1. Introduction
Among the renewable energies experiencing considerable development, marine energies need more attention. The ocean, which covers 71% of the Earth’s surface, is an underutilized energy source. The expected increase in the number and intensity of storms due to climate change, flooding along coastal areas, and the push for corporate environmental responsibility along coastal regions are opening the way for significant marine energy development. Wave Energy Converters (WEC) should be climate-proof (resistant to sea level rise and strong waves), environmentally friendly, and of low visual impact (submerged or low crested) to avoid negative impacts. Various WECs have different mechanisms and technologies for converting mechanical energy into electricity. These technologies have been reviewed by many authors [
1,
2,
3,
4,
5].
Another vital feature of WECs is their influence on the hydrodynamics near coastlines. Various numerical and experimental studies have been conducted to assess the hydrodynamic impacts of coastal protection structures on nearshore flow characteristics. Atan et al. [
6] have studied three arrays of configurations with 12 WECs on the western coasts of Ireland to measure the influence of these structures on nearshore wave climate and captured power. They found that wave height decreased by less than 1% between 1 km and 3 km from the coast and by 0.1% between 100–300 m from the coast. They also reported that wave power decreased by less than 1% between 1–3 km from the coast and by 0.2% between 100–300 m from the coastline.
Chang et al. [
7] performed a sensitivity analysis of the SWAN (Simulating Waves Nearshore) model for WEC arrangements and features. They concluded that wave height decreases of 30% and 15% were observed because of two tested scenarios for wave energy converter structures. Flow regime alterations imposed by a wave farm located on the southwestern coasts of England were investigated using SWAN and ROMS (Regional Ocean Modeling System) models by Greaves & Iglesias [
8]. They studied WECs effects on wave radiation stresses, bed shear stresses, bottom frictions, and sediment movement. The results confirmed that the wave farm influences gradients of bottom shear stress, which leads to adjusting current velocity, and wave heights (by around 5 to 10 cm). It has been reported that flow interactions and bed stress are the main factors affecting sediment transport patterns and subsequent morphological changes. Contardo et al. [
9] validated their proposed SWAN model using measured field data from a series of wave measurement devices. Their model showed that WEC impacts on the wave field and flow structure are more significant at 40 m downstream of the unit, with a maximum drop of 20% of the wave height.
Apart from the impacts of WECs on the flow field and, consequently, the morphology of a region, it is also necessary to examine the region’s potential in terms of wave energy. It can be considered the first step of the project implementation. Numerous studies have focused on the marine power potential of a region calculated from wave characteristics such as wave height and wave period [
10,
11,
12,
13,
14]. The wave parameters are determined using in situ wave measurements, satellite data, and numerical wave models.
Appendini et al. [
15] investigated the wave potential in the Caribbean Sea. To this end, they validated a 30-year wave hindcast of the region using altimetry (Globwave) and buoy (DIMAR) data. Based on their study, the Caribbean Low-Level Jet with easterly winds of 13 m/s has the highest potential for wave energy extraction with 8 to 14 kW/m. Garcia and Canals [
16] assessed wave power potential in Puerto Rico and US Virgin Islands. They used a high-resolution wave model to estimate available wave power in the region. They reported 10 to 12 kW/m as the available potential of wave power, which reveals that these sites are theoretically appropriate for wave energy harvest projects.
The extractable wave energy of the Atlantic coast of Morocco was studied by Sierra et al. [
17]. Using 44-year data series at 23 points and statistical analysis of significant wave heights, they categorized the domain of study in terms of the amount of recoverable energy. As a result, the central area of the Atlantic Moroccan coast, with the most considerable wave heights, was known as the optimal area for wave energy harvesting. This area had an annual average wave power higher than 25 kW/m.
The WECs use sensors which could pose several problems due to the possibility of simple disturbances causing errors. Future research should consider using interval observers instead of sensors. Based on the recent research by [
18,
19], interval observers can be used for control of linear and non-linear systems, and anti-disturbance controller design, in a wide range of applications such as Wave Energy Converters.
To maximize the benefits of WECs, installing them in the regions susceptible to coastal erosion is imperative. Beaches form about 20% of the planet’s coastline. Of these, nearly 70% are undergoing a phase of erosion, 20% are stable, and 10% show signs of accumulation. Moreover, Choupin et al. [
20] investigated the most significant factors affecting wave energy harvesting. As they noted local geographical specifications such as touristic features are critical in recognizing the suitable location for WEC installation. Algeria has a coastline of 1622 km, which welcomes millions of people. The beaches are a major tourist attraction, providing a primary economic interest and a natural landscape heritage of incomparable value. Since Algeria has a robust tourism industry, and considering its power demand and population density, these inputs justify the installation of WECs near its coasts. Unfortunately, this coastline is marked by degradation due to intensive erosion.
In this study, we focused on the area of Palm Beach-Azur, which constitutes a tourist site for summer visitors. High competition for using this natural environment has led to coastline degradation. Marked by long-term intensive erosion, this study evaluates the shoreline’s behaviour and the coastline’s dynamics following the installation of WECs. In addition, it determines the effect of this equipment on the hydrodynamics.
2. Materials and Methods
2.1. SWAN Mathematical Model
In this study, SWAN has been used to calculate wave height reduction and energy dissipation due to the design of the wave farm. SWAN is a third-generation wave model developed by Booij et al. [
21] that estimates wave characteristics (significant wave height, peak period, average direction, and the spectrum of directional waves) in coastal areas, lakes, and estuaries. The required inputs are wind data, the bathymetry of the region, and flow input information. The model solves the equilibrium equation of the action of the spectral waves without prior assumptions on the shape of the wave spectrum. A two-dimensional wave action density spectrum,
N (
ω,
θ), describes the wave field, where
ω is the angular wave frequency, and
θ is the direction of the wave. The wave action density spectrum is used instead of the energy density spectrum. The action density is conserved in the presence of currents, but the energy density is not. Therefore, the wave energy spectrum can be calculated from the wave action spectrum. The wave action equilibrium equation is discretized using A time-based method of finite difference, geographic space (
x,
y), and spectral space (
ω,
θ). The equilibrium equation of the action of the spectral waves is:
The first term indicates the local change rate in wave action density on the left-hand side of the equation. The second and third terms refer to the action of waves over a geographical space, with their propagation speed and direction, respectively. The fourth term quantifies the relative frequency shift due to variations in depths and currents, with a propagation speed of
cx and
cy in the
X and
Y directions. Finally, the fifth term represents the refractive effects induced by depth variations or currents, with propagation speed
cθ in the direction
θ. The explanations of propagation velocity above stem from linear wave theory. Considering the right side of the equation,
S refers to the source and sink terms in the physical processes that produce, dissipate, or redistribute wave energy:
Here, Snl4 presents to the redistribution of energy by nonlinear quadruplet wave-wave interactions, Snl3 refers to the redistribution of the nonlinear triad of wave energy, Sin is the transfer of wind energy to waves and the dissipation of wave energy that occurs as a result of white capping, Sbot is the term for background friction energy elimination, and Sbrk is the random wave energy dissipation due to depth-induced fracture.
The wave energy flow, also called wave power, is calculated on its
X and
Y components with the following two expressions:
where
E (
σ,
θ) is the directional spectral density, which specifies how energy is distributed over frequencies (
σ) and directions (
θ). The magnitude of the wave power is then calculated as follows:
SWAN model documentation [
22] describes the set of equations governing the spectral distribution of wind waves, the transmission of wave energy, the source and sinks, the effect of the ambient current on the waves, the modelling of obstacles and structures, and the configuration induced by the waves.
2.2. Wave Refraction Calculation
Approaching the coast and from a certain depth (according to the linear theory d = 1/2L0, i.e., the half-wavelength of the offshore swell), the propagation of swells is influenced by the bathymetry. As a result, wave ridges tend to become parallel to isobaths. This phenomenon is called wave refraction. This way, the energy is concentrated on the salient (heading, arrows, etc.) and spread out on the re-entrants (creeks, gulfs, etc.). The study of refraction seeks to unravel the characteristics of the swell (direction and height) as it propagates from the open sea toward the coast.
The wave refraction phenomenon is accounted for by calculating the refraction coefficients (
Kr) at several points on a coastline for the dominant swell sectors and a given swell period. Thus, we opt to calculate the Shoalling Coefficient
Ks.
The values of Ks calculated up to the coast reflect the following:
The energy attenuation when Ks < 1 (wave divergence);
The conservation of energy when Ks = 1 (rectilinear wave propagation);
The concentration of energy when Ks > 1 (convergence of waves).
The calculations of the refraction of the swell between the open sea and the coast are carried out by the digital SWAN model.
Application of the Model
The software models the propagation of the swell by considering these phenomena:
The best practice for effectively applying the model is using a smaller grid according to the area of study. Meshing is very important to reduce computation time and improve accuracy. In this study, the calculations were performed first on a coarse grid for a larger region, and then the results were used as boundary conditions for a finer grid. The grid has 31 rows, 28 columns, and 868 nodes, and the mesh dimensions are X = 2.7 m and Y = 36.65 m.
Meshing must be performed using Cartesian or Spherical coordinates. Additionally, SWAN can also simulate grids that are irregular, and consists of triangles or tetrahedra in an irregular pattern. It is helpful for shorelines with irregular contours and complex bottom topographies. Therefore, since the calculations are performed on a grid, SWAN is an Eulerian model that considers the refractive propagation over different bathymetries and flow fields. This model solves the discrete equilibrium equation. SWAN represents the directional and non-directional spectrum at any point of the computing grids through spectral and time-dependent wave characteristics, such as wave height, maximum or average period, wave direction, and energy transport.
The SWAN simulations in this study are carried out using two computational grids, a coarse offshore-to-shore grid and a high-resolution grid in the local region of interest. The resolution of the nested grid allows the precise definition of the WEC position in the array and the precise simulation of their operation. For a detailed assessment of the impacts of the wave farm, this is a prerequisite, as mentioned by Carballo and Iglesias [
23].
2.3. Bathymetry Data
The bathymetry used for the refraction study is that taken from the (GEBCO, n.d.) website [
24]. The bathymetry was extracted as a table using the SURFER software. To improve accuracy, for the coastal zone between −22 m up to 0 m, the data extracted from the GEBCO website was replaced by the data obtained during the in situ bathymetry measurement (2016).
Figure 1 represents the bathymetric data of the Palm-Beach Azur zone in the SURFER software.
As shown in
Figure 1, the contour lines are regular and parallel to the coast coming towards the coast and more spaced going towards the open sea, with the presence of a canyon, which means a fall to the depth of −23 m on the Northeast side. The general average slope of the bottom is of the order of 1%.
Two bathymetric grids were prepared, a large grid that covers deep water depths up to −100 m and a small grid of −50 m. In this study, the −50 m grid is of interest. The −100 m grid is only used to determine the characteristics of the swell in the −50 m grid. Once the bathymetry map was projected by SURFER (v18.1.186) software, the bathymetry was extracted for all the grid points. The depths were recorded as (.dat) files. Then, they were incorporated into MATLAB and imported into the SWAN model.
2.4. Offshore Swell Data
The offshore swell data used for the refraction calculation is from the Summary of Synoptic Meteorological Observations (SSMO) [
25], consisting of ships’ observations from 1963 to 1970. Statistical processing of these data provided the frequencies of swells’ appearance by direction and period. The periods were chosen according to the probability distribution of exceeding a swell of a given amplitude. Swells of high amplitude have a relatively low probability of occurrence.
Table 1 relates the swell conditions used in the context of this study.
2.5. WEC Type and Integration Data
We used the same method as Carballo and Iglesias [
23] to determine the effects of WECs installation on the erosion of the Palm Beach-Azur. The WEC we use is the WaveCat illustrated in
Figure 2 [
26]. It is a floating WEC whose operating principle is oblique overtopping. It should be deployed at sea (in 50–100 m of water) and produces a limited impact on the shoreline. It is composed of two convergent hulls with a single-point mooring to a Catenary Anchor Leg Mooring (CALM) buoy which allows the device to orient itself passively with the direction of wave propagation. The WaveCat’s bows are kept afloat, and incoming waves propagate through the space between the hulls. When the wave crests overtake the inner sides of the hull, the overflowing water is collected in tanks at a level above the external sea level. Then, the water is discharged to the sea and drives turbine-generator units. The device acts as a single-shell body by reducing the angle to 0° and effectively closing.
To study the impact on beach erosion, we are introducing 13 WaveCat Overtopping converters arranged in 2 parallel rows, the nearshore row having 7 WECs and the offshore row containing 6 WECs (
Figure 3). The WECs are installed at a depth of 20 m, and the distance between them is 2.2 times the distance
D. A WaveCat’s distance
D is 45 m between its two most distant arcs. The WEC-wave field interaction is modelled using the transmission coefficients of the waves obtained during laboratory tests carried out at the Porto laboratory by Fernandez et al. [
26]. As a result of various wave conditions, the transmission coefficients are calculated as a ratio between the wave heights measured downwind and in front of the WEC. The results showed that the wave transmission coefficient exhibited very low variability (
Kt = 0.76). Consequently, medium- and long-term analyses use constant values.. Furthermore, the limited range of wave conditions prevented the development of a frequency-dependent model.
5. Conclusions
Waves have the potential to provide a sustainable source of energy that can be transformed through energy converters into electrical energy in shallow or deep water. Erosion is a natural phenomenon mainly linked to meteorological and hydrodynamic effects. In addition, the human influence on the shore accelerates and worsens erosion patterns in coastal regions.
Palm Beach-Azur, the subject of this study, is located in the eastern part of the Bay of Bou Ismaïl. It is one of the most significant beaches on the Algerian coast. This study aimed to investigate the effect of WaveCat Wave Energy Converters (WECs) on wave hydrodynamics and marine erosion.
In this study, the presence of WECs correlated to a decrease in the shoaling coefficient, confirming that the WECs captured wave energy as wave heights declined. Moreover, it has been seen that the WECs changed the bathymetric profile so that an accumulation of sediment appeared. Therefore, we conclude that WECs can be used to protect shorelines from marine erosion while transforming wave energy into electrical power.
As observed, WECs can play a dual role in power generation and coastline protection, yet their economic feasibility still poses an issue. However, the high installation cost of WECs can be justified when considering they eliminate the need for the construction of erosion protection structures.