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The present paper aims to incorporate nonlinear amplitude dispersion effects in parabolic and hyperbolic approximation models. First, an explicit and analytical method for considering nonlinearities in parabolic approximation models is investigated. This method follows the concept of calculating spatially and temporally varying wave phase celerities within the simulation. The nonlinear dispersion relation to be applied is dependent on the local Ursell number and wave steepness, in relation to valid regions of analytical wave theories. Furthermore, nonlinearities are introduced in a hyperbolic approximation model by proposing a novel method which combines a parabolic and a hyperbolic model without a significant loss in accuracy, leading to a substantial reduction in the required simulation time. This is achieved by inputting initial boundary conditions into the hyperbolic model based on the output of the parabolic model, which is used for an initial calculation of the spatial distribution of nonlinear dispersion effects over the entire numerical domain. Numerical results were compared with measurements obtained via demanding experimental setups and illustrated satisfactory performance of the models. These concerted nonlinear models offer ease in implementation, short simulation times, and accurate results while incorporating the majority of wave transformation processes including shoaling, refraction, diffraction, reflection, bottom friction and depth-induced wave breaking.

In the present paper a thorough probabilistic methodology is presented, aiming at estimating the reliability of coastal structures, such as rubble mound breakwaters during their lifetime, based on the probabilistic representation of load environmental and resistance parameters. One of the innovative points and main objectives of this study is the estimation of the failure probability of a coastal structure based on the long-term wave climate at the structure's location, usually met in intermediate waters, using wave observations or measurements in deeper waters. This task is accomplished by applying a wave propagation statistical model in order that the joint probability density function of all random load parameters be estimated at the structure's location. Moreover, a relation between an event-based extreme value analysis and an analysis on sea-state conditions within storm events is derived in order that both of these two approaches could be compared estimating the same kind of failure probability; an unconditional one. The latter is properly defined here as the percentage of the structure's Lifetime that the structure will be in a failure situation. This unconditional failure probability provides direct information on the time period that the structure will be in a situation of failure (since it considers the total range of loadings and total lifetime), and thus can be incorporated more efficiently in an integrated risk analysis with consideration of social and economic costs. Besides, another specific issue of scientific originality could be considered the investigation on the proper time step denoting the sea state in the sea state analysis applied. In this manner, the actual history and shape of each storm event is taken into consideration. Furthermore, it is shown that these two approaches could be incorporated in the design of a coastal structure. Moreover, two different fully probabilistic methods, Direct Integration Method and Monte Carlo Method, were applied (and compared) by using a combination of variables with zero and non-zero hazard rate, referred here as a combined time-invariant and time-variant analysis. Finally, the effect of considering additional and different types of parameters as random variables on the assessed failure probability of the structure has been investigated. The aforementioned methodology has been applied to a sample of wave and sea level data at the structure's location generated for this purpose. The original wave data were derived from measurements in deeper waters than the structure's location, covering a period of 8 years, obtained from an oceanographic buoy, located in the western Mediterranean off Malaga, Spain. Sea level data were also obtained from a tide gauge, located in Malaga's harbor. Finally, it is shown that the methodology derived from this study could be incorporated into a coastal structure's design process to meet specific safety requirements.

In this paper we present recent evolvements of three robust numerical models for the simulation of the evolution of wave fields and hydrodynamic circulation in gulfs and coastal areas with large harbours and significant urban port facilities. The models are integrated into a single software suite for the development of a decision support tool to provide reliable forecasts of sea states prevailing at selected important ports worldwide. The application of the integrated modelling platform is designed to support approaching procedures of vessels to ports and it is based on co-operating, high-resolution, hydrodynamic (ocean and wave) models that derive input data and boundary conditions from global scale or regional, open sea and weather forecasts. The implementation of short-term forecasts for sea conditions includes the development, validation, coupling, and operational application of: i) the High Resolution Storm Surge (HiReSS) model for sea level variations; ii) the 3rd generation spectral wave model called TELEMAC-based Operational Model Addressing Wave Action Computation (TOMAWAC) for irregular wave propagation in offshore and coastal areas; and iii) a high resolution phase-resolving wave model (WAVE-L) for port basins, based on the hyperbolic mild-slope equations. This innovative product, designed for port-related end-users, will improve the navigation safety at ports, optimize the berth occupancy, support the port pilotage operations, mooring and towage procedures, and may facilitate the port layout upgrade or design. Hereby, pilot forecast implementations are presented concerning the Mediterranean Sea and eight selected harbours in it.

Spectral wave models have experienced constant development and vast improvements over the past decades. They are constantly being extended and refined in order to cover the complex wave transformation processes that take place in the coastal zone. Nevertheless, wave transmission due to overtopping has not been treated similarly yet. In this paper, a methodology to include wave generation due to overtopping in spectral wave models is presented. Incorporation of overtopping aims at better simulating the wave disturbance in the lee side of a system of offshore breakwaters and the induced hydrodynamic processes. So far, the waves generated due to wave overtopping were being neglected. The methodology consists of executing sequential simulations at small time step intervals and whenever wave overtopping occurs in a breakwater, waves are generated and transmitted in the lee side of the structure. This is achieved by modifying the boundary condition at the lee of a coastal structure to account for wave generation due to overtopping. Additionally, the transmitted spectrum source function was modified, to capture the observed transfer of energy in the higher frequencies of the spectrum due to the aforementioned overtopping process. The above methodology was implemented in the open source wave model TOMAWAC and verification with experimental measurements was carried out yielding satisfactory results. Inclusion of wave transmission due to overtopping in spectral wave models is considered to be a valuable asset, especially for the simulation of inshore hydrodynamic processes.

An integrated methodological approach to the development of a coastal flood early-warning system is presented in this paper to improve societal preparedness for coastal flood events. The approach consists of two frameworks, namely the Hindcast Framework and the Forecast Framework. The aim of the former is to implement a suite of high-credibility numerical models and validate them according to past flooding events, while the latter takes advantage of these validated models and runs a plethora of scenarios representing distinct sea-state events to train an Artificial Neural Network (ANN) that is capable of predicting the impending coastal flood risks. The proposed approach was applied in the flood-prone coastal area of Rethymno in the Island of Crete in Greece. The performance of the developed ANN is good, given the complexity of the problem, accurately predicting the targeted coastal flood risks. It is capable of predicting such risks without requiring time-consuming numerical simulations, the ANN only requires the offshore wave characteristics (height, period and direction) and sea-water-level elevation, which can be obtained from open databases. The generic nature of the proposed methodological approach allows its application in numerous coastal regions.

The necessity of an effective risk management in urban coastal zone increases, while the climate change creates unpredictable natural hazards. It is therefore very important to develop and implement analytical tools able to assist decision-makers to reveal vulnerable areas and prioritize relevant mitigation and adaptation measures. This article focuses on the applicability of the Coastal City Flooding Vulnerability Index (CCFVI) in zones of coastal cities belonging to the same country and incorporating industrial activities. It targets at investigating the capacity of the CCFVI to adequately take account of the impact of the industrial characteristics that are developed in the study areas on their vulnerability to coastal flooding. The results reveal the reduced discriminative capacity of the “administrative and institutional” subsystem in a centrally planned governance model like the one followed in Greece. They furthermore indicate the need for adding a separate indicators’ subsystem, which will be able to measure the special features of the case study. Specifically, the industrial activity in the urban domain could severely impact the vulnerability of the area and should therefore be considered in designing the risk management plans for these areas. Moreover, the importance of weighting the indicators used in the vulnerability index calculation is emphasized.

The ability to reliably forecast sea states (most importantly sea level, wind and wave conditions) within or close to the entrance of ports is a critical tool for all involved stakeholders. In this paper we present our work on a prototype decision support system capable of providing accurate sea state forecasts based on three high-resolution hydrodynamic models, i.e. a spectral wave model (model A), a mild-slope equation wave model (model B) and a barotropic hydrodynamic circulation model (model H). We present an end to end novel data processing pipeline, capable of handling the challenges posed by the volume of related data and capable of providing high resolution wave forecasts by exploiting parallelization.

In the present work the applicability of an extended Boussinesq-type model in simulating wave propagation over submerged porous breakwaters, as well as predicting the velocity distribution inside them was studied. The basic solver is able to reproduce wave propagation in practically any water depth over mild sloping bottom. Extension of this model is presented here to cover porous structures and predict wave kinematics in the interior of a permeable rubble mound covering 2DH configurations. Laboratory experiments were undertaken in the Hydraulic Engineering Laboratory, Department of Civil Engineering, University of Patras. Tests with a physical model were performed in order to measure the 2DH free surface elevation and 3D flow velocity in the interior of a porous submerged breakwater under regular and irregular, breaking and non-breaking, short or longer wave attack. The numerical results when compared with test data showed that adequate agreement was achieved in most cases.

The main objective of the present study is the combination of short- with long-term wave statistics in deep waters in order to achieve a more accurate description of the long-term wave climate in shallower waters. Such a description would provide vital information for many engineering applications in deep and intermediate waters, including design of coastal structures. This task can be accomplished by accumulating the statistics for all short-term sea conditions, considering the frequency of occurrence of each sea state during a certain period of years. A modification of an existing relationship has been developed aiming at achieving this purpose. More specifically, by using the relative frequencies of occurrence of the significant wave height (Hs) and mean zero-crossing wave period (Tm), measured at a specific location, as well as the short-term joint distributions of wave height (H) and period (T) associated with each sea state, the long-term joint distribution of H and T can be produced at that location in deep waters. Then, the long-term joint probability density function of Hs and Tm and the long-term joint probability function of H and T can be estimated at any intermediate water depth by considering wave directionality in deep waters and wave transformation of each individual wave, as waves propagate from the open sea towards shallower waters. Wave measurements obtained at three different locations in the Aegean (Greece) have been examined and compared. The results showed that, as waves propagate from deep to shallower waters, wave statistics differ from those in deeper waters, especially when waves become significantly depth limited. It is noted that this individual wave analysis refers to short-crested waves, thus wave directionality and refraction have been considered. However, in this approach, the nonlinear wave – wave interactions have not been taken into account.

A recently developed compound 1DH numerical model for simulating coastal sediment transport and bed morphology evolution is extended and validated in two horizontal dimensions. The wave module is a higher-order Boussinesq-type model. The bed load in the surf zone is computed from an advanced semi-empirical formula while the suspended load can be calculated through the solution of the advection-diffusion equation for the sediment or alternatively from a simplified formula. The estimation of the sediment transport in the swash zone is based on the ballistic theory. Extended simulation time is achieved through the application of the morphological accelerator factor technique. The validation tests showed a good response of the model with regard to longshore sediment transport under the combined action of waves and currents. A similarly good behaviour of the said model in the cross-shore direction was presented in a previous paper. In addition, the formation of a tombolo behind a detached breakwater is...

A simple, small array of a few elevation probes is proposed for the estimation of wave directional spreading and the mean wave direction. This technique offers the possibility of such estimations through two comparable methods, that is, the Maximum Likelihood Method and the Maximum Entropy Method. It is noted that the latter method was combined with an approximate technique, based on a simple alternative calculation of sea surface’s orthogonal slopes. The small array was proved to work well in both methods’ applications to laboratory and modeled data. In summary, this paper proposes a simple array of probes and an approximate technique for the estimation of wave directional spreading, which can be used in association with laboratory, numerical, and field measurements, and can give sufficiently accurate results.

Taking into consideration the changing climate, researchers are mainly interested in measuring this change in many different sectors. Regarding the coastal areas, the effects are related inter alias to the sea level rise, but also the increase and the severity of storms incidence. In conjunction with the astronomical tide, coastal storms can cause extreme wave runup and overtopping phenomena in ports, and coastal structures, the consequences of which may be disastrous, mainly affecting the operation and the reliability of infrastructure. Consequently, the analysis of coastal storms is necessary for any future technical study in coastal engineering, for the design of port and coastal structures and the coastal management also. Coastal storms as multivariate and extreme events necessitate a detailed and multivariate analysis of many parameters. This work aims to review and highlight the most significant issues in coastal storm analysis, to summarise the knowledge and the current trends of coastal storms research, by exploring the scientific background through a literature overview. A guiding framework of storm analysis should include the most important aspects of this work which are: the coastal storm definition, the description of their severity, the understanding of the synoptic systems formation, the storm surges and the time-series analysis, the thresholds for their identification, the impacts, their classification, and finally the impacts of coastal storms on coastal human population.

In the present work a previously presented high-order Boussinesq-type model is extended to account for wave propagation over porous beds. The resulting wave solver is coupled with a sediment transport and morphological model to form a compound numerical tool for studying coastal hydrodynamics and morphodynamics. The linear properties of the derived equations are studied analytically with respect to wave celerity and spatial damping rate. The values of relevant parameters for the improvement of linear properties are also reviewed. The model is tailored for simulating wave propagation over permeable submerged breakwaters. The effect of the inclusion of dispersive terms in Darcy-Forchheimer equation on the propagation of both short and long waves over a permeable submerged breakwater is studied numerically. A qualitative investigation of the wave-induced current field and the resulting morphological evolution of a sandy beach is also presented.

The applicability of a Boussinesq-type wave model in simulating wave propagation over submerged breakwaters is studied. The original model is able to reproduce wave propagation including wave breaking in practically any water depth over impermeable mild sloping bottom. Extension of that model is presented to cover steep slopes, permeable structures and breaking conditions typically out of the applicability range of the main solver. This extension is attained by coupling the main solver with a nonlinear Darcy–Forchheimer equation and with a modified wave breaking module. Experiments in a wave flume were conducted to measure free surface elevation for regular waves propagating over such structures. The modified model is able to accurately capture the nonlinear phenomena due to wave propagation over submerged structures of any porosity. Also, the wave breaking prediction technique, introducing breaker type categorization in terms of the dominant form, shows that the modified model is able to adequately simulate breaking effects, including spilling, plunging and collapsing breakers, for long and short waves. The numerical simulations when compared with measurements show very good agreement in most cases.

In the present work the evolution of a sandy beach in the lee of a permeable submerged breakwater was studied both experimentally and numerically. Three-dimensional laboratory experiments were performed to investigate regular and irregular wave propagation over a porous submerged structure and the resulting bed morphology evolution down-wave of it. The tests included normal wave incidence of breaking and non-breaking, long and shorter waves. The measurements were also used to validate a compound numerical model. The basic solver relies on enhanced Boussinesq-type equations extended to simulate wave propagation over porous beds. The wave module accounts for the entire nearshore zone, from deep water to the swash zone, and it is coupled with a sediment transport module including both bed and suspended loads. Adequate agreement between measurements and model results was achieved in most cases.

A modified Boussinesq-type model is derived to account for the propagation of either regular or irregular waves in two horizontal dimensions. An improvement of the dispersion and shoaling characteristics of the model is obtained by optimizing the coefficients of each term in the momentum equation, expanding in this way its applicability in very deep waters and thus overcoming a shortcoming of most models of the same type. The values of the coefficients are obtained by an inverse method in such a way as to satisfy exactly the dispersion relation in terms of both first and second-order analyses matching in parallel the associated shoaling gradient. Furthermore a physically more sound way to approach the evaluation of wave number in irregular wave fields is proposed. A modification of the wave generator boundary condition is also introduced in order to correctly simulate the phase celerity of each input wave component. The modified model is applied to simulate the propagation of breaking and non-breaking, regular and irregular, long and short crested waves in both one and two horizontal dimensions, in a variety of bottom profiles, such as of constant depth, mild slope, and in the presence of submerged obstacles. The simulations are compared with experimental data and analytical results, indicating very good agreement in most cases.

A simple model for predicting the vertical distribution of wave-induced pore pressures inside submerged porous structures is presented. A Boussinesq-type model coupled with a Darcy–Forchheimer equation was used to derive depth-averaged velocities. Then their profile was obtained by a semi-empirical approach based on energy considerations applied on a vertical distribution of the particle velocities induced by nonlinear waves in a free field. Laboratory measurements of hydrodynamic pressures were undertaken in a flume for breaking and non-breaking regular waves. The proposed model was compared with these measurements and to the results of a Reynolds Averaged Navier–Stokes equations model. Good agreement of the proposed model with the experiments was found and very good behaviour when compared with the RANS code. Increased pore pressures were identified during the experiments close to the downstream slope of the mound and a tendency of the pressures to increase with wave steepness. These effects were satisf...

In the present work a previously presented Boussinesq-type wave propagation model is extended to account for breaking waves in the surf zone. The model applies to fully dispersive and weakly nonlinear regular and irregular waves. Wave-breaking simulation includes the breaker effects in both the continuity and momentum equations by adding extra dissipative terms. Model results are compared to experimental data as well as to those of model's previous version based on surface roller breaker technique. Some improvement is observed over previous versions of the model in approximating the energy dissipated due to wave-breaking, especially for monochromatic waves.

A two-dimensional high-order Boussinesq-type model was derived to simulate wave propagation and relevant processes in the nearshore zone. Because of its enhanced nonlinear character, the model can describe more accurately the amplitude dispersion compared to its weakly nonlinear counterpart. Extension to the surf zone was accomplished using the eddy-viscosity concept for simulating breaking waves. Swash-zone dynamics were simulated by applying a modified narrow-slot technique. Bottom friction and subgrid turbulent mixing were also incorporated. The model can estimate the wave-induced current field, including the undertow effect. The numerical model relied on a generalized multistep predictor-corrector scheme, and the waves were generated using the source function method. Both the one-horizontal-dimensional (1DH) and two-horizontal-dimensional (2DH) versions were validated against a variety of experimental tests, including regular and irregular wave propagation and breaking on plane beaches and sub...

A simple model for predicting the vertical distribution of wave-induced horizontal orbital velocities inside submerged porous structures is presented. A velocity profile is formulated based on the exponential profile of the nonlinear wave theory. This velocity distribution is then fitted to the numerically-predicted depth-integrated velocity given by a Boussinesq model assuming uniform porosity. For the sake of comparison, experimental measurements of horizontal velocities were taken in a laboratory flume. The proposed model was also compared with the results of a version of the commercial program FLOW-3D dealing with linear waves in a simple manner. A good agreement of the model results with the experiments was found as well as an improved behaviour with respect to this program. Moreover, increased velocities were identified at the downstream slope of the rubble mound caused by recirculating flow.

A recent Boussinesq-type model is herein modified to account for breaking waves in shallow water. The model is based on a system of equations in terms of surface elevation and depth-averaged horizontal velocities, in two horizontal dimensions for fully dispersive and weakly nonlinear random waves over any finite water depth. The formulation involves five terms in each momentum equation, including the classical shallow-water equation terms, and only one frequency dispersion term. This work extends the model by including depth-induced wave-breaking in one horizontal dimension, based on the eddy viscosity and surface roller criteria. The modified model was applied to simulate the propagation and wave-breaking of regular and random waves using a simple explicit finite difference scheme. The simulation results were compared with experimental data and with results from one of the most widespread commercial Boussinesq wave models, indicating good agreement in most cases.

An experimental study carried out in a flume to a scale of 1/20 is presented to assess the wave height attenuation induced by submerged meadows of Posidonia oceanica. After examination of the appropriate scaling laws and selection of the model material, an extensive test programme included both regular and random waves. A semi-empirical formulation for estimating the wave height transformation along the meadow is obtained, based on energy conservation and considering that dissipation is only due to drag forces. The latter were linearized to obtain an exponential decay law. The formulation proposed depends on the drag coefficient and includes also an empirical parameter accounting for wave steepness. The model improves previous results and extends its applicability to random waves. The drag coefficient associated to the meadows is found to be better related to the Keulegan–Carpenter parameter than to the Reynolds number. Its value is given also for models proposed by others.

Three enhanced versions of two existing nonlinear Boussinesq-type models are herein derived. These models, along with two other similar solvers, were investigated with respect to their nonlinear and dispersive characteristics. In particular, this study comprises Fourier analysis at first-order, second-order, and third-order harmonics; an investigation of linear and nonlinear dispersion; linear shoaling analysis; and an estimation of transfer functions for subharmonics and superharmonics. The models are also validated against demanding experimental tests of wave propagation over a submerged bar. Conclusions of both a special and a general nature are drawn and discussed concerning the scope of nonlinear upgrade of Boussinesq-type equations, their numerical implementation, and the limitations of such models.

A hydrodynamic model was applied to calculate the flow field and the renewal time in Salman Bay, a semi-enclosed coastal water body of particular environmental significance in the region of Jeddah, Saudi Arabia. Initially the model was calibrated with field data. It was then applied to assess the effect of a series of engineering modifications of Salman Bay, involving enlarging of the cross-section of a link channel to the Red Sea, dredging of the bay, and reclamation of islands inside the bay, on the flow characteristics and the renewal of waters. Calculations showed that the channel upgrading would significantly improve the renewal of the bay waters. For tidal calculations the renewal time was reduced from 48·6 days to 12·7 days, whereas for a wind-driven regime it was reduced from extremely large values to 13–34 days.

Limenoscope is a web based database aiming at promoting the cultural heritage regarding ancient Greek harbours and disseminate the relevant information equally to the general public and to researchers with an interest in that particular cognitive field. The scope of the project is the realization of a database, where one can search for concise information relevant to the historical role, the topography, the morphology, as well as the technical works and installations of ancient harbours in the Mediterranean and the Black Sea. The Database started off with the registration of harbours located in the Aegean Sea and Cyprus, dating from Archaic to Byzantine times. Special emphasis is laid on the bibliographical update of the data forms of the harbour sites, as well as on the related references in ancient literature. The database enables the locating of these sites on a general map, where photographs, plans etc. are also archived. The principles of the database structure are briefly presented along with an example, that of the harbour of Phalasarna, among the harbours registered therein.

A non-linear wave propagation model, based on the higher order depth-integrated Boussinesq-type equations for breaking and non-breaking waves, was applied to predict irregular wave transformation in two horizontal dimensions. A new source function, adapted for the proposed equations, is introduced inside the computational domain, to generate the desired short-crested waves. The dissipation due to the roller is introduced in the momentum equation in order to simulate wave breaking. Bottom friction and sub-grid turbulent processes are also introduced in the model. At the open boundaries a damping layer is applied together with a radiation boundary condition. Model results are compared with experimental measurements, containing tests with normal or oblique to the shore long- and short-crested irregular waves. The comparisons show that the model is able to simulate successfully the non-linear evolution of a unidirectional or a multidirectional wave filed in the nearshore zone, under the effects of refraction, shoaling, and breaking.

Field measurements of directional waves were carried out during the summer of 2002 at two coastal sites in water of finite depth. A couple of general purpose instruments were used employing acoustic Doppler technology. The aim of the study was to investigate the spatial behavior of the directional movement of waves as they come ashore. In total,74 tests were carried out during which sea states of low to moderate intensity were recorded. A great number of these runs displayed bimodal characteristics of the spreading function at high frequencies. It was found that in general, the frequency-integrated directional width tends to broaden as the water shoals and when refraction effects are negligible. This is attributed to wave-wave interactions that become pronounced in shallow water. The same directional width showed, also, a tendency to increase with increasing peak frequency of the sea state spectrum. The behavior of the kurtosis of the spreading function was also examined. It was found that for higher frequencies this index tends to increase in wave spectra above a certain sea severity threshold.

An alternative to spectral description of sea waves in water of any depth is proposed based on the stochastic nature of the sea surface. The suggested short-term representation of a sea state displays a probabilistic structure in terms of joint densities of wave heights and periods that is advantageous in the design of maritime structures. Models have been developed and supported by laboratory and field data studies that are capable of providing the said stochastic description in a manageable form and with acceptable accuracy. Lines of further research are described for investigating this relatively unexplored field in maritime hydraulics.

A two horizontal dimensional compound model is developed to simulate coastal sediment transport and bed morphology evolution due to wave action. The wave module is a higher-order Boussinesq-type model. The bed load in the surf zone is computed from an advanced semi-empirical formula while the suspended load can be calculated through the solution of the advection-diffusion equation for the sediment or alternatively from a simplified formula. The estimation of the sediment transport in the swash zone is based on the ballistic theory. The unified sediment transport module is valid under combined waves and currents including the wave asymmetry and phase-lag effects. The bathymetry is updated through the sediment conservation equation and the morphological accelerator factor technique accounts for extended simulation time. The model is validated against a number of short-term tests in one horizontal dimension. The response is generally good with most of the morphological features being reproduced in the cross-shore direction. A comparison between various sediment transport formulae and a sensitivity analysis are also performed illustrating the need for inclusion of the phase-lag effects.

The short-term joint distribution of wave heights and periods gives an informative description of a sea state that is well suited for many practical applications in the coastal zone. This paper deals with modifications and extensions of recently published results, expressed in terms of the joint probability density function of wave heights and periods. The performance of the present model is shown to be improved as compared with experimental data. Waves of any bandwidth are treated in deep water as well as over a uniformly sloping bottom. The modifications of the joint distribution in deep water refer to the estimation of wave periods, the separation of swell from sea waves, and the accommodation of a breaking criterion. The modified joint distribution is then transformed as waves move in shallow water, through a wave-by-wave technique incorporating nonlinear shoaling of both Stokes third-order and cnoidal waves, depth-induced wave breaking, and wave reforming. Comparisons with experimental measurements show improved performance over past models.

In the present investigation the hydrodynamic characteristics of a vertically floating annular body in both regular and irregular waves are studied. Classical potential theory of diffraction and radiation is employed assuming linearity of the response motion. The method uses alternative forms of Green's functions depending on the distance and treats both diffraction and radiation problems in the same set of equations. Results for the hydrodynamic loading and coefficients in heave motion are produced for monochromatic waves and compared with those for a floating dock. Some resonance phenomena are identified. Corresponding results were obtained for irregular waves following narrow or broad Wallops spectra. In general, resonant effects are reduced compared to the monochromatic case of wave loading. Also, the narrowness of the wave spectrum is transmitted to the frequency distributions of both hydrodynamic forcing and heaving motion. The resonant frequencies can be supressed when the body is fully immersed, but in any case there are wide frequency bands where the loading of the body is smaller than on a floating dock of equal external diameter.

In the present paper, a package model is derived, based on a joint probability density function and on a Boussinesq-class numerical wave model. The key task was to produce joint probability density...

The short-term joint probability of wave heights and periods is of major importance in many coastal and offshore engineering problems. The existing results cover sufficiently only the limiting case of narrow band spectra, a gross approximation to real life data. This paper presents numerical evaluation of the joint probability based on the theoretical framework discussed in a companion paper. The obtained results are valid mainly for wide band spectra and compare well with the available data. The improved behaviour of the present model over past theories is demonstrated, especially in the range of high spectral width parameter.

The determination of the joint probability density of wave heights and periods in the short-term statistics of sea waves of any band-width is of great importance in modelling coastal wave processes, environmental loading on floating vessels, etc. This research is based on known probability relations as well as on simple theoretical considerations. Assuming Gaussian waves of any band-width, a set of differential equations has been formulated giving the desired probability density function of wave heights and periods. Non-symmetrical wave heights about the mean can be accommodated, while some simplifying approximations are discussed. Numerical results are presented in a companion paper appearing in this issue.

Some of the most important parts of a port structure are rubble mound breakwaters. This paper describes a study conducted in Greece, aimed at investigating the seismic response of a rubble mound breakwater. Experiments carried out used mathematical modeling. The two physical models used were one on a solid bed and the other on a layer of sand. Total of 38 tests were carried out on both models. A numerical modeling effort was undertaken in two procedures of varying complexity. The main conclusions of the study are provided.

Rubble-mound breakwaters are subject not only to wave action but, also, to other types of environmental loading, such as earthquakes. High seismic activity combined with soft foundation soil can lead to large settlements and even to failures of these structures. This paper reports on some aspects of the investigation undertaken to study the behaviour of rubble-mound breakwaters under seismic loading. The investigation comprised physical and mathematical modeling of two breakwaters: the first one sitting on a rigid bed, and the second on a yielding base of loose sand. Input earthquakes induced horizontal acceleration with increasing magnitude at consecutive tests. Measurements of hydrodynamic pressures and accelerations were taken. It was found that in general rubble-mound breakwaters resting on rigid bed are quite seismic resistant structures. However, a soft foundation soil plays a dominant role in the seismic behaviour of such breakwaters and may lead to quite high residual deformations. Extra care should be taken during the design phase whenever rubble-mound breakwaters are to be placed on soft soil in areas of high seismicity.

In order to mitigate hazards and losses due to earthquakes, seismic designmethodologies have been developed and implemented in design practice in many regions since the early twentieth century, often in the form of codes and standards. Most of these methodologies are based on a force-balance approach, in which structures are designed to resist a prescribed level of seismic force specified as a fraction of gravity. These methodologies have contributed to the acceptable seismic performance of port structures, particularly when the earthquake motions are more or less within the prescribed design level. Earthquake disasters, however, have continued to occur. These disasters are caused either by strong earthquake motions, often in the near field of seismic source areas, or by moderate earthquake motions in the regions where the damage due to ground failures has not been anticipated or considered in the seismic design.

The theory of the diffraction of water-waves has previously been limited to twosimple cases; the diffraction around a semi-finite breakwater and the diffractionthrough an opening in a rigid plane. Another useful practical configuration consideredhere is two breakwaters at an angle, with a gap at the corner in one ofthe breakwaters. The parameters are the angle, the breadth of the gap and theangle of incidence of the wave train. The waves are assumed to be of small amplitude.Numerical results agree well with the classical solution for the case wherethe two breakwaters lie in the same plane. Experiments with two sets of parametershave been made in a tank and have also shown good agreement with the theory.

A simple model for runoff estimation is presented, with particular reference to Athens basin. The method is based on assumptions of a symmetrical exponential storm profile and a linear cumulative area‐time relation, while a power law is postulated for correlating the storm peak factor with rainfall duration. A general expression is derived for the peak flow and discussed in comparison with the rational formula. Further, the outflow hydrograph from subcatchments of uniform characteristics is approximated by a triangular form. The model parameters for the Athens area are estimated from local rainfall data. Specific applications in Athens basin indicate good agreement with results of established techniques or observations, implying that the present method may constitute a useful tool in design practice.

Wave forecasting is accomplished today via numerical models. In this work we apply stochastic techniques using actual measurements to improve wave height forecast in real time. Application of these techniques in four locations of the Aegean Sea results in significant improvement of the forecast in the time domain retaining the same pattern of modifications, suggesting, thus, this method for operational use in deep and intermediate waters. The improvement is obtained by four regression models, which take into account the variable of the significant wave height as measured and forecasted by the model. Space-wise extension of the method was also investigated and applied to the Aegean Sea and the Indian Ocean, where its performance was remarkable.