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This paper presents some results of a study on the non-linear features of steep isolated 2D waves conducted at the Dept. of Naval Architecture, Ocean and Environmental Engineering of the University of Trieste in the frame of a wider research project financed by CETENA SpA on the wave loads on ships and marine structures in severe sea conditions. The analysis is here conducted by numerical simulations, thus solving the fully non-linear flow field by means of a BEM technique, and specifically it regards the non-linear effects deriving from the wave-wave interaction due to the frequency focusing of the component waves in a given spectrum [Codiglia, 2002; Contento et al., 2001]. It is shown that the shape of the wave spectrum computed at different stations in the direction of propagation is modified as a consequence of the nonlinear interaction of the component waves. In particular new high frequencies appear at positions close to the focusing station with non-negligible amplitudes. Moreover the highest wave is magnified by several unit percent (up to 15%) compared to simple linear predictions and the phase speed of the new high frequency components doesn’t fulfil the dispersion relation but it is locked to the phase speed of the highest component in the discrete input spectrum. Each numerical result here shown is supported by analogous experimental data presented by Chaplin [1996] and Chaplin et al. [1997]

It is well known that the periods of the natural modes of the inner free surface oscillations of a harbour are determined thoroughly by its plan shape. The amplitude of the induced standing or partially standing waves can be large when the outer sea spectrum shows non negligible energy at those frequencies. Depending on the relative size, the motions of the vessels in the harbour, ships or pleasure boats, can be large too, in particular roll, surge and yaw, so that up-downloading operations must be interrupted or small vessels must abandon their mooring for safety reasons. Thus the design of harbour or a marina takes on a great importance from an economic and safety point of view. In this paper we investigate the so-called harbour oscillations induced by offshore waves by means of a time domain approach. The method proposed here is able to handle an arbitrarily shaped plan view and variable water depth, so that reflection, diffraction and refraction effects can be taken into account. The mathematical model and the numerical scheme employed are presented in synthesis. The preliminary test cases regard 2 harbours with simple rectangular plan shape. Afterwards the method is applied to the harbour of Trieste (Italy-North Adriatic Sea) with regular waves coming from 270° to 330°. The effects on the wave pattern induced by the lengthening of a large pier used to berth modern cruise ships are investigated too.

This paper shows some numerical results obtained at DINMA on the fully nonlinear interaction of regular waves with four bottom-mounted circular cylinders [D’Este et al. 2001]. The phenomenon of interest is the so-called near trapping, i.e. the large magnification of the amplitude of the free surface elevation and induced pressures in the zone delimited by the cylinders surface. Linear theory [Linton & Evans, 1990] and experiments [Contento et al. 2000] show that this amplification depends strongly on the ratios of the column radius to the incident wavelength (ka parameter) and of the column radius to the side of the square (a/d parameter). In this specific case we analyse the ka condition that leads to extremely large oscillations of the second Fourier components of the free surface elevation in the inner zone and of the related pressure [Malenica et al., 1999] even in small amplitude incident waves. In particular the interest is focused on the behaviour of the higher order terms of the forces and run-up for two different configurations of the wave tank while keeping the same hydrodynamic parameters (ka, a/d). From the preliminary results shown in the present work, it seems that first order in-line terms are only weakly affected by the dimensions of the basin whereas the first order side force on the lateral cylinder shows evident interference effects. At the same time, the amplitude of the second order terms of the forces show a smoother variation with time for the larger basin.

This paper summarizes the results of experimental tests conducted at the Danish Hydraulic Institute (DHI) in the frame of the EU-IHP-ARI project “Wave Forces on an Array of Circular Cylinders: Experimental Investigation on the Higher Order Near Trapping” .The aim of this research project was to study thoroughly the so-called “near trapping”, and specifically the second order near trapping. This phenomenon regards diffraction effects of TLP like structures in waves, or in general arrays of vertical cylinders that enclose a portion of free surface (inner domain), and it shows itself with a rather large amplification of the oscillations of the mentioned portion of the free surface. These magnifications are particularly large at the fluid-body interface with associated large induced pressures; they show their maximum effect for specific ratios of the column radius a to the incident wavelength λ (diffraction parameter ka) and of the column radius to the distance between the column axis d (a/d parameter). First order near trapping occurs at the incident wave frequency, whereas second order near trapping is a double frequency phenomenon that is expected to occur when double frequency component waves, according to the dispersion relation, exhibit a wavelength comparable to that of linear waves giving first order near trapping. The paper describes the set-up of the experiments, the tests conducted and finally presents the most meaningful results obtained. As far as the in-line and out-of-line forces acting on the cylinders, the wave run-up and the free surface oscillations at selected locations in the inner domain are concerned, their behavior Vs ka shows clearly the occurrence of the second order near trapping phenomenon with impressive quantitative aspects.