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In a framework of changing climate, it is important to find alternative solutions for coastal protection. Indeed, the pressure of anthropogenic origin, combined with natural forcings, has contributed both to a worsening of the environmental quality of coastal areas, and to the triggering of erosion dynamics, with retreat of the sandy coast. Tethered floating breakwaters, built as a regular lattice of reversed pendula, can provide an alternative solution for beach management. With respect to rubble mound breakwaters, this type of structures has small impact on water circulation, and, in the presence of rising sea levels, it is much more adaptable than an artificial reef. Depending on their efficiency, the cost-effectiveness of beach protection using tethered floats is favorable compared to the current hard-engineering strategies. For this purpose, inspired by the concept of metamaterial wave control, a floating device has been tested in a wave flume with a two-dimensional periodic configuration. Metamaterials are engineered structures designed to interact with waves and manipulate their propagation properties. The device is built as an array of tethered submerged cylinders, with their axes parallel to the wave crests. The idea is to investigate the conditions which lead to the formation of bandgaps, which is the key factor for mitigating the incoming energy of the surface gravity waves. Experimental results demonstrated the feasibility of the concept, and that wave attenuation can be significant, even using a limited number of cylinders. The analysis of the results, have allowed us to assess that two leading mechanisms, dissipation and reflection, contribute to wave attenuation. If the cylinders are fully immersed, dissipation induces a broad bandgap around a resonance frequency that depends on the characteristics of the single pendulum. Instead, wave scattering (reflection) is relevant around frequencies that can be predicted using the generalized Bragg condition and the second harmonic generation, where the most significant bandgaps in attenuation can be observed. The second harmonic generation effect is a typical non-linear phenomenon, linked to the geometrical configuration of the device. In our tests, this behavior can be observed even for very small amplitude incident waves. In conclusion, these results show the possibility to tune the position of the attenuation bands in the wave spectrum by modifying system parameters, to make possible the implementation of an efficient wave absorber for coastal protection.

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Over the last decades, the evaluation of hazards and risks associated with coastal flooding has become increasingly more important in order to protect population and assets. The general purpose of this research was to assess reliable coastal flooding hazard maps due to overflow and wave overtopping. This paper addresses the problem of defining credible joint statistics of significant wave heights Hs and water levels ζ, focusing on the selection of the sample pair that characterizes each sea storm, to evaluate the occurrence probability of extreme events. The pair is selected maximizing a spatial structure variable, i.e., a linear combination of Hs and Relaix, F., Zammit, P.S. Satellite cells are essential for skeletal muscle, specific to each point of the area at risk. The structure variable is defined by the sensitivity of the flooding process to Hs and ζ, as found by analyzing a set of inundation maps produced through a Simplified Shallow-Water numerical model (SSW). The proposed methodology is applied to a coastal stretch in the Venetian littoral (Italy), by means of a 30 year-long time series recorded at the “Acqua Alta” oceanographic research tower, located in the Northern Adriatic Sea in front of the Venetian lagoon. The critical combination of Hs and ζ forming the structure variable is presented in a map, and it can be related to the topography and the presence of mitigation measures. The return period associated with the two recent large storms that occurred in this area in 2018 and 2019 is also investigated. The proposed procedure gives credible occurrence probabilities for these events, whereas other approaches would consider them extremely unlikely.

The aim of this work is to show that a significant increase of the e_ciency of aWave Energy Converter (WEC) can be achieved already at an early design stage, through the choice of a turbine and control regulation, by means of an accurate Wave-to-Wire (W2W) modeling that couples the hydrodynamic response calibrated in a wave flume to a Hardware-In-the-Loop (HIL) test bench with sizes and rates not matching those of the system under development. Information on this procedure is relevant to save time, because the acquisition, the installation, and the setup of a test rig are not quick and easy. Moreover, power electronics and electric machines to emulate turbines and electric generators matching the real systems are not low-cost equipment. The use of HIL is important in the development of WECs also because it allows the carrying out of tests in a controlled environment, and this is again time- and money-saving if compared to tests done on a real system installed at the sea. Furthermore, W2W modeling can be applied to several Power Take-O_ (PTO) configurations to experiment di_erent control strategies. The method here proposed, concerning a specific HIL for testing power electronics and control laws for a specific WECs, may have a more general validity. This work was supported by MARINET, a European Community—Research Infrastructure Action under the FP7 “Capacities” Specific Programme, grant agreement n. 262552.

This paper investigates on a Wave Energy Converter (WEC) named Energy &amp, Protection, 4th generation (EP4). The WEC couples the energy harvesting function with the purpose of protecting the coast from erosion. It is formed by a flap rolling with a single degree of freedom around a lower hinge. Small-scale tests were carried out in the wave flume of the maritime group of Padua University, aiming at the evaluation of the device efficiency. The test peculiarity is represented by the system used to simulate the Power Take Off (PTO). Such dummy PTO permits a free rotation of two degrees before engaging the shaft, allowing the flap to gain some inertia, and then applying a constant resistive moment. The EP4 was observed to reach a 35% efficiency, under short regular waves. The effects, in terms of coastal protection, are small but not negligible, at least for the shortest waves.

This paper describes 2-D numerical simulations of velocity and pressure fields generated by non-breaking waves on a vertical breakwater with a recurved parapet wall. The influence of the geometrical characteristics of the parapet is investigated. An impulsive pressure force is identified and discussed with respect to the pure vertical wall case. This force is generated by the seaward flow confinement induced by the surging wave crest. We refer to this impulsive impact as “confined-crest impact”. A large part of the vertical wall is affected by an impulsive increase in pressure caused by pulsating wave, compared to the case where the parapet is completely vertical. The maximum values of the impulsive pressures are localized under the recurved parapet. The total force increase on the entire structure may be significant when compared to the pure vertical wall case.

This note presents the Seabreath wave energy converter, basically a multi-chamber floating oscillating water column device, and the lumped model used to size its chambers, the ducts and the turbine. The model is based on extensive testing carried out in the wave flume of the University of Padova using fixed and floating models with a dummy power take off and indirect measurement of the produced power. A map with the available energy in the Mediterranean Sea is also proposed, showing possible ideal application sites. The Seabreath is finally dimensioned for a quarter scale test application in the Adriatic Sea, with a 3 kW turbine, and a capacity factor of 40%.

This paper discusses the key aspects of the recent Coastal Plan of the Veneto Region (IT). Its aim is to propose a single mitigation strategy for coastal erosion that is valid for the whole Veneto Region, and possibly elsewhere, as well as a method to assign a priority level to any action. The suggested mitigation action against erosion depends on urbanization level, beach width, as well as cross-shore and long-shore sediment transport. The criterion used to give a priority level to mitigation actions is based on a vulnerability index that takes into account erosive tendency, existing coastal flooding hazards, coast value, environmental relevance, tourist pressure, urbanization level, the presence of production activities, and cultural heritage. A sample case featuring the littoral of Rosolina is also provided and includes a site description, the sediment budget, critical issues and possible mitigation measures.

The general aim of this paper is to examine the effect of floating breakwater layouts on wave transmission, loads along moorings and connectors, under oblique waves. The specific contribution of this work is to provide novel and accurate experimental results for a configuration that is widely adopted in existing prototypes. Tests were carried out in the wave basin (3.8 m×20.6 m×0.8 m) of the Maritime Laboratory of the University of Padova, Italy. Two layouts, characterised by different degrees of complexity (I- and J-shaped), and three obliquities (0∘,30∘,60∘) were examined. With increased wave obliquity, the floating breakwater becomes more efficient thanks to the decrease of wave transmission and of the forces along moorings and connectors. Under perpendicular waves, with increasing layout complexity, no significant effect on wave transmission is observed, whereas mooring and intermodule connector forces significantly change, particularly in the case of frequent overtopping.

An experimental model test study is carried out to investigate damage pattern and progression on a rock armoured breakwater roundhead subjected to multidirectional waves. Concerning damage pattern, the most critical sector is observed to shift leeward with increasing wave period. Taking angles relative to mean wave direction, the critical sector is observed in the sector 10 degrees-55 degrees for short waves and in the sector 100 degrees-145 degrees for long waves. A probabilistic approach is developed to predict for one typical roundhead geometry the damage distribution depending on the incoming waves and structural characteristics. The damage progression is observed dependent on significant wave height and peak wave period, but not on the directional spreading and the spectral width of the incident waves. Combining the results of both damage pattern and damage progression, a stability formula for the distribution of damage over the roundhead is developed. Thus the formula also considers the shifting of the critical sector due to increasing wave period which existing formulae do not include. Finally, analysing the damage produced by double peaked spectra, it is shown that the armour may be designed by the formula when using the total significant wave height and an equivalent peak period.

One of the greatest challenges of coastal engineering today is the need for coastal protection in the changing climate scenario. Places which are nowadays protected will demand upgraded defences and more sites will require security; in all cases a large amount of resources will be needed to ensure beach maintenance and coastal safety. This may be an opportunity for the multi-purpose use of Wave Energy Converters (WECs) if the foreseen increase of energy demand in coastal areas is also considered. In this paper a group of WECs based on different operating concepts is numerically tested in front of two beaches, i.e. the Bay of Santander in Spain and Las Glorias beach in Mexico, representing two different case studies where the long-shore sediment transport is dominant. The hydrodynamics induced by these devices is represented by means of a 2D elliptic modified mild-slope model that is calibrated against new experimental results. The wave field is then used as input for the analytical calculation of the long-shore sediment transport and the coastline trend is estimated by applying the continuity of sediment equation. The characteristics of the selected numerical models give this work a first approach level. All the devices were found to produce a positive trend (accretion) at least in small areas. Recommendations are given to facilitate the selection of the device and the design of the farm layout for shore protection purpose.

The aim of this paper is to define a simple and useful formula to predict wave transmission for a common type of floating breakwater (FB), supplied with two lateral vertical plates protruding downward, named π-type FB. Eight different models, with mass varying from 16 to 76 kg, anchored with chains, have been tested in the wave flume of the Maritime Laboratory of Padova University, under irregular wave conditions. Water elevation in front and behind the structure has been measured with two arrays of four wave gauges. Our starting point for the prediction of wave transmission was the classical relationship established by Macagno in 1954. His relationship was derived for a box-type fixed breakwater assuming irrotational flow. Consequently, he significantly underestimated transmission for short waves and large drafts. This paper proposes an empirical modification of his relationship to properly fit the experimental results and a standardized plotting system of the transmission coefficient, based on a...

The design of a mooring system of a Wave Energy Converter is a challenging process that points out several unsolved technical problems, mostly related to the highly non-linear hydrodynamic phenomena occurring when high waves (e.g. 8 m high with 200 m wavelength) propagate in relatively shallow waters (e.g. 20 m). The aim of this note is to point out the relevance of the non-linear response of a WEC anchored in relatively shallow waters (shallow in the “non-linear” sense) in terms of loads applied to the mooring lines. Further, the effects of this cyclic load on the anchors is investigated. Note that to some extent it is like checking the importance of geotechnical and coastal engineers in the design process of the WEC structure and its mooring system (typically carried out by naval architects). The whole mooring design process is first outlined and then it is schematically applied to a specific case, namely a promising Italian device named SeaBreath (www.seabreath.it), in view of a possible deployment in the Adriatic Sea. The main concern of mooring designers is related to resonance effects induced by the second order drift. Therefore specific tests have been carried out in the 36 m long x 1.0 m wide x 1.3 m high wave flume of Padova University. Tests focused on the forces on the mooring lines induced by the sum of two regular waves of similar frequency. The mooring design is still far from complete: the physical model proved the relevance of the aforementioned effects but a numerical investigation (not yet performed) is required to draw final conclusions.

This note presents further experimental evidence on the effect of the layout on the mooring forces of floating breakwaters under irregular waves. The latest results, here summarized, have been obtained by means of physical model tests carried out on an L-shaped layout and are compared to data previously published by the authors. The experimental facility is located at the University of Padova, Italy. Results are given in non-dimensional form and concern the transmission phenomenon and the loads on mooring and tie rods interconnecting adjacent modules. It is confirmed that under more complex layouts, the wave transmission increases, due to smaller dissipation, maximum mooring forces decrease and link forces largely increase.

Aim of this contribution is to investigate the relevance of the layout on the performance of floating breakwater schemes under oblique waves. An experimental investigation was carried out in the wave basin of the Maritime Laboratory of Padua University, Italy. The facility dimensions are 3.8m x 20.6m x 0.8m. Several regular and irregular longcrested waves were generated and two different layouts (I- and J-shaped) and three obliquities (0°, 30°, 60°) were tested. With increasing wave obliquity, wave transmission decreases, mooring forces due to snapping decrease and link forces slightly increase. The J-shaped configuration determines basically the same effects with regards to both transmission and loads. The maxima of link forces are not much greater than the average loads and this is relevant for fatigue and reliability considerations.

Aim of this contribution is to examine the load on the mooring and on the tie rods of a set of interconnected floating bodies under extreme waves, with particular attention to the layout obliquity. Tests carried out at the IMAGE department of Padova University are briefly presented. It is doubtful how to scale the laboratory tests in the presence of impulsive loads on semi-taught moorings. In order to find proper scaling laws, a numerical model is presented where the chain and the floating body are studied as a lumped mass system. Results, compared to available laboratory tests are encouraging and it appears that the main processes in presence of impulses are correctly represented by the model. Model calibration will be carried out shortly, on the basis of specific ongoing tests on floating Wave Energy Converters.Copyright © 2009 by ASME

This study is motivated by the need of optimising generic floating wave energy converters based on the oscillating water column (OWC), principle in the framework of a new FP7 project (CORES) involving DISTART. Similarly IMAGE, that deals since long with floating breakwaters, is planning to further investigate this kind of device. The key aspect of our interest is the OWC dynamic, which affects the efficiency of the energy conversion. The dynamic response of a floating body is a typical two-way interaction problem: the body dynamics is determined by the wave pressure and the body movements essentially influence the wave and velocity field. The OWC under exam is moored with piles, so that some of the degrees of freedom of the system are restrained by the anchoring device: only heave and, to some extent, roll, is possible. This simplification of the problem, that in origin has 6 degrees of freedom, allows for the set up of an easier model, which is also appropriate for didactic purposes. This problem has been solved for instance in connection to floating breakwaters (see McCartney, 1985 for a description of this kind of structure) in a simplified form. Usually waves are assumed to propagate in an inviscid irrotational flow and behave as if having an infinitesimal height, whereas the floating body is assumed as rigid. After being extensively studied in the decade 75-85, mainly in connection with floating breakwater performance, the floating body simulation is now the subject of several new papers (according to the Sirius database, starting in 1965, 50% of journal papers regarding floating breakwater dynamics are written after 2001). The Authors compared experiments (Ruol and Martinelli, 2007) to simulations based on such simple hypotheses and found significant differences, almost 10%, which are too high for the purpose of optimising OWC devices. It seemed that wave non-linearities were the main cause of such dissimilarities and the need for a further investigation was established. Aim of this note is to evaluate the floating body dynamics under non-linear waves in 2DV (2 Dimensions, Vertical) conditions. A novel and simple model is set up that considers the exchange of forces between the (rigid) body and a fluid, actually sea water, described by equations able to account for all (wave) non-linearities. The Navier Stokes (NS) equations are solved in a moving grid through a finite element discretisation by means of the Comsol Multiphysics engine. The modeled equations are

The aim of this work is to assess, by means of available experimental results and numerical simulations, the possible extension of the range of application of the formula proposed by Ruol et al. (J. Wat. Port, Coast. Ocean Eng., 1, 2013), giving wave transmission for chain-moored -type floating breakwaters. The formula is here applied out of the range used for its calibration and even to other types of FBs. The error between predicted and measured values is described and discussed with reference to the main geometrical variables. It appears that the formula performs fairly well for the box-type FB, but not in cases characterized by very different mooring stiffness compared to the one used for calibration. For instance in case of fixed or tethered FBs, the formula significantly overestimates the wave transmission.

An original mathematical formulation for suspended sediments in a two-dimensional wave boundary layer is presented. The model accounts for non-immediate adaptation of sediments to the hydrodinamic conditions, and allows to include the effect of sorting of the different diameters considered. The mathematical model is numerically solved through a finite difference scheme. It is suitable that results compare favourably with experimental data by Staub et alii.

Aim of this note is to analyse the possible application of a Wave Energy Converter (WEC) as a combined tool to protect the coast and harvest energy. Physical model tests are used to evaluate wave transmission past a near-shore floating WEC of the wave activated body type, named DEXA. Efficiency and transmission characteristics are approximated to functions of wave height, period and obliquity. Their order of magnitude are 20% and 80%, respectively. It is imagined that an array of DEXA is deployed in front of Marina di Ravenna beach (IT), a highly touristic site of the Adriatic Coast. Based on the CERC formula, long-shore sediment transport is evaluated in presence and in absence of this array of DEXAs. The sediment transport in this site is quite large and frequently changes directions during the year. The larger North directed contribution and the more persistent South directed one are similar in magnitude and almost compensate each other, with the latter only slightly prevailing. It is shown that the DEXA could be designed so that the effect on sediment transport becomes quite significant and the direction of the net transport can be reversed.

This note presents the physical model tests carried out on the new breakwater in the fishing harbour of Mirbat (Sultanate of Oman), designed for a cyclonic wave Hs = 6.0 m and for a 200 year return period wind wave Hs = 3.2 m. Based on this experience, the behaviour of a rubble mound breakwater subject to wind waves that are much smaller than the design cyclonic wave height is discussed. We shall define the wave climate in this case as “cyclonic”. The initial interlocking (during construction) that does not “grow” during the lifetime as usual and the expected cyclonic wave is likely to produce larger damage than predicted by the design formulae, that on the contrary rely on such interlocking. Under oblique waves, the importance of unit interlocking is even greater due to the sub-horizontal loads and therefore the case of cyclonic wave climates requires a larger safety margin.

This note presents wave flume experiments, carried out at Aalborg University, measuring the horizontal sliding distance of a vertical breakwater in 1:40 scale. Horizontal and uplift wave induced pressures were accurately measured simultaneously with the caisson movements. Caissons of different weight and same geometries are tested under regular and irregular waves. It is found that, under breaking conditions, the expected inaccuracy of the prediction of the force, inherent on the variability of the breaking process, induce unacceptable errors in the prediction of the sliding. This observation endorses other previous experimental results. Conversely, when the actual measured input force is used as input, the analytical Shimosako formula fit quite well the experimental sliding distance.

In view of a potential design of a 2 kW small scale prototype of a wave energy converter named Seabreath, the dimensioning of the power take off, generator and relative electrical equipment is under investigation. This note presents an innovative research focusing on a holistic description of the behaviour of this device. Within a Marinet application (FP7 Research Infrastructure Action) named “Multi-chamber oscillating water column device for harvesting Ocean Renewable Energy” (MORE), electrical experiments have been carried out in the “hardware in the loop” test bench in Tecnalia laboratory, Bilbao, in order to test different control strategies. For these experiments, the Electrical and hydrodynamic response need to be fully coupled. The note describes how the available hydrodynamic model of the Seabreath has been modified to be coupled to the new electric experiments. Since the electrical tests are being used to calibrate an electrical numerical model, the procedure depicts an innovative and complete type of wave-2-wire model of a wave energy converter.