The coastal zone covered by this study is 170 km long, including the Port Autonomous Guinea at 4˚67 south and 11˚97 east. It is oriented on average at 320˚ - 140˚ ( Figure 1 ) in front of a continental shelf over 40 km wide [1] [14] - [16] .

The effectiveness of numerical flow modeling in coastal areas depends on the accuracy of the bathymetric data. The bathymetric data used in this study were provided by the General Bathymetric Chart of the Oceans, grid GEBCO_08. This is a global terrain model for ocean and land at intervals of 30 arc seconds ( Figure 2 ) [3] .

The wind data used for the simulations are those predicted by the De Glisse and Ça-Baigne marine weather forecasts. They provide hourly wind speed and direction at 10 m above the water surface. A series of sampling data collected over 23 hours (0h to 22h) and 7 consecutive days by the Ça-Baigne weather station was used in the validation section. The wind characteristics used were speed in m/s and direction in deg. These values can be checked via the following links: https://marine.meteoconsult.fr/meteo-marine/bulletin-detaille/spot-de-glisse-5623/previsions-meteo-pointe-noire-aujourdhui .

Pointe-Noire’s coastline is oblique in a NW-SE direction, and the inclination of the waves in relation to the shallow water is negligible. According to the national meteorology, the Pointe-Noire coast is mostly visited by swells from the South Atlantic (SW direction) [1] [2] [4] . Wave heights range from 1 to 1.5 meters. These swell data will enable us to calibrate the swells at the boundaries.

The CMS-Wave model is based on the wave action equilibrium equation. It expresses the two-dimensional evolution of wave energy in space and takes into account the effect of an ambient horizontal current on wave behavior. It is written as follows [17] [18] :

$\frac{\partial \left(C_{x}N\right)}{\partial x}+\frac{\partial \left(C_{y}N\right)}{\partial y}+\frac{\partial \left(C_{\theta }N\right)}{\partial \theta }=\frac{\kappa }{2\sigma }\left[{\left(C{C}_g{\cos }^2\theta \frac{\partial N}{\partial y}\right)}_y-\frac{C{C}_g}{2}{\cos }^2\theta \frac{{\partial }^{2}N}{\partial y^2}\right]-{ℰ}_{b}N-S$

with

$N=\frac{E\left(\sigma ,\theta \right)}{\sigma }$

where

Since this study involves analyzing the behavior of swells near the coast, it is necessary to understand the effect of the swell’s angle of incidence in relation to the coast. A swell is said to be frontal when its direction of propagation is perpendicular (an angle of incidence of 0˚) to the coast, and non-frontal for a swell with an oblique direction (an angle of incidence not zero) in relation to the coast.

SMS (Surface-water Modeling System) is a comprehensive program for building and simulating free-surface flow models. It is a graphical user interface and analysis tool that enables engineers and scientists to visualize, manipulate, analyze, and interpret numerical data and associated measurements.

Many SMS software tools are generic. They are designed to facilitate the establishment and operation of numerical models of rivers, coasts, inlets, bays, estuaries, and lakes. The site enables 1D and 2D modeling and a unique approach to conceptual models.

Models currently supported by SMS include ADCIRC, BOUSS-2D, CGWAVE, CMS-FLOW, CMS-WAVE (WABED), FESWMS, GenCade, PTM, STWAVE, TABS and TUFLOW [18] .

Boundary wave forcing condition:

Due to a lack of wave data and measurements in the Pointe-Noire coastal area for validation purposes, we were forced to use satellite information provided by weather spots in the study area.

The wind data (wind speeds and directions) predicted by the weather spots on June 24 and 24, 2024, are used as model input data. The wave outputs obtained using the model are compared with the waves predicted by the spots on these two days. The spots present hourly mean values of wave heights, periods, and directions, while the model presents these values in different areas of the Pointe-Noire coast. Three points were chosen near the Pointe-Noire coastal zone to observe changes in swell characteristics. The first point is to the north of the port (Songolo), the second is in front of the port, and the third is near the outer breakwater (Côte Sauvage).

Figures 4-9 show the changes in wave height and direction simulated by the model and those predicted by the De-glisse and Ça-baigne marine meteos for these two days on the Pointe-Noire coast. The model simulates wave heights and directions at every point in the study area, while the meteorological spots propose an average value for the entire coastal zone.

These different curves show that characteristic swell grades depend not only on bathymetry, but also on weather conditions and the location where they are observed.

Figures 4-7 show that wave heights in the Pointe-Noire coastal zone vary according to time and place for a 1 m frontal swell. The highest wave heights are observed near the open beach of Songolo, followed by those along the outer dike. The lowest wave heights were observed in the harbor area. The average values predicted by the meteorological spots remain less variable during this period. The average difference between the values simulated by the model and those predicted by the weather remains very small.

Figure 8 and Figure 9 show the evolution of wave direction for the same swell characteristics at the boundaries. Wave direction varies according to location but remains constant throughout the observation period. These observations highlight the fact that waves tend to move northwards during their propagation as they approach the shore. The values predicted by Meteo De Glisse that are compared with those simulated by the model are seen under the third dial, while those of the model are on the first dial. Reading these values on the same dial shows that they remain very close.

The evolution of the wave energy spectrum as it approaches the coast depends exclusively on the angle of incidence (see Figure 10 and Figure 11 ) or the frequency (see Figure 12 ) of the wave.

For a frontal swell, the coast receives wave energy in counter-clockwise directions from 50˚ to 320˚. For a south-westerly oblique swell, the coast receives wave energy in counter-clockwise directions from 80˚ to 340˚. For a non-frontal swell of northwest incidence, the coast is visible for wave energies in directions between 25˚ and 275˚ counter-clockwise.

The layout of the Pointe-Noire coast is such that it is in a blind spot for waves coming in a counter-clockwise direction between 275˚ and 80˚. Waves with an angle of incidence in this direction are parallel to the Pointe-Noire coast.

The test cases carried out with the three angle incidences (frontal, non-frontal, northwest, and southwest) of swell at the boundaries with significant height $H_s=1.5m$ and peak period $T_P=12s$ ( Figures 13-15 ) show that the largest waves are observed along the outer dike and near the Songolo coast. For both frontal and non-frontal swell incidence in the northwest direction, wave height decreases relative to the value set at the boundaries, while for non-frontal swell incidence in the southwest direction, wave height increases relative to the value set at the boundaries as the waves approach the coast.

Wave height remains constant during propagation to the immediate open sea, only to increase near the coast due to the elevation of the bathymetry and adjacent structure of the area. The harbor enclosure is characterized by a very calm situation, as the wave dissipates during its interaction with the protective structure of

the harbor access channel.

The presence of high wave heights at the level of the large dike (southeast zone of the port) and the Songolo coast (northeast zone) is responsible for the drift currents that cause the drainage of sediments from the savage coast and erosion in Loango Bay.