Coastal Engineering Journal

A numerical wave model for two-dimensional wave field in the vertical plane is proposed in this study. The model combines a VOF method with a non-reflective wave generator in addition to the open boundary treatment based on an added dissipation zone to achieve stable computations. Not only wave breaking due to a submerged breakwater, but also post-breaking wave deformation are numerically investigated using the proposed model. Extensive laboratory experiments were also conducted to verify the validity of the model. The breaking characteristics and the frequency spectra of wave amplitude are examined for various incident wave conditions and breakwater configurations. The computed and measured results have revealed that second harmonic free wave component is generated in the region of non-breaking reformed wave, and that a breaking wave-induced circulating flow is formed at the onshore side of the submerged breakwater. It is demonstrated that the proposed numerical wave model can reproduce well the wave deformation before and after wave breaking through comparison with the experimental results.

This study concerns the vortex motions around the base of a vertical wall-mounted circular cylinder exposed to sinusoidal oscillatory flows. The flow field is simulated using the full three-dimensional unsteady Navier-Stokes equations. First, preceding three-dimensional simulations, a series of calculations have been carried out for two-dimensional oscillatory flows around a cylinder. Several patterns of vortex shedding are identified within particular ranges of flow amplitude. Fairly good agreements have been obtained between numerical and experimental results for vortex motions and flow induced forces. Next, three-dimensional flow fields around the base of a vertical wall-mounted cylinder have been investigated. The range of Keulegan-Carpentar number (KC) is from 1 to 20. The influence of KC on the development of the horseshoe vortex is reproduced quite well. The predicted lee-wake flow regimes above the bed boundary layer are similar to the two-dimensional results, while the vortex shedding in the bed boundary layer is suppressed a little. The influence of KC on the amplification of bed shear stress beneath the horseshoe vortex and wake vortices is significant. The numerical results for the vortex motions and amplification of bed shear stress agree quite well with the experimental results by Sumer et al. (1997).

Practical two-dimensional numerical models investigating the internal characteristics of plunging breakers on a uniform slope are proposed under the assumption that the energy dissipation associated with the turbulence and vortex motions after wave breaking can be evaluated directly by the Reynolds stress terms. In these models, the Reynolds stress terms are expressed using Prandtl's mixing length model. The energy dissipation is evaluated using internal kinematic quantities (vorticity and shear distortion rate) because laboratory experiments have revealed that the energy dissipation of plunging breakers demonstrate a strong correlation to internal kinematic quantities. A new concept termed "vortex radius" is defined as the circulation divided by the local horizontal velocity, and the representative scale of length is given by this vortex radius. Even though the representative scale of length is evaluated using the zero-order turbulence model, the scale changes spatially in accordance with flow conditions. The qualitative and quantitative accuracies of the models are examined by comparing turbulence properties with experimental results for plunging breakers on a uniform slope. Furthermore, the internal characteristics of plunging breakers are numerically investigated.

Wave breaking processes inducing violent transition of wave shapes and internal kinematics are investigated through laboratory experiments using flow visualization techniques, and through numerical computations using the BIM (Boundary Integral Method) for non-breaking waves and the VOF method for breaking waves. The results show the importance of the plunging jet from wave crest into the front face, and clarify the relationships of the jet size to the characteristic values of the resultant large scale deterministic eddies, entrained air bubbles and wave height decay.

A three-dimensional large eddy simulation (LES) of wave breaking was carried out. A numerical method for LES is proposed in this paper. The following characteristics of vorticity and velocity field after wave breaking are discussed on the basis of results of the LES: (1) generation and evolution of the widthwise (shore direction) velocity component; (2) transition from a two-dimensional velocity field to a three-dimensional one after wave breaking; (3) evolution process of large-scale eddies comprised by horizontal, vertical and helical eddies; and (4) a coherent eddy structure involving a turbulent bottom and wall boundary layer.

A Lagrangian numerical simulation of breaking waves is performed by the moving particle semi-implicit (MPS) method, in which the Navier-Stokes equation is discritized based on the interaction of particles. The Eulerian numerical solvers of the Navier-Stokes equation with the volume of fluid (VOF) method have difficulties in the calculation of the free surface due to the existence of the numerical diffusion derived from the advection terms. To attenuate the numerical diffusion, the procedures of the calculation of the cells involving the free surface should be very complicated one in Eulerian models. While, the MPS method is free from the numerical diffusion, hence it can calculate the free surface clearly, even under the existence of the fragmentation and the coalescence of fluid. In this study, the breaking waves are simulated on the several bottom configurations, namely a uniform slope, a permeable uniform slope and a vertical wall with small step on its foot. The time series of the water surface profiles and the velocity fields are displayed to show the performance of the MPS method in the wave breaking simulations.

A computational method for two-phase flow with a moving boundary is presented, in which the motion of each phase is treated separately to avoid numerical instability due to high-density ratio between the phases. To capture the moving boundary, we use a GAL (Grid-Averaged Lagrangian) model, which may appreciably reduce numerical diffusion in the convective transport simulation for a fractional volume of fluid and accurately satisfy the conservation of mass. The fundamental performance of the GAL model for the capture of the moving boundary is examined through the computation for a simple moving boundary problem and comparison of the computational results with those obtained by VOF and CIP methods. Of these methods, the GAL model has higher accuracy, especially, in the case of relatively coarse grids. The present method is applied to the computation of a broken-dam problem and gives good agreement with the previous experimental and computational results. Furthermore, the present method is confirmed to accurately satisfy the conservation of mass in the computation. These facts demonstrate the validity and capability of the present method for two-phase flow with a moving boundary.