce. Tang et al. [27] investigated the effects of current velocities and reef shapes on equilibrium local scour around ARs in a flume, finding that AR geometry significantly influences local scour. Nguyen et al. [28] developed an empirical model to predict scour volume around a cubic artificial reef under steady flow, highlighting flow velocity and sediment size as key factors. Yang et al. [29] conducted a study on local scour around a cubic AR using FLOW-3D and RANS equations with the RNG k-ɛ turbulence model. They examined how the number of openings and incident angles affected scour characteristics. Zheng et al. [30] used flume experiments and FLOW-3D simulations using the RNG k-ε turbulence model to investigate local scour around cubic ARs under steady flow. The results showed that scour was most intense at the front corners of the AR, and flow velocity had the greatest influence, followed by sediment grain size and opening ratio. Yang et al. [31] examined how varying opening ratios in trapezoidal ARs influence local scour, revealing that velocity amplification at sharp corners, not horseshoe vortices, is the primary scour driver. Liu et al. [32] emphasized the significant threat posed by local scour to the stability of artificial reefs and highlighted the scarcity of research on effective scour countermeasures. They conducted flume experiments and CFD simulations to evaluate the influence of deflector plates on scour and flow dynamics around artificial reefs, emphasizing the critical role of flow–structure interaction in reef stability.

This study aims to provide a comprehensive numerical investigation of the performance of a novel AR type, the reef cube^® (RC), developed by ARC Marine, focusing on both the flow characteristics around the reef and the formation of scour around its structures. The flow field is modelled using the incompressible, unsteady RANS equations, coupled with the k-ω SST turbulence model. The temporal development of local scour around the structure is assessed through a novel hydro-morphodynamic model, utilizing the Generalized Internal Boundary (GIB) method within the OpenFOAM-based HELYX 4.0.0 software suite.

The following section, Methodology, outlines the approach used to develop the hydro-morphodynamic models. Section 3 presents model validation against experimental data from the literature, including flow fields, bed shear stress (BSS), and scouring. Section 4, Results, is divided into two parts: the first focuses on flow field modelling around various RC configurations, while the second addresses scour modelling around a single RC. Finally, the Conclusion summarizes the key findings, limitations, and contributions of this study.

2. Methodology

The numerical modelling in this study comprises two main parts. The first part involves applying hydrodynamic modelling to investigate the influence of AR presence on adjacent flow characteristics. This is accomplished by solving the incompressible unsteady RANS equations with the k-ω SST turbulence model closure, as implemented in OpenFOAM. The RANS model was selected due to its widespread use in predicting flow behaviour in practical turbulent flow cases, as it offers a balance of computational efficiency and reasonable accuracy for many engineering applications [33,34]. The second part focuses on evaluating stability performance of the AR through modelling the temporal evolution of local scour. For this purpose, a coupled hydro-morphodynamic model, following the classical approach, is developed within the OpenFOAM-based HELYX software suite. In the classical approach, the hydrodynamics of the water phase are solved using CFD, while no physical description of the sand is defined as a separate phase (as in two-phase models). In this approach, empirical sediment transport formulas are applied to display the morphology of the sandy bed at the water-sand interface, and the natural behaviour of sand is induced through sand sliding models. The implemented model is based on the previously developed and validated models in Bordbar et al. [35], Bordbar et al. [36], and Bordbar et al. [37]. The Generalized Internal Boundary (GIB) technique, developed by Karpouzas [38], is used to model the sand-water interface. Unlike the original code, where the water-sand interface was treated as the domain’s bottom boundary, GIB acts as an internal boundary. This approach offers greater flexibility in mesh deformation and enables the simulation of scouring around ARs, a capability not available in the original code developed by the authors, which was limited to modelling scour around vertical piers.

Figure 1 illustrates the coupling procedure in a flowchart for the classical approach, which needs to be repeated at every time step of the simulation. Shear stress information, resulting from hydrodynamic modelling, is used to compute sediment transport on the GIB surface, and mesh adjustments are made accordingly. During the solution process, numerical instability may arise, as noted by Stahlmann and Schlurmann [39]. To mitigate deviations caused by such instability, filtration methods are applied to suppress spurious oscillations. In this study, a dual-mesh concept and mesh-to-mesh interpolation are employed as a filtering technique to enhance the numerical stability of sediment propagation. This is followed by a sand sliding mechanism to replicate the natural behaviour of sand. Finally, the updated mesh is used as the computational mesh for the next time step in the solution process.

2.1. Bedload Sediment Transportation

In general, sediment transportation comprises bedload and suspended load sediment transport models. The bedload model computes the flux of sediments that roll, slide, or jump along the bed in a thin layer very close to the bed surface, while the suspended load model accounts for sediments that are lifted into the water column and carried by the flow over greater distances, depending on factors such as flow velocity and sediment size. In the present study, the sedimentation only includes bedload transport model. The bedload transport rate, $\overrightarrow{q_B}$, is computed using the vectorial form of the equation proposed by Engelund and Fredsøe [40] for non-cohesive sediments:

$$\overrightarrow{q_B}= {\displaystyle \frac{\pi }{6}}dp\overrightarrow{u_B}$$

(1)

where $d$ is the mean sediment particle diameter, $\overrightarrow{u_B}$ is the mean transport velocity vector of the moving particles, calculated in a vectorial form based on the model proposed by Roulund et al. [41] for a two-dimensional bed, and $p$ stands for the probability of the particle transport [42,43].

2.2. Sediment Continuity Equation

In numerical modelling using the classical approach, two factors, erosion, and deposition of materials, alter the morphology of the water-sand interface level (i.e., GIB) under non-equilibrium conditions. The deformation of the water-sand interface or, in essence, the changes in the morphology of the GIB, are conducted by solving the sediment continuity equation over a 2D mesh of the GIB surface, utilizing the results of the sediment transport models. For this task, the Exner [44] equation is employed:

$${\displaystyle \frac{\partial h}{\partial t}}={\displaystyle \frac{-1}{1-n}}\left[\nabla .\overrightarrow{q_B}\right]$$

(2)

where $h$ represents the local water-sand interface level height, and $n$ denoted the sand porosity, taken as 0.4. Equation (2), the sediment continuity equation, is structured as a hyperbolic equation and has the wave-like nature. Consequently, filtration methods may be used to suppress spurious oscillations.

2.3. Sand Sliding Modelling

Analysis of the natural behaviour of sand-covered ocean (or river) beds during local scouring around offshore structures reveals that when the bed slope exceeds a critical angle relative to the horizontal plane, gravitational forces surpass frictional resistance at that point. This causes a downslope movement of sand until the slope reduces to below the critical angle. To replicate this natural behaviour of sand in the classical approach, a sand sliding mechanism must be implemented by incorporating the angle of repose as the threshold for initiating sliding. Bordbar et al. [37] critically investigated two different techniques for the purpose of numerically mimicking the sand sliding process, namely, Artificial Transport Rate Method (ATRM) and Geometry-Based Method (GBM). The full description of the methods, the applied test cases and the results of the comparisons are available in Bordbar et al. [37]. In the proposed approach, ATRM was applied as a sand sliding model, as it offers a solution with a considerably lower numerical error in compared to that of GBM.

3. Validation

A series of experimental data were employed to verify different aspects of the applied model, including the flow field, Bed Shear Stress (BSS) (i.e., shear stress at the GIB surface), and the evolution of local scour. The details of each test and its outcomes are provided below.

3.1. Hydrodynamic (Flow Field) Modelling

Wang et al. [16] investigated the flow velocity distribution around a symmetrical AR both numerically and experimentally. The configuration of the AR is presented in Figure 2. The experiment took place in a tank measuring 7 m in length, 0.3 m in width, and 0.7 m in depth with the AR positioned at the symmetry plane. The mean flow velocity was measured to be U = 0.085 (m/s). Particle Image Velocimetry (PIV) technique was applied to measure the velocity distribution at different heights from the bed ($z$ = 0.06, 0.10, 0.15 cm) at the symmetry plane. The experimental data were compared with the outcomes of CFD modelling using RANS in combination with Standard k-ε turbulent model. Yang et al. [45] has also utilized Wang’s results to validate their CFD model, which adapted RANS with RNG k- ε turbulent model.

A computational domain measuring 8 m in length, 0.3 m in width, and 0.7 m in depth was generated, with the AR positioned at the symmetry plane and 5 m downstream of the inlet boundary. A mesh dependency study was conducted, and a mesh with approximately 8.5 × ${10}^6$ cells is employed for numerical modelling, with the smallest cell size around wall surfaces (bottom/AR). The near-wall cells were generated to ensure that the cell centres were located within the logarithmic region of the boundary layer, allowing appropriate wall treatment for smooth and rough surfaces in all simulation cases.

Table 1. Applied boundary condition for model validation against the experimental test conducted by Wang et al. [16].

Boundaries	Sides	Top	Bed	Inlet	Outlet	AR
Velocity ($u$)	no-slip	Slip	no-slip	fixedValue	inletOutlet	no-slip
Pressure ($p$)	zeroGradient	Slip	zeroGradient	zeroGradient	fixedValue	zeroGradient
Turbulent ki-netic energy ($k$)	kqRWallFunction	Slip	kqRWallFunction	fixedValue	inletOutlet	kqRWallFunction
Specific turbu-lent dissipation rate ($\omega$)	omegaWallFunction	Slip	omegaWallFunction	fixedValue	inletOutlet	omegaWallFunction
Kinematic tur-bulent viscosity ($v_t={\mu }_t/\rho$)	nutkWallFunction	Slip	nutkWallFunction	calculated	calculated	kqRWallFunction

presents a full list of applied boundary conditions for the test case.

The simulation results, Figure 2a–c, from the present study show satisfactory agreement with the experimental data. However, discrepancies are observed across all turbulence models in predicting the formation of eddies upstream of the AR, as illustrated in Figure 2a. This limitation can be attributed to the inherent constraints of the turbulence models used. Employing a more accurate numerical approach, such as Large Eddy Simulation (LES), could potentially improve the prediction quality. However, due to the size of the computational domain in modelling of RC and the large number of cases modelled, the use of higher-fidelity methods was beyond the available computational resources in this study. Nevertheless, k-ω SST outcomes produced by this study, and RNG k-ε turbulent model results by Yang et al. [45] show better agreement with the experimental data in the wake region compared to Standard k- ε turbulent results by Wang et al. [16].

3.2. Bed Shear Stress (BSS) Modelling

In the modelling of scouring using the coupled hydro-morphodynamic approach, the hydrodynamic and sediment transport models are interlinked via the BSS, which acts as the key input parameter for the sediment transport model. Therefore, accurate calculation of BSS is essential for obtaining realistic sediment transport results. In the current numerical setup, the BSS ($\overrightarrow{{\tau }_w}$) acting on the surface is calculated in vectorial form as the inner product of the stress tensor (T) and the unit normal vector of the wall face, $\overrightarrow{N}$:

$$\overrightarrow{{\tau }_w}=\mathit{T}.\overrightarrow{N}$$

(3)

$$T=\left({\vartheta }_t+\vartheta \right)(\nabla \overrightarrow{u}+\nabla \overrightarrow{u^T})$$

(4)

where ${\vartheta }_t$ and $\vartheta$ are Kinematic turbulent viscosity and molecular kinematic viscosity, respectively, and $\overrightarrow{u}$ is the velocity vector.

Experimental data from Sadeque et al. [46] are utilized to validate the numerical model for the BSS test. Sadeque et al. [46] investigated flow around a cylinder in an open channel and reported normalized mean BSS contour adjacent to the circular cylinder. The experiments were carried out in a horizontal flume 18 m in length, 1.22 m in width, and 0.65 m in depth. A smooth circular cylinder with a diameter of 114 mm and a height of 300 mm was positioned on the rigid flume bed, 8.5 m downstream from the inlet. Further details of the test case are provided in

Table 2. Details of experiment test by Sadeque et al. [46].

Water Depth ($\mathit{H}$) [m]	Discharge [L/s]	Mean Velocity ($\mathit{U}$) [m/s]	Cylinder Reynolds Number [-]
0.220	50	0.186	21,000

.

For the numerical modelling, a computational domain matching the dimensions of the experimental flume was created, with the domain height limited to the water–air interface ($H$ = 0.22 m). A mesh dependency study was conducted, and a mesh consisting of approximately 4.9 × ${10}^6$ cells was selected for the simulations. The smallest cell sizes were concentrated around wall surfaces (i.e., the bottom and the cylinder). Near-wall cells were generated to ensure that their centres lie within the logarithmic region of the boundary layer, allowing for the appropriate application of wall functions.

Table 3. Applied boundary condition for model validation against the experiment conducted by Sadeque et al. [46].

Boundaries	Sides	Top	Bed	Inlet	Outlet	Cylinder
Velocity ($\mathit{u}$)	Symmetry	Slip	no-slip	fixedValue	inletOutlet	no-slip
Pressure ( $p$)	Symmetry	Slip	zeroGradient	zeroGradient	fixedValue	zeroGradient
Turbulent kinetic energy ($k$)	Symmetry	Slip	kqRWallFunction	fixedValue	inletOutlet	kqRWallFunction
Specific turbulent dissipation rate ($\omega$)	Symmetry	Slip	omegaWallFunction	fixedValue	inletOutlet	omegaWallFunction
Kinematic turbu-lent viscosity ($v_t={\mu }_t/\rho$)	Symmetry	Slip	nutkWallFunction	calculated	calculated	kqRWallFunction

provides a complete list of the boundary conditions applied in this test case.

Figure 3 shows the Normalized Mean Bed Shear Stress (NMBSS) contours obtained from numerical modelling using the RANS equations in combination with the k-ω SST turbulence model. The NMBSS is calculated by normalizing the time-averaged bed shear stress (BSS) by the BSS of the undisturbed flow field. The results are compared with experimental data reported by Sadeque et al. [46]. In the experimental data, the maximum NMBSS occurs at 100° from the stagnation point, near the cylinder surface, with a peak value of 5.5. In comparison, the numerical simulations predict the maximum NMBSS at 80° from the stagnation point, with a corresponding value of 4.7. Despite these differences, there is strong agreement between the experimental and numerical results in predicting the overall shear stress patterns both upstream and downstream of the cylinder.

3.3. Hydro-Morphodynamic Modelling Around a Circular Pile in Live-Bed Conditions

To investigate local scour, an experimental study on the evolution of scouring around a circular pile in live-bed condition by Roulund et al. [41] was adapted. This experiment was conducted in a flume 10 m length and 4 m in width. A pile with a diameter of 0.1 m was fixed at a distance of 6.6 m downstream of the inlet section. The bed was covered with loose sand with a particle diameter of $d_{50}$ = 0.26 mm and a Nikuradse equivalent sand roughness of $k_s$ = 0.55 mm. The test was conducted on a mobile bed and under steady current flow conditions. The water depth in the experiment was maintained at $H$ = 0.4 m, and the depth-averaged velocity was $U$ = 0.46 m/s. Further details of the test can be found in Roulund et al. [41].

The generated computational domain is depicted in Figure 4. A mesh dependency study was carried out and a 3D mesh with approximately 820,000 cells was selected. The applied boundaries are listed in

Table 4. Applied boundary condition for model validation against experimental data obtained by Roulund et al. [41].

Boundaries	Sides	Top	GIB/Rigid-Rough Apron	Inlet	Outlet	Pile
Velocity ($\mathit{u}$)	Symmetry	Slip	no-slip	fixedValue	inletOutlet	no-slip
Pressure ($p$)	Symmetry	Slip	zeroGradient	zeroGradient	fixedValue	zeroGradient
Turbulent kinetic energy ($k$)	Symmetry	Slip	kqRWallFunction	fixedValue	inletOutlet	kqRWallFunction
Specific turbulent dissipation rate ($\omega$)	Symmetry	Slip	omegaWallFunction	fixedValue	inletOutlet	omegaWallFunction
Kinematic turbu-lent viscosity ($v_t={\mu }_t/\rho$)	Symmetry	Slip	nutkRoughWallFunction	calculated	calculated	kqRWallFunction

. The symmetry boundary condition was considered at the sides of the computational domain for all quantities. This assumption is valid due to the small ratio of the cylinder diameter (D) to the flume width ($w_F$) in the experimental setup (D/$w_F$ = 0.026). Consequently, the effects of the flume width are negligible in the flow field, particularly in the area of interest where the cylinder interacts with the sandy bed.

The GIB was used to model the mobile water-sand interface, and a rigid-rough apron was also taken into account between the inlet and sandy region of the domain. Both of these boundaries were treated as rough surfaces with a roughness factor of $k_s$ = 0.55 mm. The inlet boundary was supplied with the velocity profile obtained from curve fitting of the provided profile by Roulund et al. [41]. The implemented coupled hydro-morphodynamic model is solved to simulate local scour progression adjacent to the pile.

The hydro-morphodynamic model simulation was very time-consuming even when run in parallel. Due to the resource’s limitation, the model was only run for 10 min of physical time, which required around 1 week of simulation time in 36 CPU cores. Nevertheless, this 10 min period is justifiable as scour progression in this period is remarkably fast, with around two-thirds of the equilibrium scour hole depth forming in such a limited time, whereas the experimental test reached the equilibrium scour stage after around 1 h. Figure 5a illustrates the simulated scour formation at the water-sand interface (GIB) at t = 10 min. The results show that bed deformation and scouring adjacent to the pile begin in the early stages of the simulation and progressively increase in both depth and affected area. In Figure 5b, the evolution of the simulated scour hole, measured by the maximum scour depth near the circular cylinder, is compared with the experimental results of Roulund et al. [41]. CFD results were recorded at 5 s intervals. The developed model successfully simulates the formation of the scour hole around the cylinder as well as the downstream sand deposition, aligning with the overall process of scour progression around piles under current flow [47,48]. The model demonstrates strong agreement with experimental data in terms of the temporal evolution of scour depth. However, it slightly underestimates the maximum scour depth by approximately 25%. This discrepancy between the CFD results and experimental data may be attributed to the fact that the present study only considers bedload sediment transport, whereas a more comprehensive approach would also account for suspended sediment transport.

4. Results

4.1. Flow Field Simulation Results Around the Reef Cubes

The validated hydrodynamic model, RANS model in combination with k-ω SST turbulence closure model, was employed to simulate flow field hydrodynamics and BSS for several different scenarios. In each scenario an impact of one parameter, comprise variation in the orientation angle, and arrangement, is evaluated.

Figure 6 presents the geometry of the Reef Cube^® designed by ARC Marine, along with its various sizes and arrangements used in the hydrodynamic simulation scenarios. The RCs are deployed at a depth of 30 m in Torbay, UK, where the influence of surface waves is considered negligible. According to Fennessy [49], the maximum average tidal current speed in the Torbay region is approximately $U_{mean}$ = 0.2 m/s. This flow speed is applied to all flow field simulations, as understanding flow characteristics around the RC under dominant conditions is a primary focus of this study.

To mimic Torbay water environment for the simulations, a three-dimensional computational domain with 18 $\mathrm{m}$ long, 12 $\mathrm{m}$ wide, and 7 $\mathrm{m}$ height is generated, whereas the RC structure is placed 10 $\mathrm{m}$ away from the inlet and at the symmetry plane. The applied boundary conditions for all hydrodynamic simulations are listed in

Table 5. Applied boundary condition for modelling flow behaviour around RCs.

Boundaries	Sym	Top	Bed	Inlet	Outlet	RC
Velocityb ($\mathit{u}$)	symmetry	Slip	no-slip	fixedValue	inletOutlet	no-slip
Pressure ($p$)	symmetry	Slip	zeroGradient	zeroGradient	fixedValue	zeroGradient
Turbulent kinetic energy ($k$)	symmetry	Slip	kqRWallFunction	fixedValue	inletOutlet	kqRWallFunction
Specific turbulent dissipation rate ($\omega$)	symmetry	Slip	omegaWallFunction	fixedValue	inletOutlet	omegaWallFunction
Kinematic turbu-lent viscosity ($v_t={\mu }_t/\rho$)	symmetry	Slip	nutkRoughWallFunction	calculated	calculated	nutkRoughWallFunction

. The bottom boundary is satisfied using OpenFOAM built-in boundary conditions; no-slip is used for the bottom boundary and the turbulence properties are treated using different wall functions for smooth and rough-surfaces, see Cebeci and Bradshaw [50] and Cebeci and Chang [51], with respect to the applied turbulence models. Nikuradse’s equivalent sand roughness, $k_s$, for the sandy bed is suggested to be equal to $2d_{50} \mathrm{or} 3d_{50}$ [41,52]. Therefore, considering the seabed of Torbay as a mixture of non-cohesive sand and silt with ${\mathrm{d}}_{50}= 1 \mathrm{mm}, k_s= 2 \mathrm{mm}$ was estimated in the simulation for sandy bed. The roughness of the RC surfaces is also defined, $k_s$ = 2 mm, provided by ARC Marine. The inlet flow is defined $U$ = 0.2 m/s, similar to the maximum mean tidal flow velocity measured in Torbay water.

The mesh for all test cases is generated using snappyHexMesh method in OpenFOAM^®. An initial mesh dependency study is carried out for modelling of flow field around each arrangement, where the volume of upwelling region is compared for different generated meshes. In this study, the upwelling region is determined using the method proposed by Wang et al. [16]. It is defined as the area where the magnitude of the upflow, $u_z$ (in the direction perpendicular to the seabed), is greater than 10% of the mean undisturbed flow.

In the following sections, the results of variations in orientation angle and arrangement are reported and discussed in detail.

4.1.1. Reef Cubes with Different Orientation Angles to the Flow

RCs with a side length of D = 1.5 m were analyzed with two different orientation angles, 90° and 45°, as shown in Figure 6c,d.

Table 6. Generated meshes for mesh dependency study.

Name	Mesh Size	Background Mesh Size [${\mathbf{m}}^2$]	Volume of Upwelling Region [${\mathbf{m}}^3$]
Coarse	5.4 × ${10}^6$	0.3 × 0.3	5.844
Medium	6.9 × ${10}^6$	0.25 × 0.25	6.088
Fine	8.8 × ${10}^6$	0.2 × 0.2	6.152

presents the results of the calculated upwelling region volume for the RC with a 90° orientation to the flow as part of the mesh independence study. The outcomes indicate a high degree of mesh independence, particularly in cases with medium and fine mesh resolutions (showing changes of approximately 1% in the volume of the upwelling region). Figure 7 shows horizontal and vertical slices of the generated mesh in the region of interest around the RC with a 90° orientation to the flow. Therefore, the fine mesh results were selected for post-processing. The same mesh generation setup, as described above, was applied to all other simulations.

For each case, 90° and 45°, flow field contours at different horizontal planes, z = 0.375, 0.75, 1.125 m, are demonstrated in Figure 8. Figure 9 demonstrates the flow field contours in vertical planes (Y = 0 m and Y = 0.375 m). A significant difference in flow field behaviour is observed due to the change in the orientation angle. However, in both cases, an area with high flow velocity at the side edges, jet flow behaviour within the RCs aligned with the main flow direction, and a wake region downstream of the structure can be observed. Therefore, compared to the relevant literature, in addition to the upwelling and wake regions, an additional region of high flow velocity within the RC can be identified, attributed to the large openings of the RC.

An upwelling flow region is evident in both cases; however, in the 45° orientation, the upwelling flow adheres to the top surface of the structure, while in the 90° orientation, the flow separates from the top surface. This flow separation can be related to the fluid dynamics over the leading edges of the cube at a 90° orientation, where boundary layer separation occurs due to adverse pressure gradients. For both the 90° and 45° orientation angles, the wake region is larger near the bed and gradually diminishes in size with height. The jet flow through the RC openings interacts with and disturbs this wake region. The results also indicate that the presence of a front opening significantly reduces the likelihood of horseshoe vortex formation at the front of the cubes. The internal region of the RC exhibits a combination of high and low velocity zones in both cases, creating a favourable habitat that supports a diverse range of marine flora and fauna. This environment provides shelter, spawning grounds, and feeding areas while enhancing nutrient transport, supporting the food chain, and facilitating fish settlement.

Table 7. Magnitude of volume of upwelling and wake regions for single RCs with 90° and 45° orientation angles to the flow.

Orientation Angle to the Flow	Volume of Upwelling Region [${\mathbf{m}}^3$]	Volume of Wake Region [${\mathbf{m}}^3$]
Single cube—90°	6.152	3.135
Single cube—45°	11.172	4.668

reports the magnitudes of the volume of upwelling and wake regions for a single RC with 90° and 45° orientation angle to the flow, respectively. The wake region was calculated using the proposed method by Wang et al. [16]. Based on that, the wake region was determined as the area where the magnitude of $u_x$ (in the direction aligned with the undisturbed flow) is negative. The result indicates that the RC with 45° orientation angle provides larger upwelling and wake regions which can potentially lead to more favourable condition for marine organism growth.

The potential of formation of scour hole around the structures were measured by monitoring the NMBSS contours adjacent to the structures, presented in Figure 10. In the case of the RC with a 45° orientation angle, the maximum NMBSS occurs adjacent to the outer corners of the structure, whereas in the 90° orientation angle case, it occurs near the front corners. This is because the flow cannot follow the sharp 90-degree turn at the front edges, resulting in abrupt separation. The separation causes the flow to accelerate around the corners, forming localized high-velocity and low-pressure regions.

The simulation predicted higher NMBSS magnitude with larger area of impact around the RC with 90° orientation angle which means higher potential of scouring around the structure.

4.1.2. Group of Two, Four, and Six Reef Cubes

In this section, the flow field and BSS around arrangements of two, four, and six RCs, each with cubes with a side length of D = 0.75 m, as shown in Figure 6e–g is studied. Figure 11 and Figure 12 illustrate the flow field contours for a horizontal plane at Z = 0.375 m, and vertical planes at Y = 0 m and Y = 0.375 m corresponding to different arrangements of the RCs. Roughly the same flow characteristics observed around all different arrangements in terms of side flow adjacent to the front edges of structures and upwelling flow. As seen in the case of a single RC with a 90° orientation angle to the flow, the flow separates from the front edges where boundary layer separation occurs due to adverse pressure gradients. In terms of wake formation, a larger wake area is detected downstream of the two-RC arrangement compared to the other two arrangements (i.e., four and six RCs). This behaviour is associated with the flow dynamics over the front edges of the cubes, where strong adverse pressure gradients and backward flow are generated downstream in the case of two RCs. The results also reveal that changes in the arrangement, the number of back-to-back RCs, do not significantly affect the flow profile of the jet flow within the cubes at the frontal openings. However, differences are observed on the rear side of the arrangements. In the case of two RCs, the jet flow at the rear is directed towards the outer sides and rises downstream of the structure. This behaviour diminishes as the number of back-to-back RCs increases, with four and six RC arrangements showing a less pronounced jet flow. This pattern can be related to the strength of the backward flow downstream of the arrangements, which diminishes as the number of back-to-back RCs increases.

Table 8. Magnitude of volume of upwelling and wake regions for the arrangement of a group of two, four, and six RCs.

Group of RCs	RC Volumes	Volume of Upwelling Region [${\mathbf{m}}^3$]	Dimensionless Volume of Upwelling	Volume of Wake Region [${\mathbf{m}}^3$]	Dimensionless Volume of Wake
Two	0.48	3.585	7.469	1.460	3.042
Four	0.96	3.164	3.296	1.175	1.225
Six	1.44	3.208	2.228	1.239	0.860

presents the calculated volumes of the upwelling and wake regions for each arrangement. Larger volumes of both upwelling and wake regions are observed in the arrangement with two RCs compared to the other two configurations. These differences become more pronounced when the values are expressed as dimensionless quantities. This suggests that increasing the number of back-to-back RCs does not enhance their performance in terms of upwelling and wake region volumes. However, in general, a greater number of RCs provides more shelter for marine organisms.

The NMBSS contours for RCs with different configurations are shown in Figure 13. The maximum NMBSS value and the affected area slightly decrease as the number of back-to-back RCs increases. This indicates that increasing the number of back-to-back RCs may enhance the long-term stability of the structures by providing greater resistance to scouring.

4.1.3. Group of Ten Reef Cubes

In this subsection, the flow field and BSS around a group of ten RCs, each with a side length of D = 0.75 m, arranged in different configurations as shown in Figure 6h–j, are analyzed. Flow field contours for both horizontal and vertical planes are presented in Figure 14 and Figure 15. The findings indicate substantial changes in the flow patterns around the structures, particularly influenced by adjustments in the positioning of the top row of RCs. The results indicate that positioning the top four cubes at the front leads to stronger side flow in the corners and a jet flow within both the bottom six and top four RCs. When the top four cubes are moved to the middle or back, the flow characteristics change significantly. With the top four RCs in the middle, the altered opening arrangement allows the flow to enter from various directions, inhibiting jet flow formation and considerably reducing flow velocity in the corners, although high flow velocity remains within the top four RCs. Moving the top four RCs to the back results in a weaker flow in the corners and within the bottom six RCs, while strong flow persists around and within the top four RCs. The formation of wake regions is also influenced by the positioning of the top four RCs. Among all configurations, placing the top four cubes at the back generates a stronger backward flow downstream, closer to the bed. This backward flow acts as a driving force, steering the jet flow toward the sides downstream of the structure, a phenomenon that is notably less pronounced in the front and middle arrangements.

Table 9. Magnitude of volume of upwelling and wake regions for a group of ten RCs with different arrangements of top four cubes in (a) front, (b) middle, and (c) back.

Group of Ten RCs	Volume of Upwelling Region [${\mathbf{m}}^3$]	Volume of Wake Region [${\mathbf{m}}^3$]
The top four in the front	6.702	2.725
The top four in the middle	6.723	2.460
The top four in the back	7.149	2.616

presents the volumes of upwelling and wake regions for each arrangement, with results showing a high degree of similarity. However, it can be argued that these calculated values represent the total upwelling and wake regions around the structures, and comparing these scalar values alone may not fully capture how these regions facilitate interactions with marine flora and fauna. As this analysis does not account for how the formation of each individual region may specifically influence such interactions.

The NMBSS results are presented in Figure 16. Higher values of maximum NMBSS and a larger area of impact are observed when the top four cubes are located at the front. The results indicate that these behaviours weaken when the top four cubes are moved backward.

4.2. Modelling of Development of Scour Around a Single Reef Cube

The developed hydro-morphodynamic model was applied to predict the progression of scour around a single RC under conditions similar to those at Torbay Water. In this study, an RC with a side length of D = 0.5 m was considered and mounted on a sandy bed, as illustrated in Figure 17. To assess the sensitivity of scour hole development around the RC, two different depth-averaged flow velocities $U$ = 0.2 m/s and $U$ = 0.4 m/s, were applied, each representing a fully developed flow profile, defined by:

$$u={\displaystyle \frac{U_f}{\kappa }}\mathit{ln}\left({\displaystyle \frac{30 z}{k_s}}\right)$$

(5)

where $U_f$ is friction velocity, Kármán constant, $\kappa$ = 0.41, and bed roughness factor $k_s$ = 2 mm. The boundaries were treated with conditions similar to those employed in the modelling of scouring around a circular cylinder detailed in Table 4. A 3D mesh, which included around 980,000 cells, was generated.

Figure 18 illustrates the temporal evolution of maximum scour depth and deposition height around the RC for different flow velocities. Data were collected at 10 s intervals. The simulations were conducted over the first 10 min of physical time, during which a rapid progression in scour hole development occurs. Figure 19 presents the simulated water-sand interface displacement contours for the two flow velocities at t = 10 min. The primary scouring impact is concentrated at the upstream corners of the RC, while sediment deposition predominantly occurs downstream and along the sides of the structure. This pattern aligns with the simulated BSS distribution contours, which predict the highest BSS magnitudes near the upstream corners. intensifies scouring, leading to a scour hole approximately ten times deeper. These results underscore the importance of accounting for extreme flow conditions in scour progression analyses, as short-duration events can have severe implications for the stability and failure risk of AR structures.

Table 10. The hydro-morphodynamic model results after 10 min of simulation.

Mean Flow Speed	RC Reynolds Number [-]	Undisturbed Shields Parameter [-]	Max. Scour Depth [mm]	Max. Deposition Height [mm]
U = 0.2 (m/s)	${10}^5$	0.015	6.8	2.6
U = 0.4 (m/s)	${2\times 10}^5$	0.06	63.9	37.2

summarizes the hydro-morphodynamic model results for the RC case. The RC Reynolds number and Shields parameter are provided for each case. The Shields parameter θ is calculated as:

$$\mathrm{\theta }={\displaystyle \frac{{U_f}^2}{(s-1)g{d}_{50}}}$$

(6)

where $U_f=U/\alpha$ and α = 9. The flow is fully turbulent, as the transition threshold to turbulent flow over rough surfaces occurs at significantly lower Reynolds numbers. The values of the undisturbed Shields parameter indicate that the flow is in clear-water conditions, since the threshold for transition to live-bed conditions is approximately θ = 0.06. The findings highlight the significant influence of flow velocity on scour development, both in terms of depth and the extent of the affected area. At $U$ = 0.2 m/s the mean flow velocity is barely sufficient to mobilize sediment particles. However, doubling the flow velocity to $U$ = 0.4 m/s, intensifies scouring, leading to a scour hole approximately ten times deeper. These results underscore the importance of accounting for extreme flow conditions in scour progression analyses, as short-duration events can have severe implications for the stability and failure risk of AR structures.

5. Conclusions

This study presented a comprehensive numerical investigation of the flow dynamics and local scour around a seabed-mounted AR structure, specifically, the Reef Cube^® developed by ARC Marine and deployed in Torbay, UK.

All flow simulations were carried out using the average tidal current speed in the region ($U_{mean}$ = 0.2 m/s) to replicate the prevailing conditions that are most relevant for establishing habitats capable of supporting a diverse range of marine flora and fauna. The analysis focused on evaluating hydrodynamics and bed shear stress under various structural configurations, including different orientation angles and spatial arrangements of the RCs. The key findings from the investigation of flow dynamics are summarized below:

Compared to prior studies, the presence of large openings in the RC was found to generate an additional region of high flow velocity within the structure, in addition to typical upwelling and wake zones. This creates a mixture of high- and low-speed flows inside the RC, potentially enhancing habitat suitability for marine organisms.

An RC oriented at 45° to the flow produced larger upwelling and wake regions than one aligned at 90°, suggesting more favourable conditions for biological growth. Conversely, a 90° orientation intensified scouring, with peak bed shear stress observed at the upstream corners.

Simulations involving groups of 2, 4, and 6 RCs exhibited distinct flow behaviours. Two-RC configurations generated outward and upward jet flows at the downstream of the RCs, not observed in denser arrangements. Larger dimensionless upwelling and wake volumes were found in the two-RC group. Increasing the number of cubes slightly reduced maximum bed shear stress, indicating improved long-term structural stability.

In the ten-cube arrangement, the position of the top four RCs significantly affected flow patterns. Placing them at the front enhanced side flows, while rear placement promoted backward flow downstream. Regardless of position, similar flow behaviours, such as jet and side flows, were consistently observed, though higher bed shear was associated with front-mounted configurations.

The hydro-morphodynamic model was then used to simulate local scouring around a single RC under two flow conditions: the typical tidal velocity ($U_{mean}$ = 0.2 m/s) and a stronger current ($U_{mean}$ = 0.4 m/s), representing potential extreme marine events. Simulations over the first 10 min of physical time demonstrated that the higher flow speed substantially accelerated scour hole development, resulting in a depth approximately ten times greater than that observed under normal conditions. These findings underscore the critical importance of accounting for extreme flow events in scour progression analyses, as short-duration high-velocity conditions can have severe implications for the stability and failure risk of AR projects.

While the study offers valuable insights into the flow and scour behaviour around reef cubes, several limitations should be acknowledged:

The calculated upwelling and wake volumes, as recommended in the literature, represent aggregate scalar values that may not fully capture the spatial complexity or ecological significance of these flow features in supporting marine ecosystems.

The presence and growth of marine flora on RC surfaces during real-world deployment can significantly alter flow behaviour. This aspect was not investigated in the present study and would require a separate investigation employing alternative modelling approaches.

Although the incompressible unsteady RANS equations coupled with the k-ω SST turbulence model provided reliable results for engineering-scale simulations, higher-fidelity approaches such as Large Eddy Simulation (LES) could offer improved accuracy. However, resource limitations and computational demands precluded their use in this study.

While the applied hydro-morphodynamic model successfully captured the influence of flow speed on local scour formation, it lacked suspended sediment transport modelling and comprehensive validation. Future work should incorporate more advanced sediment transport formulations and validation cases to enhance predictive accuracy.