**6. Numerical Modelling of the Bay and Results**

Numerical modelling of the bay has been performed through the wave driver MIKE 21 BW (DHI), which allows for obtaining the growth of the wave fronts leeward of the headland. In order to follow the method used in the numerical trial, the bay has been modelled in such a way that wave fronts could extend leeward the headland without any interference: the real bathymetry of the area has been employed until the diffraction point location, where the water depth is about 3 m, then a gentle slope of 1:100 has been adopted; the coastline has been shifted and cut landward and a sponge layer has been used, in order to avoid reflection phenomenon (Figure 17).

**Figure 17.** Model setup of case study bay.

Numerical simulations have been performed wave detecting the equivalent direction of 205◦ N, since it is representative of the effects of the entire wave climate on long-shore sediment transport [41]. As concerns wave period, the average measured omni-directional peak period (5.9 s) has been investigated.

Simulations have been carried out using regular waves, which wave height has been set at 0.8m; the breaking phenomenon has been neglected. Fine grid has been used (square cells with grid spacing 3 m), for which the orientation coincides with wave direction, with a time step of 0.1. A wave generation line has been used and wave absorbing sponge layers have been applied at the lateral boundaries. Grid geometric characteristics are summarized in Table 3.

**Table 3.** Grid geometric characteristics.


Comparison between equilibrium profile and wave fronts carried out through BW model, shown in Figure 18b, demonstrates that wave fronts' direction in the illuminated zone matches shoreline orientation, confirming the goodness of the LDR equivalent wave to represent the entire wave climate in the act of shape the beach planform. Specifically, simulations results confirmed the behaviour observed in the previous section: the shoreline planform of the headland bay is placed on more wave fronts, the downdrift section overlaps the wave front while the curved section is placed on the wave front closer to the headland (Figure 18a).

**Figure 18.** (**a**) Wave fronts generated by means BW; (**b**) comparisons between wave fronts (green lines) and shoreline (red line).

In order to attain an effective validation of the *wave-front-bay-shape equation*, Equation (15) has been applied. The minimum distance between the diffraction point and the asymptote has been measured (distance c in Figure 19a) and it has been standardised with respect to the local wave length, *c/L*. Applying Equation (15), we obtained the value of the shift, *s*, which represents the distance needed to superimpose the whole wave front on the shoreline. After shifting the wave front, as shown in Figure 19b, it is perfectly superimposed on the bay shoreline, thus verifying the correlation found between wave fronts and shoreline profile, reached by Equation (15).

**Figure 19.** (**a**) Wave front (green line) that overlaps the shoreline (red line) in the downdrift section and the latter's distance, c, from the diffraction point; (**b**) wave front shifted by s, which was derived from Equation (15).
