**3.1 Experimental set up**

The results obtained from the numerical model outlined in the previous section have been validated against extensive experimental data [14], and then used to obtain further insight in the physics of the flow here analyzed.

The detailed experimental setup has been given in De Serio and Mossa [14]. Here only some important parameters are summarized.

Experiment was carried out in the wave flume 45 m long and 1 m wide of the *Department of Civil, Environmental, Land, Building Engineering and Chemistry* (DICATECh) of the *Polytechnic University of Bari* (Italy). A beach with constant slope of 1/20 is connected to a region with constant water depth of *h* = 0.7 m. The wave generating system is a piston-type one, with paddles producing the desired wave by providing a translation of the water mass, according to the proper input signal. The instantaneous Eulerian velocities were acquired by a backscatter, twocomponent, four beam Laser Doppler Anemometer (LDA) system and a Dantec LDA signal processor (58 N40 FVA Enhanced) based on the covariance technique. The wave elevations were measured with a resistance probe placed in the transversal section of the channel crossing the laser measuring volume.

**Figure 1a**–**f** show the different parts of the complex experimental apparatus, which comprises the LDA system, the resistance wave gauge system and the wavemaker system. Further details about the experimental tests can be found in [14].

A sketch view of the experimental setup is shown in **Figure 2**.

**Table 1** shows the main parameters of the examined waves listed for each experiment, such as the offshore wave height *H0*, the wave period *T* and the deepwater wavelength *L0*, estimated in section 76, where the bottom is flat and the mean water depth *h* is equal to 0.70 m. In the experiments, the regular wave had a height *H0* = 11 cm and a period *T* = 2.0 s for the spilling breaker case (T1), while *H0* = 6.5 cm and *T* = 4.0 s were used to generate a plunging breaker (T2). **Table 1** shows also the Irribarren number *ξ0*, computed for the two tests from the following equation

$$\xi\_0 = \frac{\tan \beta}{\sqrt{\frac{H\_0}{L\_0}}} \tag{7}$$

in which *β* is the bottom slope angle.

Water surface elevations and velocities were measured at six different sections along the longitudinal axis of symmetry of the wave channel named 76, 55, 49, 48, 47, 46 and 45 (see **Table 2**). Specifically, for all two tests, section 48 was in the prebreaking region, section 47 was where the incipient breaking occurred, while in sections 46 and 45, the wave re-arranged into a bore.

### **3.2 Numerical model setup and validation**

The WCSPH method coupled with a *k–ε* turbulence model has been employed to reproduce the above experiment. The computational domain has been reduced to be 20.0 m long so as to save computing expenses (**Figure 3**).

**Figure 1.**

*Experimental apparatus: (a) LDA probe; (b) DANTEC FVA signal processor and process computer; (c) laser coherent Innova and Dantec 2D fiber flow optics; (d) process computer with a AD/DA board for the wavemaker control; (e) a part of the wave channel; (f) the wavemaker.*

**Figure 2.**

*Sketch view of experimental setup.*


**Table 1.**

*Experimental parameters of the analyzed regular waves.*
