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This paper presents a new methodology to reproduce the interaction between waves and floating objects over mildly variable bathymetry. The elliptic mild slope equation solves the fluid velocity potential over a domain, which does not include the near field around each object. The waves scattered by the floating bodies are considered by means of boundary conditions at the edges of the near field areas. The coefficients of these boundary conditions are obtained nesting the solution of a near field three dimensional solver with the elliptic model solution. Comparison with a 3D numerical model, which solves the potential flow field over the whole domain, is used to validate the proposed approach. An example of application to reproduce the wave field around an array of wave energy converters is presented.

We consider a ap gate farm, i.e. a series of P arrays, each made of Q neighbouring ap gates, in an open sea of constant depth, forced by monochromatic incident waves. The eect of the gate thickness on the dynamics of the system is taken into account. By means of Green’s theorem a system of hypersingular integral equations for the velocity potential in the uid domain is solved in terms of Legendre polynomials. We show that synchronous excitation of the natural frequencies of Sammarco et al. (Applied Ocean Research 43, 206{213, 2013) yields large amplitude response of gate motion. This aspect is fundamental for the optimisation of the gate farm for energy

In this paper we test two different numerical models for the assessment of the long waves climate inside a harbour, induced by nonlinear interaction of short waves. One model is based on the nonlinear Boussinesq Type Equations; given the properties of the incoming short waves it is able to model the growth of the long waves, and their propagation and amplification inside the harbour basin. The other model uses a simplified formula for the calculation of the incoming long waves, and solves the linearized Mild Slope Equation to reproduce the long waves penetration into the harbour. The models are applied to the harbour of Marina di Carrara (Italy), where a field measurement network of both short and long waves is operational since 2005. Short waves records are obtained by a directional buoy deployed at about 1 km offshore the harbour entrance, whereas the long waves measurements inside the basin are obtained from 8 pressure transducers installed along the harbour inner perimeter. About 3 years of measurements (December 2005 to October 2008) are considered in this paper. Both the models are shown to provide reasonable estimates of the long waves climate inside the harbour. Advantages and disadvantages of each are discussed.

Semi-analytical and fully numerical modelling is developed in the framework of the inviscid potential flow theory to investigate the dynamics of a wave farm made by flap-type wave energy converters in the nearshore. The hydrodynamic parameters and the efficiency of the system in typical layouts are calculated with both models. Good agreement is shown between the two approaches. Parametric analysis undertaken with the semi-analytical model allows to identify a near-resonant phenomenon which is responsible for increasing the absorbed power by the single elements of the array. Such result could be used as a preliminary design criterion. The numerical model is then applied to analyse a configuration of practical engineering interest, i.e. an array of two staggered converters. The dynamics arising in this more complex system is explained, showing that non-symmetric layouts can be less effective.

This paper presents a novel technique for the computation of eigenvalues and eigenvectors of partially enclosed basins such as harbours and bays. The procedure makes use of the finite element approximation of the linear shallow water equations, and converts the time-depending problem into an eigenvalues one. The main point of novelty of this research is the mathematical condition used at the boundary that separates the computational domain from the open sea. While classical techniques impose a zero surface elevation (i.e. a nodal line), here an approximate radiation condition is applied. The use of a radiation condition at the open boundary gives a quadratic eigenvalue problem that admits as solution complex eigenvalues and eigenvectors, thus describing the flow in terms of both standing and progressive waves. The new method is applied to an idealized long and narrow harbour, for which an analytical solution of long wave resonance exists, and to the harbour of Marina di Carrara (Italy), for which measurements and previous numerical computation results are available. In both cases the results show good agreement with the available data.

We present a depth integrated numerical model for the simulation of the generation and the propagation of tsunamis generated by submerged landslides. The model is able to reproduce at low computational costs the full frequency dispersion of the waves and uses an ad hoc treatment for the incorporation of the effects of the moving seafloor to reproduce the generation of the waves. We also compare the present approach with some simplified techniques used in the past for the generation of these waves in depth integrated models, and we highlight the different behavior of frequency-dispersive and non-dispersive model equations. Reference solutions for comparison and discussion are obtained from the application of a three dimensional solver of the Laplace equation. All the numerical models used in this research are based on linearized model equations and boundary conditions and are therefore expected to provide reliable results for problems involving small amplitude waves and small thickness landslides. The model seems to be useful for rapid and accurate estimation of the properties of landslide generated waves, and can be used to support a tsunami early warning system. (C) 2009 Elsevier Ltd. All rights reserved.

A numerical model based on the mild-slope equation is applied to reproduce the propagation of small-amplitude transient waves. The model makes use of the Fourier Transform to convert the time-dependent hyperbolic equation into a set of elliptic equations in the frequency domain. The results of two available experimental studies on tsunamis generated by landslides are used to validate the model, which appears to be able of carefully reproducing the effects of the frequency dispersion. An example application of tsunamis propagating around the Stromboli island is also presented to show the applicability of the present approach to real life scenarios. It is finally discussed how this model could be applied as support to a tsunami early warning system. (C) 2008 Elsevier B.V. All rights reserved.

In this note, a description of swash zone boundary conditions for implementation in wave-resolving and wave-averaging long-wave models is given along with a discussion of the role of such conditions on the modelling of the entire surf zone hydromorphodynamics. (c) 2005 Elsevier B.V. All rights reserved.

Although in the last years, several numerical models have been shown to be able to reproduce rip currents around discontinuous submerged barriers, only few simple methods of practical use are available for estimating main flow parameters, like the current intensity and the mean water levels, in terms of geometrical (barrier and gap dimensions) parameters and wave characteristics. The aim of this paper is to present a simplified model to be used for an easy estimate of these important rip currents parameters. The model, which is based on rough simplifications, considers the area between the shoreline and the barrier as a reservoir in which water is pumped by breaking short waves across the barrier and from which water flows out at the gap. Four equations (mass and momentum conservation across the barrier, free discharge at the gap and balance of water pumped towards the shore and freely flowing offshore) are used to derive one single model equation that can be solved for the wave set-up and subsequently used for rip current velocity calculation. Two free parameters appear in this equation which respectively account for energy losses at the gap (C-v) and bed friction (mu). The proposed model is validated against available laboratory experiments to show its ability in providing reasonable estimates of the desired parameters, that may be considered by engineers adequate at the preliminary design stage of submerged breakwaters and that can be used for evaluating hydrodynamics on barred beaches. (C) 2004 Elsevier B.V. All rights reserved.

Two different types of shoreline boundary conditions which can be used in either wave-resolving or wave-averaging models of waves and currents propagation in the nearshore are compared here. The two techniques are essentially different: in the first case the velocity of the shoreline is obtained by the momentum equation and the shoreline position is tracked by changing the grid position, while in the other case the velocity of the shoreline is obtained by a modified Riemann solver and the shoreline is defined as an interface between dry and wet fixed grid points. A number of test cases are described to compare the performance of the two techniques. (C) 2002 Elsevier Science B.V. All rights reserved.

The aim of this paper is to illustrate the results of a preliminary study on aerial landslide-generated waves, which has been mainly intended to establish a method for analyzing water surface records. Some simple physical experiments, reproducing the Scott Russell's wave generator, were carried out in a small two-dimensional wave flume; the Wavelet Transform (WT) is applied to analyze wave measurements and it is shown that useful information can be obtained by means of this technique, The celerity of impulsively generated waves, reflection by an overflow structure and seiching phenomena of the flume are studied. A discussion of the results along with some remarks about ongoing research is also given. (C) 2002 Elsevier Science B.V. All rights reserved.