*Hydrodynamics of Regular Breaking Wave DOI: http://dx.doi.org/10.5772/intechopen.94449*


## **Table 2.**

*Location of measurement sections.*

**Figure 3.**

*Sketch of the computational domain wave channel with location of the seven investigated sections, used to calibrate the numerical model.*

### **Figure 4.**

*Instantaneous SPH velocity field in the SPH simulation of spilling wave (T1): (a) before; (b)–(c) during and (d)–(e) after breaking.*

The adopted offshore boundary condition guarantees a regular development of the wave train before the sloping section of the channel and, therefore, does not influence the quality of the numerical solution, as shown by [32].

For both the two tests, the offshore boundary condition has been treated as dynamic boundary condition modeled by a numerical wave paddle also composed of ghost particles whose motion has been forced to obtain the frequency and amplitude of the wave paddle needed to generate the desired sinusoidal wave [76]. The initial water depth was set equal to 0.70 m. In the present simulations, the initial particle spacing Σ = 0.022 m, the value of η/Σ = 1.5 and *φ* = 0.01, recommended by De Padova et al. [32], have been adopted.

The instantaneous SPH particle distribution and velocity magnitude snapshots of the breaking wave are shown in **Figures 4a–e** and **5a–e**, respectively, for the spilling and plunging breakers. These results show that the general features of wave breaking, collapsing and a turbulent bore propagating have been well captured by the SPH computations.

In order to further verify the accuracy of the SPH model the time series of wave elevations, horizontal and vertical velocities at the investigated sections (**Figure 3**)

**Figure 5.**

*Instantaneous SPH velocity field in the SPH simulation of plunging wave (T2): (a) before; (b)–(c) during and (d)–(e) after breaking.*

### **Figure 6.**

*Instantaneous computed and measured (a) wave elevations, (b) horizontal and (c) vertical velocities in section 48 and section 45 for T1.*

have been compared with the experimental data of De Serio and Mossa [14]. As an example, in **Figure 6a**–**c** both laboratory and numerical wave surface elevations, and velocities at vertical sections 48 and 45 are plotted for T1, referring to the point located at 1 cm from the bottom. The agreement between the calibrated numerical results and the laboratory measurements is fairly good.
