# Modelling of a Wave Energy Converter Impact on Coastal Erosion, a Case Study for Palm Beach-Azur, Algeria

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. SWAN Mathematical Model

_{x}and c

_{y}in the X and Y directions. Finally, the fifth term represents the refractive effects induced by depth variations or currents, with propagation speed c

_{θ}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:

_{nl4}presents to the redistribution of energy by nonlinear quadruplet wave-wave interactions, S

_{nl3}refers to the redistribution of the nonlinear triad of wave energy, S

_{in}is the transfer of wind energy to waves and the dissipation of wave energy that occurs as a result of white capping, S

_{bot}is the term for background friction energy elimination, and S

_{brk}is the random wave energy dissipation due to depth-induced fracture.

#### 2.2. Wave Refraction Calculation

_{0}, 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.

_{r}) at several points on a coastline for the dominant swell sectors and a given swell period. Thus, we opt to calculate the Shoalling Coefficient K

_{s}.

_{s}calculated up to the coast reflect the following:

- The energy attenuation when K
_{s}< 1 (wave divergence); - The conservation of energy when K
_{s}= 1 (rectilinear wave propagation); - The concentration of energy when K
_{s}> 1 (convergence of waves).

#### Application of the Model

- Refraction on the bottoms and around the structures;
- Friction on the bottom;
- Surge.

#### 2.3. Bathymetry Data

#### 2.4. Offshore Swell Data

#### 2.5. WEC Type and Integration Data

_{t}= 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.

## 3. Zone of Study

#### 3.1. Geographical Location

#### 3.2. Sedimentology of The Zone of Study

#### 3.3. Climate and Wind Data

- I.
- A winter period (October-March), with prevailing winds from the west, with a frequency ranging from 60 to 80%;
- II.
- During summer (April-September), the prevailing winds are from the east and the northeast, with 45 to 75% frequencies for the northeast direction.

#### 3.4. The Sea Swells

- The highest appearance frequencies are related to those swells from the west, east, and northeast. The weakest ones are recorded for swells in the north and north-west directions;
- The frequencies of observations over the year of the easterly and westerly swells are roughly identical. However, a slight predominance of the eastern sector exists.

- I.
- In winter: western swells dominate with the majority of amplitudes of 1 and 3 m and can reach up to 4 m;
- II.
- In summer: The most dominant swells come from the northeast sector with smaller amplitudes, and the swells from the west are quite significant.

## 4. Results

#### 4.1. Wave Modelling

#### 4.2. Sedimentation Pattern near Wave Energy Converters

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 2.**Schematic of the WaveCat energy converter [26].

**Figure 4.**Geographical location of the Palm Beach-Azur area [27].

**Figure 5.**Sedimentology of the bay of Bou-Ismail [28].

**Figure 6.**Annual wind distribution in percent, Dar-El-Beida province, 1995–2015 [29].

**Figure 7.**Swell direction summary roses off the sector (275°–55°) [30].

**Figure 9.**Contours of Hs obtained using the SWAN model for a direction of 280° N, Hs = 5 m, and T = 7s: (

**a**) before the integration of the WECs; (

**b**) after the integration of the WECs.

Offshore Swell Direction | Peak Period (S) | Significant Height Offshore (m) |
---|---|---|

N 340° | 8 | 6.8 |

N 30° | 9 | 7 |

N 280° | 10 | 8 |

Parameters | No WECs | With WECs |
---|---|---|

Average of Hs (m) | 2.56 | 2.26 |

Average ΔHs (m) | 0.3 | |

Average ΔHs (%) | 30% | |

Shoaling Coefficient Ks | 0.512 | 0.452 |

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**MDPI and ACS Style**

Moradi, M.; Chertouk, N.; Ilinca, A.
Modelling of a Wave Energy Converter Impact on Coastal Erosion, a Case Study for Palm Beach-Azur, Algeria. *Sustainability* **2022**, *14*, 16595.
https://doi.org/10.3390/su142416595

**AMA Style**

Moradi M, Chertouk N, Ilinca A.
Modelling of a Wave Energy Converter Impact on Coastal Erosion, a Case Study for Palm Beach-Azur, Algeria. *Sustainability*. 2022; 14(24):16595.
https://doi.org/10.3390/su142416595

**Chicago/Turabian Style**

Moradi, Mehrdad, Narimene Chertouk, and Adrian Ilinca.
2022. "Modelling of a Wave Energy Converter Impact on Coastal Erosion, a Case Study for Palm Beach-Azur, Algeria" *Sustainability* 14, no. 24: 16595.
https://doi.org/10.3390/su142416595