Numerical Investigation into the Hydrodynamic Performance of a Biodegradable Drifting Fish Aggregating Device

Abstract

Drifting fish aggregating devices (DFADs) can significantly enhance fishing efficiency and capability. Conventional drifting devices are prone to degradation in harsh marine environments, leading to marine waste or pollution. In this study, we develop a biodegradable DFAD (Bio-DFAD) to minimise negative impacts on marine ecology. To investigate the hydrodynamic performance of the proposed device, numerical modelling involving the unsteady Reynolds-averaged Navier–Stokes equation has been conducted, in which a realisable k–ε model is applied to consider the turbulence effect. The response amplitude operators, which are key parameters for design, are obtained for heave and pitch motions. The hydrodynamic performance is found to be sensitive to the relative length, relative diameter, and wave steepness, but they are less sensitive to the relative current velocity. This work provides some scientific insights for practical applications.

1. Introduction

Globally, tuna purse-seine fleets use a significant quantity of drifting fish aggregating devices (DFADs) to increase fishing effectiveness by attracting tuna and other non-commercial species in open oceans [1]. Recently, the global catch of tuna with DFADs has reached an all-time high, comprising over 50% of the entire quantity of tuna catch [2,3,4]. Annually, statistically, 0.1 million DFADs are implemented in the ocean [5,6]. Typically, DFADs are composed of floating structures at sea surface, such as rafts, and submerged structures, such as ropes or old purse-seine nets. The submerged section of the structure can extend to a length exceeding 100 m [6]. The structure is susceptible to damage from the impact of waves and currents, eventually contributing to marine debris and pollution. To clarify the risks and value of DFADs, it is necessary to examine their hydrodynamic characteristics in the marine environment [7].

Conventional DFADs comprise primarily materials that are unlikely to naturally degrade over the years, resulting in a significant accumulation of marine debris in recent decades [1,5,8]. Regional fishery management organisations state that DFADs should have a design that is both biodegradable and completely non-entangling in tuna purse-seine fisheries [9,10]. However, DFADs made from biodegradable materials and non-entangling structures are more prone to breaking in harsh maritime settings.

Investigators have recently conducted experimental and numerical analyses to examine the hydrodynamic performance of offshore aquaculture [11,12,13,14,15]. For DFADs, one study simplified DFADs to a small raft with a rope, thereby performing experimental and numerical analysis on the raft’s motion response in regular waves [7]. Researchers have also examined the drift velocity and turbulence intensity of DFADs with varying submerged entanglement characteristics under a steady uniform current [15,16]. Furthermore, the degradation of submerged structures has been assessed in the actual oceanic environment [13].

These existing studies have primarily focused on wave conditions only and treated the DFADs as rigid bodies, while waves in the ocean are usually followed by currents, and DFADs could change in shape [17,18,19]. It is necessary to conduct a more in-depth analysis of the hydrodynamic characteristics of DFADs considering the combined effects of waves and currents.

Compared to controlled laboratory environments with simple and manageable single-variable situations, DFADs are usually subjected to intricate patterns of waves, as well as currents. Whereas the motion responses of DFADs tend to be directly observed in waves, the inclusion of currents has a noticeable effect on the hydrodynamic properties. Laboratory and numerical methods have generally used the six degrees of freedom data to analyse the motion responses of DFADs based on linear wave theory [7]. Based on this, it is necessary to numerically replicate the hydrodynamic properties of DFADs when subjected to both waves and currents. Prior studies have demonstrated that the responses of the DFADs can be dominated by either waves or currents [7,16].

In summary, the hydrodynamic performance of DFADs under the combined excitation of waves and currents and the development of biodegradable designs have not been adequately addressed. Building upon our earlier research [7], we use numerical models herein to examine the hydrodynamic performance of biodegradable DFADs (Bio-DFADs) subjected to the combined effects of waves and currents. Further, we aim to quantitatively assess the effects of currents on DFADs. This study helps clarify the hydrodynamic characteristics and serves as a guide for the practical implementation of Bio-DFADs.

2. Description of the Proposed Concept

The Bio-DFADs Model

To investigate the hydrodynamic performance of Bio-DFADs and help devise experiments, a numerical model is developed here at a scale of 1:12. The Bio-DFADs used in this study comprise two main components, the raft and rope, as shown in Figure 1 (at model scale). The raft is constructed with balsa wood and contains two perpendicular layers, with each layer consisting of five balsa wood pieces evenly spaced apart. Balsa wood is biodegradable and favourable for both floating and degradation in the marine ecosystem. It can also be used to construct marine structures in actual oceanic conditions [20,21]. The raft is also equipped with five buoys, positioned on the top area. One buoy is installed centrally, while the other four buoys are firmly attached to the frame established by both the top and bottom, as represented in Figure 1. The length of the Bio-DFADs (L_F), the diameter of the balsa wood (D_F), the width of the Bio-DFADs (B), and the length of the rope (d_F) are also depicted in Figure 1. The balsa wood diameters measure 0.03, 0.04, 0.05, 0.06, 0.07, and 0.08 m. A 2.00 kg iron sinker (W_Sinker) in the shape of a sphere is connected to the raft using a cotton rope measuring 0.60 m in length.

3. Numerical Methodology

3.1. Governing Equations

To streamline the numerical simulation, we assumed that the fluid was incompressible. The fluid’s heat exchange was disregarded, and the water temperature was set at a constant 25 °C. The unsteady Reynolds-averaged Navier–Stokes was employed. The relative equations governing the flow of unstable incompressible fluids are as follows:

Continuity equation

$$\frac{\partial \left(\rho \overline{u_i}\right)}{\partial x_i}=0$$

(1)

Momentum equation

$$\frac{\partial \left(\rho {\overline{u}}_i\right)}{\partial t}+\frac{\partial }{\partial x_j}\left(\rho \overline{u_i{u}_j}+\rho \overline{u_i^{\prime }{u}_j^{\prime }}\right)=-\frac{\partial \overline{P}}{\partial x_i}+\frac{\partial {\overline{\tau }}_{ij}}{\partial x_j}$$

(2)

where $\overline{P}$ denotes the mean pressure, $\overline{u_i}$ represents the averaged velocity vector, $\overline{{\tau }_{\mathit{ij}}}$ is the mean viscous stress tensor components, and $\rho \overline{u_i^{\prime }{u}_j^{\prime }}$ indicates the Reynolds stress. A non-linear eddy viscosity model is used to model the Reynolds stress [22]. The fluid flow was calculated using the finite volume method.

3.2. Turbulence Model

The numerical simulation was based on the realisable k–ε model, using all y+ wall treatments. The turbulent viscosity is determined using an enhanced approach. Compared with various turbulence models, the one chosen is deemed superior in accurately forecasting the dissipation rate distribution [23,24]. In addition, the model, which is used in this study, offers an improved prediction of boundary layer features in situations including significant pressure gradients, separated flows, and recirculating flows [25]. The k and ε equations had been mentioned in our prior research [7]. Notably, the volume of fluid (VOF) model was used to accurately represent the free surface motions [26].

3.3. Computational Setup

Figure 2 and Figure 3 display the computational setup. The construction of the three-dimensional wave tank was based on previous research conducted by Wan et al. (2022) [7]. The wave and current were generated using the first-order wave model developed by Fenton in 1985 [27]. The origin of the coordinate system is consistent with the centre of the raft. To optimise computational resources, a symmetry boundary was implemented. The symmetry border was estimated at half the width of the design. The velocity inlet was designated as the boundary for the rest boundaries, while the pressure outlet was assigned as the boundary for the top. The surfaces of the Bio-DFADs were designated as no-slip wall-type surfaces. The computational domain has a bottom border located 0.80 m from the surface of calm water, which corresponds to a water depth, h, of 0.80 m. The domain’s height was specified as 1.6 m. The Bio-DFADs were placed 1.5 L and 3.0 L from the inlet and the outlet, respectively. In addition to the consequence of adopting symmetric boundary conditions, the domain had a width of 2 B from 4 B.

The DFBI module was implemented to model the motion of the Bio-DFAD in response to force, with six degrees of freedom. The Bio-DFADs in this investigation were allowed to experience heave, pitch, and surge motion.

Figure 4 illustrates the use of the catenary coupling method to imitate the cotton rope connecting the raft and sinker. The shape of the rope is determined using the following equations, which are based on a local Cartesian coordinate system:

$$x=au+b\sinh \left(u\right)+\alpha$$

(3)

$$y=a\cosh \left(u\right)+\frac{b}{2}{\sinh }^2\left(u\right)+\beta$$

(4)

$$u_1\le u\le u_2$$

(5)

$$a=\frac{c}{{\lambda }_{0}g}$$

(6)

$$b=\frac{ca}{D{L}_{eq}}$$

(7)

$$c=\frac{{\lambda }_0{L}_{eq}g}{\sinh \left(u_2\right)-\sinh \left(u_1\right)}$$

(8)

where λ₀ and L_eq are the mass per unit length and the relaxation length of the rope, respectively, D is the stiffness of the rope, and α and β are integration constants depending on the position of the two endpoints of the rope. u₁ and u₂ are the positions of the rope’s endpoints P₁ and P₂, respectively. The equation for curve parameter u and inclination angle Φ is as follows:

$$\tan \varphi =\sinh \left(u\right)$$

(9)

The total length of the rope, L_T, is defined as follows:

$$L_T={\displaystyle \underset{x_1}{\overset{x_2}{\int }}\sqrt{1+{\left(\frac{dy}{dx}\right)}^{2}dx}}$$

(10)

where y is the catenary curve, and x₁ and x₂ are the endpoints where the rope is attached. The length of the catenary with respect to the relaxation length L_eq is as follows:

$$r=L_T-L_{eq}$$

(11)

The forces F₁ and F₂ can be expressed as follows:

$$F_{1,x}=c$$

(12)

$$F_{1,y}=c\sinh \left(u_1\right)$$

(13)

$$F_{2,x}=-c$$

(14)

$$F_{1,y}=-c\sinh \left(u_2\right)$$

(15)

Several scholars have investigated the impact of boundary-reflected waves [28,29,30,31]. Herein, we employed the VOF wave-forcing method, as proposed by Kim et al. (2012) [31], to generate waves.

Figure 5 depicts the influence area of the wave-forcing method. The wave-forcing method effectively prevents the occurrence of flow reflections at borders. This is accomplished by incorporating a source term into the momentum equation, as follows:

$$q_{\varphi }=-\gamma \rho \left(\varphi -{\varphi }^{*}\right)$$

(16)

where γ denotes the forcing coefficient, ϕ denotes the current solution, and ϕ* indicates the value to which the solution has been forced.

3.4. Mesh Generation

The overset mesh was used in the computational domain to accurately represent and track the intricate characteristics and motion of the Bio-DFADs. Figure 6 illustrates the computational domain, which consists of two primary regions. The Bio-DFADs model was located within the overset region. The computational domain was based on volume mesh models, including the trimmed model, prism layer, and polyhedral mesh. The surface remesher was used to retriangulate the model’s surfaces and enhance the surfaces for the volume mesh models. The hexahedral mesh of the trimmed model was used to create meshes in the background region. Given that the simulation focused on the surfaces of the Bio-DFADs and the surrounding area, special treatment was applied to the meshes on the model’s surfaces. Specifically, the prism layer and polyhedral mesh were used in the overset region. Overall, a configuration of five layers was established.

3.5. Simulation Matrix

Table 1. Parameters for the different test conditions.

Wave Period, T (s)			Wave Height, H (m)			Current Velocity Vcurrent (m/s)
1.5	2.0	2.5	0.10	0.15	0.20	0.05	0.10	0.15	0.20	0.25

presents the wave and current conditions typically observed by tuna purse-seine fleets. The selected range of wave conditions (T, H) and current velocity (V_current) were representative. To ensure consistency in the wave tank test, the water depth was adjusted to 0.80 m.

4. Results and Analysis

4.1. Verification of the Numerical Model

Validating the precision of the CFD model is vital for assessing the accuracy of the outcomes. The time step and mesh size were crucial considerations in ensuring convergence and accuracy during the numerical simulation. Thus, we conducted a mesh sensitivity analysis and a time step analysis. A wave case was chosen as the test condition (T = 1.5 s, H = 0.2 m). There were six monitors positioned at distances of 0.5, 1.0, 1.5, 2.0, 2.5, and 3.0 L from the inlet boundary to observe changes in wave elevation.

4.1.1. Mesh Sensitivity Analysis

Various mesh sizes were examined to elucidate the impact of the mesh number. The details about mesh are provided in

Table 2. Details of the mesh parameters.

Region	Mesh Number, N
Wave height (1 H)	5, 10, 20, 30, 40
Wavelength (1 L)	44, 88, 176

, which includes five alternative mesh numbers for each wave height (5, 10, 20, 30, and 40) and three mesh numbers for each wavelength (44, 88, and 176). Within the range of the free surface, various mesh values were used. The computational domain had a fixed base size of 0.64 m, and the time step remained constant at 0.0025 s.

Figure 7 depicts the analysis of the mesh sensitivity. The results show the correlation between wave elevation and mesh size, specifically, L/Δx within the wavelength range and H/Δz within the height range. According to Figure 7, the precision of the wave elevation improved as the ratios L/Δx and H/Δz increased. Nevertheless, the numerical simulation requires a larger computational capacity for dealing with higher mesh numbers and incurs more cost. Our findings show that when the L/Δx ratio is 88 and the H/Δz ratio is 30, the numerical simulation exhibited a relatively lower computational expense and greater efficiency.

4.1.2. Time Step Sensitivity Analysis

The time step plays a crucial role in ensuring the accuracy. Therefore, the sensitivity of the time step was also examined. The mesh sensitivity analysis revealed that H/Δz = 30, L/Δx = 88. Then, various time steps were used to determine the appropriate time step.

According to Figure 8, the time step significantly influenced the wave elevation. When the time step was 0.005 s, the wave elevation was recorded with greater precision.

In our prior investigation [7], we employed an identical numerical model, which produced precise results with regard to the tests. The findings indicate that the numerical process employed in this study exhibited high accuracy, along with consistent results.

Figure 9 shows that the wave elevation values differ according to computational and mathematical calculations. The numerical model demonstrated a high level of accuracy and was well-suited for this investigation, exhibiting an error rate of less than 0.5%.

Figure 10, Figure 11, Figure 12, Figure 13 and Figure 14 illustrate the modifications that occur in the hydrodynamic characteristics when subjected to waves and currents. The specific conditions for this case are T = 1.5 s, H = 0.10 m, and V_Current = 0.1 m/s. The Bio-DFADs exhibited consistent periodic motion in all three dimensions. Regarding these figures, it can be concluded that the motion response and the flow field around it, as well as the pressure imposed on it, experienced periodic variations.

4.2. Effect of Relative Length on the Hydrodynamic Performance

Figure 15 illustrates how the motion responses (i.e., heave and pitch) of the Bio-DFADs are influenced by the relative length (L_F/B). In this study, three lengths of the raft are tested (L_F = 0.50, 1.00, and 1.50 m, respectively). The current velocity in this section remained constant at a value of 0.1 m/s, denoted as VCurrent. According to Figure 15, the heave RAO dropped as the L_F/B ratio grew, but the trend of the pitch RAO became more complex with an increase in L_F/B. Nevertheless, when the wave time rose, the trend exhibited a progressive decline. When L_F/B = 0.5 and T = 1.5 s, the motion RAOs exhibited an increase with increasing wave height H. This is due to the varying weights of L_F/B, which developed as the relative length increased. Therefore, the two RAOs became minimised as the L_F/B increased, even while the wave condition and wave force remained the same. Meanwhile, as the wave period grew, the disparity in motion RAOs between various wave heights diminished, as did the disparity in motion RAOs between different relative lengths. The increase in wave period led to an increase in wave force, particularly in the vertical direction of the model. As a result, the heave RAO grew and eventually reached a consistent value. In contrast, the wave force exerted on the model intensified, resulting in increased difficulty for the model to pitch. Therefore, the pitch RAO exhibited a decrease, while the wave period demonstrated an increase. The findings demonstrated that the RAOs were significantly influenced by the relative length and wave parameters.

Figure 16 shows the relationship between relative length L_F/B and relative velocity V/V_Current. The V/V_Current fell with increasing L_F/B and rose with increasing wave height. The velocity ratio V/V_Current declined as the wave period grew, whereas the disparity in V/V_Current between distinct L_F/B values under varying wave heights decreased and approached saturation. The weight of the model increased with the rise in L_F/B, which in turn caused a drop in V/V_Current under the same wave force. Nevertheless, the wave force and V/V_Current escalated proportionally with increasing wave height. As the period of the wave increased, the velocity relative to the current dropped. The model experiences greater wave forces that induce vertical movement, but wave forces diminish horizontally, leading to a reduction in drift velocity V/V_Current. The findings demonstrated that the relative length and wave conditions significantly influenced the relative velocity. This conclusion is consistent with our prior research [7].

Figure 17 illustrates the correlation between the relative length L_F/B and the relative wetted area S_Wetted/S_Total. Accordingly, the relative wetted area (S_Wetted/S_Total) fell as the ratio of the length (L_F) to the width (B) grew and increased with increasing wave height. The relative wetted area dropped with the rising wave period. Furthermore, the distinction in S_Wetted/S_Total between different L_F/B values under varying wave heights decreased and approached a constant value. The model’s surface area increased with the rise in L_F/B. However, as L_F/B grew, the surface area in contact with the flow dropped because of the greater buoyancy. Consequently, under the same wave condition, the S_Wetted/S_Total decreased. This is consistent with the previous finding on relative velocity, indicating that the relative velocity increases as the relative wetted area increases. The findings demonstrated that the relative length and wave conditions significantly influenced the relative wetted area (S_Wetted/S_Total) of the Bio-DFADs.

Figure 18 depicts the correlation between the relative length and the relative rope tension F/W_Sinker. Accordingly, the relative rope tension F/W_Sinker decreased as the L_F/B increased and increased with rising wave height. The magnitude of the relative rope tension (F/W_Sinker) dropped as the period of the wave grew. However, the variation in F/W_Sinker between different low frequencies (L_F/B) under different wave heights decreased and approached saturation. The increase in the model’s weight resulted in a decrease in F/W_Sinker as the L_F/B grew under the same wave force. Nevertheless, the wave force exhibited a positive correlation with the wave height, resulting in a rise in F/W_Sinker with increasing wave height. The F/W_Sinker decreased with an increasing wave period. The model experiences greater wave forces that induce vertical movement, but wave forces diminish horizontally, leading to a reduction in drift velocity. This is also consistent with the previous finding that an increase in heave RAO results in a corresponding rise in F/W_Sinker. The findings demonstrated that wave conditions and relative length had an important impact on the relative rope tension.

4.3. Effect of Wave Steepness on the Hydrodynamic Performance

Figure 19 shows the effect of wave steepness on motion RAOs when the current velocity is held constant at 0.1 m/s. Accordingly, the heave RAO rose with an increase in wave steepness, but the pitch RAO became more complex as wave steepness grew. Nevertheless, when the wave time rose, the trend exhibited a progressive decline. At a wave steepness of 0.016 and T = 2.0 s, the motion RAOs dropped as L_F rose. The weight of L_F rose proportionally with its length owing to the variations in length across different LF. Therefore, when L_F rose, the motion RAOs decreased while keeping the wave condition and wave force constant. However, as the wave period grew, the variation in motion RAO between different lengths L_F decreased, and the variation in motion RAO between different wave steepness dropped. The wave force increased with the increase in wave period, particularly in the vertical direction. This resulted in a rise in the heave RAO, forcing all values to converge to the same value. In contrast, the force exerted on Bio-DFADs intensified, resulting in increased difficulty for the model to pitch. Therefore, the pitch RAO decreased with increasing wave period. The findings demonstrated that the wave steepness and relative length had an important impact on the motion responses of the Bio-DFADs.

Figure 20 shows the correlation between wave steepness and relative velocity V/V_current. Accordingly, the V/V_current increased as the wave steepness increased and decreased with the increase in length L_F. The velocity ratio V/V_current decreased as the wave period grew, whereas the disparity in the V/V_current between different wave steepnesses under various lengths L_F decreased. The rise in L_F resulted in an increase in the weight of the model, causing a drop in the V/V_current under the same wave force. Meanwhile, the magnitude of the wave force grew in tandem as wave steepness increased, subsequently resulting in an increase in the V/V_current. As the wave period rose, the velocity relative to the current dropped. The model experiences greater wave forces that induce vertical movement, but wave forces diminish horizontally, leading to a reduction in the drift velocity V/V_current. The findings demonstrated that the wave steepness and wave period significantly influenced the V/V_current.

4.4. Effect of Current Velocity on the Hydrodynamic Performance of the Bio-FADs

This section presents a simple derivation of the analysis of current velocity. The wave situation remained consistent with H = 0.20 m and T = 1.5 s. Figure 21 depicts the correlation between the current velocity V_current/V and the motion RAO. Accordingly, the heave and pitch RAOs exhibited a small increase when the V_current/V increased. As observed in Figure 22, the V_current/V had a marginal impact on the S_Wetted/S_Total, V/V_0.10, and F/W_Sinker. Furthermore, the V/V showed a notable increase with an increase in the V_current/V, revealing a direct relationship. This phenomenon can be elucidated by the influence of the current, whereby the force exerted on the model escalated in tandem with the augmentation of the current velocity. Subsequently, the relative drift velocity escalated in tandem with the augmentation of the force. An increase in the horizontal force pressing on the model results in an increase in wave steepness. Additionally, the heave RAO, pitch RAO, relative wetted area, and rope tension increased with the increase in the V_current/V. The findings indicate that the relative current velocity had an impact on the motion RAOs, relative wetted area, rope tension, and drift velocity.

4.5. Effect of Balsa Wood Diameter on the Hydrodynamic Performance

Next, the wave and current conditions were kept constant, with a current velocity of 0.10 m/s, H = 0.20 m, and T = 1.5 s. Figure 23 depicts the correlation between the balsa wood relative diameter and the motion RAOs. In this study, six diameters of balsa wood are employed (D_F = 0.03, 0.04, 0.05, 0.06, 0.07, 0.08 m, respectively). Accordingly, the heave and pitch RAOs initially increased and subsequently reached a point of stability as the relative diameter of the balsa wood D_F/B increased. The solid lines depicted in Figure 24 indicate that D_F/B had a minimal impact on the relative wetted area S_Wetted/S_Total, the relative drift velocity V/V_Current, and the relative rope tension F/W_Sinker. The relative wetted area S_Wetted/S_Total decreased dramatically with increasing D_F/B and finally reached a stable state. The influence of DF/B on the relative drift velocity V/V_Current and rope tension F/W_Sinker was significant and complex. Conversely, the values of the relative drift velocity V/V_Current and the relative rope tension F/W_Sinker exhibit a more intricate pattern as D_F/B grows. As D_F/B increases, the V/V_Current first increases and then decreases. As the value of D_F/B increases, the value of F/W_Sinker follows a pattern of increasing, then decreasing, and then increasing again. The reason for this is that the wave force remained constant in the vertical direction, whereas the weight and buoyancy of the model rose proportionally to the D_F/B. As the diameter of the balsa wood increases, the weight of the raft does indeed become heavier, but the buoyancy it experiences also increases. Regarding the decreasing trend in the relative wetted area, our previous research yielded similar conclusions [15]. In this numerical simulation experiment, the wetted area and surface area of the raft corresponding to different diameters of balsa wood were as follows: 30 mm (0.35/1.49), 40 mm (0.27/1.89), 50 mm (0.25/2.30), 60 mm (0.27/2.70), 70 mm (0.30/3.11), and 80 mm (0.33/3.52). It is clear that as the diameter of the balsa wood increases, the wetted area first decreases and then increases. However, as the diameter increases, the surface area increases significantly, leading to a decrease and stabilization in the non-dimensional ratio of wetted area to surface area.

Regarding the heave and pitch RAOs, as the diameter of the balsa wood increases, the surface area of the raft increases, the permeability decreases, and the hydrodynamic forces acting on the raft increase, resulting in an increase in heave and pitch RAOs.

The findings indicate that the balsa wood's relative diameter had an important impact on the motion RAOs, relative wetted area, tension of the rope, and drift velocity.

5. Conclusions

To investigate the hydrodynamic performance of Bio-DFADs, this study develops a series of numerical simulations based on the realisable k–ε turbulence model. The effects of different components of relative length, wave steepness, relative current velocity, and diameter on motion response, relative velocity, wetted area, and rope tension are the main focus, which can provide scientific guidance for the eco-friendly and safe design of the DFADs.

(1) The motion responses were significantly influenced by the relative length, wave period, and wave height. The relative velocity and relative wetted area were particularly affected. The heave and pitch RAOs decreased with the increasing relative length. As the wave period rose, the trend of pitch and heave RAOs steadily decreased. The relative velocity, relative wetted area, and relative rope tension dropped with rising relative length and increased with rising wave height.

(2) The wave steepness, wave period, and relative length had an important impact on the motion responses and relative velocity of the Bio-DFADs. The motion RAOs increased with the rise in wave steepness. The relative velocity grew with rising wave steepness and decreased with rising relative length.

(3) The relative current velocity had an impact on the heave RAO, pitch RAO, relative wetted area, rope tension, and particularly, the drift velocity. The balsa wood's relative diameter significantly affected the heave RAO, pitch RAO, relative wetted area, rope tension, and drift velocity.