This paper presents a numerical model for simulating wave interaction with porous structures. The model calculates the mean flow outside of porous structures based on the Reynolds averaged Navier-Stokes equations. The corresponding turbulence field is modeled by an improved k-ε model. The flow in porous structures is described by the spatially averaged Navier-Stokes equations. The drag forces caused by the presence of a solid skeleton are modeled by the empirical linear and nonlinear frictional forms. The numerical model is first calibrated by simple experiments for flow passing through a porous dam with different porous media. Excellent agreements are obtained for the case using gravels with mean sizes of O(1 cm) to O(10 cm) as the materials for the porous dam. Reasonably good agreements are also obtained when small uniform glass beads with diameters of 3 mm are used. The calibrated numerical model is then employed to investigate the breaking wave overtopping a caisson breakwater, protected by a layer of...

This paper presents a combined experimental and numerical effort to study solitary wave runup and rundown on beaches. Both nonbreaking and breaking solitary waves are investigated. A two-dimensional numerical model that solves both mean flow and turbulence is employed in this study. For the nonbreaking solitary wave on a steep slope, numerical results of the present model are verified by experimental data and numerical results obtained from the boundary integral equation method model, in terms of both velocity distribution and free surface profiles. The characteristics of flow patterns during runup and rundown phases are discussed. The vertical variations of the horizontal velocity component are large at some instances, implying that the shallow water approximation may be inaccurate even for the nonbreaking wave runup and rundown. For the breaking solitary wave on a mild slope, numerical results of the present model are compared with experimental data for free surface displacements. The present model is found to be more accurate than the depth-averaged equations models. Using this numerical model, the mean velocity field and turbulence distribution under the breaking wave are discussed.

The fluid particle velocities in the overturning jet of a breaking wave have been measured by the Particle Image Velocimetry (PIV) technique. Monochromatic waves with wave height of 14.5 cm and wavelength of 121 cm were generated in the water depth of 20 cm. The measured fluid particle velocity at the tip of the overturning jet reached 1.68 times of the phase velocity calculated from the linear wave theory. Fluid particle accelerations were estimated from the velocity data with the following results: The overturning jet enters the horizontal water surface with an acceleration of 1.1 g at an angle of 88° downward. The PIV technique was also used to measure the instantaneous vertical vorticities generated by breaking waves. The number and locations of the vortices on the horizontal plane appear to be random. The maximum instantaneous vorticity was in the order of magnitude of 20–30 s${}^{\text{−1}}$ , whereas the ensemble-averaged vorticity was quite small.

This paper reports a set of laboratory data for breaking waves in the water of intermediate depth. A monochromatic wave train with a wave height of 14.5 cm and a wavelength of 121 cm was generated in a water depth, $\mathrm{h,}$ of 20 cm. The wave train breaks consistently at a distance of about 2$h$ from the wave generator. The instantaneous velocity fields under the breaking waves on a two-dimensional vertical plane were measured by using the particle image velocimetry (PIV) technique. By repeating the same experiments twenty times and performing the ensemble average, mean velocity, mean vorticity, turbulence intensity, and other flow properties such as the Reynolds stress and the mean strain rate were calculated. Outside the aerated region, where the density of air bubbles is high, the experimental data show that the mean vorticity was of the same order of magnitude as $\mathrm{(C/h)}$ $\text{(≈6}$ ${\mathrm{s}}^{\text{−1}})$ with $C$ being the phase speed. The maximum turbulence intensity outside the aerated region was in the order of magnitude of 0.1 $C$ $\text{(≈11}$ cm/s). The time-averaged (over one wave period) turbulence intensity under the wave trough level was one order of magnitude smaller, i.e., it was about 0.04 $C$ $\text{(≈4.8}$ cm/s). Based the experimental data, the transport equation for turbulent kinetic energy was further examined. The turbulence dissipation rate and its time scale were also estimated. Under the trough level at the measurement section, which was about 3$h$ downstream from the breaking point, the turbulence production, and dissipation were of the same order of magnitude, but not identical. The turbulence advection, production, and dissipation were equally important, while the turbulence diffusion was almost negligible.