# Offshore-to-Nearshore Transformation of Wave Conditions and Directional Extremes with Application to Port Resonances in the Bay of Sitia-Crete

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Geographical and Offshore Wave Data in the Studied Area

#### 2.1. Offshore Wave and Wind Data

#### 2.2. Bathymetry and Coastline Data

## 3. Offshore-to-Nearshore Wave Transformation

#### Wave Climatology in the Sitia Gulf Area

- (i)
- At nearshore point 1, the wave directions concentrated around the north-northwestern directions, due to the effects of refraction, diffraction, and sheltering by the Sitia peninsula. However, a secondary population of waves from the eastern directions also appeared, which were mainly attributed to wind from eastern directions.
- (ii)
- Moving closer to the shore, the effects of refraction due to bathymetric variations become more significant. These are clearly depicted in Figure 6, Figure 7 (which presents the wave statistics based on the wave data calculated at nearshore points 2 and 3, respectively), and, in particular, in the corresponding wave-rose diagrams. As a result, there was a concentration of the majority of the waves in the northeastern sector. Moreover, a secondary peak of waves from the eastern directions appeared.
- (iii)
- As we move closer to the entrance of the port area of Sitia, at nearshore point 3, a secondary peak of waves from the eastern directions was present.

## 4. Directional Extreme Wave Data Analysis at Offshore and Nearshore Points

#### 4.1. Directional Model and Parameter Estimation

#### 4.2. Design Values

## 5. Study of Port Resonances in the Enclosed Small Port of Sitia, Crete

_{elem}= 24960, are shown in Figure 15, using open circles. The bars in the figure indicate the peak periods obtained from the analysis of wave data at nearshore point 3 in front of the entrance of the Sitia port, corresponding to the energetic sea states from the eastern directions, which could excite port resonances. The closest MMS eigenperiods of the enclosed port obtained from the solution of Equation (14) were {9.92 s, 9.50 s, 8.66 s, 8.49 s, 8.34 s}; shown in Figure 15, using rectangles. The corresponding calculated eigenmodes in the port area are plotted in Figure 16. It was noted, however, that the wave periods calculated from the wave transformation were dependent on frequency discretization of the models, and the matching should have been performed using a small bandwidth permitting overlapping with the identified eigenperiods.

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Appendix A. Offshore-to-Nearshore (OtN) Wave Transformation Technique

^{2}is the acceleration due to gravity, the parameter $\alpha $ is defined by means of the formula,

_{p}and the highest value at 3f

_{p}. Furthermore, the rest of parameters used in SWAN were as follows—(i) bed roughness 0.0015, (ii) wave breaking constants—rate of dissipation 0.5, breaker parameter 0.668, and (iii) for wave–wave interaction proportionality coefficient 0.25 and maximum frequency 2.50 (default values). More details about the SWAN model formulation, implementation, and validation can be found in [4,5,15].

**Figure A1.**The OtN wave transformation technique—spatial distributions of (

**a**) significant wave height with mean direction and (

**b**) mean wave period with mean direction in the studied area for offshore wave data ${H}_{S}\text{}=\text{}0.53\text{}\mathrm{m},\text{}{T}_{-10}\text{}=\text{}4.5\text{}\mathrm{s},\text{}{\theta}_{m}\text{}=\text{}{340}^{\circ}$.

**Figure A2.**Spatial distributions of (

**a**) significant wave height with mean direction and (

**b**) mean wave period with mean direction in the offshore wave data of the studied area (same as in Figure A1), but from the east ${\theta}_{m}\text{}=\text{}{115}^{\circ}$.

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**Figure 1.**(

**a**) The nearshore area of Sitia in the northeastern part of the Crete island. (

**b**) The port of Sitia including the enclosed touristic marina (map tiles: © OpenStreetMap contributors 2019; https://www.openstreetmap.org/copyright, bathymetric data: GEBCO Compilation Group (2019) GEBCO 2019 Grid).

**Figure 2.**(

**a**) Aerial map of the Sitia gulf from Google Earth, showing the location of the ERA-Interim offshore grid point; and (

**b**) Bathymetry and coastline data used for the offshore-to-nearshore transformation of wave data.

**Figure 4.**Bathymetric data in the area of interest and the set-up of the SWAN model for calculating the offshore-to-nearshore wave transformation. Results are stored for the three indicated nearshore target points. The offshore point is shown by a red dot.

**Figure 9.**(

**a**) Conditional distribution of wave periods and wave heights at nearshore point 3 in the eastern wave sector 75°$\le \theta \le $105°, and; (

**b**) corresponding distribution of wave periods at the same point, as calculated by offshore-to-nearshore transformation.

**Figure 12.**(

**a**) Bathymetry (depth in meters) of the Sitia port and the nearshore/coastal area. The location of nearshore point 3, where the wave data were calculated by using the offshore-to-nearshore wave transformation was indicated by using a circle; and (

**b**) detailed bathymetry and solid-wall boundaries in the enclosed port, including the small marina. Horizontal distances are in meters.

**Figure 13.**Intermediate finite element method (FEM) mesh in the enclosed Sitia port (no. of elements was 6240). Horizontal distances are in meters.

**Figure 14.**Calculated (

**a**) first; (

**b**) second; (

**c**) third; (

**d**) fourth eigenmode in the Sitia enclosed port area. Horizontal distances are in meters.

**Figure 15.**Calculated modified mild-slope (MMS) eigenperiods in the Sitia enclosed port in the range $8.2\text{}\mathrm{s}T10\text{}\mathrm{s}$, denoted by open circles. The bars indicate peak periods obtained from the analysis of wave data at nearshore point 3 in front of the entrance of the Sitia port, corresponding to the energetic sea states from east, which could excite port resonances. The closest eigenperiods of the enclosed port were {9.92 s, 9.50 s, 8.66 s, 8.49 s, 8.34 s}; denoted by rectangles.

**Figure 16.**The calculated eigenmodes corresponding to the eigenperiods (

**a**) 9.92 s; (

**b**) 9.48 s; (

**c**) 8.68 s; (

**d**) 8.46 s; (

**e**) 8.33 s; (

**f**) 8.30 s in the enclosed port, as obtained from the MMS model, using FEM with N

_{elem}= 24,960. Horizontal distances are in meters.

Wave Parameters | N | m | s | min | max | Sk | Ku |
---|---|---|---|---|---|---|---|

${H}_{S}$ (m) | 5186 | 1.06 | 0.64 | 0.09 | 5.20 | 1.44 | 2.84 |

${T}_{-10}$ (s) | 4.93 | 1.03 | 2.23 | 9.66 | 0.59 | 0.32 | |

${\theta}_{m}$ (deg) | 315.3 | 58.0 | 0 | 360 | 0.72 | 1.18 |

Point | ${\mathit{H}}_{\mathit{S}}$ (m) | ${\mathit{T}}_{-10}$ (s) | ${\mathit{\theta}}_{\mathbf{peak}1}$ (deg) | ${\mathit{\theta}}_{\mathbf{peak}2}$ (deg) |
---|---|---|---|---|

Offshore | 1.06 | 4.93 | 345 | 285 |

Nearshore point 1 | 0.63 | 4.64 | 345 | 105 |

Nearshore point 2 | 0.38 | 4.35 | 15 | 105 |

Nearshore point 3 | 0.35 | 4.39 | 15 | 95 |

Parameter | Lower CI | Estimate | Upper CI |
---|---|---|---|

${A}_{10}$ | −0.22 | −0.12 | −0.05 |

${A}_{11}$ | −0.05 | 0.02 | 0.11 |

${A}_{21}$ | −0.18 | −0.04 | 0.10 |

${B}_{10}$ | 0.63 | 0.71 | 0.78 |

${B}_{11}$ | −0.03 | 0.04 | 0.13 |

${B}_{21}$ | −0.18 | −0.01 | 0.10 |

**Table 4.**First Laplace eigenvalues and corresponding eigenfrequencies in the Sitia small harbor domain as calculated for the mean constant depth $h\text{}=\text{}3.22$ m.

Mode | ${\mathit{k}}_{\mathit{n}}$ (m^{−1}) | ${\mathit{\omega}}_{\mathit{n}}$ (rad/s) | ${\mathit{T}}_{\mathit{n}}$ (s) |
---|---|---|---|

1 | 0.003457 | 0.0194 | 323.3903 |

2 | 0.012237 | 0.0688 | 91.3808 |

3 | 0.016172 | 0.0909 | 69.1592 |

4 | 0.022362 | 0.1256 | 50.0359 |

5 | 0.024986 | 0.1403 | 44.7908 |

6 | 0.027347 | 0.1535 | 40.9325 |

7 | 0.031044 | 0.1742 | 36.0713 |

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**MDPI and ACS Style**

Karathanasi, F.; Karperaki, A.; Gerostathis, T.; Belibassakis, K.
Offshore-to-Nearshore Transformation of Wave Conditions and Directional Extremes with Application to Port Resonances in the Bay of Sitia-Crete. *Atmosphere* **2020**, *11*, 280.
https://doi.org/10.3390/atmos11030280

**AMA Style**

Karathanasi F, Karperaki A, Gerostathis T, Belibassakis K.
Offshore-to-Nearshore Transformation of Wave Conditions and Directional Extremes with Application to Port Resonances in the Bay of Sitia-Crete. *Atmosphere*. 2020; 11(3):280.
https://doi.org/10.3390/atmos11030280

**Chicago/Turabian Style**

Karathanasi, Flora, Angeliki Karperaki, Theodoros Gerostathis, and Kostas Belibassakis.
2020. "Offshore-to-Nearshore Transformation of Wave Conditions and Directional Extremes with Application to Port Resonances in the Bay of Sitia-Crete" *Atmosphere* 11, no. 3: 280.
https://doi.org/10.3390/atmos11030280