In this paper we propose a three-dimensional numerical study of the coastal currents produced by the wave motion in the area opposite the Cetraro harbour (Italy), during the most significant wave event for the coastal sediment transport. The aim of the present study is the characterization of the current patterns responsible for the siltation that affects the harbour entrance area and the assessment of a project solution designed to limit this phenomenon. The numerical simulations are carried out by a three-dimensional non-hydrostatic model that is based on the Navier–Stokes equations expressed in integral and contravariant form on a time-dependent curvilinear coordinate system, in which the vertical coordinate moves in order to follow the free surface variations. The numerical simulations are carried out in two different geometric configurations: a present configuration, that reproduces the geometry of the coastal defence structures currently present in the harbour area and a project configuration, which reproduces the presence of a breakwater designed to modify the coastal currents in the area opposite the harbour entrance.

A new three-dimensional high-order shock-capturing model for the numerical simulation of breaking waves is proposed. The proposed model is based on an integral contravariant form of the Navier–Stokes equations in a time-dependent generalized curvilinear coordinate system. Such an integral contravariant form of the equations of motion is numerically integrated by a new conservative numerical scheme that is based on three elements of originality: the time evolution of the state of the system is carried out using a predictor–corrector method in which exclusively the conserved variables are used; the point values of the conserved variables on the cell face of the computational grid are obtained using an original high-order reconstruction procedure called a wave-targeted essentially non-oscillatory scheme; the time evolution of the discontinuity on the cell faces is calculated using an exact Riemann solver. The proposed model is validated by numerically reproducing several experimental tests of breaking waves on computational grids that are significantly coarser than those used in the literature to validate the existing 3D shock-capturing models. The results obtained with the proposed model are also compared with those obtained with a previously published model, which is based on second-order total variation diminishing reconstructions and an approximate Riemann solver usually adopted in the existing 3D shock-capturing models. Through the above comparison, the main drawbacks of the existing 3D shock-capturing models and the ability of the proposed model to simulate breaking waves and wave-induced currents are shown. The proposed 3D model is able to correctly simulate the wave height increase in the shoaling zone and to effectively predict the location of the wave breaking point, the maximum wave height, and the wave height decay in the surf zone. The validated model is applied to the simulation of the interaction between breaking waves and an emerged breakwater. The numerical results show that the proposed model is able to simulate both the large-scale circulation patterns downstream of the barrier and the onset of quasi-periodic vortex structures close to the edge of the barrier.

We propose a two-equation turbulence model based on modification of the k − ε standard model, for simulation of a breaking wave. The proposed model is able to adequately simulate the energy dissipation due to the wave breaking and does not require any “a priori” criterion to locate the initial wave breaking point and the region in which the turbulence model has to be activated. In order to numerically simulate the wave propagation from deep water to the shoreline and the wave breaking, we use a model in which vector and tensor quantities are expressed in terms of Cartesian components, where only the vertical coordinate is expressed as a function of a time-dependent curvilinear coordinate that follows the free surface movements. A laboratory test is numerically reproduced with the aim of validating the turbulence modified k − ε model. The numerical results compared with the experimental measurements show that the proposed turbulence model is capable of correctly estimating the energy dissipation induced by the wave breaking, in order to avoid any underestimation of the wave height.