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A small-scale field experiment was conducted on a U-OWC incorporated into a model of caisson breakwater at the NOEL laboratory of Reggio Calabria (Italy). The U-Oscillating Water Column (U-OWC) or REWEC (REsonant Wave Energy Converter) is a device belonging to the family of OWCs. Such a device is very innovative, being able to absorb a very percentage of incoming sea waves and to produce electrical energy via proper PTO. The focus of the paper has been the analysis of the impact wave loads acting on the modified U-OWC structure during extreme wave events. It has been observed the occurrence of both “quasi-standing wave” loads due to non-breaking waves and “impulsive wave loads” with different wave impacts exerted by a wave breaking against the U-OWC model.

This paper proposes a new approach for the calculation of extreme wind speed. Specifically, the storm approach widely employed for long-term statistics of ocean storms is reviewed and adapted for the analysis of windstorms. This approach is based on the substitution of the sequence of real event at a given site with a sequence of simplified events characterized by a kind of equivalence with the actual ones. Basing on that, analytical solution for the calculation of the return period of a storm event whose peak exceeds a given threshold is developed. The windstorm model characterizes the simplified windstorm event by means of two parameters which are the maximum average wind speed over the windstorm and a duration parameter determined by imposing that the maximum expected gust in the simplified event is the same of that in the actual one. First, an attempt is made to assimilate the peak gust to a “maximum expected gust” and to relate this quantity to the windstorm duration. Then, in order to validate the new model, a data analysis is carried out to estimate average wind speed return values with the proposed approach and results are compared with those provided by well-established peak over threshold method.

The paper proposes an approach for estimating the long-term statistics of random wave crests occurring over a certain space–time domain. Such a problem is relevant for a number of marine engineering applications, as classical analyses based, exclusively, on time domain approaches underestimates wave crest amplitudes associated with a given return period. The return period of a certain wave crest is derived by combining the Trapezoidal Storm (TS) Model, based on DNV GL storm profile, with the Euleric Characteristic (EC) of an excursion set concept, recently applied to the study of sea wave statistics. By computing the average EC, an explicit solution for the probability distribution of the wave crests during a sea storm can be derived by an approximation of the EC. Return period of linear wave crests is derived in the paper. The proposed solution is applied for the calculation of extreme waves during an ocean storm over a certain area. The results presented can be used as good approximation in design work of offshore installations. An extension of the proposed approach to account for nonlinearities of sea surface will be a subject of future research.

This paper introduces a theoretical and experimental study of a wave energy converter (WEC) that combines the two innovative concepts of U-oscillating water column (U-OWC) and dielectric elastomer generator (DEG) power take-off (PTO). The U-OWC is a type of oscillating water column that features a U-shaped duct that is introduced to tune its dynamics to a certain wave period without active means of phase-control. The DEG is a compliant polymeric generator that makes it possible to convert mechanical energy into electrical energy by exploiting the large deformations of elastomeric membranes. A lumped-parameter mathematical model of the proposed WEC has been set-up and a small-scale model/prototype has been preliminary tested in a benign real-sea environment. During experiments, relevant experimental data have been collected and used for assessing the reliability of the modelling approach. Beside the model validation, specific experiments have been conducted to test a simple but yet effective load shedding system based on the progressive opening of an air valve. Finally, a preliminary design of a full-scale U-OWC equipped with DEG-PTO has been studied through wave-to-wire analysis. The obtained numerical results show an overall performance that is comparable with that of more conventional, expensive and complex PTO technologies.

The paper addresses the problem of deriving the nonlinear, up to the second order, crest wave height probability distribution in front of a vertical wall under the assumption of finite spectral bandwidth, finite water depth and long-crested waves. The distribution is derived by relying on the Quasi-Deterministic representation of the free surface elevation in front of the vertical wall. The theoretical results are compared against experimental data obtained by utilizing a compressive sensing algorithm for reconstructing the free surface elevation in front of the wall. The reconstruction is pursued by starting from recorded wave pressure time histories obtained by utilizing a row of pressure transducers located at various levels. The comparison shows that there is an excellent agreement between the proposed distribution and the experimental data and confirm the deviation of the crest height distribution from the Rayleigh one.

An ongoing two-year research is performing with the general objective to assess the feasibility of a system integrating the production of green-energy and its consumption inside and close to port areas for mobility services. The system is composed by two elements: (a) a “sea-to-grid” technological component harvesting and producing electrical energy from sea waves; and (b) a “green” logistic service based on the use of Fully Electric Vehicles (FEVs). A pilot study will be conducted near an Italian port area supporting passengers and freight mobility between a port and a backward (sub)-urban area. The proposed system is within the environmental goals set by the EU (Europe 2020 Strategy) and the Italian Government (National Energy Masterplan). Indeed, the energy-producing technology reduces dependence from traditional energy sources (coal, gas, oil) and consequently reduces their negative effects (greenhouse gases, air pollution, etc.). Considering that the energy is produced by sea waves, the system transfers the entire amount of produced (green) energy to the electric vehicles. The system will be experimented in a medium size urbanized area and the energy will be produced in a small size port.

The objective of this paper is to investigate the reliability of the mathematical model used for estimating the U-Oscillating Water Column (U-OWC) response in the time domain. This device is a wave energy harvester belonging to the family of Oscillating Water Columns. It comprises a water column, an air chamber with a self-rectifying turbine and a vertical U-shaped duct connecting the water column to the open wave field. The model used for describing the water column oscillations is based on the application of the unsteady Bernoulli equation for a real fluid and involves the determination of energy losses occurring over the entire duct length. The reliability of this mathematical model is assessed against experimental data. For this purpose, a U-OWC experimental model is installed in a benign natural basin, the Natural Ocean Engineering Laboratory NOEL. The experimental model is exposed to waves stochastically characterized. Thus, its response is described by relevant statistics. The paper shows that the current mathematical model may yield relevant overestimations of the system response. This relates to the approximate representation of the head losses, which are based on the Darcy-Weisbach formula traditionally employed in the analyses of steady flows. For overcoming these limitations, the paper proposes the utilization of the instantaneous acceleration-based model, which includes unsteady head losses proportional to the water column inertia. In this context, the model shows a general good agreement with the experimental measurements and demonstrate a superior capability of predicting the U-OWC response in all the processed records.

The REWEC3 (Resonant Wave Energy Converter) is a fixed oscillating water column (OWC) wave energy converter (WEC) incorporated in upright breakwaters. The device is composed by a chamber containing a water column in its lower part and an air pocket in its upper part. The air pocket is connected to the atmosphere via a duct hosting a self-rectifying air turbine. In addition, a REWEC3 includes a vertical U-shaped duct for connecting the water column to the open sea (for this reason it is known also as U-OWC). The working principle of the system is quite simple: by the action of the incident waves, the water inside the U-shaped duct is subject to a reciprocating motion, which induces alternately a compression and an expansion of the air pocket. The pressure difference between the air pocket and the atmosphere is used to drive an air turbine coupled to an off-the-shelf electrical generator connected to the grid. The main feature of the REWEC3 is the possibility of tuning the natural period of the water column in order to match a desired wave period through the size of the U-duct. The REWEC3 technology has been theoretically developed by Boccotti, later tested at the natural basin of the Natural Ocean Engineering Laboratory (NOEL, Italy), and finally proved at full scale with REWEC3 prototype built in the Port of Civitavecchia (Rome, Italy). The objective of this paper is to select and optimize a turbine/generator set of a U-shaped OWC installed in breakwaters located in the Mediterranean Sea, such as the Port of Civitavecchia, where the first prototype of REWEC3 has been realized, or the Port of Salerno or Marina delle Grazie of Roccella (Italy). The computations were performed using a time domain model based on the unsteady Bernoulli equation. Based on the time-domain model of the power plant, the following data is computed for the turbines: i) the ideal turbine diameter; ii) the generator feedback control law aiming to maximize the turbine power output for turbine coupled to the REWEC3 device for Mediterranean applications.

The paper introduces a parameterization of the DNV GL storm profile for developing an analytical model for calculations of the return period of a storm whose peak exceeds a given threshold. The DNV GL storm evolution is represented via an isosceles trapezoidal shape in which the minor base represents the storm peak duration, the major base the total storm duration and the height is half of the highest significant wave height in the actual storm. In this representation, the storm duration is not related to the storm intensity and it is fixed constant and equal to 42 hours, while the peak duration is assumed to be 6 hours. The parameterization proposed in the paper consists in expressing the peak duration as a fraction of the total storm duration allowing to investigate the effects of storm peak duration on long term estimates. The analytical solution for the return period is derived by following the classical approach of Equivalent Storm Models that is referring to the equivalent storm sequence, with the only difference that all the Trapezoidal Storm durations are identical whatever the storm intensity is. This assumption leads to significant simplification on the model development and potential employment as well. Further, a closed form solution is achieved for the return period which is also a generalization of the triangular shape. Finally, data analysis with NDBC buoys data is carried out for validating the model and elucidating analogies and differences with respect to classical Equivalent Storm approach. Results have shown that the Trapezoidal Model can be thought as a triangular one with a prudential factor on the storm peak duration which results in a reasonable overestimation of maximum expected wave height and return values.

The objective of this paper is to compare two methodologies adopted in the context of long-terms statistics: Equivalent Triangular Storm (ETS) and Peak Over Threshold (POT), applied both with the Goda model and with the Generalized Pareto Distribution. Both methodologies are currently used for conducting long-term statistics oriented to the determination of relevant input parameters adopted in the design of coastal structures. The paper proposes a dissemination of the key characteristics of the methods and elucidates the fundamental steps necessary for mechanizing the methods starting from available wave data. Then, it discusses numerical results pertaining to both Mediterranean and Ocean data. In this context, the paper focuses on the stability of the methods with respect to the (subjectively) selected storm thresholds. It shows that the ETS method is more stable than the POT. Results pertain to both omnidirectional and directional return values.

This paper presents an approach for estimating the long-term statistics of random wave crests occurring over a certain space–time domain. Such a problem is relevant in a number of marine engineering applications, as classical analyses based, exclusively, on time domain approaches underestimate wave crest amplitudes associated with a given return period. The return period of a certain wave crest is derived by combining the Equivalent Power Storm model, used in long-term statistical analyses, with the Euler Characteristic (EC) of an excursion set concept, recently applied to the study of sea wave statistics. In this regard, the paper shows that by computing the average EC, the probability distribution of the wave crests can be derived. Specifically, an explicit solution valid for finite crest thresholds can be derived by an approximation of the EC. Thus, removing the limitation of actual solutions, which are valid only for extremely large wave crests. In addition, return period of nonlinear wave crests are derived. In this context, Forristall distribution is adopted and introduced on a heuristic basis in the EC framework. The EC approximation and the reliability of the nonlinear crest distribution is assessed against Monte Carlo data by comparing distributions of maximum wave crests both in a sea state and in a sea storm. Then, return value estimations are discussed for a number of cases.

To withstand the local wave climate, coastal structure design relies on our understanding of the wave characteristics at the structure wall and the forces they impose onto the wall. However, despite the vast number of protective structures along our coasts, detailed field observations of waves measured directly at the structure wall are virtually absent. In this study, rare observations of wave characteristics at a vertical wall are presented. Contrary to linear wave theory, results suggest that the standing waves are highly nonlinear. Waves at the wall have considerably larger kurtosis and skewness compared to the incoming wave field and the wave steepness at the wall is observed to exceed the theoretical wave steepness limit of standing waves.

This paper describes the results of an experimental campaign conducted on a U-Oscillating Water Column (U-OWC) wave energy converter equipped with Dielectric Elastomer Generator (DEG) Power Take-Off (PTO) system. The considered PTO technology has the potential for overcoming some of the limitations associated with the use of traditional self-rectifying turbines. Experiments have been performed in the benign sea test site of the Natural Ocean Engineering Laboratory (NOEL), where the DEG/U-OWC was exposed to sea states with a significant wave height in the range of 0.15 m – 0.45 m and peak spectral periods in the range of 1.8 s – 3.3 s. The aim of this work is to analyze the dynamic response of the coupled DEG-PTO and U-OWC system. The analysis of the experimental data shows that the presence of the DEG determines a slight decrease in the natural period of the water column oscillations. Through the tests, we also demonstrate that a relief valve can be successfully used to actively tune the dynamic response of the system to ensure the safety of the DEG in severe sea-states.

The Resonant Wave Energy Converter 3 (REWEC3) is a wave energy converter belonging to the family of Oscillating Water Columns (OWCs). It comprises an oscillating water column and an air pocket connected to a turbine, as in the traditional OWCs. In addition, it has a small vertical U-shaped duct connecting the water column to the open wave field. Because of this particular geometrical configuration, it is also known as U-Oscillating Water Column (U-OWC). The first full-scale prototype was constructed in the Port of Civitavecchia (Rome, Italy), in the context of a major port enlargement. This paper shows some results of the monitoring activity pursued on one U-OWC chamber equipped with sensors measuring water and air pressures. The activity has been conducted for about 1 year. The energetic performance of the plant is investigated in the paper, via the estimation of the capture width ratio.

The paper concerns the statistical properties of extreme ocean waves in the space-time domain. In this regard, a solution for the exceedance probability of the maximum crest height during a sea state over a certain area is obtained. The approach is based on the Adler's solution for the extremal probability for Gaussian random processes in a multidimensional domain. The method is able to include the effects of spatial variability of three-dimensional sea waves on short-term prediction, both over an assigned area XY and in a given direction. Next, the storm-term predictions in the space-time are investigated. For this purpose, the exceedance probability of ηmax⁡ during an ocean storm over an assigned area A is derived. This solution gives a generalization to the space-time of the Borgman's time-based model for nonstationary processes. The validity of the model is assessed from wave data of two buoys of the NOOA-NDBC network located along the Pacific and the Atlantic U.S. coasts. The results show that the size of the spatial domain A remarkably influences the expected maximum crest height during a sea storm. Indeed, the exceedance probabilities of the maximum crest height during an ocean storm over a certain area significantly deviate from the classical Borgman's model in time for increasing area. Then, to account for the nonlinear contributions on crest height, the proposed model is exploited jointly with the Forristall's distribution for nonlinear crest amplitudes in a given sea state. Finally, Monte Carlo simulations of a sea storm are performed showing a very good agreement with theoretical results.

The random ocean waves have a natural tendencyto form groups of waves that produced due to the interaction of lower and higher frequency wave components. In this paper H ilbert H uang T ransformationis considered, which is the result of the empirical mode decomposition (EMD) and the Hilbert spectral analysis (HSA). HHT uses the EMD method to decompose a signal into so-called intrinsic mode functions, and uses the HSA method to obtain instantaneous frequency data. Using EMD method, any non-stationary data set can be decomposed into a finite and often small number of components, which are intrinsic mode functions ( IMF ). This decomposition method operating in the time domain is adaptive and highly efficient. Since the decomposition is based on the local characteristic time scale of the data, it can be applied to nonlinear and nonstationaryprocesses. This method is applied to the field data collected in the Natural Ocean Engineering Laboratory (NOEL, Reggio Calabria, Italy) and results on the wave groups in crossing sea are discussed.

The Resonant Wave Energy Converter 3 (REWEC3) is a wave energy converter belonging to the family of Oscillating Water Columns (OWCs). It comprises an oscillating water column and an air pocket connected to a turbine, as for traditional OWCs. In addition, it has a small vertical U-shaped duct used for connecting the water column to the open wave field. Because of this particular geometrical configuration, it is also known as U-Oscillating Water Column (U-OWC). During the past decade, small scale field experiments and theoretical analyses proved its potential for full scale applications. Currently, a full-scale prototype has been operating in the Port of Civitavecchia (Rome, Italy), where a REWEC3 was constructed within the context of a major port enlargement. This paper shows some results of the monitoring activity on a single chamber equipped with pressure gauges. The results show some initial energetic performances of the REWEC3 in wind-generated seas.

The objective of this paper is to investigate the long-term statistics associated with extreme nonlinear sea wave crests. For this purpose, an equivalent power storm methodology is exploited for modeling the non-stationary time variability of the significant wave height. The method involves the identification of the real storm time histories and a subsequent replacement of each real storm by a fictitious storm that is equivalent to the real one in a statistical sense. Such an approach allows deriving the closed form expression of the return period of a nonlinear wave crest. Numerical results pertain to the calculation of this quantity starting from wave data recorded at the Gulf of Mexico and comparison with alternative methodology recommended in the practice. Next, the paper investigates effects relevant to the design of marine structures in the proximity of a coast. Specifically, the paper considers the effect of the water depth on the return values of the significant wave height and of the maximum expected crest height. The water depth influence relates to a magnification of the return values of wave crest despite the fact that the offshore significant wave height is larger than the near-shore one for a certain value of the return period, due to shoaling-refraction effects.

The paper suggests a generalized approach to the analysis of second-order three-dimensional random wave fields that can represent either ocean waves in an undisturbed field or standing ocean waves. A nonlinear stochastic family is introduced that has a linear stationary Gaussian random contribution and a second-order correction exact in a Stokes expansion. This family can describe the nonlinear mechanics of a random wave field. Subsequently, in the considered random ocean field, the nonlinear mechanics of wave groups can be investigated conditional to the occurrence of a very high wave. The free-surface displacement and velocity potential may be obtained, as well as the nonlinear wave velocity and acceleration, for both the stochastic family and the very high wave groups. The results are of interest for the analysis of nonlinear wave kinematics when extreme surface wave events occur and thus for Morison′s wave forces on slender structures.

This paper proposes a parameterization of the Det Norske Veritas and Germanischer Lloyd (DNV GL) storm profile for the development of analytical solution for the calculation of the associated return period. This solution allows the possibility of calculating the design wave for marine structures by means of a very simple approach. The basic concept is to substitute the sequence of actual storms at a given site with a sequence of trapezoidal storms (TS) defined on the basis of the DNV GL storm temporal evolution and derive analytically the return period referring to the TSs sequence. The DNV GL storm is represented by a trapezium which may be totally defined by means of three parameters: the trapezium height related to the storm intensity, and its minor and major bases, which represent two durations Dp, D* pertaining to the maximum significant wave height Hsmax and to 50% of Hsmax, respectively. It is assumed that the parameters Dp, D* are uncorrelated to the storm intensity and are the same for all the storms. With this assumption, the return period is obtained in a closed form as a function of the ratio n between Dp and D*, D* itself, and of the exceedance probability distribution of significant wave height. The model is validated by comparison with Equivalent Triangular Storm (ETS) model by processing buoys data at four locations representative of different wave climates: Haltenbanken in North Sea, Alghero in Mediterranean Sea, stations 41001 and 46006 in Atlantic and Pacific Oceans, respectively. Results reveal that although its significant simplicity, the TS model provides reliable estimate of return values which are in agreement with those achieved by ETS model. Further, the employment of TS model with the values of parameters n and D* corresponding to the DNV GL profile is suitable for any location.

An analytical non-linear theory is presented for the interaction between three-dimensional sea wave groups and a seawall during an exceptionally high crest or deep trough in the water elevation. The solution to the second-order of the free-surface displacement and the velocity potential is derived by considering an irrotational, inviscid, incompressible flow bounded by a horizontal seabed and a vertical impermeable seawall. From this, an analytical expression for the non-linear wave pressure is obtained. The resulting theory can fully describe the mechanics at the seawall and in front of it, which are represented by a strongly inhomogeneous wave field, and demonstrate that it is influenced by characteristic parameters and wave conditions. The theoretical results are in good agreement with measurements conducted during a small-scale field experiment at the Natural Ocean Engineering Laboratory in Reggio Calabria (Italy). Comparisons of the theoretical and experimental results show that some distinctive phenomena involving the wave pressures of very high standing wave groups at a seawall, in the absence of either overturning or breaking waves, may be associated with non-linear effects.

The paper deals with the analysis of severe storms in the central Mediterranean Sea and in the US coasts of the Atlantic and Pacific Ocean. Firstly, we introduce a model for the representation of the sea storms by means of two parameters: the former is given by the maximum value of significant wave height in the actual storm and defines the storm intensity, the latter gives the storm duration. The analysis considers buoy data with different sampling Δt between two consecu- tive records, which varies in the range 0.5 - 6 hours. The sensitivity analysis of the modelled sea storm with the varia- tion of Δt shows as the structure of storms is strongly modified with large values of Δt of order of 3 - 6 hours: both the intensity and the duration may change significantly. The results are of interest to investigate the extreme events in the storms obtained with WAve Model, starting from meteorological data, where the value of Δt of 6 hours is widely applied. The conclusion is that structure of severe storms should be represented with continuous data, with Δt = 0.5 hours; a good representation is also obtained with Δt = 1 hour. The errors with increasing values of Δt are investigated.

Using Morison's equation and the directional spectrum of surface waves, it is possible to create a stationary random process that is statistically equivalent to the random process of the force exerted by wind-generated waves on a rigid cylinder. This was validated by the results of two small-scale field experiments dealing with wave forces on truncated vertical cylinders and submerged horizontal cylinders.

A small-scale field experiment was conducted on wave forces on upright breakwaters, and the following observations were made. The largest waves in a sea state yield one of two very characteristic time histories of the horizontal force, F, according to whether or not there is overtopping. With a large overtopping, F has a very sharp peak at the instant at which water reaches beyond the top of the wall. Without overtopping, F has a smooth history with its maximum when the water reaches the highest elevation on the wall. The sharp peaks of the wave-force per unit of length at a given section of a breakwater are estimated to have a negligible effect on the force on one caisson, provided that the wave crest makes an angle of only a few degrees with the breakwater. The dimensionless pressure distributions are not very sensitive to the ratio between the Hs of the incident waves and the elevation of the wall above the mean water level. Our field experiment confirms that Goda’s model (GM) is very effective for est...

A method for obtaining the directional spectrum, on assuming that the frequencies of the elementary waves are all different from one another, is re-proposed in a form suitable for applications to sea states near a coast. The method is applied to an interval of 10 h during which the sea state remained basically steady state off the beach at Reggio Calabria (east coast of the Straits of Messina). It is shown that the directional spectrum converges as the length of the time series data grows. A numerical simulation of a 10 h sea state confirms that the directional spectrum converges as the length of the time series grows, and the convergence is onto the known directional spectrum used to make the numerical simulation. Through the numerical simulation, it is proved that the method, generally, is suitable for applications even with short time series of wind waves (duration of about 100Tp). Finally, it is shown that the method is not necessarily inadequate even with short records of multimodal sea states with different modal directions, modal amplitude ratios and intermodal distances.

High waves at ocean occur during a complex space–time evolution of wave groups. In this paper the nonlinear structure of three-dimensional sea wave groups at intermediate water depth is investigated. To this purpose, the Boccotti's Quasi-Determinism theory is firstly applied to describe the linear wave groups when a given exceptionally high crest occurs. Then, the second-order correction to the linear solution is derived for the general condition of three-dimensional wave groups, at a finite water depth. Several numerical applications, finally, have been carried out in order to show how both the spectral bandwidth and the directional spreading modify the nonlinear high waves at different water depth.

The design of an energy harvester involves achieving the two following objectives: to install a safe structure with a reasonable safety margin; and to install an effective device which is able to capture energy in a variety of environmental conditions. In this context, the long-term modelling of the environmental variables plays a crucial role. In the context of wave energy harvesters, the occurrence of sea storms is a critical element in the design process. Indeed, its identification is required for determining extreme loads as well as controlled de-activations of the device for preserving the mechanical components into the device. Considering these issues, the paper proposes an analysis of the wave climate oriented to the determination of the downtime and of the energy losses. Specifically, the paper provides expressions: for calculating the average deactivation time of a wave energy device, given that it must be deactivated if the significant wave height is larger than a certain threshold; and for calculating the energy “lost” (as it is not absorbed by the device) during a storm in which the maximum wave height is larger than the mentioned threshold. The paper shows that closed-form expressions can be obtained by relying on the Equivalent Triangular Storm (ETS) model and that the adequacy of the estimations improves for larger values of the significant wave height threshold.

This paper deals with the implementation of a control algorithm for a turbine equipped into a U-Oscillating water column (U-OWC) plant. The open literature has largely ignored the problem of coupling the U-OWC behaviour to the turbine behaviour with the objective of maximizing the energy harvesting. Therefore, this paper has the objective of assessing the reliability of a Maximum Power Point Tracking (MPPT) algorithm. The paper uses a numerical algorithm for estimating the energy produced by a U-OWC in real seas. In this regard, the computations rely on long time domain analyses that allow testing a variety of environmental conditions. The MPPT is proved adequate for controlling the turbine behavior in conjunction with U-OWCs. In this context, it is shown that a reference parameter, used for determining the reference rotational speed, can be the significant wave height.

The objective of this paper is to provide a synthetic tool for determining expeditiously the wave climate conditions in several areas of the Mediterranean Sea. In the open literature, several authors have already conducted this specific analysis also for the area under examination in this paper. However, the need of discussing aspects strictly related to the design of wave energy harvesters is still relevant. Therefore, considering the variety of devices and the amount of information needed for conducting both an energy-wise optimization and a structural reliability assessment, a holistic view on the topic is provided. Specifically, the paper elucidates the theoretical aspects involved in the estimation of wave energy statistics and in the calculation of relevant return values. Next, it provides synthetic data representing the mean wave power and the return value of extreme events in several coastal areas of the Mediterranean Sea. In this regard, the paper complements information available in the open literature by discussing the influence of the directional pattern of the sea states in the determination of sea state statistics as well as in the design of a wave energy harvester. © 2014 Elsevier Ltd.

Since the nineties, the OWC (Oscillating Water Column) plants were developed at full scale to produce electrical power from ocean waves [1]. A prototype was built into a caisson breakwater of the Sakata Port, in Japan; other plants were built in India, in Scotland at Islay, in Portugal at the Azores. A new plant was built in Mutriku (Spain) recently. A new kind of OWC caisson, named U-OWC or REWEC3, was proposed by Boccotti [2]. With respect to a traditional OWC, a U-OWC plant includes an additional vertical duct, which enables to tune the eigenperiod of the plant to the peak period of the wave pressures acting on the converter-breakwater. In this way, resonance conditions can be reached without phase control devices and the wave pressures into the air pocket are increased in amplitude, amplifying the performance of the plant. In 2012, a full scale U-OWC (REWEC3) breakwater has been designed in Italy, for the harbour of Civitavecchia (the port of Rome – Port Authority of Civitavecchia). Such a breakwater embodies 19 caissons, each including 8 cells, 34m long. The paper disseminates the key issues pertaining the design stage. Further, it describes the main phases of the construction stage. The building of the caisson started in October 2012. The first caisson has been completed at the end of 2012. It is the first device for wave energy in the Mediterranean Sea and one of the biggest in the world.Copyright © 2013 by ASME

In the last decades, the research has directed its efforts and resources paper is to investigate towards the possibility to incorporate wave energy converters, into the traditional maritime breakwaters to combine classical use with new opportunities and developments (for example, the Green Ports). Since the nineties, the OWC (Oscillating Water Column) plants were developed at full scale to produce electrical power from ocean waves. For instance, a new plant was built in Mutriku (Spain) recently. A new kind of OWC caisson, named U-OWC or REWEC3, which has the advantage to obtain an impressive natural resonance without any device for phase control, has been patented by Boccotti [1]. This new U-OWC device gives performances better than those of a conventional OWC either with small wind waves or with high waves [2,3,4]. The properties of the REWEC3 have been verified with two small-scale field experiments carried out in the natural ocean engineering laboratory NOEL of Reggio Calabria off the eastern coast of the Sicily Channel [5–7]. The aim of the present two sites along Italian coasts for possible installations of REWEC3 devices: i) the port of Civitavecchia (Rome, Italy)in the Tyrrhenian sea; ii) the port of Pantelleria, in the Sicily Channel.

Practical applications in ocean engineering require the long-term analysis for prediction of extreme waves, that identify design conditions. If extreme individual waves are investigated, we need to combine long-term statistical analysis of ocean waves with short-term statistics. The former considers the distribution of standard deviation of free surface displacement in the considered location in a long-time span, of order of 10 years or more. The latter analyzes the distribution of individual wave heights in a sea state, which is a Gaussian process in time domain. Recent advanced approaches enable the combination of the two analyses. In the paper the analytical solution is obtained for the return period of a sea storm with at least two individual waves higher than a fixed level. This solution is based on the application of the Equivalent Triangular Storm model for the representation of actual storms. One of the corollaries of the solution gives the exact expression for the probability that at least two waves higher than fixed level are produced during the lifetime of a structure. The previous solution of return period and the relative probability of exceedance may be effectively applied for the risk analysis of ocean structures.

This paper investigates the steepness of large ocean waves. Different steepness and asymmetry parameters of the highest wave in a time series recorded in severe storms as well as nonlinearity of the records were investigated in Guedes Soares et al (2003, 2004). Here the steepness of high waves will be investigated by considering the ocean wave groups, both to the first and to the second order in a Stokes expansion, and some conclusions are obtained with wave data generated in an offshore basin. In particular, some parameters of wave steepness defined in Guedes Soares et al. (2004) are obtained with an analytical approach, by starting from the Boccotti’s linear Quasi-Determinism theory, including the second-order component derived by Arena (2005) for wave groups in undisturbed wave field. Furthermore, the wave field is analyzed in the space domain, to determine the actual steepness of the highest waves. These results, achieved starting from either the time or the space domain, will be analyzed for different wave spectra.Copyright © 2009 by ASME

This paper deals with the random forces produced by high ocean waves on submerged horizontal circular cylinders. Arena [Arena F, Interaction between long-crested random waves and a submerged horizontal cylinder. Phys Fluids 2006;18(7):1–9 (paper 076602)] obtained the analytical solution of the random wave field for two dimensional waves by extending the classical Ogilvie solution [Ogilvie TF, First- and second-order forces on a cylinder submerged under a free surface. J Fluid Mech 1963;16:451–472; Arena F, Note on a paper by Ogilvie: The interaction between waves and a submerged horizontal cylinder. J Fluid Mech 1999;394:355–356] to the case of random waves. In this paper, the wave force acting on the cylinder is investigated and the Froude Krylov force [Sarpkaya T, Isaacson M, Mechanics of wave forces on offshore structures, Van Nostrand Reinhold Co.; 1981], on the ideal water cylinder, is calculated from the random incident wave field. Both forces represent a Gaussian random process of time. The diffraction coefficient of the wave force is obtained as quotient between the standard deviations of the force on the solid cylinder and of the Froude Krylov force. It is found that the diffraction coefficient of the horizontal force C d o is equal to the C d v of the vertical force. Finally, it is shown that, since a very large wave force occurs on the cylinder, it may be calculated, in time domain, starting from the Froude Krylov force. It is then shown that this result is due to the fact that the frequency spectrum of the force acting on the cylinder is nearly identical to that of the Froude–Krylov force.

The upright fully reflective wall-types breakwaters have been widely adopted for development of harbours. The design of these structures depends on the characteristic wave field resulting from the interaction of the sea waves with the reflective structure, which is strongly irregular and nonlinear. This paper deals with the mechanics of long-crested wave groups in front of a vertical wall. For this purpose the ‘Quasi Determinism’ theory, particularized for the reflection of sea wave groups, is extended up to the second-order. The nonlinear processes free surface displacement and velocity potential, when a large wave crest occurs on the vertical wall or in front of it, are obtained. In the application some properties of nonlinear wave groups in reflection, when a high wave crest occurs on the wall or in front of it, are investigated.Copyright © 2007 by ASME

In this paper a new solution for non-linear random wave groups in the presence of a uniform current is obtained, by extending to the second-order the Boccotti’s ‘Quasi-Determinism’ (QD) theory. The second formulation of the QD theory gives the mechanics of linear random wave groups when a large crest-to-trough wave height occurs. Here the linear QD theory is firstly applied to the wave-current interaction. Therefore the nonlinear expressions both of free surface displacement and velocity potential are obtained, to the second-order in a Stokes’ expansion. Finally some numerical applications are presented in order to analyze both the wave profile and the wave kinematics.Copyright © 2006 by ASME

The paper proposes the directional analysis of the severest storms recorded by the Italian Wave Measurement Network (RON). For this purpose the buoy data have been processed and all the storms have been selected; for the strongest storms, the direction of the sea states, which form them, has been analyzed. The directional return period of sea storms in which the maximum significant wave height exceeds a threshold is then obtained, by applying the ETS model. It is found that, for the prediction of extreme storms off Italy, it is possible to assume the duration of storms constant, with an error smaller than 4%.Copyright © 2006 by ASME

Arena, F.; Malara, G.; Barbaro, G.; Romolo, A., and Ghiretti, S., 2013. Long-term modelling of wave run-up and overtopping during sea storms. This paper is concerned with the determination of the return period of a sea storm in which response (run-up or overtopping) of a coastal structure exceeds a fixed threshold. The method is based on long-term statistical analysis of the sea states interacting with the structure and on practical formulas proposed in the past decades for determining response of coastal structures. The proposed methodology accounts for nonstationarity of sea states in time domain by the equivalent triangular storm model, which allows us to determine closed-form solutions of the return period of a storm where maximum significant wave height is larger than a fixed threshold. In this paper the analytical solution is supplemented by a practical application pertaining calculation of the response of a coastal structure. A rubble-mound breakwater is supposed to be placed at a known wa...

Nonlinear random wave groups interacting with a vertical wall are investigated. The analytical solution for the second-order free surface displacement and velocity potential when a high crest occurs at some fixed point on, or close to, the vertical wall is obtained. The solution is exact for any water depth, and it is given as a function of the frequency spectrum of the incident waves. It is obtained that the effects of nonlinearity strongly modify the linear structure of wave groups both in the space and the time domain. The maximum effect of nonlinearity occurs when the high wave hits the wall. Furthermore, it is shown that in finite water depth, the nonlinearity increases as the bottom depth decreases. Finally, a validation by means of Monte Carlo simulations of nonlinear random waves in reflection is given.

An analytical nonlinear theory is presented for the interaction between three-dimensional sea wave groups and a seawall during the occurrence of an exceptionally high crest or deep trough of the water elevation. The solution to the second order of the free surface displacement and of the velocity potential is derived by considering an irrotational, inviscid, incompressible flow bounded by a horizontal seabed and a vertical impermeable seawall. The analytical expression of the nonlinear wave pressure is derived. The resulting theory is able to fully describe the mechanics at the seawall and in front of it, which represents a strongly nonhomogeneous wave field, then demonstrating that it is influenced by characteristic parameters and wave conditions. The theoretical results are in good agreement with measurements carried out during a small-scale field experiment at the Natural Ocean Engineering Laboratory in Reggio Calabria (Italy). The theoretical and experimental comparisons show that some distinctive phenomena regarding wave pressures of very high standing wave groups at a seawall, in the absence of either overturning or breaking waves, may be associated with nonlinear effects.

The paper proposes an analysis of ocean storms carried out starting from significant wave height time series of HOMERE sea-states hindcast database based on WAVEWATCH III model. Considering that wave spectra often exhibit multiple peaks due to the coexistence of wind waves and swells, here sea states are described by partitioned sea states that can be interpreted physically as representing independent wave systems. The analysis presented here in the paper deals with the contribution of swells to the storm peaks and on how they influence the long term statistics. The sensitivity of return values of significant wave height to swell contribution is investigated via an application of the Equivalent Triangular Storm Model (ETS). The ETS model provides analytical solution for the calculation of the return period R(Hs>h) of a sea storm whose maximum significant wave height exceeds a given threshold h. The approach of ETS consists in substituting each actual storm with an ETS described by two parameters: the storm intensity, that is the triangle height and it is equal to the maximum significant wave height during the actual storm; the storm duration, that is achieved imposing the equality between the maximum expected wave height of actual and equivalent storms. It has been experimentally proved that the actual storm and associated ETS are statistically equivalent because they have the same maximum significant wave height and the same probability P(Hmax>H) that the maximum wave height exceeds a given threshold H. The sequence of ETSs obtained in this way represents the equivalent sea, while the sequence of actual storms is the actual sea. The equivalent and actual seas present the same wave risk because they are characterized by the same number of storm events, each of them with the same intensity and the same P(Hmax>H). For the proposed analysis a set of four points from open sea to the coast is considered in area of the Gulf of Biscay (France). The results show that the contribution of swells is more significant for the storms of small and medium intensity and decreases for increasing storm intensities. Further return values variability neglecting swell is less than 7% at any point for return periods up to 100 years.