# Optimum Coastal Slopes Exposed to Waves: Experimental and Numerical Study

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

_{2}and the temperature of the Earth. The European Union has pledged to reduce greenhouse gas emissions by 20% compared to 1990 by 2020 while improving energy efficiency by 20% and increasing the share of renewable energy by 20%. In October 2014, EU Energy agreed to reduce greenhouse gas emissions by at least 40% below 1990 levels by 2030 [1]. Renewable energies are divided into several different categories, one of which is the energy of sea waves. The energy of sea waves is also divided into several different categories, one of which is a point absorber. The point absorber transfers the energy of sea waves to linear generators, linear converters, mechanical rotors, or hydraulic pumps using a float that is much smaller than the wavelength [2].

## 2. Experimental Wave Tank

#### 2.1. Wave Generation

#### 2.2. Wave Energy Dissipation

#### 2.3. Wave Gauges

## 3. Simulation Method

#### 3.1. Governing Equations

#### 3.2. Numerical Method

#### Dynamic Mesh

Algorithm 1 Computer programming codes provided for flap in Fluent software. |

#include “udf.h” DEFINE_CG_MOTION (Case1, dt, vel, omega, time, dtime) { if (time < 14.0801) omega [2] = −0.3722 ∗ cos(5.7120 ∗ time−2 ∗ atan(1.0)); else if (time < 66) omega [2] = −0.3722 ∗ cos(5.7120 ∗ (time + 0.2199)−2 ∗ atan(1.0)); else omega [2] = 0; |

## 4. Simulation Results and Discussions

#### 4.1. Mesh Independence

#### 4.2. Model Validation

#### 4.3. Wave Generation Results

_{s}represents the wave height in millimeters, which is given to the device software, and H is the depth of water from the beginning of the flap. These cases are chosen to investigate the effect of different wave heights (H

_{s}) and frequencies of the waves on the experimental and numerical simulation results.

_{s}of the wave, in this case, is reduced more than in the previous cases to 20 mm. Figure 20 illustrates that the discrepancy between the numerically simulated results and the experimental ones has increased compared with cases 1 and 2. From Figure 19 and Figure 20, it can be concluded that the accuracy of the simulation wave is reduced by decreasing the height of the wave.

_{s}or it is like case 3 but with higher frequency. A comparison of Figure 22 with previous results shows that there is a high discrepancy between the numerical and experimental results of this case, and especially at a distance of 5 m, this difference becomes very large. The reason as can be seen in the next part is the coast slope of 1:3. When the wave is not completely dampened, the reflected waves fall into the numerical wave tank and cause a disturbance in the waves. This disturbance is lower at a distance of 3 m from the flap because the reflected waves need more time to reach the distance of 3 m from the flap, while it is large at a distance of 5 m from the flap (Figure 22).

#### 4.4. Study of the Beach Slope

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**An overview of the experimental wavemaker tank: (

**a**) a real picture and (

**b**) schematic illustration.

**Figure 23.**Wave height of case 3 for different beach slopes at a distance of (

**a**) 3 m and (

**b**) 5 m from the flap.

**Figure 24.**Wave height of case 5 for different beach slopes at a distance of (

**a**) 3 m and (

**b**) 5 m from the flap.

**Figure 25.**Results of the wave reflection coefficient for different beach slopes in different cases.

Cell height (m) | 0.008 | 0.005 | 0.004 | 0.003 | 0.002 | 0.001 |

Mesh number produced | 25,213 | 37,686 | 54,355 | 64,659 | 86,555 | 210,883 |

Case Number | Period (s) | Stroke (cm) | Still Water Depth (m) | H/S | 2πd/L |
---|---|---|---|---|---|

Small wave steepness | |||||

1 | 2.1 | 8.45 | 0.3 | 0.25 | 0.5481 |

2 | 1.4 | 8.45 | 0.3 | 0.43 | 0.8746 |

3 | 1.05 | 3.15 | 0.45 | 0.88 | 1.7449 |

4 | 1.5 | 2.4 | 0.8 | 1.25 | 2.9351 |

5 | 1.4 | 8.57 | 0.5 | 0.65 | 1.2212 |

High wave steepness | |||||

6 | 0.84 | 8.47 | 0.4 | 1.003 | 2.3242 |

7 | 1.05 | 8.45 | 0.3 | 0.67 | 1.2783 |

8 | 0.84 | 8.45 | 0.3 | 0.84 | 1.8051 |

9 | 1.05 | 6.3 | 0.9 | 1.3 | 3.2925 |

10 | 1.05 | 4.69 | 0.67 | 1.13 | 2.4789 |

Case | 1 | 2 | 3 | 4 | 5 |
---|---|---|---|---|---|

H_{s} (mm) | 90 | 60 | 40 | 60 | 40 |

H (m) | 0.62 | 0.62 | 0.62 | 0.62 | 0.62 |

Frequency (Hz) | 1.1 | 1.1 | 1.1 | 1.2 | 1.2 |

Wave period (s) | 0.9 | 0.9 | 0.9 | 0.83 | 0.83 |

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**MDPI and ACS Style**

Zandi, R.; Lari, K.; Najafzadeh, M. Optimum Coastal Slopes Exposed to Waves: Experimental and Numerical Study. *Water* **2023**, *15*, 366.
https://doi.org/10.3390/w15020366

**AMA Style**

Zandi R, Lari K, Najafzadeh M. Optimum Coastal Slopes Exposed to Waves: Experimental and Numerical Study. *Water*. 2023; 15(2):366.
https://doi.org/10.3390/w15020366

**Chicago/Turabian Style**

Zandi, Reza, Khosro Lari, and Mohammad Najafzadeh. 2023. "Optimum Coastal Slopes Exposed to Waves: Experimental and Numerical Study" *Water* 15, no. 2: 366.
https://doi.org/10.3390/w15020366