*3.3. Boussinesq Wave Module Set Up*

The primary aim of this research is to investigate the relationship between headlandbay static equilibrium profile and wave propagation characteristics (diffraction and refraction). Therefore, we created different numerical simulations scenarios, in order to generate different wave fronts, by varying wave direction, wave period and refraction conditions.

First, to evaluate refraction conditions, two bathymetry configurations were been investigated. The first one (called "*gentle slope*") is characterised by a linearly varying cylindrical bathymetry, with a gentle bottom slope of 1/100 and a diffraction point, modelled through a breakwater, located at a water depth of 3 m. The water depth at the offshore boundary is 20 m (Figure 6a). A gentle slope has been adopted to allow an expansion of the wave fronts without the influence of bottom abrupt raising. The second configuration (called "*flat bottom*") exhibits a bottom with a constant water depth equal to 10 m (Figure 6b).

**Figure 6.** (**a**) Gentle slope configuration bathymetry; (**b**) flat bottom configuration bathymetry.

Secondly, numerical experiments have been conducted considering the possible effect of wave period and wave direction; conversely, the influence of wave height was not explored. This is because the correlation function describing the relationship between static equilibrium profiles and wave characteristics, at this first stage of the research, is obtained through a "linear approach" based on simple geometric consideration. Therefore, the only parameters that could geometrically affect the aforementioned correlation are period, wave direction and bottom inhomogeneity. Conversely, wave height does not represent a variable of the problem. Three different wave directions have been investigated; one is normal to the breakwater, while the other two are angled of 25◦ and −35◦ with respect to being perpendicular to the structure. For each direction, three wave periods have been tested: 5.9 s, a typical wave period of the Mediterranean wave climate; and 10 s and 15 s, which simulate swell conditions. The wave height used was 0.8 m for each numerical scenario. Since the predominant wave shapes the crenulated beach, for the numerical experimentation the value of wave height has been chosen equal to the LDR equivalent wave height value for the case study of Bagnoli bay (see Section 5.2). Simulations have been implemented using regular waves. It is important to underline that the effect of breaking waves was not considered in the trials. For each bathymetry configuration ("gentle slope" and "flat bottom"), the scenarios analysed are summarized in Table 1.

**Table 1.** Scenarios analysed in the numerical experimentation.


Models are made up of a fine grid (square cells with grid spacing 3 m), upon which orientation coincides with wave direction; the time step used is 0.1 s. The wave generation line has been used and wave absorbing sponge layers have been applied at the model boundaries. Near the land, one sponge layer has been applied in order to avoid the occurance of wave reflection which could influence the expansion of the wave fronts. Geometric characteristics are summarized in Table 2, and are valid for both bottom configurations.

**Table 2.** Grid geometric characteristics.

