Design and Deployment of a Floating Porous Screen Breakwater in a Mesotidal Environment

Abstract

The performance of an intermediate-scale modular, permeable, floating breakwater comprised of an array of vertical screens is optimized and tested. A distinctive attribute of this breakwater design is its adaptive capacity to fluctuating water levels owing to its floating configuration, thereby preserving its efficacy during high tide and storm tide scenarios—an advancement over conventional bottom-mounted structures. The initial validation of the concept was tested in a laboratory wave basin in regular waves, which demonstrated promising results for three porous panels. Next, the breakwater’s design parameters were optimized using a finite difference computational fluid dynamics software, (FLOW-3D version 2023R2), considering porosity, spacing, and panel count. A scaled prototype, representative of a 1:2 ratio was then deployed during the summer of 2022 along the coast of Castine, ME, within a mesotidal, semi-sheltered system characterized by tidal currents and waves. Notably, the breakwater succeeded in attenuating half of the wave energy for periods shorter than 4 s, evidenced by transmission coefficients below 0.5, making this technology suitable for locally generated waves with shorter periods. During storm events, instantaneous transmission coefficients decreased to as low as 0.25, coinciding with significant wave heights exceeding 0.8 m. Additionally, the efficacy of wave attenuation improved slightly over time as biofoulants adhered to the structure, thereby enhancing drag and mass.

1. Introduction

Breakwaters are a form of coastal protection that mitigate erosion and damage to coastal environments by limiting the wave energy [1,2]. Most breakwaters are permanent structures, and may be classified as sloping, vertical, composite, or horizontally composite, while some structures, such as floating breakwaters, are temporary [3]. Among these categories, breakwaters may be conventional, providing full wave protection, or nonconventional, providing partial protection. To provide full protection, conventional breakwaters may be hundreds of meters long, cost thousands of dollars per linear meter, and have a high level of wave reflection that can interfere in the cycle of the marine biosphere, disrupt sediment transport, and may even create a higher energy wave environment outside of the area they are meant to protect [4,5,6]. For this reason, nonconventional breakwaters are a growing area of research within coastal engineering to provide partial wave protection while limiting environmental disturbances [7,8,9].

Floating breakwaters are most effective in short-period wave environments or over deeper water where the construction of bottom-mounted permanent breakwaters is not practical [10,11,12]. Floating breakwaters can attenuate short-period wave energy, but if the wavelength is too long, the floating breakwater may be carried with wave motion instead. This effect may be mitigated by increasing the width of the breakwater in the dimension perpendicular to the wave crest, but this can be costly for production and create difficulties in deployment [13].

Floating breakwaters have distinct categories, such as box, pontoon, frame, mat, and tethered float. Among these, the box type stands out as the most prevalent. Wave attenuation primarily relies on reflection within the box structure. Hales [14] demonstrated that for any structure, a width to wavelength ratio of 0.3 is crucial for efficacy. Conventionally, a breakwater is considered effective if it attenuates waves by 50%, corresponding to a transmission coefficient ($K_T$), which is the ratio of the transmitted wave energy divided by the incident wave energy, of 0.5. However, effectiveness may vary based on local implementation constraints. Traditionally, for floating breakwaters to be deemed efficient coastal defenses, they must be sizable, exceeding 14 m in width for a depth of 10 m and a period of 6 s. The primary drawbacks of box floating breakwaters lie in their substantial size requirements for effective wave attenuation and the issue of wave reflection. Reflection can exacerbate wave action, posing challenges for naval navigation and contributing to coastal erosion.

The pontoon breakwater comprises two box breakwaters rigidly connected by a platform, resembling a pontoon or catamaran boat. Increasing the distance between the pontoons enhances the moment of inertia and stability without adding mass [7]. Reflection serves as the primary attenuation mechanism for pontoon breakwaters, with additional dissipation occurring between the two pontoons. The degree of reflection is heavily influenced by pontoon draft, width, spacing, and mooring line stiffness [15]. Past research has focused on optimizing floating breakwaters to enhance effectiveness while minimizing size. Modifications to conventional designs have been explored for simplicity. For instance, Peña et al. [16] experimented with adding fins to standard pontoon breakwaters and creating catamaran structures by joining two pontoons. Yan [17] optimized box breakwaters by incorporating cantilevers at various positions. He et al. [18] integrated pneumatic chambers into floating box breakwaters to boost performance. Ji et al. [19] tested a model featuring a hollow rubber float topped with a mesh cage. Introducing slotted barriers was found to diminish transmission and pitch response in waves with shorter periods [20]. While these innovations have shown promise, they predominantly rely on reflection as the primary attenuation mechanism.

A frame floating breakwater is a box- or pontoon-style breakwater with a rigid frame connected to the structure that extends into the water column. The upper part of the structure reflects wave energy while the extended portion induces a second mode of wave attenuation; for example, a wave fence of pressure-treated timber attached to the bottom of a concrete pontoon [21]. The spacing of the timber in the fence allows water to pass through while generating turbulence to dissipate energy. A mat floating breakwater (Figure 1) is commonly made of a large number of floating scrap tires connected together. This structure dissipates energy by creating friction along the wetted surface as well as disrupting particle orbits [7]. The width of the floating tire breakwater has to be at least 80% of the wavelength to achieve a transmission coefficient of 0.5 [22]. A tethered float breakwater has a large number of smaller floats attached to the sea floor or a submerged structure via tethers. With this type of structure, reflection is a minor contributor, with the primary attenuation mechanism being drag [23].

Previous research has explored alternative methods to enhance wave attenuation. Ji et al. [24] examined a cylindrical floating breakwater composed of two cylindrical floats bridged by a mesh cage filled with hollow rubber balls, converting wave energy into mechanical energy. Another approach involved attaching three to five skirt walls to the keel of a box breakwater, effectively halving its effective width [25]. The modification of twin pontoon breakwaters with nets and sinkers attached to the keel demonstrated a decrease in the transmission coefficient with an increasing number of nets [26]. Mani [27] investigated a Y-Frame floating breakwater, consisting of a trapezoidal float and closely spaced large cylinders attached to the keel, achieving a transmission coefficient of 0.5 with a width to wavelength ratio below 0.2. Modifications to pontoon breakwaters, such as the addition of wing plates and porous materials on the sides, led to reductions in incoming wave energy by up to 80% [28]. Wang and Sun [29] explored the use of porosity in breakwaters made of diamond-shaped blocks. While these studies indicate the potential for reducing the width to wavelength ratio using alternative attenuation methods, many still rely predominantly on reflection. Moreover, the materials employed in these models are not necessarily suitable for full-scale, long-term field deployments. Further research is needed to investigate alternative materials capable of producing lighter, more easily deployable breakwaters.

To boost the effectiveness of a floating breakwater in transitional and shallow water wave conditions, inspiration can be drawn from panel-type breakwaters. These breakwaters typically consist of vertical or horizontal arrays of thin plates. These plates are typically fixed and made of permeable or impermeable materials. Permeable plates have several advantages over impermeable plates, including reduced wave reflection and less interference with the tidal currents, sediment transport, and marine animal movement, at the cost of increased energy transmission [30,31]. Fixed panel vertical breakwaters, having larger dimensions in draft than in width, have undergone a significant evolution of modeling and experimentation over the last several decades. A vertical, impermeable barrier structure fixed to the sea floor significantly decreased wave transmission when the breakwater draft to the water depth ratio increased [32]. Introducing porosity into the fixed panel design reduces flow obstruction. A three-row vertically slotted fixed breakwater with impermeable upper and lower panels separated by a permeable interior panel was shown to attenuate a wide range of wave environments when the draft was similar to the water depth [1]. The impermeable lower panel enhanced wave reflection in intermediate and shallow wave environments, while the upper panel significantly influenced shorter period waves. While a fixed, vertical panel breakwater design is more effective than a horizontal breakwater for short and intermediate wave environments, because of its extension into the water column [33], the effectiveness is likely reduced during storm tide conditions when increased water depth becomes larger than the draft. Previous research on dual-body surface-fixed breakwater structures with heave motion has been studied in a scaled laboratory setting, intended to mimic a floating panel breakwater [34]. Wave transmission was found to follow a parabolic trend that increased with increasing wave periods, while wave reflection remained unaffected by wave period. They observed reflection coefficients of less than 30% due to high energy dissipation in the free-body breakwater structure. Generally, energy dissipation and attenuation from the heave of the breakwater should lead to lower reflection. The previous studies were primarily conducted in a scaled laboratory setting, vulnerable to scaling effects that may bias the results.

The introduction of the permeable panel-type floating breakwater offers several benefits over the traditional porous breakwaters previously discussed in the literature [35,36,37]. One of the key distinctions is its ability to combine wave attenuation with reduced environmental impact. Unlike conventional porous breakwaters, which rely heavily on wave reflection and often disrupt natural coastal processes, permeable breakwaters allow for the passage of water, reducing reflection while dissipating energy through internal turbulence. This not only diminishes wave forces but also lessens interference with sediment transport and marine habitats, making it a more ecologically sustainable solution. Moreover, the flexibility of permeable breakwaters—designed to respond to a range of wave conditions without the need for large-scale, rigid structures—offers a more cost-effective and adaptable approach to coastal defense. The reduced material requirements and easier deployment, compared to traditional bulky porous breakwaters, further enhance their practicality for real-world applications where both performance and environmental preservation are critical.

This study focuses on the design and testing of a permeable, panel-type floating breakwater in a 1:2-scale field setting, aiming to minimize the scaling effects commonly encountered in laboratory experiments [38]. The floating suspended design penetrates the water column while self-adjusting to changes in mean water levels, such as storm tide conditions [39,40]. The design is modular, where panels can be added to increase or decrease the water column penetration based on the local wave environment [41,42]. The research objectives are to (1) optimize the design of a porous floating screen breakwater through laboratory experiments and simulations and (2) use an intermediate scale field demonstration to analyze wave attenuation under varying forcing conditions.

The paper begins detailing a proof of concept 1:6-scale model constructed from PVC and tested in a laboratory wave basin, where specifications that need improvement were identified. Then, the FLOW-3D computational fluid dynamics software was used to optimize the breakwater design and minimize the transmission coefficient. A 1:2-scale field prototype was constructed and deployed off the coast of Castine, Maine, to establish the efficacy and reproducibility of this breakwater design in reducing wave transmission in a field setting. The numerical model is used to examine fluid–structure interactions to understand the impacts of the porous structure’s wave orbital velocities. The discussion compares the performance of the breakwater with previous floating breakwater experiments and discusses secondary influences such as tidal currents and biofouling. Finally, conclusions are drawn on the efficacy of the prototype and areas of future research are posed.

2. Materials and Methods

2.1. 1:6-Scale Laboratory Test

Testing was conducted in the Harold Alfond Wind and Wave Basin (${\mathrm{W}}^2$) at the University of Maine’s Advanced Structures and Composites Center (ASCC). The ${\mathrm{W}}^2$ is a 30 m long by 9 m wide by 5 m deep water wave basin. The 16-paddle multi-directional wave generator can create regular, directional (±60 degrees relative to the basin centerline), or irregular waves with varying frequencies and wave heights with a maximum wave height of 0.8 m at a period of 2.3 s. An energy dissipating beach is at the opposite end of the basin.

Six model assemblies were built using a 1:6 Froude scale, where each assembly consisted of a porous PVC sheet with buoyant PVC tubes (Figure 1a). A porosity of 23% with centimeter-scale circular pores was chosen to allow waves to pass through the structure inducing turbulence, while reducing reflection and mooring forces. The water plane area was reduced by lowering the horizontal flotation tubes below the still water line. This was carried out to allow the structure to function more like a fixed bottom wave attenuator by reducing the heave response. The full test matrix was run with one assembly, located 15 m from the wave maker, for a duration of 15 min with a wave probe sampling at a frequency of 64 Hz (Figure 1b). Once the test was completed, a second assembly was added 1 m behind the first. The entire test matrix was then repeated with one assembly added at a time until all six were installed and tested. Water surface elevations were measured using nine Edinburgh resistance wave probes. Three probes were located upstream of the assemblies to measure the incident and reflected wave heights. The remaining wave probes were located 0.5 m behind each assembly to measure the transmitted wave height. Mooring lines were attached horizontally to fixtures suspended from the tow carriage and bridge. Each test matrix consisted of regular, irregular, and pink noise wave cases, with full-scale frequencies ranging from 3 to 7 s and wave heights ranging from 1 to 1.5 m. These data were used to validate the computational model presented in the following section. Wave attenuation was evaluated using an energy transmission coefficient, $K_T={(H_t⁄H_i)}^2$, comprising the ratio of transmitted ($H_t$) to incident wave height ($H_i$), calculated from a zero-crossing analysis.

2.2. Computational Fluid Dynamics Simulations

FLOW-3D uses a Reynolds-Averaged Navier–Stokes (RANS)-based finite volume method to solve the continuity and Navier–Stokes equations [43]. The RANS method is used to model turbulent flows by decomposing the flow variables into mean and fluctuating components. It simplifies the Navier–Stokes equations by averaging the turbulent effects, allowing for practical simulations of complex, time-averaged flow behavior. This method is computationally efficient and suitable for a wide range of applications, including free surface flows and multiphase interactions. The volume of fluid (VOF) method in FLOW-3D simulates fluid–solid interactions by tracking the free surface of immiscible fluids using a fractional volume approach, accurately capturing surface tension and interface behavior between different phases in complex flows. FLOW-3D simulates porous media using a generalized form of Darcy’s Law, which models the flow through porous materials by incorporating permeability and porosity properties.

Each breakwater screen is represented as a solid rectangular object with a defined porosity in the x-direction, and the software simulates the flow of water through the screen without the necessity of simulating pore geometry. The model was first validated by replicating the conditions of the 1:6-scale laboratory tests (Figure 1c). The breakwater was simulated with 23% porosity and moored to fixed suspended beams at the surface. The simulation environment had the dimensions of 35 m × 15 m × 6 m, with an adaptive mesh size of 0.2 m near the breakwater and 0.3 m elsewhere. Preliminary convergence tests demonstrated that water level measurements converged at a rate proportional to mesh size, and at a mesh size of 0.5 m, the simulation results had converged within a tolerance of 0.1%. We reduced the mesh size by half again to avoid any potential issues with resolution. The incident wave generator was located at x = 0, and a numerical wave dampener was placed at x = 35 to mitigate reflecting waves. The simulation was run for 10 min after the initial wave generation, and at each $(x,y)$ coordinate, the free surface elevation was recorded. Each simulation was run on an 8-core Intel processor and took approximately 8 h of wall-clock time. The computational cost of each simulation scaled with the mesh size to the fourth power. We ran the simulation multiple times, with full-scale wave amplitudes of 0.5 m, wave periods ranging from 3.0 s to 6.8 s, and the number of porous screens ranging from 1 to 6.

We computed the wave amplitude at a probe located 0.5 m downstream of the assembly using a regression algorithm. Finally, we compared the ratio of transmitted to incident wave height between our simulations and laboratory experiments (Figure 2). The FLOW-3D simulations were successfully validated in predicting the transmission coefficients of the breakwater, with a root mean square error of 13%. The noted discrepancies between the laboratory and simulation results are likely due to friction and advection forces, which were present in the laboratory test but are very difficult to accurately simulate. This validated model was then used to optimize the final breakwater design, from which the efficacy will be tested in an intermediate-scale field demonstration.

2.3. Field Observation Data Processing

Field observations were collected around the intermediate-scale prototype, including five Sofar Ocean Spotter buoys that collected vertical surface displacements at 2.5 Hz. Both a spectral and a zero-crossing method were employed to analyze wave characteristics. A wave spectrum was used to temporally calculate the significant wave height, peak period, and dominant wave direction, as well as wave energy. The zero-crossing method was used to calculate wave-by-wave heights and periods to determine Beaufort sea-states and check spectral wave conditions. Bulk wave parameters were calculated temporally in hour long segments with a 50% overlap. Observations from the wave buoys showed substantial red noise in calm wave conditions, when wave heights were less than 0.25 m. Therefore, time periods where the significant wave height, $H_{sig}$, is less than 0.25 m were omitted from analysis.

Wave spectral analysis was used to calculate a frequency-dependent wave attenuation transmission coefficient for the breakwater [44]. This analysis allows for the determination of how waves of varying periods (i.e., frequencies) are attenuated as they pass through the structure. For each hour-long segment, a Welch’s power spectral density estimate, $S_{zz}$, was calculated on vertical displacements, with an input sampling frequency of 2.5 Hz. The spectrum was then binned into 20 equal frequency bins. The wave energy by frequency bin was calculated using the following equation:

$$\mathrm{W}\mathrm{E}\left(f\right)={\int }_{{\omega }_1}^{{\omega }_2}{S}_{zz}d\omega ,$$

(1)

where ${\omega }_2$ and ${\omega }_1$ are the upper and lower bound of each frequency bin.

A frequency-dependent energy transmission coefficient $K_T\left(f\right)$ was calculated by the following equation:

$$K_T\left(f\right)={\displaystyle \frac{W{E}_{transmitted}\left(f\right)}{W{E}_{incident}\left(f\right)}}.$$

(2)

The energy reflection coefficient is calculated similarly, using the ratio of reflected to incident wave energy. The frequency-binned average wave energy transmission coefficient was calculated for the breakwater by averaging the energy density for each frequency bin across all usable sampling periods during the entire deployment.

3. Results

3.1. Scaled Laboratory Test

Wave attenuation was assessed using the energy transmission coefficient $K_T$, where higher values signify less wave attenuation. As the wave period increases, screen configurations 1 through 6 exhibit decreased attenuation capacity (Figure 2). With just one screen, there is minimal attenuation across the entire range of wave periods tested. However, upon introducing a second screen, the $K_T$ reduces to 0.5 for a 3 s wave, indicating a 50% reduction in energy. Overall, attenuation capacity improves with the addition of more screens, particularly evident with longer period waves, where six screens attenuated 20% of the wave energy for 6-second waves compared to 10% with one screen. For wave periods shorter than 4 s, additional screens did not enhance wave attenuation beyond the effectiveness of three screens. A numerical model is used next to understand how porosity and distance between the screens can enhance wave attenuation.

3.2. Breakwater Optimization

After validating the 1:6-scale model, the numerical model was Froude-scaled up to 1:2 and the simulation environment was enlarged to 70 m × 70 m × 20 m, with an adaptive mesh size of 0.3 m close to the breakwater and 0.5 m elsewhere. The initial laboratory and simulation tests demonstrated that there is little benefit in wave attenuation for more than three screens in the breakwater structure. Using monochromatic linear waves with an amplitude of 1 m and a period of 2 s, we utilized a black box optimization technique with a gradient descent algorithm to determine the ideal breakwater specifications to minimize transmitted wave energy (Figure 3). The optimization procedure follows Ruder [45]. To reduce manufacturing costs, the optimized design was limited to three screens. The initial model parameters are based on the 1:6-scale laboratory design, with a screen porosity of 23%, screen width of 4.83 m, screen height of 5.56 m, and horizontal spacing of 3 m. For each iteration of the optimization process, we randomly generated 20 alternative designs, in which for each design, the parameters were within 0% and 200% of the original values. We simulated each randomly generated breakwater and computed its transmission coefficient $K_T$ (Figure 3b).

If the original parameter set is the best optimized out of the selection of designs, then the algorithm has converged and we have found the optimized parameter set. Otherwise, we next interpolated over the parameter space $\theta$ to compute the gradient of $K_T$, and then iteratively updated the parameter space as

$${\theta }_{new}=\theta -\eta \ast \nabla K_T$$

(3)

where $\theta$ and ${\theta }_{new}$ represent the original and updated set of parameters, and $\eta$ is a calibration parameter [45]. We then ran the algorithm again, using the new parameter set, and narrowed the parameter space by a factor of 25%. We repeated this process until the transmission coefficient converged, which typically took about three iterations. Note that the optimal design is also weighted by the material cost, so the algorithm will show preference to a smaller structure that achieves nearly the same energy dissipation as larger structures.

Finally, the optimized breakwater was simulated with Beaufort scale conditions ranging from 0 to 5 (calm wind to fresh breeze), using a JONSWAP wave energy spectrum with the wind speed ranging from 0.5 m/s to 10.7 m/s, a fetch of 20,000 m, and a peak enhancement factor of 7. The free surface elevation time series at each $(x,y)$ coordinate and the transmitted wave energy, $K_T$, were recorded by computing a fast Fourier transform of the time series, treating each frequency band as a discrete wave amplitude, and adding the individual wave energy contributions of each band.

The breakwater design optimization demonstrated that the most important factor in wave attenuation effectiveness is the horizontal spacing between the screens (Figure 3). The screens must be spaced sufficiently far apart so that the waves do not overtop the individual screens, and the spacing between screens must be proportional to the wavelength of the incident waves. In general, the distance between the first and last screen should ideally be roughly equal to one wavelength. In a variable wave environment, the wavelength associated with the peak wave frequency may serve as a guideline. It was also determined that screen width and screen height do not affect the magnitude of wave attenuation, but they do affect the area and extent of the attenuation. If the breakwater screens are too narrow in the along-crest direction, the two diffracted wave crests will recombine directly behind the structure, increasing the wave amplitude. The screens just need to be deep enough to encompass the wave crest and trough.

Wave attenuation improves with the number of screens in the structure, but returns are diminished after three screens, which was consistent with the laboratory experiment. More than three screens will accomplish slightly improved wave attenuation but are likely not worth the added cost. It was also determined that a lateral array of floating structures, with the spacing between them equal to the width of each structure, is just as effective as one wide structure in creating a broad zone of attenuation. This lateral arrangement requires several more mooring lines but considerably less construction material and is easier to transport and deploy. It was also determined that there is little correlation between mooring line strength and wave attenuation if the mooring lines are sufficiently strong to hold the structure in place and prevent excessive movement.

Finally, it was determined that lower porosity screens are more effective at wave attenuation and completely solid screens are the most effective in an irregular wave environment (Figure 4). This was compared using changes in wave energy from before and after the structure.

$$\Delta E={\displaystyle \frac{\int S_{zz\left(transmitted\right)}\left(f\right)df}{\int S_{zz\left(incident\right)}\left(f\right)df}}-1.$$

(4)

However, low porosity screens also tended to produce stronger reflective waves ($\Delta E>0$), an undesirable side effect for the surrounding area. The breakwater with 10% porosity screens avoided producing reflective waves of higher amplitudes than the incident waves and still achieves nearly 50% transmitted wave energy attenuation in standard wind-wave conditions. The 10% porosity screens provided a larger area of attenuation behind the structure, evidenced by $\Delta E<0$, compared to the 23% porosity simulation in Figure 4.

3.3. Wave Attenuation Mechanisms

The semi-permeable design of the wave screen breakwater suggests that wave attenuation is influenced by reflection, diffraction, and dissipation. With a porosity of 10%, it is anticipated that wave orbital velocities passing through the voids create turbulence, consequently forming a wake behind the structure. To understand the dissipation effects on wave attenuation, wave orbital velocities, turbulent kinetic energy (TKE), and TKE dissipation are compared (Figure 5). The wave orbital velocities experience a decline near the breakwater, dropping from 0.2 m/s to 0.1 m/s within 8 m directly behind the structure (Figure 5a). Beyond this point, they begin to rise again, reaching 0.15 m/s for the subsequent 15 m, presumably influenced by wave diffraction. TKE dissipation takes place following the first screen, reaching its peak at the second screen with values around ${10}^3$ J/kg (Figure 5b). The dissipation remains notably high in the surface layer, with the wake extending up to 5 m behind the structure. While the observed values can be significant, they are confined to the structure and its immediate surroundings.

To differentiate reflected versus dissipated wave energy, the total incident wave energy is compared in front of the structure with that within and behind the structure. The total incident wave energy can be computed as follows:

$$E_{incident}=\rho g{\int }_0^{\infty }S\left(f\right)df,$$

(5)

where $\rho$ is the water density, g is acceleration of gravity, and $S\left(f\right)$ is the wave energy frequency spectrum. For the breakwater model with 10% porosity in Beaufort Scale 2 conditions (wind speed = 5 m/s), the incident wave energy that the model is forced with is about 198 J/m. Using the same formula, the reflected wave energy directly in front of the structure is 240 J/m, roughly 42 J/m more than the incident wave energy. This suggests that 21% of the incident wave energy is being reflected.

The integral of TKE within the area covering the structure and the wake can be compared with the integral of TKE dissipation over the same area; we compute that about 47 J/m of energy, or 23% of incident wave energy, is lost to turbulence. This indicates that, in total, about 46% of incident wave energy is mitigated by the porous breakwater either through reflection or turbulence.

3.4. Field Demonstration

To study whether the laboratory and simulation results are impacted by scaling effects and tidal currents, the 1:2-scale breakwater was constructed throughout the month of May 2022 and deployed for field testing from 31 May to 5 August. All design parameters followed the optimized design in Figure 3, except the screens were spaced 2.95 m apart to match the characteristic wavelength of the field site in Beaufort sea-state 2 conditions. Units were constructed of wood, steel, aluminum, as well as poly-plastic pontoons and floating dock components for buoyancy (Figure 6). Each unit weighed approximately 5200 kg before deployment. Two units that were arranged laterally formed a complete breakwater assembly, which visually attenuated wave energy in the lee of the structure (Figure 6c,d).

To measure the effectiveness of the half-scale prototype, five wave buoys were placed in front, behind, and to the side of the assemblies (Figure 7a). Buoy 1 was placed in front of the prototype and provides an estimate of wave energy affected by reflection. Buoy 2 is positioned alongside, providing a measure of incident wave energy unaffected by reflection or diffraction. Buoy 3 is located between the two assembles and will measure the greatest amount of wave transmission, while buoys 4 and 5 are directly behind one unit.

Three transmission coefficients, $K_{T3}$, $K_{T4}$, $K_{T5}$ were calculated as the frequency-dependent wave energy ratio between buoy 3 (the modified wave field), buoy 4 (the leeward shadow zone), and buoy 5 (the leeward transition zone), respectively, to buoy 2 (the incident). Additionally, a reflection coefficient $K_R$ was calculated as the wave energy ratio between buoy 1 (the reflected wave field) and buoy 2 (the incident). Error bars for each of these transmission and reflection coefficients were calculated by taking a 95% confidence interval of the sampled data within each frequency bin. Frequency-binned hour samples all had over 1500 samples after notable outliers were removed.

The field deployment site was located off the coast of Castine, Maine, in the upper Penobscot Bay (Figure 7). Penobscot Bay is a mesotidal system (tidal range varying from 2.9 to 4.9 m) that is part of the longest estuary in Maine and features a mean annual river discharge of 350 ${\mathrm{m}}^3$/s [46]. The topography of upper Penobscot Bay is complicated, marked by islands that limit the available fetch for wave growth. The predominate wind direction during the summer months is from the south/southwest [47]. To understand the wave response during storm events, wind and barometric pressure data were collected from the NOAA Buoy in Penobscot Bay, 44033, stationed in Southern Penobscot Bay to the East of Islesboro, approximately 40 km from the site (Figure 7b). Velocity data were collected at a 2 m depth from the UMaine NERACOOS Buoy F0135 in West Penobscot Bay at a more offshore location. Currents are tidally modulated and asymmetric, biased to being offshore due to the influence of river discharge. This is evidenced by flood velocities that reach up to 0.50 m/s, while ebb velocities reach up to −0.75 m/s (Figure 8 (top panel)). The wave environment closer to the mouth is often a wind-sea environment, with peak wave periods $<7$ s, with limited swell events (Figure 8 (bottom panel)). Significant wave heights varied from typical values of 0.25 m during calm winds and could reach up to 1.5 m during storm events.

The deployment area for the breakwater is situated further inshore, featuring semi-sheltered conditions created by the presence of Islesboro and North Haven islands. This area experiences a fetch-limited wave environment alongside significant tidal currents. The deployment occurred over a 14 m depth at mean high waters with a 3.5 m tidal range. Considering the mean water depth and tidal height, the wave regime was mostly transitional to deepwater ($0.13<d/L<2.33$), with typical wavelengths ranging from 6.23 m and 106 m at high tides to 6.23 m and 94.3 m at low tides. Most of the waves do not reach the bottom at these depths, which allows for the reflection and transmission of waves to be influenced by the breakwater and not refraction.

To understand wave attenuation and reflection induced by the breakwater, the results are presented in an environment that has been scaled to match the breakwater. Throughout the deployment, the incident wave environment exhibited a bimodal nature. Predominantly, conditions were characterized by wind sea, where the peak period ($T_p$) was typically around 4 s (Figure 9a). However, there were occasional occurrences of swell conditions, with $T_p$ ranging between 7 s and 10 s, commonly around 8 s. The scaled significant wave heights ranged from 0.2 m to 1.6 m (during storm events), with common $H_{sig}$ ranging from 0.6 m to 0.8 m.

The frequency-dependent transmission coefficient, $K_T$, was calculated for every hour of data and averaged over the entire deployment period to understand how the breakwater-attenuated waves of varying frequencies at different spatial locations (Figure 9b). The general trend at all spatial locations was a reduction in $K_T$ from swell frequencies ($f<0.14$ Hz) to wind sea (0.14 Hz $<f<$ 0.5 Hz), indicating increasing wave attenuation. Directly behind the breakwater (buoy 4), $K_{T4}<0.5$ for the predominate wave environment (2 s $<T_p<4$ s), indicating that 50% of the wave energy was attenuated. The greatest attenuation occurred at 0.325 Hz $<f<$ 0.425 Hz, where $K_{T4}$ = 0.4. Farther behind the breakwater at buoy 5, $K_{T5}$ increased to 0.53 at f = 0.325 Hz, indicating that diminished wave attenuation likely influenced by diffracted waves. Directly between the two floating structures, $K_{T4}$ = 0.48 at f = 0.325 Hz. The reflection coefficient, $K_R$, varied from 1.17 to 1.04, indicating 4% to 17% wave amplification in front of the breakwater from reflection.

While on average, the breakwater attenuated at least 50% of the wave energy, it is important to understand the performance during different forcing conditions, such as storm versus non-storm conditions. From 25 June 2022 to 3 August 2022, seven frontal passages (28 June, 1 July, 6 July, 12 July, 19 July, 25 July, 2 August) were identified by drops in barometric pressure, P, greater than 5 hPa and wind speeds in excess of 5 m/s (Figure 10 (top)). During these periods, the wave environment was energetic compared to non-storm conditions, where $H_{sig}>0.8$ m and $T_P>4$ s (Figure 10 (middle)). The frequency-dependent transmission coefficient at f = 0.4 Hz was near 0.27 during storm events immediately behind the structure at buoy 4, indicating 73% wave attenuation at these frequencies, compared to $K_{T4}>$ 0.25 during non-storm conditions (Figure 10 (bottom)). Breakwater performance improved beyond the average $K_{T4}=0.4$ during storm events when wave heights were larger.

After the deployment, the two assemblies had masses of 6600 kg and 6300 kg. Beyond minor additions from metal components of the connections between assemblies, any additionally significant weight can be attributed to biofouling (Figure 11). The community of biofouling species present on each were distinct, due to the depth and wave exposure affecting the community composition [48]. From photo and video footage, microalgae (slime), barnacles, mussels, wormweed (Ascophyllum nodosum, f. scorpioides), and fucus (Fucus vesiculosus) were identified on both structures [49,50,51]. However, macroalgae such as wormweed and fucus were more common on the 6600 kg assembly, and barnacles appeared to be more densely dispersed. A kelp species, which was identified as Alaria esculenta, was present on the heavier assembly and absent on the other.

4. Discussion

The half-scale breakwater performed well for short-period waves typical in fetch-limited environments. For periods smaller than 3.7 s, the breakwater featured an average transmission coefficient of less than 0.5 directly behind one of the structures, meaning that at least half of the wave energy was attenuated. Farther behind the structure or between the two structures, the transmission coefficient were generally below 0.6 for wave periods smaller than 3.7 s. The average reflection off the structure was generally minimal, ranging between 5% to 17%, which suggests that wave attenuation is also influenced by attenuation and dissipation. Performance was improved for a narrow band of wave frequencies during storm events, when large enough wave heights ($H_{sig}$ > 0.8 m) produced transmission coefficients as small as 0.25 at the f = 0.4 s wave frequency (2.5 s period).

The 1:2-scale breakwater generally performed as well as or better than various breakwater designs tested experimentally in terms of wave energy transmission. Koutandos et al. [34] used a laboratory experiment to test a box breakwater fixed at the surface with a porous plate beneath. In an irregular wave field, they found transmission coefficients for periods of 2.67 s, 3.16 s, and 5.04 s of approximately 0.6, 0.7, and 0.8, respectively. The 1:2-scale screen breakwater demonstrated improved performance at the same frequencies on average, with transmission coefficients of 0.41, 0.45, and 0.7, respectively. Comparison with the results of the various box and board-net floating breakwaters with additional chain lengths tested by Dong et al. [52] in a laboratory experiment with regular waves was only possible for the 20 m wavelength for $H/L$∼$0.3$ using H∼$0.6$ m. Transmission coefficients were as low as 0.8 (single-box), 0.65 (double-box breakwater), and 0.6 (board-net with 4 rows). At a similar wavelength, the transmission coefficient of the 1:2-scale screen breakwater was ∼$0.45$, demonstrating improved performance. Ding et al. [53] tested the performance of three surface-fixed vertical plates that were not porous. The fixed rigid plates featured a transmission coefficient that was higher (0.98) than the 1:2-scale breakwater (0.89) at 80 m wavelengths. At 20 m wavelengths, the fixed rigid plates outperformed the floating porous breakwater with a transmission coefficient of 0.1 compared to 0.45. It is expected that fixed, non-porous plates would outperform a floating porous structure due to differences in reflection.

Overall, the results of the floating, porous breakwater are promising. The structure is best suited in a semi-sheltered environment where the dominant wave regime is a wind-sea regime. This technology would not perform well in a coastal environment where swell waves dominate. The floating nature of this design is particularly advantageous in regions with large tidal fluctuations or under storm tide conditions. The specifications of the breakwater can be adjusted based on ambient wave conditions, where additional panels can be added either vertically or horizontally. By reducing the porosity of the screens, a higher fraction of incident wave energy can be mitigated, at the expense of higher reflected waves and a greater risk of drift from tidal forces. The zone of greatest attenuation is local to the structure. If this technology were to be used to protect a larger area, additional arrays would be necessary to create a breakwater field. Future research could evaluate how these structures affect tidal and subtidal flows and assess what the consequences would be for material transport. Additionally, research into robust materials that could survive repeated deployments is needed.

5. Conclusions

The goal of this research was to evaluate the efficacy of a modular, floating, porous breakwater that could attenuate wave energy while reducing the overall footprint. This was accomplished through comprehensive laboratory, numerical, and field experiments. The breakwater was designed as three porous screens that are modular in nature and can be modified depending on the environment. Results indicate that the floating structure can attenuate as much as 75% of the wave energy for ∼4 s waves during storm events and features transmission coefficients $<0.5$ for wave periods lower than 3.7 s on average. By implicit design, the nature of these floating breakwaters enables them to retain effectiveness during high and storm tide conditions, in contrast with bottom-mounted breakwaters. They are most appropriate for semi-sheltered wave environments such as estuary mouths or bays, where the sea state is dominated by shorter periods of wind sea.

Despite these promising results, several limitations should be noted. The performance of the breakwater was tested primarily in environments with short-period waves, which may not fully represent the conditions in areas dominated by long-period swell waves. The breakwater’s efficacy in such environments remains untested, and further investigation is required to understand its potential limitations. Additionally, the localized attenuation of wave energy means that larger areas would require multiple breakwater arrays, potentially increasing costs and logistical complexity. Future research should explore the effects of breakwater fields on tidal and subtidal currents, as well as their influence on material transport, which could have ecological and sedimentary consequences. Moreover, the durability of the materials used for repeated deployments in harsh conditions remains an open question, warranting further studies on the development of more resilient materials for long-term use.