**1. Introduction**

Wave breaking is one of the most important process for coastal engineers since it greatly influences both the transport processes and the magnitudes of the forces on coastal structures [1, 2]. Wave breaking in the surf zone drives complicated turbulent structures and for this reason breaking is possibly the most difficult wave phenomenon to describe mathematically [3–5].

Pioneering experimental studies were carried out by [6–11], who described the velocity field under plunging breakers in the outer region of the surf zone; more recently by [12–17]. As observed experimentally by [18], during the pre-breaking stages, the maximum turbulence intensity appears at the core of the main vortex and decreases as the vortex moves downstream. Additional turbulence is then generated near the free surface during the breaking process.

Moreover, the difficulties of measuring velocity due to the existence of air bubbles entrained by the plunging jet have hindered many experimental studies on wave breaking encouraging the development of numerical model as useful tool to assisting in the interpretation and even the discovery of new phenomena. One of the great advantages of the numerical models is their ability to disclose the evolutions of undertow currents and turbulence quantities in the spatial and temporal domains, which are too expensive to be investigated by experiments. Therefore, the main emphasis for research is placed on the application and development of numerical methods. Furthermore, for consistent and accurate results, it is essential to calibrate the numerical models with experimental data.

The numerical models can be classified as Eulerian or Lagrangian method. In Eulerian method, the space is discretized into a grid or mesh and the unknown values are defined at the fix points, while a Lagrangian method tracks the pathway of each moving mass point. The Eulerian methods such as the finite difference methods (FDM), finite volume methods (FVM) and the finite element methods (FEM) have been widely applied in many fields of engineering because are very useful to solve differential or partial differential equations (PDEs) that govern the concerned physical phenomena [19–23]. Despite the great success, grid based numerical methods suffer from difficulties in some aspects such as the use of grid/ mesh makes the treatment of discontinuities (e.g., wave breaking, cracking and contact/separation) difficult because the path of discontinuities may not coincide with the mesh lines.

Therefore, during the last years, research has been focused on Lagrangian techniques such as Discrete Element Method (DEM) [24], Smoothed Particle Hydrodynamics (SPH) [25], Immersed Particle Method (IPM) [26, 27]. The development and applications of the major existing Lagrangian methods have been addressed in some review articles such as [28–30]. In general, the Lagrangian methods provide accurate and stable numerical solutions for integral equations or partial differential equations (PDEs) with all kinds of possible boundary conditions using a set of arbitrarily distributed nodes or particles. During the last years, Smoothed Particle Hydrodynamics (SPH) has become a very powerful method for CFD problems governed by the Navier–Stokes equations such as fluid-dynamic problems with highly non-linear deformation [31–37]; multi-phase flows for coastal and other hydraulic applications with air-water mixture sand sediment scouring [38–42]; oscillating jets inducing breaking waves [43] and nonbuoyant jets in a wave environment [44–46]; fluid/structure/soil-interaction [47–49]; hydraulic jumps [50–53]; multi-phase flows and oil spill [54–55].

The present chapter is organized as follows. First, an WCSPH method is developed using the RANS equations and a two-equation *k–ε* model is formulated using the particle approach. Then the numerical model is employed to reproduce breaking in spilling and plunging waves in a sloped wave channel. The experimental data by [14] are used to check the model results. This reveals the importance of experimental data in these studies. The present chapter is aimed to describe some recent results obtained within the frame of numerical and experimental analyses of wave breaking. The new insight is the investigation of the ability of WCSPH with a *k–ε* turbulence closure model to disclose the turbulence dispersion and the temporal and spatial evolutions of turbulence quantities in different types of breakers.
