Search

In this work, a new numerical model for cross-shore beach profile evolution, IH2VOF-SED, is developed. It consists in the bidirectional coupling of a 2D RANS hydrodynamic solver and a sediment transport module. The resulting model is extensively validated against three benchmark cases at different scales, attending to the hydrodynamics, bottom shear stress and bathymetry evolution. Comparisons between experimental and numerical results show a good agreement for both the flow variables and the seabed evolution in all the validation cases without making use of calibration parameters. Additionally, the qualitative analysis of the results is in accordance with previous experimental observations of sediment transport induced by breaking waves. The computational cost is greatly reduced to about 1/10 of other available RANS models. As a novel aspect regarding RANS models, the model is able to simulate the swash zone and changes in the position of the coastline. A good compromise between precision and computational cost is achieved, allowing for an in-depth analysis of the processes leading to the cross-shore profile evolution. The writers are grateful to Iván Cáceres (Polytechnic University of Catalunya) and Tom Baldock (University of Queensland) for providing experimental data for the validation cases. Also, to Moisés Álvarez Cuesta for performing the XBeach simulations. J. García-Maribona is indebted to the MECD (Ministerio de Educación, Cultura y Deporte, Spain) for the funding provided in the FPU (Formación del Profesorado Universitario) studentship (FPU17/04356). M. Maza is sincerely grateful to the Spanish Ministry of Science, Innovation and Universities for the funding provided in the grant Juan de la Cierva Incorporación (BOE de 27/10/2017). The work leading to this paper has been partially funded under the Retos Investigación 2018 (grant RTI2018-097014-B-I00) program of the Spanish Ministry of Science, Innovation and Universities.

This paper presents the stability analysis of a non-conventional breakwater cross-section integrating an overtopping wave energy converter, named OBREC. The device consists of a traditional rubble-mound breakwater in which the upper part of the armour layer is replaced by a smooth ramp and a reservoir. The analysis of the structure is carried out by combining model scale experiments and numerical simulations based on the Volume-Averaged Reynolds Averaged Navier-Stokes (VARANS) equations. The numerical analysis is used to complete and extend the results of the physical model test campaign, providing a deeper understanding of the pressure distribution and resultant force behaviour in locations where laboratory measurements were difficult to obtain or not available. Results show that the maximum vertical and horizontal total forces on the device are not simultaneous. At the time instant of the maximum total horizontal force, the vertical force is zero or directed downward, due to the significant positive contribution of the force acting on the sloping ramp. Additional numerical simulations show the influence of the submerged ramp length on the forces acting on the structure using the global and local stability analysis. The presence of the shaft contributes positively to the global stability against the sliding failure mode by reducing the uplift force exerted on the horizontal base. Moreover, the stability analysis shows that the critical conditions for the global failure modes occur at different time instants.

Understanding the hydrodynamic performance of floating energy converters is a complex challenge. Hence, physical modelling is necessary to evaluate the performance of innovative designs and validate them. The present paper shows the experimental work performed to validate a new floating semisubmersible structure which combines wave energy converters (3 Oscillating Water Columns, OWC) and wind harvesting (5 MW wind turbine). To characterize the global response of the platform, as well as the OWCs’ performance, an innovative wave tank testing campaign was carried out at the Cantabria Coastal and Ocean Basin (CCOB). The multi-use platform was characterized under the incidence of regular wave tests (with and without wind), operational sea states and survival sea states (combining waves, currents and wind). During the tests wind was reproduced with a portable wind generator and the wind turbine was simulated as a drag disk. The OWC air turbines were experimentally conceptualized by different diameter openings on the upper part of each OWC. This paper describes the experimental testing campaign carried out at the CCOB and presents the most significant experimental results obtained, such as natural periods, movements, loads on the mooring system or accelerations, which are representative of the performance of the multi-use platform presented.

This paper explores the role of wave spectral characteristics and wave time history on the estimation of extreme mooring loads on floating offshore wind turbines. This research is applied to the DeepCwind semi-submersible platform located at the BiMEP test site in the North of Spain. Extreme sea states are selected using the inverse first-order reliability method (I-FORM). Mooring loads are modelled by quasi-static and dynamic numerical approaches. Different wave time series are generated numerically for each sea state to investigate the variability in predicted peak loads. All cases simulated incorporate the combined effect of wind and waves. Differences of approximately 30% in peak loads are found for the mooring system, reaching 40–79% for the most extreme sea states. Safety factors are proposed to account for sensitivity to wave groupiness in modelling loads under extreme work conditions of the DeepCwind platform (e.g., pitch and velocity control). A comparison between theoretical and real-sea wave spectra is also modelled to investigate possible differences due to the presence of multiple spectral peaks associated with swell and wind seas. In general, results show differences below 12% in the prediction of loads between both assumptions.

This paper and its companion (Di Paolo et al., 2020b) present near-far field coupling schemes of Navier-Stokes (NS) equations for high-fidelity numerical modelling of wave generation, transformation and interaction with structures. The computational domain is subdivided into near and far field zones (2D and 3D subdomains, respectively) in which the NS equations are solved adopting the Finite Volume Method. The couplings can be made through the one-way or two-way exchange of flow information, thus providing a complete tool for studying one or bi-directional processes in which the three-dimensional flow is expected to be confined in the near field. The global coupled system, which is built on the OpenFOAM® platform, is based on a multi-domain approach in which the sub-domains (i.e., 2D and 3D meshes) are built independently. In Part I, the coupling methodologies have been validated against full 3D models taking into account wave propagation under different conditions with excellent results and high efficiency. Part 2 (Di Paolo et al., 2020b) involves the validation and application of the proposed methodologies to complex wave-structure interaction studies.

In this paper, an extended numerical analysis of the “confined-crest impact” (hereinafter referred as “C–CI”), induced by non-breaking waves on recurved parapet walls, is presented to better understand the physics and characteristics of this impulsive wave phenomenon, which significantly depends on the geometry of the parapet (here made by a sector of circumference) as well as on non-breaking wave steepness. A dimensional analysis of the forces has been carried out and used to analyse the results obtained by numerical CFD computations. The numerical simulations, performed for different radii of curvature, opening angles and incoming wave characteristics (changing both the wave height H and wave period T), have shown that the maximum impulsive pressure: (i) takes place on the top of the recurved parapet and decreases moving towards the S W L , where it tends to vanish; (ii) tends to decrease as the radii of curvature and the incoming wave characteristics (wave height H and period T) increase. However, this reduction in the maximum pressure, is always accompanied by an increase of the forces acting on the recurved parapet and a decrease of the wave overtopping volumes. Moreover, the maximum wave induced pressures have been examined by means of regular and irregular wave conditions in order to analyse the possibility of schematising the effects (i.e. forces) of an irregular sea state with those of a regular one, providing an equivalent force and therefore saving computational time. Based on the new results, a schematization of the pressure diagram induced by the C–CI impact has been proposed, used to extend the Goda-Takahashi pressure diagrams, valid for vertical walls in non-breaking wave conditions, including recurved walls.

One approach to identifying and mapping the state of marine biophysical conditions is the identification of large-scale ecological units for which conditions are similar and the strategies of management may also be similar. Because biological processes are difficult to directly record over large areas, abiotic characteristics are used as surrogate parameters. In this work, the Mediterranean Sea was classified into homogeneous spatial areas based on abiotic variables. Eight parameters were selected based on salinity, sea surface temperature, photosynthetically active radiation, sea-wave heights and depth variables. The parameters were gathered in grid points of 0.5° spatial resolution in the open sea and 0.125° in coastal areas. The typologies were obtained by data mining the eight parameters throughout the Mediterranean and combining two clustering techniques: self-organizing maps and the k-means algorithm. The result is a division of the Mediterranean Sea into seven typologies. For these typologies, the classification recognizes differences in temperature, salinity and radiation. In addition, it separates coastal from deep areas. The influence of river discharges and the entrance of water from other seas are also reflected. These results are consistent with the ecological requirements of the five studied seagrasses ( Posidonia oceanica , Zostera marina , Zostera noltei , Cymodocea nodosa , Halophila stipulacea ), supporting the suitability of the resulting classification and the proposed methodology. The approach thus provides a tool for the sustainable management of large marine areas and the ability to address not only present threats but also future conditions, such as climate change.

This study presents IH-LANS (Long-term ANthropized coastlines Simulation tool), a numerical model for addressing long-term coastline evolution at local to regional scales in highly anthropized coasts. In IH-LANS, a hybrid (statistical-numerical) deep-water propagation module and a data-assimilated shoreline evolution model are coupled. Longshore and cross-shore processes are integrated together with the effects of man-made interventions. For every simulation, shoreline changes in response to time varying wave conditions and water levels are evaluated while reducing calibration uncertainty by means of an extended Kalman filter that allows to assimilate shoreline observations. To test model performance, IH-LANS is applied to a highly anthropized 40 km stretch located along the Spanish Mediterranean coast. The model is run during the period 1990–2020 using high space-time resolution climate data and satellite-derived shorelines in order to calibrate the free parameters and validate model outputs. Shoreline evolution is successfully represented (

Although mangroves reduce the daily risk of flood for millions of people, it is still difficult to estimate the protection they provide for variable wave conditions and forest characteristics. This aspect is crucial for the promotion of conservation and restoration of mangrove forests and for the estimation of how the coastal protection service they provide will evolve over time. This paper presents evidence and a new method for the estimation of the relationship between mangrove forest age and wave attenuation. The forest under analysis is characterised by the age of the Rhizophora mangrove trees, where consideration is given to the differences in the maturity of its individual trees and the density of the forest. Environmental conditions are defined by water levels and incoming wave height and period. A set of empirical and analytical relations expressing wave attenuation as a function of the submerged solid volume fraction (SVF) are presented. Changes is tree morphology and forest characteristics with forest age, as well as the contribution of the tree canopy, are taken into account. Results indicate that, after restoration, it may take only 5 years to obtain a forest's maximum coastal protection capacity. Additionally, such capacity appears to be maintained throughout the forest's lifetime with minor variations, provided the forest is not affected by any conditions altering its health, such as extreme wave events or anthropogenic action that may modify its habitat. Our findings present a new approach to quantifying the protection provided by mangroves without requiring any calibration. These findings can also assist in planning mangrove restoration and assessing associated benefits by providing the incorporation of nature-based solutions or ecosystem-based adaptation into coastal management.

Global wave hindcasts provide wave climate information for long time periods which helps to improve our understanding of climate variability, long term trends and extremes. This information is extremely useful for coastal studies and can be used both directly or as boundary conditions for regional and local downscalings. This work presents the GOW2 database, a long-term wave hindcast covering the world coastline with improved resolution in coastal areas and along ocean islands. For developing the GOW2 hindcast, WAVEWATCH III wave model is used in a multigrid two-way nesting configuration from 1979 onwards. The multigrid includes a global grid of half degree spatial resolution, specific grids configured for the Arctic and the Antarctic polar areas, and a grid of higher resolution (about 25 km) for all the coastal locations at a depth shallower than 200 m. Available outputs include hourly sea state parameters (e.g. significant wave height, peak period, mean wave direction) and series of 3-h spectra at more than 40000 locations in coastal areas. Comparisons with instrumental data show a clear improvement with respect to existing global hindcasts, especially in semi-enclosed basins and areas with a complex bathymetry. The effect of tropical cyclones is also well-captured thanks to the high resolution of the forcings and the wave model setup. The new database shows a high potential for a variety of applications in coastal engineering.

In this work, we present several applications of the 2D-3D multi-domain couplings for Navier-Stokes models developed and validated in its companion (Di Paolo et al., submitted). The methodology is used to carry out some relevant simulations which include long regular and irregular waves, solitary wave propagation on a shallow foreshore, focused wave group transformation on a planar beach, wave impact on a cylinder and finally, the numerical twin of a complex laboratory experiment to analyse the performance of a perforated breakwater under wave action. Results agree well with the full 3D simulations and laboratory experiments and demonstrate the feasibility of using the 2D-3D coupled methodologies presented in Part I to successfully replace full 3D modelling. For all the cases considered, the application of coupled methodologies have resulted in a drastic reducing of the computational time without decreasing the accuracy of the full solution.

This paper presents a methodology to assess the walk-to-work accessibility of a floating wind turbine. The system composed by the vessel and the platform is modelled in the frequency domain as a rigid, possibly constrained multibody system. Non-linear actions, such mooring and viscous forces are linearised. Extreme maxima for the response variables are calculated assuming that crests are Rayleigh distributed. Two vessels are studied: a catamaran equipped with fender, and a supply vessel mounting a motion-compensated gangway. For the catamaran, accessibility is possible when no-slip conditions between the vessel fender and the ladder landing platform are ensured. For the supply vessel, accessibility is possible when the gangway motions are below the hydraulic system compensation limits. The catamaran is able to handle wave heights up to 2 m, provided that it can work under head sea conditions and take advantage of the shielding effect of the platform. The supply vessel allows personnel transfer with wave heights up to 5 m, but it is important that roll motions are not excited. The proposed methodology and the calculated maps are a valuable source of information for decision-making during personnel transfer to and from offshore floating platforms.

Based on energy conservation a new analytical formulation for the evaluation of wave damping under the combined effect of waves and both following and opposing currents is presented. The formulation obtained for regular and random waves allows the derivation of analytical expressions for the vegetation drag coefficient as a function of wave damping parameters. These parameters are calibrated using a unique experimental set obtained in a large-scale wave basin considering the interaction of waves and currents with real vegetation representative of salt marshes, namely Spartina anglica and Puccinellia maritime. Comparisons show the quality of the analytical formulation under different hydrodynamic conditions, vegetation species and various Reynolds numbers formulated in terms of plant characteristics such as the deflected plant length accounting for the flow-induced bending of the vegetation. The new formulation can be useful to be implemented in phase averaged and phase resolving numerical models of wave propagation.

A new solver for wave and structure interaction is used for three-dimensional simulation of an Oscillating Water Column (OWC). The CFD model solves the Reynolds Averaged Navier–Stokes equations for two incompressible phases (water and air). Laboratory experiments are conducted on a small scale to validate the numerical results. Air and water pressures and velocities as well as the free surface evolution inside and outside the chamber are modeled with notably good agreement. The model is further used to improve understanding of relevant processes and shows potential for use detailed analysis. Even if the experimental problem analyzed had a two-dimensional behavior, the three dimensional domain of the wave flume was numerically simulated in order to prove the capabilities of OpenFOAM ® .

This paper presents an innovative vertical breakwater cross-section integrating an overtopping wave energy converter, named OBREC-V, and the analysis of its hydraulic performance and stability response to hydraulic loading. The structure is composed of a vertically-faced caisson with a sloping ramp on the top, a reservoir and a set-back crown-wall. The analysis of the structure is carried out by performing numerical simulations based on the Volume-Averaged Reynolds Averaged Navier-Stokes (VARANS) equations. The numerical simulations are performed to compare the performance of a traditional and innovative vertical caissons under the action of irregular waves, in terms of wave reflection, overtopping and wave acting forces. Results show that the reflection coefficients are lower than those computed in front of the traditional breakwater, with a reduction of up to the 40%. New formulations are proposed to better estimate the reflection coefficient and the wave overtopping at the rear side of the structure taking into account the non-conventional geometry of the device. The analysis of the forces indicate that the non-conventional geometry of the innovative OBREC-caisson increases the overall stability of the structure. The values of the safety factor against sliding, Cs, on innovative caissons are similar or greater than those calculated on the traditional vertical structure for almost all the tests. The downward force on the ramp and reservoir and the time lag between the vertical and horizontal forces, lead to a significant reduction of the maximum destabilizing forces Fs in the innovative breakwater, whose values range between 60 and 80% of the ones computed on the traditional structure. The obtained results show the co-benefits, in terms of functionality and hydraulic stability, that an OBREC-V entails with respect to a traditional vertical breakwater.

Climate change is and will continue altering the world's coasts, which are the most densely populated and economically active areas on earth and home for highly valuable ecosystems. While there is considerable relevant research, in the authors' experience this problem remains challenging for coastal engineering. This paper reviews important challenges in this respect and identifies three key actions to address them: (a) refocusing traditional practice towards more climate-aware approaches; (b) developing more comprehensive risk frameworks that include the multi-dimensionality and non-stationarity of their components and consideration of uncertainty; and (c) building bridges between risk assessment and adaptation theory and practice. We conclude that the way forward includes numerous activities including increased observations; the attribution of coastal impacts to their drivers; enhanced climate projections and their integration into impact models; more impact assessments at the local scale; dynamic projections of spatially-distributed exposure and vulnerability; and the exploration of inherently adaptive options. Given the complexity of the possible solutions, more practical guidance is required.

Mooring systems are under a cyclic loading process caused by the randomness of metocean conditions, which could lead to a fatigue failure of the station keeping system. The present paper presents an innovative methodology for the assessment of floating offshore wind turbine mooring system fatigue considering the full lifetime of the structure. The method integrates the impact of the life cycle metocean conditions over the dynamic performance of the platform thanks to coupled numerical models, selection and non-linear data interpolation techniques and commonly accepted fatigue approaches. One of the benefits of using this methodology is that there are no uncertainties due to the selection of a reduced set of sea states. The methodology is applied to a set of moorings with different properties in the DeepCwind platform to evaluate the solution which offers the best compromise between size and fatigue damage. Results show that the best long-term mooring behaviour is achieved with a weight of approximately 300 kg/m. A comparison is conducted between the fatigue damage obtained through the life-cycle method and conventional methods. The mean differences observed between the standard and the new method proposed are between 13% and 49% depending on the use of the S–N or T-N curves.

To estimate coastal risk it is necessary to integrate the joint probability density function, including extremes, of the sea condition variables over a function that defines the consequences, typically economic damage. The use of Monte Carlo methods is common practice to undertake this integration; however, it can introduce a high computational burden for use in practical applications. Hence, a simplifying assumption of full dependence between the sea condition variables is often made. This paper describes a method that overcomes this simplifying assumption through the use of two techniques. A hybrid emulator of the simulating waves nearshore model is used to increase the computational efficiency associated with the wave transformations. In addition, a computationally efficient dynamic inundation model has been incorporated to further reduce the computational burden. To demonstrate the system, it has been applied to an urban coastal area located in northern Spain.

In this work the numerical model IHFOAM is extended to incorporate moving-boundary wave generation and absorption capabilities. The goal is to obtain a solver that includes free surface flow through porous media, able to replicate the wave generation procedures of physical wave basins. For this purpose a new boundary condition to mimic the action of multi-paddle piston wavemakers is developed and the dynamic mesh capabilities present in OpenFOAM® are enhanced. A set of experiments is carried out in the laboratory and is reproduced numerically to validate the correct operation of the new module. Additional numerical experiments are carried out to test the efficiency of active wave absorption. The results indicate a high degree of accordance between the experimental and numerical results and a correct performance of active wave absorption at the moving boundary.

Rubble mound breakwaters dissipate the incident energy of waves using friction through different layers of porous media. The porosity of these layers decreases from the external slope to the core. The flow through the breakwater induces high internal pore pressures, which might cause breakwater failures. Indeed, high pressure in the core can provoke failure of the armor layer and geotechnical instability. The experimental study of the pressure evolution inside a breakwater is tough and the existing semi-empirical approximations diverge. Consequently, the analysis of pore pressure damping through a porous media is still an open task. However, nowadays there are powerful numerical models that can be used with that aim. Therefore, pressure evolution inside the breakwaters is analyzed in this work by means of a combination of experimental, numerical and previously existing semi-empirical formulations. Hence, a hybrid modeling of pore pressure damping in rubble mound breakwaters is presented here, taking advantage of the strengths of each approach. After a validation of the numerical modeling using the experimental data, the numerical model is used to analyze the pressure field inside the breakwater. Numerical and physical model results are also compared with existing semi-empirical formulae.

A three dimensional numerical approach based on IHFOAM to study the interaction of tsunami waves with mangrove forest is presented. As a first approximation, the problem is modelled by means of solitary waves impinging on emergent rigid cylinders. Two different conceptual approaches are implemented into IHFOAM. Solving the URANS equations provides a direct simulation of the flow field considering the actual geometry of the array of cylinders. A modified version of the volume-average URANS equations by introducing a drag force to model the momentum damping created by the cylinders is used in the second approach. Both the direct and macroscopic simulations are validated against laboratory experiments for wave damping with very high agreement. A large set of numerical experiments to analyse flow parameters and uniform and random cylinder array distributions are analysed and use to compare pros and cons of the different approaches. Large differences are found in the forces exerted on the vegetation for uniform and random distributions. Generalizations obtained from uniform arrangements could lead to underestimation of wave-exerted forces, especially for low dense configurations. Wave forces calculated with the macroscopic approach by means of the drag coefficient yields clear underestimations. M. Maza is indebted to the MEC (Ministerio de Educación, Cultura y Deporte, Spain) for the funding provided in the FPU (Formación del Profesorado Universitario) studentship (BOE-A-2012-6238). This work has been partially funded under the RETOS program of the Spanish Ministry of Economy and Competitiveness (BIA2014-59718).

This study presents a comprehensive methodology for the reanalysis, characterization and propagation of wave bound infragravity waves (1/300 Hz to 1/30 Hz) in the nearshore. A deep water short wave reanalysis has been modified analytically to include the energy input associated with infragravity waves (full spectrum), through the decomposition and energy balance of the radiation stress of waves in deep water. A hybrid clustering-numerical wave propagation downscaling technique was used, forced by the modified full wave spectra previously obtained, resulting in hourly series of high spatial resolution nearshore ocean waves, including short and bound long waves. The methodology has been applied to the northern coast of Spain and validated by comparing buoy and pressure gauge records in the coast, for short wave (agitation) and infragravity wave (resonance) responses in open harbours, with very satisfactory results.

This paper presents a study of the factors that influence array layout on wave energy farms. The WEC considered is a two-body heave converter extracted from Babarit et al. (2012) . Simulations were run through a time domain model from de Andres et al. (2013) with irregular waves considering different sea states. Factors analyzed in this paper are array layout, WEC separation, number of WECs and wave directionality. Results show that wave directionality is very important in order to achieve constructive interference. When looking at the number of WECs the conclusion is that as the larger the number of WECs, more interactions are possible and therefore, the higher the interaction factor is. Regarding array layout, triangle and square configurations were found to be similar and the efficiency of each one depends on the most probable peak period. Separating distance was found to be a key factor and L 10 / 2 was set as the optimal one. Finally, wave climate was classified in different subtypes around the globe. The optimum layout in these sites was assessed. The influence of directionality was studied and the triangular configuration was found to be the most favorable for multidirectional climates while square configurations were most adequate in unidirectional climates.

A methodology to identify the state-space matrix and the vectors which solves the Cummins equations directly using free surface temporal series, obtained from laboratory or CFD codes, avoiding the use of potential flow solvers, is presented. The new methodology is applied to the solution of the piston-like movement of an Oscillating Water Column (OWC) moving in heave, assuming that sloshing is negligible, to incorporate flow effects that are not captured with traditional methods using potential flow solvers. The identification of the state-space components is done in two steps. The first step uses the solution of the state-space for decay tests, no forcing terms, obtaining a possible solution. This solution is used in the second step to solve regular waves, nonzero forcing term and no initial condition. The solution obtained in the second step is the component of the state-space that characterizes the movement of the OWC. The numerical series used to compute the solution are obtained using IH2VOF in this study, but they can be obtained by means of other sources, such as different numerical codes or laboratory measurements. Once the solution is found, the resulting state-space is validated against numerical results of IH2VOF for regular and irregular wave trains.

In this paper and its companion (Higuera et al., 2014--this issue), the latest advancements regarding Volume-averaged Reynolds-averaged Navier–Stokes (VARANS) are developed in OpenFOAM® and applied. A new solver, called IHFOAM, is programmed to overcome the limitations and errors in the original OpenFOAM® code, having a rigorous implementation of the equations. Turbulence modelling is also addressed for k-ϵ and k-ω SST models within the porous media. The numerical model is validated for a wide range of cases including a dam break and wave interaction with porous structures both in two and three dimensions. In the second part of this paper the model is applied to simulate wave interaction with a real structure, using an innovative hybrid (2D–3D) methodology.

This paper and its companion Higuera et al. (2014--this issue) introduce the formulation of Volume-Averaged Reynolds-Averaged Navier–Stokes (VARANS) equations in OpenFOAM® to simulate two-phase flow through porous media. This new implementation, so-called IHFOAM, corrects the limitations of the original OpenFOAM® code. An innovative hybrid methodology (2D–3D) is presented to optimize the simulation time needed to assess the three-dimensional effects of wave interaction with coastal structures. The combined use of a 2D and a 3D model enables the practical application of the 3D VARANS code to simulate real cases, contributing to a significant speed-up. This is highly convenient and especially suitable for non-conventional structures, as it overcomes the limitations inherent to applying semi-empirical formulations out of their range or 2D simulations only. A detailed study of stability and overtopping for a 3D porous high-mound breakwater at prototype scale subjected to oblique irregular (random) waves is carried out. Pressure around the caissons, overtopping discharge rate and turbulent magnitudes are presented in three dimensions. The mean pressure laws present a high degree of accordance with the formulation provided by Goda–Takahashi. Furthermore, local effects due to three-dimensional processes play a significant role, especially close to the breakwater head.

A simplified time-domain model for a fixed detached Oscillating Water Column (OWC) device is presented as a first step towards modeling a floating multi-chamber OWC device. The motion of a floating body in the time-domain is expressed by Cummins integro-differential equation, and based on it, water mass motion inside the chamber has been modeled here as a piston-like motion. Radiation, hydrostatic, excitation and viscous forces have been considered, as well as the added mass of the water in the chamber and the effect of the air pressure inside it. The equation of the floating body in the time domain has been approximated by a state-space method, which comes from the extension of the state-space system corresponding to the convolution integral of the radiation force. Experimental data have been used for model calibration and validation. Furthermore, the model has also been validated with a widely used Computational Fluid Dynamics (CFD) model (IH-2VOF). These show that the model presented is reliable and computationally efficient allowing for massive simulations for a statistical design or economic feasibility studies.

This study presents a methodology to obtain the power performance of a two-body heave converter. First, the methodology relies on a time domain model which represents the motion of the two bodies throughout the time. This time model was built substituting the entire equation system with a state-space system, thereby avoiding the convolution integral of the radiation force. This technique is demonstrated to be a reliable and very efficient method in terms of speed. Then, based on this model the instantaneous power of the device can be obtained. The performance of the device is shown through the power production matrix and the 60 year series power production statistics. This long series is obtained by means of using the MaxDiss selection technique in order to compute only the power of the most representative sea states and the Radial Basis Function (RBF) interpolation technique which interpolates in order to obtain the complete power series.

This work presents a new model for wave and submerged vegetation which couples the flow motion with the plant deformation. The IH-2VOF model is extended to solve the Reynolds Average Navier–Stokes equations including the presence of a vegetation field by means of a drag force. Turbulence is modeled using a k–e equation which takes into account the effect of vegetation by an approximation of dispersive fluxes using the drag force produce by the plant. The plant motion is solved accounting for inertia, damping, restoring, gravitational, Froude–Krylov and hydrodynamic mass forces. The resulting model is validated with small and large-scale experiments with a high degree of accuracy for both no swaying and swaying plants. Two new formulations of the drag coefficient are provided extending the range of applicability of existing formulae to lower Reynolds number.

The present paper and its companion (Higuera et al., 2012) introduce OpenFOAM® as a tool to consider for coastal engineering applications as it solves 3D domains and considers two-phase flow. In this first paper, OpenFOAM® utilities are presented and the free surface flow solvers are analysed. The lack of specific boundary conditions for realistic wave generation is overcome with their implementation combined with active wave absorption. Wave generation includes all the widely used theories plus specific piston-type wavemaker replication. Also standalone active wave absorption implementation is explained for several formulations, all of which are applicable to 3D cases. Active wave absorption is found to enhance stability by decreasing the energy of the system and to correct the increasing water level on long simulations. Furthermore, it is advantageous with respect to dissipation zones such as sponge layers, as it does not increase the computational domain. The results vary depending on the theory (2D, Quasi-3D and 3D) but overall performance of the implemented methods is very good. The simulations and results of the present paper are purely theoretical. Comparisons with laboratory data are presented in the second paper (Higuera et al., 2012).

In the present work, the OpenFOAM® newly developed wave generation and active absorption boundary condition presented in the companion paper (Higuera et al., submitted for publication) is validated. In order to do so the simulation of some of the most interesting physical processes in coastal engineering is carried out and comparisons with relevant experimental benchmark cases presented. Water waves are found to be generated realistically and agreement between laboratory and numerical data is very high regarding wave breaking, run up and undertow currents.

This paper evaluates the energy transfer between short and long waves resulting from nonlinear interactions of the radiation stress with the low-frequency motion in the nearshore. Shoaling and breaking of irregular waves over different slopes are investigated by means of numerical simulations with the Reynolds Averaged Navier–Stokes model IH-2VOF. The low-frequency energy flux is enhanced up to the outer surf zone where dissipation starts. Seaward of the inner surf zone, the rate of work done by the radiation stress roughly balances the low-frequency energy flux gradients, indicating that nonlinear interactions with sea–swell waves are responsible for both the enhancement and the damping of low-frequency energy. In the inner surf zone, interactions between short- and long-wave fields are weak and the low-frequency energy loss appears to be largely due to self–self nonlinear interactions.

Over the last decades, population densities in coastal areas have strongly increased. At the same time, many intertidal coastal ecosystems that provide valuable services in terms of coastal protection have greatly degraded. As a result, coastal defense has become increasingly dependent on man-made engineering solutions. Ongoing climate change processes such as sea-level rise and increased storminess, require a rethinking of current coastal defense practices including the development of innovative and cost-effective ways to protect coastlines. Integrating intertidal coastal ecosystems within coastal defense schemes offers a promising way forward. In this perspective, we specifically aim to (1) provide insight in the conditions under which ecosystems may be valuable for coastal protection, (2) discuss which might be the most promising intertidal ecosystems for this task and (3) identify knowledge gaps that currently hamper application and hence need attention from the scientific community. Ecosystems can contribute most to coastal protection by wave attenuation in areas with relatively small tidal amplitudes, and/or where intertidal areas are wide. The main knowledge gap hampering application of intertidal ecosystems within coastal defense schemes is lack in ability to account quantitatively for long-term ecosystem dynamics. Such knowledge is essential, as this will determine both the predictability and reliability of their coastal defense function. Solutions integrating intertidal ecosystems in coastal defense schemes offer promising opportunities in some situations, but require better mechanistic understanding of ecosystem dynamics in space and time to enable successful large-scale application. © 2013 Elsevier B.V.

Wind wave reanalyses have become a valuable source of information for wave climate research and ocean and coastal applications over the last decade. Nowadays, wave reanalyses databases generated with third generation models provide useful wave climate information to complement, both in time and space, the instrumental measurements (buoys and alimetry observations). In this work, a new global wave reanalysis (GOW) from 1948 onwards is presented. GOW dataset is intended to be periodically updated and it is based on a calibration of a model hindcast with satellite altimetry data, after verification against historical data. The outliers due to tropical cyclones (not simulated due to insufficient resolution in the wind forcing) are identified and not taken into account in the process to correct the simulated wave heights with the altimeter data. The results are validated with satellite measurements in time and space. This new calibrated database represents appropriately the wave climate characteristics since 1948 and aims to be the longest and up-to-date wave dataset for global wave climate variability analysis as well as for many coastal engineering applications.

This paper presents the validation results for the IH-3VOF model presented in Part I (del Jesus et al., 2011) of this paper. Initially the validation procedure is focused on wave-breaking conditions. A dam-break interacting with a prism is considered as a simplified approach to the study and analysis of wave-breaking conditions. Two different turbulence models are used in order to investigate flow separation prediction and its influence on the net forces exerted on the prism. Single and two-phase flow simulations are carried out to investigate the importance of trapped air within the fluid in the development of the forces acting on the prism. In addition, both a porous and a solid prism are considered for the study. Surface gravity waves interacting with a vertical structure in a narrow flume are presented next. Comparisons between experimentally and numerically obtained free surface elevation, pressure distribution and velocity around the structure are carried out. The hydrodynamics around the structure are studied in detail and compared with the numerical model predictions. Finally, the interaction of regular and solitary waves with a vertical breakwater in a wave basin is studied. The comparison between the laboratory tests and the numerical simulations are carried out for free surface elevation and pressure distribution over the structure under solitary and regular waves. The different results show a good performance of the IH-3VOF model, reproducing the most important processes that appear in the interaction of surface gravity waves with porous structures; therefore validating the new equations and the numerical implementation of the model.

Desalination has gained importance as an alternative water source. Brine effluent is a sub-product of desalination and can have negative effects on marine ecosystems. Numerical modelling is a prediction tool useful for the design of discharge configurations and for environmental impact assessment. The models CORMIX, VISUAL PLUMES and VISJET can be used for simulating negatively buoyant jets arising from brine discharges. A detailed analysis of the major assumptions, capabilities, limitations and reliability of these models is presented. Some important conclusions and recommendations have been elucidated. In a companion paper [1], an exhaustive validation of these commercial tools is carried out against experimental data found in the literature, focusing on brine jets discharged into both stagnant and dynamic environments. These two papers represent global research of the state of the art and the degree of reliability of existing commercial tools, using the most reliable experimental data available, and provide useful information for the technical and scientific communities. As such, they aim to improve the design and modelling of brine discharges. The conclusions outlined in the paper will improve the quality of environmental impact assessments of desalination projects and reduce the uncertainty associated with the use of numerical models.

Brine discharge is a recent environmental concern in countries where desalination production has been increased and there are protected marine ecosystems. Numerical modeling is an efficient tool useful for predicting brine behavior in seawater. CORMIX, VISUAL PLUMES and VISJET are some of the most used commercial software for modeling negatively buoyant effluents, such as brine. A detailed analysis of these models has been carried out in the companion article: “Near Field brine discharge modeling Part I: Analysis of commercial tools” (Palomar et al., submitted for publication) [1] , including the most important aspects to consider when using the models. This manuscript completes the companion paper (Palomar et al., submitted for publication) [1] by including an exhaustive validation of these commercial tools, using published experimental data. The validation focuses on the near field region of dense single port jets discharged into both stagnant and dynamic environments. An estimation of the discrepancies obtained by these models for different designs is also included. Conclusions are provided relating to the reliability and accuracy of the commercial models. This paper, together with its companion, represents the global research which aims to improve the quality of environmental impact assessments of desalination plants, while reducing the degree of uncertainty associated with the use of these commercial models for simulating brine discharges.

Solitary wave evolution over a shelf including porous damping is investigated using Volume-Averaged Reynolds Averaged Navier–Stokes equations. Porous media induced damping is determined based on empirical formulations for relevant parameters, and numerical results are compared with experimental information available in the literature. The aim of this work is to investigate the effect of wave damping on soliton disintegration and evolution along the step for both breaking and non-breaking solitary waves. The influence of several parameters such as geometrical configuration (step height and still water level), porous media properties (porosity and nominal diameter) or solitary wave characteristics (wave height) is analyzed. Numerical simulations show the porous bed induced wave damping is able to modify wave evolution along the step. Step height is observed as a relevant parameter to influence wave evolution. Depth ratio upstream and downstream of the edge appears to be the more relevant parameter in the transmission and reflection coefficients than porosity or the ratio of wave height–water depth. Porous step also modifies the fission and the solitary wave disintegration process although the number of solitons is observed to be the same in both porous and impermeable steps. In the absence of breaking, porous bed triggers a faster fission of the incident wave into a second and a third soliton, and the leading and the second soliton reduces their amplitude while propagating. This decrement is observed to increase with porosity. Moreover, the second soliton is released before on an impermeable step. Breaking process is observed to dominate over the wave dissipation at the porous bottom. Fission is first produced on a porous bed revealing a clear influence of the bottom characteristics on the soliton generation. The amplitude of the second and third solitons is very similar in both impermeable and porous steps but they evolved differently due to the effect of bed damping.

Recent advances in the description of environmental and geophysical extreme events allow incorporating smooth time variations for the parameters of the GEV distribution using harmonic functions, long-term trends and covariates (North Atlantic Oscillation, El Nino, etc.). Most of the proposed models rely on the maximum likelihood estimation method for a given parameterization. However, finding the best parameter selection for each case is not an easy task, since the number of possible combinations grows exponentially with the number of possible parameters to be considered. This problem is usually overcome by assuming simplified models based on experience or using heuristic approaches, which are computationally very expensive. In this paper, a method to obtain a pseudo-optimal parameterization using the maximum likelihood method is presented. The proposed algorithm automatically selects the parameters which minimize the Akaike Information Criterion within an iterative scheme, including one parameter at a time based on a score perturbation criteria. The process is repeated until no further improvement in the objective function is achieved. The proposed method is applied for the adjustment of monthly maximum significant wave height at different locations around the Atlantic coast and results are compared with those obtained using an existing heuristic approach, showing an important reduction in computational time and comparable results in terms of fitting quality.

The significant unbalance between water resources and the huge demands in Mediterranean area in Spain (especially for irrigation and tourist infrastructures) entails the necessity of a careful water management. The Spanish Water Resources National Plan (PHN, 2005) foresees to achieve 3 Mm³/day of water resource through a significant increase in the desalinated water production, water recycling and modernization of irrigation and supply infrastructures. With respect to desalination, this plan foresees an additional flow rate of 1.55 Mm³/day. The plants projected under the PHN (2005) use reverse osmosis technology with conversion rates between 40% and 50%, with the amount of fresh desalinated water and brine effluent being similar. The brine is discharged into the Mediterranean coastal waters, causing a potentially harmful impact on the marine environment, especially on the stenohaline benthic communities: Posidonia oceanica and Cymodocea nodosa seagrasses. In this paper, the evolution and growth of desalination in Spain is summarised. Brine behaviour, environmental evaluation methodologies, marine monitoring programs and action protocols set up to guarantee the protection of the marine environment are described. A few examples of recently built desalination plants are explained. Based on this experience, some recommendations to improve the discharge system designs are given to minimize impacts.

This work aims to demonstrate an advancement towards the integrated modelling of surf zone hydrodynamics by means of a VOF-type numerical model (COBRAS-UC) based on the Reynolds-Averaged Navier–Stokes equations. In this paper, the numerical model is adapted and validated for the study of nearshore processes on a mildly-sloping beach. The model prediction of wave energy transformation and higher order statistics (skewness and asymmetry) are in good agreement with detailed laboratory observations from a barred beach [Boers, M. (1996). “Simulation of a surf zone with a barred beach; Report 1: Wave heights and wave breaking”. Tech. Rep.96-5, Comm. on Hydrol. and Geol. Eng., Dept. of Civil Engineering, Delft University of Technology]. Moreover, the numerical model allows us to study the low-frequency motions inside the surf zone. It is found that in order to achieve a satisfactory simulation of both short- and long-wave transformation, the numerical model must achieve: (i) the simultaneous second-order wave generation and absorption, (ii) the energy transfer between triad of components, (iii) the short- and long-wave energy dissipation inside the surf zone, and (iv) the wave reflection at the shoreline. Comparisons between numerical and experimental results demonstrate the model capability to satisfactorily simulate all the aforementioned processes.

The numerical model COBRAS-UC [Losada, I.J., Lara, J.L., Guanche,R., Gonzalez-Ondina, J.M. (2008). Numerical analysis of wave overtopping of rubble mound breakwaters. Coastal Engineering, Vol 55 (1), 47–62.] is used to carry out a two-dimensional analysis of wave induced loads on coastal structures. The model calculates pressure, forces and moments for two different cross-sections corresponding to a low-mound and a conventional rubble-mound breakwater with a crown-wall under regular and irregular incident wave conditions. Predicted results are compared with experimental information provided in Losada et al. [Losada, I.J., Lara, J.L., Guanche,R., Gonzalez-Ondina, J.M. (2008). Numerical analysis of wave overtopping of rubble mound breakwaters. Coastal Engineering, Vol 55 (1), 47–62.] and Lara et al. [Lara, J.L., Losada, I.J., Guanche, R. (2008). “Wave interaction with low mound breakwaters using a RANS model”. Ocean engineering (35), pp 1388–1400; doi:10.1016/j.oceaneng.2008.05.006.] on a 1:20 scale. Good agreement is found, and the differences between both typologies are explained in detail. Additionally, numerical results are also compared with several semi-empirical formulae recommended for design at both the 1:20 model scale and two prototype cross-sections. Results suggest that COBRAS-UC is able to provide realistic stability information that can be used to complete the approach based on currently existing methods and tools.

A time-dependent generalized extreme value (GEV) model for monthly significant wave heights maxima is developed. The model is applied to several 3-hour time series from the Spanish buoy network. Monthly maxima show a clear non-stationary behavior within a year, suggesting that the location, scale and shape parameters of the GEV distribution can be parameterized using harmonic functions. To avoid a possible over-parameterization, an automatic selection model, based on the Akaike Information Criterion, is carried out. Results show that the non-stationary behavior of monthly maxima significant wave height is adequately modeled, drastically increasing the significance of the parameters involved and reducing the uncertainty in the return level estimation. The model provides new information to analyze the seasonal behavior of wave height extremes affecting different natural coastal processes.

Using COBRAS-UC, a numerical model based on the Volume-Averaged Reynolds Average Navier–Stokes (VARANS) equations, 2-D wave interaction with low-mound breakwaters is analyzed. The model uses a Volume of Fluid (VOF) technique method to capture the free surface which allows the modeling of complicated processes such as breakwater overtopping. Furthermore, thanks to the VARANS equations, the flow in the permeable layers underneath the caisson is quantitatively correct. In order to validate the model's performance, a new set of experimental studies are carried out in a wave flume at a 1:20 scale using regular and irregular waves. Comparisons between numerical and experimental free surface, pressure time histories, and overtopping layer thickness for regular and irregular waves show a good agreement. Further comparisons of numerically predicted overtopping magnitudes with existing semi-empirical formulae and experimental data indicate that the model can be used as a complementary tool for the functional design of this kind of structures.

The paper describes the results of a two-dimensional (2-D) numerical modelling investigation of the functionality of rubble mound breakwaters with special attention focused on wave overtopping processes. The model, COBRAS-UC, is a new version of the COBRAS (Cornell Breaking Waves and Structures) based on the Volume Averaged Reynolds Average Navier–Stokes (VARANS) equations and uses a Volume of Fluid Technique (VOF) method to capture the free surface. The nature of the model equations and solving technique provides a means to simulate wave reflection, run-up, wave breaking on the slope, transmission through rubble mounds, overtopping and agitation at the protected side due to the combined effect of wave transmission and overtopping. Also, two-dimensional experimental studies are carried out to investigate the performance of the model. The computations of the free surface and pressure time series and spectra under regular and irregular waves, are compared with the experimental data reaching a very good agreement. The model is also used to reproduce instantaneous and average wave overtopping discharge. Comparisons with existing semi-empirical formulae and experimental data show a very good performance. The present model is expected to become in the near future an excellent tool for practical applications.

This paper assesses the influence of different flow and vegetation parameters on the wave attenuation provided by two contrasting salt marsh species: Puccinellia maritima and Spartina anglica . Different water depths and wave parameters (height and period) are considered for both regular and irregular waves with and without an underlying uniform current coming from different directions. The study of the submergence ratio ( h / h v ) influence shows that wave damping coefficient rapidly decreases as the plant submergence ratio increases. The high nonlinearities found in the wave–current interaction lead to different wave damping patterns in comparison to wave-only conditions. A smaller wave damping is found for waves and current acting in the same direction and an increase in the wave damping rate is obtained for waves and current flowing in the opposite direction. These wave and current tests allow for the studying of the energy dissipation produced by the vegetation, increasing our knowledge about flow and plant interaction in estuarine conditions. The biomechanical properties of the two real salt marshes used in the experiments are also evaluated and related to wave damping revealing a higher attenuation for stiffer vegetation. Both, the vegetation density and the biomass strongly influence wave damping. Higher density and biomass values lead to higher attenuation rates for both species.

This paper is the second part of the work presented by Garcia et al. [Garcia, N., Lara, J.L., Losada, I.J., 2004. 2-D numerical analysis of near-field flow at low-crested breakwaters. Coastal Engineering 51 (10), 991–1020]. In the mentioned paper, flow conditions at low-crested rubble-mound breakwaters under regular wave attack were examined, using a combination of measured data of free surface, bottom pressure and fluid velocities from small-scale experiments and numerical results provided by a VOF-type model (COBRAS) based on the Reynolds-Averaged Navier–Stokes (RANS) equations. This paper demonstrates the capability of the COBRAS model to reproduce irregular wave interaction with submerged permeable breakwaters. Data provided by the numerical model are compared to experimental data of laboratory tests, and the main processes of wave–structure interaction are examined using both experimental and numerical results. The numerical model validation is carried out in two steps. First, the procedure of irregular wave generation is verified to work properly, comparing experimental and numerical data of different cases of irregular wave trains propagating over a flat bottom. Next, the validation of the numerical model for wave interaction with submerged rubble-mound breakwaters is performed through the simulation of small-scale laboratory tests on different incident wave spectra. Results show that the numerical model adequately reproduces the main aspects of the interaction of random waves with submerged porous breakwaters, especially the spectral energy decay at the structure and the spectrum broadening past the structure. The simulations give good results in terms of height envelopes, mean level, spectral shape, root-mean-square height for both free surface displacement and dynamic pressure inside the breakwater. Moreover, large-scale simulations have been conducted, on both regular and irregular incident wave conditions. The overall pattern of the wave interaction with a large-scale submerged breakwater is adequately reproduced by the numerical model. The processes of wave reflection, shoaling and breaking are correctly captured. The good results achieved at a near prototype scale are promising regarding the use of the numerical model for design purposes.

A description of the progress achieved within DELOS (environmental DEsign of LOw-crested coastal defence Structures) EU project in the modelling of wave interaction with low-crested structures (LCS) is presented in this paper. Emphasis is put on the description of the near-field flow, especially the velocity and turbulence distribution around and inside LCS, as required by other researchers in the project. Two-dimensional (VARANS) and three-dimensional (LES) numerical modelling has been considered. The two-dimensional model has been extensively validated with DELOS laboratory data as shown in Garcia et al. [Garcia, N., Lara, J.L., Losada, I.J., 2004. 2-D Numerical analysis of near-field flow at low-crested breakwaters. Coastal Engineering, ELSEVIER, 51 (10) 991–1020.]. A system of flow recirculation is included in both the experimental and numerical set-ups for a correct description of the 2DV velocity field in the vicinity of the structure. Further validation is presented in this paper. Laboratory tests on two values of crest width have been simulated in order to analyse relevant near-field flow features related to a variation of the geometric configuration of the structure. The width of the breakwater crest is seen to significantly influence the wave breaking-induced flow pattern at the structure. Magnitudes such as turbulent kinetic energy (TKE), TKE dissipation rate, shear stresses and Reynolds stresses are computed around and inside the breakwater. The three-dimensional model numerical results are compared with results of wave basin experiments, showing a good agreement for instantaneous free surface. Numerical results of the flow over the breakwater and around the breakwater head are also presented.

This paper describes the capability of a numerical model named COrnell BReaking waves And Structures (COBRAS) [Lin, P., Liu, P.L.-F., 1998. A numerical study of breaking waves in the surf zone. Journal of Fluid Mechanics 359, 239–264; Liu, P.L.-F., Lin, P., Chang, K.A., Sakakiyama, T., 1999. Numerical modeling of wave interaction with porous structures. Journal of Waterway, Port, Coastal and Ocean Engineering 125, 322–330, Liu, P.L.-F., Lin, P., Hsu, T., Chang, K., Losada, I.J., Vidal, C., Sakakiyama, T., 2000. A Reynolds averaged Navier–Stokes equation model for nonlinear water wave and structure interactions. Proc. Coastal Structures '99, 169–174] based on the Reynolds Averaged Navier–Stokes (RANS) equations to simulate the most relevant hydrodynamic near-field processes that take place in the interaction between waves and low-crested breakwaters. The model considers wave reflection, transmission, overtopping and breaking due to transient nonlinear waves including turbulence in the fluid domain and in the permeable regions for any kind of geometry and number of layers. Small-scale laboratory tests were conducted in order to validate the model, with different wave conditions and breakwater configurations. In the present study, regular waves of different heights and periods impinging on a wide-crested structure are considered. Three different water depths were tested in order to examine the influence of the structure freeboard. The experimental set-up includes a flow recirculation system aimed at preventing water piling-up at the lee of the breakwater due to overtopping. The applicability and validity of the model are examined by comparing the results of the numerical computations with experimental data. The model is proved to simulate with a high degree of agreement all the studied magnitudes, free surface displacement, pressure inside the porous structure and velocity field. The results obtained show that this model represents a substantial improvement in the numerical modelling of low-crested structures (LCS) since it includes many processes neglected previously by existing models. The information provided by the model can be useful to analyse structure functionality, structure stability, scour and many other hydrodynamic processes of interest.

In this work, a model for wave transformation on vegetation fields is presented. The formulation includes wave damping and wave breaking over vegetation fields at variable depths. Based on a nonlinear formulation of the drag force, either the transformation of monochromatic waves or irregular waves can be modelled considering geometric and physical characteristics of the vegetation field. The model depends on a single parameter similar to the drag coefficient, which is parameterized as a function of the local Keulegan–Carpenter number for a specific type of plant. Given this parameterization, determined with laboratory experiments for each plant type, the model is able to reproduce the root-mean-square wave height transformation observed in experimental data with reasonable accuracy.