The paper employs a Reynolds-averaged Navier–Stokes (RANS) approach to investigate the time-dependent wave breaking processes. The numerical model is the smoothed particle hydrodynamic (SPH) method. It is a mesh-free particle approach which is capable of tracking the free surfaces of large deformation in an easy and accurate way. The widely used two-equation k-∊ model is chosen as the turbulence model to couple with the incompressible SPH scheme. The numerical model is employed to reproduce cnoidal wave breaking on a slope under two different breaking conditions–spilling and plunging. The computed free surface displacements, turbulence intensities and undertow profiles are in good agreement with the experimental data and other numerical results. According to the computations, the breaking wave characteristics are presented and discussed. It is shown that the SPH method provides a useful tool to investigate the surf zone dynamics.

Summary: A numerical model based on the smoothed particle hydrodynamics method is developed to simulate depth‐limited turbulent open channel flows over hydraulically rough beds. The 2D Lagrangian form of the Navier–Stokes equations is solved, in which a drag‐based formulation is used based on an effective roughness zone near the bed to account for the roughness effect of bed spheres and an improved sub‐particle‐scale model is applied to account for the effect of turbulence. The sub‐particle‐scale model is constructed based on the mixing‐length assumption rather than the standard Smagorinsky approach to compute the eddy‐viscosity. A robust in/out‐flow boundary technique is also proposed to achieve stable uniform flow conditions at the inlet and outlet boundaries where the flow characteristics are unknown. The model is applied to simulate uniform open channel flows over a rough bed composed of regular spheres and validated by experimental velocity data. To investigate the influence of the bed roughness on different flow conditions, data from 12 experimental tests with different bed slopes and uniform water depths are simulated, and a good agreement has been observed between the model and experimental results of the streamwise velocity and turbulent shear stress. This shows that both the roughness effect and flow turbulence should be addressed in order to simulate the correct mechanisms of turbulent flow over a rough bed boundary and that the presented smoothed particle hydrodynamics model accomplishes this successfully. © 2016 The Authors International Journal for Numerical Methods in Fluids Published by John Wiley & Sons Ltd