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We present a study of wave overtopping of barriers. The phenomenon of the wave overtopping over emerged structures is reproduced both numerically and experimentally. The numerical simulations are carried out by a numerical scheme for three-dimensional free-surface flows, which is based on the solution of the Navier–Stokes equations in a novel integral form on a time-dependent coordinate system. In the adopted numerical scheme, a novel wet–dry technique, based on the exact solution of the Riemann problem over the dry bed, is proposed. The experimental tests are carried out by adopting a nonintrusive and continuous-in-space image-analysis technique, which is able to properly identify the free surface even in very shallow waters or breaking waves. A comparison between numerical and experimental results, for several wave and water-depth conditions, is shown.

The aim of coastal structures for the defense from erosion is to modify the hydrodynamic fields that would naturally occur with the wave motion, to produce zones of sedimentation of solid material, and to combat the recession of the coastline. T-head groin-shaped structures are among the most adopted in coastal engineering. The assessment of the effectiveness of such structures requires hydrodynamic study of the interaction between wave motion and the structure. Hydrodynamic phenomena induced by the interaction between wave motion and T-head groin structures have three-dimensionality features. The aim of the paper is to propose a new three-dimensional numerical model for the simulation of the hydrodynamic fields induced by the interaction between wave fields and coastal structures. The proposed model is designed to represent complex morphologies as well as coastal structures inside the domain. The numerical scheme solves the three-dimensional Navier–Stokes equations in a contravariant formulation, on a time-dependent coordinate system, in which the vertical coordinate varies over time to follow the free-surface elevation. The main innovative element of the paper consists in the proposal of a new numerical scheme that makes it possible to simulate flows around structures with sharp-cornered geometries. The proposed numerical model is validated against a well-known experimental test-case consisting in a wave train approaching a beach (non-parallel with the wave front), with the presence of a T-head groin structure. A detailed comparison between numerical and experimental results is shown.

In this paper, we simulate the sea bottom modifications produced by the presence of a T-head groin. We present a simulation model of sea bottom modifications composed of two sub-models: a two-dimensional phase-resolving model that simulate the variation of the fluid dynamic variables inside the wave; a second sub-model to simulate the sea bottom modifications, in which the suspended sediment concentration is calculated by the wave-averaged advection-diffusion equation. The fluid motion equation and the concentration equation are expressed in a new contravariant formulation. The velocity fields from deep water up to just seaward of the surf-zone are simulated by a new integral contravariant form of the Fully Nonlinear Boussinesq Equations. The new integral form of the proposed continuity equation does not contain the dispersive term. The Nonlinear Shallow Water Equations, expressed in an integral contravariant form, are solved in order to simulate the breaking wave propagation. The momentum equation, integrated over the turbulent boundary layer, is solved to calculate the near-bed instantaneous flow velocity and the intra-wave hydrodynamic quantities. Starting from the contravariant formulation of the advection–diffusion equation for the suspended sediment concentration, it is possible to calculate the sea bottom modification. The advective sediment transport terms in the advection-diffusion equation are formulated according to a quasi-three-dimensional approach