Coastal Engineering 1996

The aim of this paper is to study the transformation of irregular directional waves over a circular shoal. An experimental study has been carried out. The resulting data has been used to test the accuracy of an existing refraction-diffraction model. Model to data comparisons have been carried out for the entire basin region including about 3 shoal diameters downwave of the shoal, with satisfactory results. Several physical processes have been identified which lead to possible disparities in the comparisons.

Random sea waves are described by directional spectra which sometimes have bimodal distributions. Frequency spectra are often expressed in standardized forms which contain several parameters. This makes it easy to accumulate and analyze a large number of data obtained in various fields and to specify incident wave conditions in designing practice. In the present study, a method is proposed for estimating directional spectra in the form of a standardized bimodal distribution. The validity of the method is verified by numerical simulation for a three-component array (water surface elevation and horizontal two components of the water particle velocity). Furthermore, several applications to field data are shown.

To investigate the effects of currents on estimations of directional wave spectra, the problems with the existing methods for obtaining directional wave spectra are discussed when they are applied to wave fields in the existence of currents. The characteristics of distortion of the estimated spectra by current effects are examined through numerical simulations and analyses of experimental data. Both the numerical and experimental tests with wave gages, show that the directional spread of estimated spectra becomes narrower than that of the actual wave field and the value of the spectral peak is overestimated for the case of adverse currents. The extent of these distortions depends on the relative speed and direction of the current and waves. The relation of the error and these factors is summarized in the present study.

A method for estimating the directional spectrum as well as the reflection coefficient in a incident and reflected random wave field is developed for practical use. In the method, the directional spectrum is assumed to be expressed by a circular normal distribution which includes three parameters. Then the parameters are estimated by the maximum likelihood method. The present method is applied to laboratory data, and the parameters are estimated for two kinds of wave gauge arrays. A measure of accuracy of the estimated parameters is also proposed.

The development of a control system for active absorption of multidirectional waves is described. The present work is an extension of a two-dimensional flume system to include the wave propagation direction. The hydrodynamic feedback necessary for the active absorption is taken to be the surface elevation measured at each segment of the multidirectional wavemaker. A frequency-direction domain transfer function relating the paddle position to the measured and desired elevations is derived. For practical applications a two-dimensional digital filter is used for a time-space realization of the generation/absorption procedure. Experimental verification is made in a numerical wave tank using a Boundary Element Model. The numerical setup includes a moving boundary representing a segmented wavemaker. This ensures a realistic reproduction of evanescent wave modes, which can be important for the system performance. The numerical tests show that a quasi three-dimensional system consisting of an array of absorbing wavemakers developed for wave flumes is far better than having no active absorption. The present fully three-dimensional absorption system is shown to further reduce spurious reflections to around one third in the examples treated. Although the system is capable of simultaneous wave generation and active absorption, only the absorption ability was used in these preliminary tests.

A wave-averaged model for simulating wave transformation and associated mean flow circulation in coastal regions is presented. To develop the governing equations for wave height, wave setup and mean flow, an analysis method used in turbulent shear flow is adapted where the variables are decomposed into a slowly varying mean flow and a fluctuating residual which includes both wave and turbulent components. The conservation equations of mass, momentum and energy are averaged over a wave period and integrated over water depth. The time-averaging introduces apparent stress- or Reynolds stress-style terms corresponding to the time scale of the wave period.

The difficulty with traditional wave data needed for variety of applications may be overcome by using the large amounts of data collected in recent years by the US Navy Geostationary Satellite (GEOSAT). Global oceanographic information for some 30 oceanographic parameters were recorded every second. These data are processed and disseminated to the user community. Significant wave height measure by an onboard altimeter were calculated as an average of 10 values recorded every second.

Two sets of Boussinesq type equations with high accuracy in dispersion as well as in nonlinearity are presented. The first set, which is expressed in terms of the depth-averaged velocity, includes up to fifth-derivative terms in the momentum equation, while the second set, which is expressed in terms of the velocity at an arbitrary z-level, includes up to third-derivative terms in the continuity equation as well as in the momentum equation. Both sets of equations provide linear dispersion characteristics, which are accurate for wave numbers (kh) up to 6, and nonlinear characteristics which are superior to previous Boussinesq formulations. The high quality of dispersion is also achieved for the Doppler shift in connection with wave-current interaction. A numerical model based on the new equations in two horizontal dimensions is presented and verified with respect to nonlinear transformation of waves in shallow water and refraction-diffraction in deep and shallow water.

Existing Boussinesq models are extended to include the computation of the vertical structure of the horizontal velocity. A time-domain model is tested against laboratory measurements of the vertical profile of the horizontal velocity in regular waves; good results are obtained, especially in the near-bed zone. A spectral model, which includes a dissipation formulation to account for wave breaking, is tested against laboratory measurements of bottom velocities in (partially) breaking irregular waves. For moderately long waves, the comparison on velocity variance and skewness, which are relevant to sediment transport, yields good results.

We investigate the effects mode truncation and dissipation characteristics have on predictions of wave shape statistics such as skewness and asymmetry. We demonstrate the effect of mode truncation by calculating wave shape statistics for data from a laboratory experiment using an increasing number of frequency components each calculation. We find that the values of skewness and asymmetry converge to a maximum as more components are retained, with the maximum values attained when components out to the Nyquist frequency are kept. We run a lowest order Boussinesq shoaling model and a nonlinear dispersive shoaling model with the data, retaining more components with each simulation. Both models show the same convergence characteristics as the data as the number of retained frequency components increases. The lowest order Boussinesq model, despite its shallow water formalism, yields skewness and asymmetry values closer to those of the data than those of the dispersive model. This is likely due to the phase mismatches in the dispersive model, which become large in deep water and thus violate the slowly-varying amplitude assumption. We also investigate the effect of spectral dissipation on these predictions. We run the lowest order Boussinesq shoaling model with different proportions of frequency-dependent dissipation and calculate wave shape statistics. We find that the distribution must take into account some aspect of (f)² variation in the dissipation for reliable wave shape statistics.

Bottom sounding data collected from 1983 to 1993 on the Shizuoka coast were analyzed. The results reveal the existence of a sand body moving downcoast at a velocity of about 233m/yr. It is the first time that this kind of phenomenon was observed in the quantitative sense including the spatial and temporal changes in longitudinal profile of the beaches, and this propagation mode is a very interesting phenomenon. In this study, sand movement shoreward and offshoreward of the detached breakwaters is modeled, and a model to predict successive contour line changes is developed, taking into account of time lag caused by the obstruction effect of longshore sand transport due to the detached breakwater. The new phenomenon observed on the Shizuoka coast is well explained by the present model. The propagation velocity of the sand body reproduced by this model is 230m/yr and it is well in agreement with the field observation value.

Experiments were conducted with regular wave groups incident on a plane beach to analyze the behaviour of the groups in the breaking region and in the surf-zone. The groups were composed of individual cnoidal waves. Emphasis was laid on obtaining measurements in the breaking region and in the surf-zone. It was found that the location of the start of breaking of the individual waves was affected by the groupiness of the waves. The structure of the groups were also seen to be different inside the surf-zone, which changes the forcing for the long wave. The long wave motion is forced at the group frequency and can be resolved into two components, an incident forced wave, which varies along the tank and a free standing wave. The standing wave is generated because the free outgoing long wave is reflected at the wavemaker, where there was no absorption of waves. A conservation model was developed using the kinematic conservation equation and the energy conservation equation. The dispersion relation was used to close the system of equations. Cnoidal theory was used in the shoaling region and bore theory was used in the surf-zone. It was found that the model accurately predicts the group structure and the individual wave location in the shoaling region, but does not do well in the surf-zone.

Propagating nonlinear waves can be computed with a time-domain numerical method based on a boundary element method. For the simulation of propagating wave groups a domain decomposition method is used to increase the efficiency of the model and to enable simulation over many wave periods. In the computations described in this paper several nonlinear formulations for an initial wave group signal are used to investigate their ability to describe a wave group of fixed form. A difficulty consists of the imposition of the boundary conditions at the unknown free-surface elevation. The nonlinear contributions to the first-order signal are related to the generation of free waves as computed by the model.

Results obtained from a laboratory experiment on shear instabilities in wave-driven longshore currents were used to analyse the cross-shore structure of the shear instability induced momentum flux. As the shear instabilities grew in the downstream direction, a significant cross-shore momentum flux occurred. However, the expected changes in the mean longshore current velocity profile were not observed.

A brief review is given of the initial development of two approaches to the modelling of the flow that occurs after a water wave breaks. The first approach aims to model the turbulence generated by a spilling breaker riding on an unsteady wave. The turbulent volume of water in a spiller is modelled as a thin layer.

The second approach is applied to model the region of strong vorticity generated by a plunging breaker. The vorticity is modelled using two-dimensional discrete vortices. The behaviour of both a single vortex and a 'cloud' of vortices near a free surface is described.

This paper presents the formulation and solution of a numerical model for breaking waves on uniform sloping bottoms. The model is based on the two-dimensional vertical (2DV) Reynolds-averaged Navier-Stokes equations. The effect of breaker-generated turbulence is modeled by the Reynolds stress terms in the momentum equations, together with an eddy viscosity model. A transformation technique is utilized to solve numerically the governing equations in a variable grid system. At each time level of computation, it is possible to determine directly the following wave quantities for the surf zone: water surface elevation, pressure field and velocity field. The numerical results are verified with various cases of laboratory data.

Turbulence due to breaking waves is an important factor in the ocean as it has a direct effect on coastal erosion, sediment transport and marine life. The laboratory study of this phenomenon is important to produce controlled simulations of processes that occur at sea, and has mainly consisted of temporal point measurements. In this paper the results obtained from using PIV to study the turbulence in the laboratory are presented. PIV is a spatial technique and yields unique information on the turbulence structure in such a flow. Of particular interest in this paper are the evolution of the wavenumber spectra and the form of the turbulent energy decay with time and space. This is used to characterise the decay of turbulence from 2-d to 3-d. Separation of the turbulence from the mean motion is important and the method used here is justified. The main results and conclusions are compared with other research, with similarities and differences emphasised and discussed.

Traditional depth-limited criteria for design of structures in shallow water were found not to be valid in hydraulic model tests with irregular waves. An extensive series of experiments showed that in addition to the height of the short period waves and the depth at the structure, the design wave height is a function of long wave action and wave setup at the structure. The additional effects are related to incident wave height and they result in an increase in depth at the structure. Thus, a simple design expression was developed by introducing a depth modification into a standard depth-limited design equation.

A time-dependent quasi-3D numerical model is developed to predict the temporal and cross-shore variations of the free surface elevation and fluid velocities in the surf and swash zones under obliquely incident waves. This model, which includes the dispersion due to the vertical variations of the instantaneous horizontal velocities, is an extension of the two-dimensional model of Kobayashi and Karjadi (1994, 1996). The developed model is compared with available laboratory and field data for planar beaches as well as field data for a barred beach. For planar beaches, the dispersion effects on the longshore current are significant for regular waves but secondary for irregular waves. For a barred beach, the model under the assumption of alongshore uniformity cannot predict the broad peak in the longshore current profile. The small alongshore variation of wave setup induced by a small alongshore variation of obliquely incident irregular waves is shown to significantly modify the driving force and longshore current profile in the bar trough region. On the other hand, for planar beaches, the alongshore current profile is shown to be insensitive to the small alongshore variation of obliquely incident waves. This may explain why existing longshore current models based on the assumption of alongshore uniformity were regarded to be adequate before their comparisons with the barred beach data.

Models for wave height and the fraction of breaking waves were developed; the models employ a wave-by-wave approach, in which the shoaling, breaking and reforming of individual waves are calculated. The performance of the models calibrated with experimental data was not satisfied; the fractions of breaking waves estimated by the models were smaller than the values measured over troughs in the field. The models therefore were calibrated and verified with the field data. Furthermore, the validity of the models calibrated with the field data was confirmed by comparison with large-scale experiment data.

The process of wave energy dissipation after breaking has been investigated with a number of random wave tests. To obtain the data for wave breaking and its deformation, experiments have been conducted by utilizing a horizontal step adjoining to a combined slope of 1/20 and 1/10.

After breaking, the wave height decreases by dissipation but attains a certain value at some distance from the breaking point. Experimental results show that the stable wave height is not constant but affected considerably by the wave period. The study has yielded a general formulation of stable wave height due to the random wave breaking.

A new one-dimensional random wave deformation model is proposed, being coupled with nonlinear shoaling coefficient formula before wave breaking and the new energy dissipation term after breaking. The model is compared with the experimental data, large wave tank data, and field data. It predicts well the wave height deformation and the change of mean water level before and after wave breaking on arbitrary bottom profiles.

This study deals with the comfortableness of wave sounds from physiological and psychological aspects. Firstly, the difference of wave sound generation mechanisim between plunging and spilling breakers is discussed on basis of the variation characteristics of sound pressure level and the volume of air bubbles in water. Secondly, the comfortableness of wave sounds is investigated based on the generation characteristics of the brain wave and the result of questionnaire surveys of auditory test.

Many experiments have been carried out on wave breaking in the past, but these have mainly been for regular, normally-incident waves. This paper describes experiments in the UK Coastal Research Facility in which over a hundred separate tests were carried out, covering regular, random, normally-incident, angled and multidirectional waves. Measurements were made of wave parameters as the waves underwent breaking in shallow water on a 1:20 slope. Analysis of the data to determine the wave breaking criterion, γ, for three random wave categories is presented.

Experiments in a wave flume(1m × 2m × 65m) with 16 wave gages and numerical simulations using a fully nonlinear BIM(Boundary Integral Method) in a super-computer(VP2600) are conducted to make clear the characteristics and occurrence condition of a new type breaker. Further, its deformation and wave height decay after breaking are investigated. It is shown that the new type breaker forms a giant jet with the size exceeding three times of the maximum jet size of usual type breakers and therefore is very efficient to wave control because of strong turbulence excited by plunging of the giant jet and the resultant remarkable absorption.

El Niño-Southern Oscillation (ENSO) events are major factors in changing wave climate at coastal sites. These events are triggered by extreme anomalies in the global seasonal climate; and in recent years they have become quasi-predictable from certain antecedent conditions. Judicious application of the global concepts leading to (ENSO) events will improve our understanding and prediction of wave climate.

Design wave heights are estimated for the Atlantic coasts of Southern Africa and the Iberian peninsula using the best available recorded data sets from the more exposed sites along these coasts. By spatial integration of the available data for a region and relaxing conditions with respect to independent sampling, stable estimates of design wave heights are obtained. Clear patterns are found in which the predicted design wave heights are strongly correlated with latitude. The recommendations of the IAHR committee on methods for design wave estimation are discussed and reservations are expressed about their recommendation to use only one method for design wave estimation.

The forecasting of wave conditions in the oceans off Southern Africa is important for both offshore and coastal marine operations in the area. The accuracy of wave forecasts for the area from models operated in Europe has, however, not been high. One of the main reasons is that the local measurement of waves has not been taken into account. Since the necessary infrastructure for operational wave forecasting is locally available in South Africa, a decision has been taken to establish a local facility whereby a numerical wave forecast model will be implemented. This paper focuses on the comparison of two operational wave forecast models in order to assist in the selection of an appropriate model for the South African region.

The South China Sea has been a prolific fishing ground and a busy shipping lane, and has recently become an important source of offshore oil and a center of rapidly growing economic activities. However, little systematic scientific study of the area has been carried out (Anonymous 1985 and Wyrtki 1961). Recently, several Metocean (meteorological and oceanographic) studies were performed to support the offshore petroleum production in the area. This paper summarizes these and other studies, and then, describes a comprehensive Metocean measurement program (Sharma et. el. 1991). Many distinctive and unique features of the measurement program are presented and discussed. Published samples of wind, waves, and current data are used to illustrate the complexity of oceanographic conditions in the area. Economic benefits of the measurement program are estimated approximately and found to be many times the cost of the program. While many important design decisions can be made with the 18 months of data, many other decisions need to be made conservatively in the absence of a multi-year Metocean dataset. A comparison with the condition in the Gulf of Mexico reveals many similarities and some differences. Future data needs and their possible benefits are also discussed briefly.

Both the univariate and joint distributions of the significant wave height (H_s) and the zero-crossing wave period (T_z) are studied using 16 years of hourly wave data measured from five National Data Buoy Center (NDBC) buoy stations. For the univariate distribution, the log-normal distribution fits both the H_s and the T_z well. The modified log-normal distribution proposed by Fang and Hogben (1982) does improve the fit at the high H_s end and at the peak for some stations. For H_s, the Weibull distribution, with parameters computed from the maximum likelihood (ML) method, fits the upper tail of the cumulative distribution; however, it underpredicts both the probability peak and the probability density at the high end. For the joint distribution, the marginal Weibull/conditional log-normal distribution best describes the measured data of the steeper sea states and has the best overall fit.

The purpose of this paper is to investigate the effect of large structures in the vicinity of small structures in the determination of wave forces on the small structures. The structures considered in this study are circular cylinders and analytical expressions are derived. It is shown that if the small cylinders are placed in close proximity of large cylinders (center distance/ caisson radius < 2.0), the wave forces on the small cylinder are largely influenced by the large cylinder.

The development of third generation wave models is needed for a detailed study of wave dynamics and impact at coastal structures. This would require the modelling of wave flows with high distortion of the free surface at confined boundaries. In our opinion, the Volume of fluid method, which uses concepts of local advection of fluid in free surface flow modelling, is the prime candidate for simulating realistic flows at sea defences and walls. In this paper, the numerical techniques for the simulation of waves with highly distorted water/air interfaces at a slope, using the volume of fluid method, are considered.

The significance of oxygen transfer across the air-water interface with its associated impact on water quality and environmental pollution control in coastal zones has become a matter of concern for coastal engineers. In the present paper experimental data on oxygen transfer obtained in the large scale facility of Delft Hydraulics have been presented. The obtained oxygen transfer coefficients have been compared to existing models for gas transfer under breaking and non breaking waves. Scale effects are found to be an important factor which needs to be considered when laboratory results are translated to field conditions.

The wave actions on a vertical cylinder in multi-directional random waves are experimentally studied in this paper. The two-dimensional (2-D) wave method is extended to calculate the three-dimensional (3-D) wave forces. The variation of various hydrodynamic coefficients with KC number and wave directional spreading are investigated. The three-dimensional wave forces are compared with that of two-dimensional waves.

The S.M.B. prediction model is used worldwide to hindcast sea wave characteristics using wind data. Even though wave parameters showed that qualitative similarities are present between ocean and small basin waves, major weather factors such as the wind speed and barometer pressure gradients in relation with the topography should be considered as calibration factors.

In the hydraulic model test in a wave basin, reflected waves from models of structures and walls of the basin reflect again at the wave maker. The re-reflected waves disturb wave field in the basin and consequently reduce the accuracy of experiments. We developed a non-reflected multi directional wave maker theory. By taking into account both current and past water elevation data in front of the wave paddles, the theory makes the wave makers possible to absorb reflected multi directional waves. Numerical simulations and experiments show that this theory is superior to the conventional theory in its efficiency of the absorption.

It has been over fifty years since the public release of the well-known monograph of Navy H.O. 601, prepared by Sverdrup and Munk (1947) during World War II. In celebrating 50th anniversary of the International Coastal Engineering Conference that was started in 1948, it is of interest to revisit the wave growth curves developed in H.O. 601 and compare them with a recent study on wave growth curves (Donelan et al. 1992). It is clear that while significant progress has been made over the last 50 years, Sverdrup and Munk’s original idea still prevails in light of modern developments.

A numerical third-generation wave model dedicated both to deep water and near-shore applications is presented and applied to several test-cases to highlight its capabilities. Among its main features, this model uses a finite-elements technique for the discretization of the modelled area, which makes it suitable to represent complex bottom topographies and irregular shorelines. Furthermore, the piece-wise ray method used for wave propagation allows to use rather large time-steps, which in turn allows to keep the computational time at a very moderate level. The implementation of shallow-water physics in the model is also described, in particular with respect to depth-induced breaking. Several applications of the model are presented and compared to field or laboratory data for their validation. Finally, the main research and development items are mentioned and discussed.

Uniformity of monochromatic oblique waves in a wave basin is investigated. A new method, using non-linear least square formulation, to determine individual wave paddle motions of multi-directional wavemaker to improve uniformity, is proposed. The possibilities and limitations of the method are discussed. Trial computations and comparisons with experiments demonstrate the validity and usefulness of the method.

Generation of second-order long waves at a wave maker by non-periodic wave group is analyzed in time series by Mizuguchi (1995). The analysis, which include a way to control the long wave generation, is briefly described. Then confirmation by using a single wave packet is successfully undertaken both in numerical simulation by Boussinesq equation and in laboratory experiment.

The present paper concerns the description of extreme waves in shallow water, and in particular contrasts the success of two recently developed wave theories (Sobey, 1992 and Baldock and Swan, 1994) to model the maximum water particle velocities arising beneath a highly nonlinear and transient (or unsteady) wave event. To achieve these comparisons exact numerical calculations were undertaken using the lime-stepping procedure outlined by Dold and Peregrine (1984). Comparisons between this numerical “data” and the kinematics models confirm the importance of both the non-linearity and the unsteadiness, and further suggest that the nature of the wave-wave interactions has important implications for the accuracy of the kinematics predictions. In particular, the local Fourier series solution (Sobey, 1992) is shown to be unable to model the global wave frequency-difference terms, and therefore tends to over-predict the fluid velocities beneath the still water level. In contrast, the double Fourier series solution (Baldock and Swan, 1994) explicitly incorporates both the nonlinearity and the unsteadiness of the wave, and typically provides a good description of the flow field beneath the still water level. However, this solution is limited in terms of the total number of Fourier components included, and consequently the largest velocities arising close to the water surface are typically under-predicted in the largest wave events. Nevertheless, both kinematics models provide a significant improvement over the existing design solutions.

The results of a field experiment aimed at investigating the evolution of fetch limited waves in water of finite depth are presented. In particular, non-dimensional growth curves, the parametric form of the one dimensional spectrum and the directional spreading of the spectrum are investigated.

Particle Image Velocimetry (PIV) has been proven to be a powerful tool for two-dimensional instantaneous velocity measurement. Tens to hundreds of velocity measurements using the Laser Doppler Velocimetry (LDV) can be done in one single measurement using the PIV. The LDV is the most common tool for non-intrusive velocity measurements. By using the LDV and the phase average method, hundreds of points were measured under a plunging breaker on sloping beaches. The flow fields of the mean and the turbulence velocity were formed and the vorticity were calculated. Turbulent structures in surf zone were also studied using either the phase-averaged method or the moving-averaged method and the differences between these two methods were demonstrated.

Two practical formulations from Isobe and Horikawa (1982) and Swart and Crowley (1988) are tested against laboratory measurements: seven cases with monochromatic waves and two cases with random waves. It appears that the Isobe and Horikawa formulation can be used with confidence over a large range of wave conditions except in the surf zone when monochromatic waves are considered. The covocoïdal theory from Swart and Crowley provides a more comprehensive description of wave properties but abnormal results have been noticed in a few cases. The use of one representative wave height and period in random waves may lead to an underestimation of velocity moments with low steepness waves.

A numerical model is developed to predict the time-dependent, two-dimensional velocity field under normally incident breaking waves on beaches and coastal structures. Use is made of the depth-integrated continuity and horizontal momentum equations, where the momentum equation includes the momentum flux correction due to the vertical variation of the horizontal velocity. The third equation for the momentum flux correction is derived from the depth-integrated wave energy equation together with a cubic horizontal velocity profile. The three equations are solved using the MacCormack finite difference method. The quasi two-dimensional model is compared with two laboratory data sets and is found to predict the vertical variation of the horizontal velocity measured below the trough reasonably well. However, the energy dissipation in the model is primarily numerical for breaking waves on gentle slopes despite the explicitly modeled energy dissipation due to wave breaking.

In offshore and ocean engineering it is often of interest to be able to model particle velocities in the so-called splash zone, in which during a wave cycle, a given point is sometimes submerged, sometimes in air. (Emergence effects.) This paper applies the so-called Gerstner wave theory, extends it to narrow banded irregular waves, and presents it in an Eulerian description to second order in wave amplitude, so that the results may be compared with measurements made at fixed positions in the fluid. Mean horizontal velocities have been determined, and shown to compare excellently to laboratory measurements, both for regular and irregular waves. At this point in time, it can not be said whether the fit will be equally good in real ocean waves.

A comparison of a range of wave pressure analysis methods has been conducted using both numerical data generated by a Fourier steady wave method and experimental data gathered in a wave flume. The results show that the local methods (local sinusoid approximations and local polynomial approximations) are more accurate than the traditional global linear spectral method. A new local polynomial approximation method shows improvement compared to similar methods developed previously.

Employing the Hamitonian theory, the canonical equations of water waves is used to derive a nonlinear model. In this paper, a unified non-linear model for water wave propagation is presented. This model can be simplified to the mild-slope equation in the linear case. It is consistent with Stokes wave theory when water depth is deep and reduces to an equation of Boussinesq’s type in shallow waters. Results of numerical computations of nonlinear water waves propagating over a submerged bar and a rectangular step are also presented in one-dimensional case. Nonlinear behaviors of water waves are captured, but further works are needed.

For the two-dimensional case of waves normally incident on a beach, a variety of techniques have recorded velocities in surf zone flows. Tracer techniques incorporating particles and film are used to provide significant qualitative information, but it generally suffers from poor spatial resolution and generally provides Lagrangian information where an Eulerian perspective is desirable. Recently, several investigators have employed velocity measurement using laser Doppler anemometry (LDA). Early significant data sets using this technique in the surf zone was discussed. LDA offers very high precision and spatial resolution.

Throughout the history of society’s attempts to build on the beach, waves have been the principal antagonist. Engineers soon learned that to be successful, they had to understand the nature of the waves that attacked their structures. That understanding has led to many efforts to measure or estimate waves to develop a climatology useful in coastal design.

Over the past 25 years, our ability to accurately and cost-effectively measure waves has improved considerably. This has resulted in an increasing number of gauging networks worldwide. This paper is a summary of many of those networks. Information on the networks will include, where available, the type gauges used, locations of stations, additional data collected, and data distribution means.

This paper presents an improved submerged Doppler-type directional wave meter which has the capability of measuring water surface elevations and multiple current velocity components. These components are determined from Doppler frequency shifts of ultrasonic waves in water. The improved system has proven to be capable of successfully obtaining tide, current and directional wave data. In addition, this directional wave meter has accurately estimated directional wave spectra in severe sea conditions with the use of some techniques introduced in this paper.

A simple criterion was derived for evaluation and comparison of directional wave data quality from two underwater measuring systems – a point gage system consisting of a pressure transducer and a bi-axial current meter (PUV gage), and a slope array consisting of four pressure transducers. By using this criterion to the measured field data, it was demonstrated that directional wave data analyzed from PUV gage contain absolutely better quality than those from pressure array gages. Further examination of the pressure array data alone showed that the resolved directional wave quality was worser for long waves than short waves. However, the flaw of directional wave data quality from pressure array gages can be mended by forcing simple linear corrections on the analyzed directional data with a maximal tolerance to the criterion introduced in the present study.

This paper presents the method for the digital simulation of the second-order nonlinear random waves including strongly nonlinear shallow water waves and near breaking waves, which can be considered to be non-Gaussian random process. The method generates time series of the second order nonlinear random waves from the given energy spectrum and bispectrum obtained from the wave records. Numerical examples indicate that the procedure is basically worked well and generated time series of waves having the similar target spectral density function and probability distribution function. The proposed method has a wide range of applicability to problems involving the second-order nonlinear systems where outputs have strongly nonlinear and non-Gaussian characteristics.

The numerical model SWAN (Simulating WAves Nearshore) for the computation of wave conditions in shallow water with ambient currents is briefly described. The model is based on a fully spectral representation of the action balance equation with all physical processes modelled explicitly. No a priori limitations are imposed on the spectral evolution. This makes the model a third-generation model. In Holthuijsen et al. (1993) and Ris et al. (1994) test cases for propagation, generation and dissipation have been shown without currents. Current effects have now been added and academic cases are shown here. The model is also applied in a fairly academic case of a shallow lake (Lake George, Australia) and in a complex, realistic case of an inter-tidal area with currents (Friesche Zeegat, the Netherlands). The results are compared with observations. A new development to formulate the model on a curvi-linear grid to accommodate linkage to hydro-dynamic circulation models is presented and a first test is shown.

It is shown that by determining wave group back tracks for recorded data it is possible to determine whether the waves were generated in deep, intermediate, or shallow water depths. The general movement of a storm can be tracked if a storm moves through water of intermediate depths. For the examples shown reasonable results were obtained by approximating the geometric group velocity by the conventional group velocity.

Wave climate parameters are estimated in a coastal area in the South Aegean Sea with the use of wave hindcast, wave transformation and spectral transformation models. The relative performance of these models is judged with the aid of a field measurements campaign. It is shown that most models can give the correct prediction in the intermediate depth waters, whereas only models taking into account nonlinear phenomena can match the measurements in the very shallow water area.

In this paper the development of a parametric transformation linking the meteorological conditions with the sea response for the Irish Sea and the southern North Sea regions is presented. The method of empirical orthogonal functions and system identification procedures are used to develop the parameterization. The reference data sets used in the investigation consist of high quality hindcast data (41 storm events) and field measurements (13 years) covering meteorological and sea state parameters. The method of empirical orthogonal functions is applied to the wind velocity field and it is shown that the wind field time history can be adequately represented by the first few principal components. These wind field principal components together with atmospheric pressure parameters are used to synthesise the meteorological input for system identification. The system identification procedures are then applied to develop a new efficient form of parametric model linking spatial meteorological data with sea state response.

Shoaling of finite amplitude periodic waves over a sloping bottom is calculated in a numerical wave tank which combines: (i) a Boundary Element Model to solve Fully Nonlinear Potential Flow (FNPF) equations; (ii) an exact generation of zero-mass-flux Streamfunction Waves at the deeper water extremity; and (iii) an Absorbing Beach (AB) at the far end of the tank, which features both free surface absorption (through applying an external pressure) and lateral active absorption (using a piston-like condition). A feedback mechanism adaptively calibrates the beach absorption coefficient, as a function of time, to absorb the period-averaged energy of incident waves.

Shoaling of periodic waves of various heights and periods is modeled over 1:35, 1:50, and 1:70 slopes (both plane and natural), up to very close to the breaking point. Due to the low reflection from both the slope and the AB, a quasi-steady state is soon reached in the tank for which local and integral properties of shoaling waves are calculated (K_s, c, H/h, kH, η_m, S_xx, …). Comparisons are made with classical wave theories and observed differences are discussed. Parameters providing an almost one-to-one relationship with relative depth kh in the shoaling region are identified. These could be used to solve the so-called depth-inversion problem.

Small irregular water depth variations may cause relatively large variations of the wave field, which may affect the results of various water wave models. Statistical properties of depth variation are obtained from real bathymetry and idealized water depths are generated to study this influence on wave fields. An angular spectral model and a parabolic model are examined for their sensitivity to depth variations. It is shown that diffraction and nonlinear effects are dominant to the wave energy scattering. Correlation functions, especially correlation lengths, play an important role in the wave field variation.

In the present study a technique for assimilating observed wave data in numerical wave predictions is developed that exploits (a) the efficiency of a limited number of integral control variables and (b) the effectiveness of variational (model-consistent) assimilation. The formal procedure is independent of the type of control variables and of the wave model. The integral control variables in this study are chosen to represent large-scale errors in the driving wind fields and uncertainties in the wave model. The assimilation technique is validated with observations of the ERS-1 satellite altimeter and two waverider buoys in two consecutive storms in the Norwegian Sea. The assimilation of the observations reduced the errors in the predicted significant wave height at the buoy locations typically from 25% to 15%. The technique is also demonstrated with an simulation of swell prediction in the Indian Ocean based on simulated buoy data and satellite data.

The method for determining coefficients in the rational approximation is improved and a numerical method is developed for application of time-dependent mild-slope equation for random waves to two-dimensional wave fields. The validity of the method is verified through comparisons with analytical solutions in typical situations and an experimental result of wave transformation around man-made island on a uniform slope.

A nonlinear model of wave transformation due to a submerged breakwater is developed on the basis of the nonlinear mild-slope equations. Numerical computation shows that significant amount of wave energy can be transferred from the fundamental component to higher harmonics by adjusting configuration of the submerged breakwater. In case of oblique incidence, wave direction as well as wave period changes due to the breakwater. These results implies the possibility to control wave period and direction as well as wave height.

Wave conditions in hurricanes have been difficult to study because of a lack of high-quality wave data and poor descriptions of the wind field. In the 1994 and 1995 hurricane seasons, two Category 1 hurricanes (Gordon and Felix) approached the North Carolina coast and stalled for a period of about 2 days. Although the storms were minimal hurricanes they produced large swell that persisted for several days. A wave gauging network of two to five directional instruments in water depths ranging from 8 to 50 m operated throughout the storms. Because of their proximity to land, both storms were extensively observed by radar and aircraft so that the wind fields are well described. The data set offers an opportunity to evaluate two prediction methods to examine the wave field during these most unusual hurricanes.

The NMI method proposed by Kuwashima and Hogben (1986) for estimating the wave persistence statistics and Mathiesen’s Model (1994) which was expected to develop the NMI method were applied to the wave data observed at four sites at Japanese coast to investigate the validity of the models. Mathiesen’s model was found not to be superior to NMI method. We show the modification of the NMI parameters based on the data improve the accuracy of the estimated persistence statistics.

Utilizing eight years of wave measurements from the U.S. Army Corps of Engineers Field Research Facility (FRF), this study develops a long-term probabilistic model for the energy-based significant wave height (H_mo) based on the shifted gamma distribution. The method of moments is used in best-fit model parameter estimation. Shifted gamma distributions are developed for the entire eight years of H_mo data, as well as for the individual years in the data set. The shifted gamma distribution represents the FRF H_mo data for both the total and yearly data sets. Further, the distribution which represents the total, or long-term, data also effectively models the yearly data, indicating that the shifted gamma distribution is a useful engineering tool for predicting long-term wave climate.

To develop the nearshore wave condition in Southern California, six meteorological weather patterns including extratropical cyclones of the northern hemisphere, northwest winds in the outer coastal waters, west to northwest local sea, pre-frontal local sea, tropical storm swell and extratropical cyclones of the southern hemisphere were identified and classified. Wave characteristics in deep water, corresponding to the categorized weather patterns, were computed and then transferred to the nearshore target sites via a spectral back-refraction transformation model. A Monte Carlo simulation technique was applied to generate a synoptic atlas of the nearshore wave climate in this region.

The effect of bottom friction dissipation and of the different formulations used for this term on the wave evolution has been investigated in the Belgian coastal regions. Two eddy viscosity models for the bottom friction dissipation, the Madsen et al. (1988) model and Weber's (1991a) model have been implemented in the Cycle 4 version of the third generation WAM model (Günther et al., 1992). The wave conditions for the area of the southern North Sea were hindcasted for the February 1993 storm. The results are compared with buoy data. It is found that the net effect of bottom friction dissipation on the significant wave height hindcast is quite big, in the order of 80% (of the wave height when the bottom frictiion dissipation is taken into account) along the Belgian coast. Different formulations for the bottom friction dissipation have a quite significant effect on wave evolution in storm conditions. The use of equivalent dissipation coefficients (Luo et al., 1994) results in nearly identical wave hindcasts.

The wave height distribution with Edgeworth's form of a cumulative expansion of probability density function (PDF) of surface elevation are investigated. The results show that a non-Gaussian model of wave height distribution reasonably agrees with experimental data. It is discussed that the fourth order moment (kurtosis) of water surface elevation corresponds to the first order nonlinear correction of wave heights and is related with wave grouping.

In this paper, a prediction method based on the chaos theory is applied to wave forecasting. First, it is investigated whether a time series data of the significant wave is chaotic. The correlation integral and the Lyapunov exponent are calculated for this purpose. In the second part of the paper, the prediction for the time series of the significant wave is attempted on the basis of the chaos theory.

The purpose of this paper is twofold. The first is to clarify the transition of stochastic characteristics of waves; in particular, the transition from a Gaussian to non-Gaussian random process in the nearshore zone as a function of water depth and sea severity, and the second is to develop a method to estimate the non-Gaussian properties of waves at a specified water depth in the nearshore zone from knowledge of the sea severity in deep water. The probability density function applicable to non-Gaussian waves in finite water depth is applied to more than 1,000 samples of wave data obtained by the Coastal Engineering Research Center, U.S. Army, during the ARSLOE Project. From analysis of the data, the limiting water depth is defined below which wind-generated waves can no longer be considered Gaussian for a given sea severity. Furthermore, by presenting the parameters of the probability density function as a function of water depth and sea severity, it is possible to estimate the sea condition at a specified water depth in the nearshore zone from knowledge of sea severity in deep water.

Physical modelling with 3-D basins have mainly been used in relation with wind wave propagation, which input are irregular and multidirectional trains obtained from a directional system in the prototype, to test harbour structures. Very few applications are been developed to test the spectral propagation over a beach from deep waters to surf zone neither to study the relationship between spectral directional characteristic of time series obtained in prototype and in the basin. The aim of this study has been the study of the propagation of real data obtained in El Saler beach along the beach slope towards the bar and compare these results with real data, employing the 3-D basin, with the real beach profile. These data have been obtained from the Monitoring Campaign developed by CEDEX, partially sponsored by the contract MAST2, CT92-0027, G8M project, on El Saler Beach.

Based on statistical analysis of extreme wave height data generated with a Monte-Carlo simulation technique for the prescribed parent probability distributions, a preferable method for the parameter estimation was determined for each of 8 distributions. It is also verified that a jackknife method is applicable to the correction of bias and the estimation of variance irrespective of parameter estimation method in most parent distributions, and that the information matrix methods inherent to the maximum likelihood method give generally satisfactory results in the estimation of variance of return wave height for samples of size greater than around 50.

Random wave fields were generated both numerically using a computer algorithm, and mechanically through a computer-controlled irregular wave generator. Statistical properties of these synthesized random waves are then compared with measured field results. It is shown that, irrespective of the methodology used, wave heights obtained from simulation always have a Rayleigh distribution, and surface elevations are approximately normally distributed, measured field data can, however, show other trend for the former with a large percentage of possibility.

A numerical method to solve the second-order interaction between a multi-component random wave and a submerged obstacle is presented by using Stokes’ wave expansion and Green’s second identity. The wave is unidirectional random wave, but nonlinear interaction up to the second-order is strictly considered. Laboratory experiments with several multicomponent random waves for several different wave powers are conducted. The transmitted wave spectra obtained both in the experiment and in the numerical calculation are compared. The effects of wave breaking on the obstacle to the transmitted wave spectra are also investigated.

A time-dependent mild-slope equation is derived, based on the formal derivation of Smith & Sprinks (1975), from which the higher-order dispersion relation for waves over uneven bottom is obtained. If only linear dispersion is used for steady waves, the equation (2.12) of Chamberlain & Porter (1995), referred as the modified mild-slope equation (MMSE), is recovered from this equation. To the leading-order solution, it is found that the modified curvature terms of the MMSE have significant effects, while the slope square terms are negligible in accordance with mild-slope assumption. Therefore, retaining all the modified curvature terms neglected in the MSE, the uniform model is developed.

A numerical model using the finite element method (FEM) is developed to predict wave scattering by a varying bottom. In general, the uniform model can predict salient features of waves over various sea beds, such as sinusoidal beds and man-made bars. For sinusoidal beds, the results of the uniform model are in closer agreement with the experimental data than other established models. For man-made bars, the results of both the MMSE and uniform model are in closer agreement with the experimental data than the results of Kirby (1986). An important result of the FEM model is application to transformation of waves over arbitrarily-varying bathymetry.

In this study a set of governing equations describing the evolution of modulated shallow-water waves over a sinusoidally varying topography on a sloping beach is derived. The governing equations include the nonlinear interactions among different wave components as well as the shoaling effect over a slowly varying topography. It has been shown that the incident waves could be resonantly reflected by the interaction with the rippled seabed under the Bragg reflection condition. The magnitude of the resonantly reflected wave is almost equal to those of the incident and the transmitted waves.

During physical model tests in a wave flume an accurate determination of the incident waves is crucial. Normally, the determination of the incident waves is conducted by a traditional reflection analysis and in this case the influence of any cross modes is ignored. The present paper concerns the advantage of including the possible presence of cross modal activity in the reflection analysis when determining the incident waves. It is shown both analytically and numerically how the cross modes affect the results of a traditional reflection analysis, and that ignoring cross modal activity can lead to an inaccurate determination of the incident waves. A new method is introduced where the cross modes are separated in the reflection analysis. This method requires at least three wave probes while a traditional reflection analyses only requires two wave probes. The applicability of the method is verified both numerically and by physical flume tests at the Hydraulic Laboratory of Aalborg University, Denmark. In both cases the new method seems to give very good results.

Runup on beaches is an important topic in coastal engineering because it defines the upper limit of direct wave influence on land. It is also a phenomenon that has proved very difficult to analyze and characterize in a quantitative manner. The reason for this difficulty is the more general problem of understanding the response of beaches to waves. This paper develops formulas to estimate the approximate upper limit of wave runup on sand and gravel beaches. The relationship between these formulas and recent progress in quantifying beach profile response to waves and the morphodynamics of beaches is discussed. It was found that estimates of wave runup on sand beaches could be improved if sediment sizes in both swash zone and surf zone are known.

This paper deals with a comprehensive field research program on wave runup, which is ongoing at different locations at the landside borders of the Wadden sea (tidal flats) and the tidal estuaries of the German Bight since 1991. The field measurement equipment is described and an overview about first results is given.

The paper deals with wave run-up on revetments and seadykes with composite slopes. The presented data were obtained from large scale laboratory tests with different wave climate characteristics in the "Large Wave Channel" (GWK) at Hannover, Germany. The results are discussed with respect to slope angle transformation mode to be used in the well-known HUNT-formula.

A landward transport process of spray generated from a wave absorbing sea wall under a strong wind has been investigated experimentally. Near the wall, the concentration of spray decays exponentially both in the leeward direction and in the upward direction. The profiles are determined by the equilibrium between the advection of spray and the sedimentation. The characteristic quantities on the profiles have been related to the experimental parameters.

A local Fourier approximation method is presented for the prediction of the complete kinematics of irregular waves from a submerged pressure trace. The method seeks a potential function and local water surface elevation that fit the pressure record and the full nonlinear free surface boundary conditions very closely in a small window in time. The result is a complete prediction of the kinematics of the waves throughout the water column that satisfies the complete nonlinear equations for irrotational gravity waves. Comparisons with the predictions of steady wave theory are excellent.

A nonlinear dispersive wave model recently introduced by the authors is used for sample simulations of directional wave transformations over gently varying depths. Various forms of the generic equation are presented first, and the dispersion and nonlinear characteristics of the model are investigated analytically. Following the numerical descriptions, the experimental data for linear wave propagation over a circular shoal and for nonlinear wave propagation over a topographical lens are compared to the model predictions with satisfactory agreements. Finally, as a demonstration of the unified character of the model, the unidirectional version of the wave equation is implemented for simulating the gradual transformation of an initially second-order Stokes wave train over decreasing depth into a cnoidal wave train.

Boussinesq-type equations with improved dispersion characteristics for the combined motion of waves and currents are introduced. The ambient current is assumed to be uniform over depth and to have a magnitude as large as the shallow water wave celerity, allowing for the consideration of wave blocking of fairly long waves. The temporal variation of the current is ignored, while the spatial variation is assumed to vary on a larger scale than the wave-length scale. Boussinesq-type equations are derived by explicit use of four scales ν, Δ, ε and μ representing the particle velocity and the surface elevation of the total wave-current motion, as well as the wave-nonlinearity and the wave-dispersion, respectively. Firstly, equations are derived in terms of the depth-averaged velocity to obtain a generalization of the equations of Yoon & Liu (1989) to allow for stronger currents. Secondly, these equations are formulated in terms of the velocity variable at an arbitrary z-location resulting in an improved dispersion relation which corresponds to a Padé [2,2] expansion in the wave number of the squared intrinsic celerity for the fully dispersive linear theory. For vanishing currents, these equations reduce to the equations of Nwogu (1993). Finally, this formulation is enhanced to achieve Padé [4,4] dispersion characteristics. Model results for monochromatic and bichromatic waves being fully or partly blocked by opposing currents are given and the results are shown to be in reasonable agreement with theoretical calculations based on the wave-action principle.

Short waves in a channel can present navigational problems and may excite harbor oscillations. Channel sidewalls may reduce much of this wave energy, if they are sufficiently porous or they are sloped. Previously we presented a model for wave propagation in prismatic channels of arbitrary cross-section utilizing a numerical eigenfunction expansion. Here a series of small scale laboratory experiments were conducted to verify the numerical model. Comparisons of the numerical model to the experimental data are made for water surface profile and for eigenfunctions. The possibility of resonance between the edge wave and the second harmonic of the incident wave is also studied.

The feasibility of a statistical approach to model the effect of triad interactions on the evolution of wave spectrum is investigated. The approach is based on the Zakharov kinetic integral for resonant triad interactions in capillary gravity waves. For application to dispersive gravity waves, the kinetic integral is modified by inclusion of a spectral filter (smeared delta function), to allow for the cross-spectral energy transfers in dispersive wavefields, with bandwidth to be determined empirically. Numerical investigation of the resulting expression indicates that the energy flux from the spectral peak region toward higher harmonics increases with decreasing water depth.

The interaction integral has been cast into an energy source/sink term and implemented in an energy balance equation that describes the evolution of a unidirectional energy spectrum in shoaling regions. The evolution model is investigated using observations of harmonic generation. Qualitatively the comparisons have shown the ability of the model to generate higher harmonics and a consequent upward shift in the mean frequency. However, quantitatively the model performance needs improvement.

A method that is valid for three dimensional fluid motion is developed. The velocity potential is represented in the vertical by a polynomial of arbitrary degree and a set of differential equations results for a local polynomial approximation (LPA) to the exact solution. The simplicity of the formulation simplifies the changing of the level of approximation, and thus the accuracy of the method. Computations over varying topography showed good accuracy for highly unsteady, nonlinear cases. The LPA proved to be an excellent tool for accurate flow computations in three dimensions.

A fully nonlinear Boussinesq-type model with dispersion accurate to O((kh)⁴) is derived. As an extension to the second order extended model proposed by Nwogu (1993), a new dependent variable is defined as a weighted average between the velocity potential at two distinct water depths to force the model to have a (4,4) Padé approximation of the exact dispersion relationship. The present model is similar to the fully nonlinear extension of Nwogu’s model proposed by Wei et al (1995), except that the dependent variable is expanded in a fourth (rather than second) order polynomial in the vertical coordinate.

Accurate nonlinear numerical methods for wave propagation have existed for some years. Most of these are very demanding of computer resources as they use global means of approximation which usually requires the costly solution of a full matrix equation at each time step. It is the aim of the present paper to describe and to compare the features of two new methods for the two-dimensional propagation of nonlinear waves over varying topography. A method based on local polynomial approximation is presented, which was found to be efficient, cheap and accurate. A novel boundary integral method is also presented, which was capable of good accuracy even for waves which overturned. For practical purposes, the local polynomial approximation method is to be preferred and may have some useful contributions to make.

We consider the form of a breaking wave dissipation term for use in spectral or stochastic wave evolution models. A time-domain Boussinesq model is tested for accuracy in modelling evolution of second and third moment statistics in shoaling and breaking waves. The structure of the dissipation term in the time domain is then used to infer the corresponding structure of the term in the frequency domain. In general, we find that the dissipation coefficient is distributed like 1/S_η(f), where S_η(f) is the spectral density of the surface displacement η. This implies an f² dependence for the coefficient in the inner surfzone, as opposed to a constant distribution over frequency as suggested by Eldeberky and Battjes (1996).

Evolution equations for nonlinear long waves are considered from an approximation to the exact Hamiltonian (total energy) for the water waves. The approximation which is used here has two distinct advantages over many other formulations which are commonly used for the same purpose. Further, a variation of these evolution equations is considered in order to incorporate higher-order nonlinearity. Numerical solutions of the evolution equations have been carried out for both the systems. Application of these models is illustrated in some practical cases. Comparisons between experimental measurements and computed results show that the model can be used for satisfactory prediction of nonlinear transformation of non-breaking waves over varying depth. Two features for further investigation are: (i) inclusion of both short-wave and long-wave nonlinearity so that the model can be used with uniform validity from deep to shallow water and (ii) modifications of the evolution equations so that they can be applied to propagation of breaking waves in a robust way.

The wave-induced shear stresses, which result from the correlation between horizontal and vertical components of the oscillatory velocity after time-averaging the horizontal momentum balance equations, are shown in this paper to play an important role in vertical circulation analysis, having the same order of magnitude than other wave-induced (normal) stresses. The model of Rivero and Arcilla (1995) to calculate the wave-induced shear stress for a 2DV situation, based on a mathematical identity that relates this stress to the wave-induced normal stresses and the oscillatory vorticity, is now extended to a general 3D flow. The consequences of neglecting the wave-induced shear stresses are shown to be an overprediction of the waves effect on the description of the vertical profiles of the mean (current) velocity. Theoretical examples of such effects are presented and discussed for some simplified situations (the undertow and longshore current vertical profiles).

In this paper we shall study and model various nonlinear interaction processes in the surf zone on the basis of a two-dimensional time-domain depth-integrated Boussinesq type model, which features the possibility of wave breaking and a moving boundary at the shoreline. Phenomena to be studied include breaking and runup of bicromatic wave groups on gentle slopes with emphasis on the evolution of surface elevations, the shoreline motion and the low frequency waves generated and released in the surf zone. The model results are compared with laboratory experiments by Mase (1994), and the agreement is generally found to be very good. Special details in the surf beats are investigated, e.g. the motion of the breaker line and of the shoreline, change of wave group modulation through the surf zone, and the sensitivity of surf beats to group frequency, modulation rate and bottom slope.

The paper describes a breaking wave model based on the classical assumptions for long, moderately nonlinear Boussinesq waves. It is shown that wave breaking can be described by accounting for the effect of vorticity generated by the breaking process. This leads to two additional terms in the momentum equation, both of which represent the enhancement of the momentum flux associated with the extra particle velocities found at and around the turbulent front of the breaking waves. In addition to the wave height decay and profile deformation predicted by earlier breaker models, the present model also provides information about particle velocity profiles including the undertow. Comparisons are made to measurements for these quantities. The similarities and differences between various breaker models are also examined and explained.

Two independent approaches are discussed whereby inverse modelling is employed as a means of better quantifying roller contributions in the near shore. A so-called integral approach utilizes a coupling between the extended wave energy and momentum balance equations to make inferences regarding roller properties based on wave height and set up measurements. In a somewhat more indirect inverse modelling approach, as first discussed in Mocke et al. (1994), the roller properties are obtained from predicted vertical distributions of internal flow properties such as turbulent kinetic energy, suspended sediment concentrations and undertow velocities which are optimally fitted against measured profiles. An intercomparison between the two approaches is made to get an indication of the validity of the applied theories and inverse modelling techniques. The integral approach further serves to evaluate a new conceptual model for dissipation due to wave breaking.

Laboratory experiments were conducted in a flume to study wave-current interaction at the entrance to an inlet. Regular and irregular waves were studied with and without ebb and flood currents. These data are being used to develop a parameterization of the wave breaking criterion in the presence of currents in inlets, provide guidance to the field on the effects of currents on waves, and improve the predictive capability of numerical models for enhancing navigation in inlets.

Since impounding of the various reservoirs of the La Grande Complex in northern Quebec, the riprap of several dams and dykes has suffered some damage during the fifteen-year period that followed. A mandate was given to the Societe d'energie de la Baie James (SEBJ) in January 1992 to review the riprap design and evaluate the necessary repairs. This paper focuses on the revaluation of the design wave with revised wave hindcast formulas based on the large amount of wind and wave data collected.

Waves travelling against an increasing opposing current tend to dissipate energy and part of the energy reflects back (in blocking conditions). The kinematic behaviour of these waves can be approximated with the linear theory for surface gravity waves. This theory has been implemented for random, short-crested waves in the third-generation wave model SWAN with numerical schemes that are fully implicit. Ad hoc assumptions that are made in other, similar models for blocking conditions are therefore not required and the model is consistent with the underlying theory. To represent the dissipation of the breaking waves in these blocking conditions, the pulse-based model of Hasselmann (1974) as adapted by Komen et al. (1984) has been chosen. Computations have been compared with the flume observations of Lai et al. (1989) in which random waves are blocked with violent breaking by an increasing counter current in relatively deep water. The computations underestimate the dissipation considerably but the addition of the bore-based model of Battjes and Janssen (1978) for steep, breaking waves in deep water improves the agreement with the observations significantly although some discrepancy remains.

Various sources of uncertainties contributing to the difficulties in the validation of harbor wave models with field measurements are discussed in this paper. Some aspects of a new theoretical formulation for removing these uncertainties for estimates of waves in harbors are presented. Implementation of the new formulation is illustrated for waves incident on a planar beach by comparing numerical model predictions to the closed-form analytical solution for normal incident waves and to the results from an one-dimensional Helmholtz equation for oblique waves.

A series of simultaneous field measurements for long and short-period waves under storm and calm wave conditions were made to understand harbor resonances in a partially enclosed harbor. During storm condition the frequency spectra show peaks of considerable magnitude around the wave period of 1 ~ 5 minutes, which are bounded long waves and their harmonics. They are strongly related with storm waves but longer period (free long) waves are not in the harbor. Numerical tests were also carried out by using the hybrid element model including entrance separation losses in a simple rectangular harbor to validate the model for a mostly constricted entrance case. Further the model was used to simulate the long period oscillation in Muko harbor. Comparisons were made between field data and numerical results to discuss the effect of storm waves on the long period oscillations. Tests demonstrate the effect of input parameters on model results and proper choice of them are stressed.

A wave resonator, which has a comparatively wide opening and still keeps effectiveness for a wider range of wave frequency, is newly developed based on the Wave Filter Theory. Applying this resonator both to a long channel and a harbor entrance, the sheltering effect for incoming waves was examined by the numerical and physical experiments. It was confirmed that the Wave Filter theory is very effective to design a wave resonator for required conditions, such as an effective band width of wave frequency.

The response of Skagway Harbor to wave events after a landslide is reported. A harbor response model is developed for the moored-floating docks response to incident waves and the parting of the mooring chains observed at Skagway. An impulsive wave generated by a simple motion of a section of the coast induced groups of complex waves composed of a wide range of frequencies. The frequency content of the transient waves generated by the boundary motion is dependent on location. Different forms of boundary motion generates similar spectral energy distributions at the same location in the harbor. The damage to the floating ferry dock observed at Skagway occurred due to the combined effect of mooring dynamics and the frequency content of the waves.

Laboratory experiment is conducted to investigate the long waves generated by time-varying breakpoint. We focus our attention on the variation of plunging point as well as the variation of breaking point. The results show that free long waves (BFLW) are really generated by the variation of the starting point of wave set-up which coincide with the plunging point and that the BFLW observed can be quantitatively evaluated by Mizuguchi(1995) model, which is more direct and realistic model. The generation mechanisms of long waves of other origins, such as bound long waves to wave groups and free long waves generated during shoaling process of wave groups, are also discussed.

Laboratory experiments were performed to investigate generation of long waves in the surf zone. Amplitude of long waves generated by time-varying breaking points was found to be nearly same as that of incoming bounded long wave. The generated long waves showed phase difference with the incoming long waves. The difference of the phases reached to 3/4 π through π at the shoreline.

In this paper the depth-integrated, short wave-averaged nearshore circulation model SHORECIRC is used to study the generation of infragravity waves due to normally incident short wave groups on a plane beach. After linear separation of the incident and reflected long waves, it is shown that the incoming long wave shoals faster than Green’s Law predicts for free waves. This indicates that energy is transferred from the short wave groups to the long wave. However, it does not shoal as quickly as Longuet-Higgins & Stewart’s (1962) steady state theory for bound waves suggests. The outgoing long wave deshoals according to Green’s Law but it is shown that energy is traded back and forth with the incoming short wave groups. Different shoaling and deshoaling curves can be found for different parameter choices. The work term in the long wave energy equation is used to explain these differences and ratio of the number of short wave groups to the surf zone width is confirmed to be an important parameter. As a consequence, the energy of the outgoing long wave can be larger or smaller than that of the incoming long wave, depending on the value of that parameter. Finally, the nonlinear version of the model shows the importance of the mean set-up on the generation of long waves, in particular very close to the shoreline.

The impacts of sea-level rise induced by global warming on sandy beaches and sediment deposition around the river mouth are assessed. The exacerbated erosion by sea-level rise is evaluated in a national scale for Japan, on the basis of the Bruun Rule assuming the existence of the equilibrium beach profile. The eroded area reaches 56.6, 81.7, and 90.3% of the total area of the existing beaches for the sea-level rises of 30, 65, and 100cm, respectively. The effects on sandy beaches is extremely large, since such erosion superposes on the already existing erosion. The effect of sea-level rise on the river mouth is also examined by a numerical model. The place of sand deposition changes from the river mouth to the upper reaches along the river as the mean sea level rises higher. Higher risk of flooding is anticipated because of the rise of river floor and the backwater effect of sea-level rise.

This paper describes the application of a model of the two dimensional shallow water equations to the growth of instabilities of the longshore current at Superduck on October 18th. Simulations are carried out using two initial current profiles. In the first case the initial longshore current profile results from a balance between bottom friction, the radiation stress gradient and lateral mixing due to turbulence. In the second case lateral mixing is neglected. The shear wave climates resulting from both simulations are analyzed and compared to data. In the first case the energy in the shear wave band is underpredicted whereas in the second case, it is overpredicted. In both cases, the initial longshore current profile changes due to lateral mixing induced by the shear instabilities. The resulting longshore current profile after shear instabilities have reached finite amplitude is found to be very similar for both cases.

NEPTUNE is an EU-research project under the MASTII framework. It involves seven partners: British Maritime Technology, Delft Hydraulics, Department of Mathematics & Statistics, University of Lancaster, Climate Research Unit, University of East Anglia, Econometrics Institute, Erasmus University, National Institute for Coastal and Marine Management of Rijkswaterstaat (RIKZ), and Forschungszentrum Geesthacht GmbH (GKSS). The purpose is to investigate a new integrated approach for modelling the statistics of NW European coastal extremes by first characterising the coastal impact and then linking it through a process model chain with the causative storm involved. The project methodology recognises that the North-European storm climate is made of several different storm types which impact on the coastline in different ways. The project strategy is described and some of the main results are presented.

This paper presents a system for estimating extremes of storm surge height and wave height associated with typhoons, which consists of a Monte-Carlo simulation model for probabilistic generation of typhoon characteristics, termed a stochastic typhoon model, a parametric typhoon model for wind estimation, numerical models for the computation of storm surges or waves and an extreme analysis model for estimation of their return values. The system is applied to the estimation of 50 to 1000-year return values and their confidence intervals based on the computations over a period of 1000 years for storm surge heights in Ise Bay connecting to the Pacific Ocean, and for wave heights at some representative locations around the Pacific coast of Japan.

A concept for the design of high water protection (HWP) walls under storm surge conditions has been developed and is applied to the geometry found in the harbour of Hamburg, Germany. However, the design methods used have been generalized so that they may be used for a wide range of cases with similar geometries. Many gaps in standard design formulae have been filled by developing engineering approaches or formulae as reflection by steep berms, new breaker criterion, design formulae for impact breakers, reduction of loads by overtopping and soil pressure distribution in front of the wall.

Some ideas for improving the accuracy of storm surge prediction models are discussed. A detailed coastal flooding model is applied to the flooding of Chittagong in the April 1991 disaster, but results are only illustrative due to the lack of good topography data. The influence of waves on wind stress forcing and bottom friction is discussed. Some recent results from a coastal observation tower taken during a typhoon show enhanced stress compared with values from empirical formulae in the literature. A new model for improving the representation of typhoon wind fields in areas surrounded by mountains is presented. Its applicability for storm surge computation is demonstrated using observations of a typhoon and surge in Osaka Bay.

This paper presents an analysis of physical model tests of the swash zone. A mild, impermeable slope was used to create a wide swash zone. Bichromatic and irregular waves with varying wave heights, wave periods and wave grouping were tested. The experiments showed the swash zone to be dominated by low frequency motions, which were closely related to the incident wave groups. The incident waves were still grouped in the surf and swash zones.

An empirical relationship was determined, relating the long wave height at the shoreline to the deep water wave parameters. The long waves were found to be partially reflected from the swash zone and this partial reflection was successfully simulated by the superposition of an absorbed and a reflected long wave. The generation of spurious long waves and the seiche at the natural frequency of the equipment were also investigated.

Tsunami! () is a WWW site developed at the University of Washington with collaborative support from the global tsunami research community. The site originated as an on-line documentation of the 1994 East Java tsunami survey. The field survey documentation was developed to serve as a prototypical WWW resource whose form can be amended and improved upon for future on-line tsunami survey documentation. Educational and hazard mitigation resources were added to the site to provide the general public with an on-line source of tsunami information. The site’s content and interface design were strongly influenced by the wide range of network connections and browser applications utilized by the target audience.

We present a general method for determining the runup and the amplification explicitly for nonbreaking long waves propagating over piecewise linear topography, using the linear shallow water wave equations. We associate each constant-depth segment and each linearly-varying depth segment with (2×2) matrices and we calculate the transmitted wave amplitude after propagating over any number of segments explicitly. We then extend our methodology to the three dimensional topography of a conical island. Our method is applicable in the design of dikes, sea-walls and other coastal structures.

This paper presents offshore tsunami profiles observed by NOWPHAS (Nationwide Ocean Wave Information Network for Ports and Harbours) wavemeasuring instruments installed at various coastal wave stations and tide stations in Japan. Included are wave profiles of damage-inflicting tsunamis generated by the 1993 Hokkaido-Southwest Earthquake, the 1994 Hokkaido-Eastoff Earthquake, the 1996 Iri-Anjaya Earthquake, and other smaller recently occurring tsumamis. Also presented are characteristiscs and phenomena of interest clarifed through various analyses performed on observational data.

Tidal waves or tsunamis are long water waves of small steepness generated by impulsive geophysical events of the seafloor or by coastal landslides. Whereas their coastal evolution is now well-understood, their generation is not. Until recently (Tadepalli and Synolakis 1994a, 1996), numerous anecdotal records of historic tsunamis where shorelines significantly retreated before the tidal waves advanced up the coastline have been disregarded; the prevailing paradigm for tsunami studies is the modeling of the evolution and runup of a single-hump leading-elevation waves which offshore have solitary-wave profiles. We propose a model for the leading-wave of tsunamis to explain why the coastal manifestation of most tsunamis suggests a leading-depression N-wave, a waveform which causes the shoreline to recede before advancing up the beach. Farfield, we use the Korteweg-De-Vries equation, and we find that N-waves of geophysical scales do not fission over transoceanic propagation distances and no leading solitary waves emerge. Nearshore, we use shallow water theory to calculate the evolution and runup of emerging non-breaking waves, and we observe that they evolve according to Greens' law (Green, 1837, Lamb, 1945, Synolakis, 1991). We discuss the effects of certain ground deformation parameters and provide one application of our theory by modeling the Nicaraguan tsunami of September 1, 1992.

A nonlinear model for predicting the resonant oscillations in a harbour due to typhoon is developed and its validity is evaluated through the comparisons with filed measurements obtained in Yui Fishery Harbour facing Suruga Bay in Japan. The numerical model is based on a time domain solution of Boussinesq equations proposed by Nwogu(1993) with an additional Forchheimer resistance term in the momentum equation to take account of the reflection characteristics of permeable seawalls in the field. It is shown that the numerical model predicts well the low-frequency oscillations inside the harbour exited by incident wave groups.

Field measurement of sea surface elevation for analysis of wave groups have been carried out at the 4 wave observation points around Japan about for 6 months. As the result of analysis of coefficient variation of wave group parameter, that a record length of wave data needs more than 60 minutes for the reliable statistics of wave groups. Using the wave record of the enough length for wave groups analysis, the empirical relationship between wave group statistics and wave climate statistics is estimated.

The characteristics of the reflection coefficients of a step-shaped slit caisson on the rubble mound are examined by experimental data. A numerical analysis which combines the method of matched asymptotic expansions with a boundary element method has been applied for the calculation of the reflection coefficients of the caisson on the rubble mound. Numerical results are compared with experimental data to show the validity. Dimensions of the preferable cross-section of the step-shaped slit caisson on the rubble mound are discussed and obtained through the numerical results.

Comprehensive three-dimensional model tests with a berm breakwater roundhead and the adjacent trunk section were carried out at the Danish Hydraulic Institute (DHI) and at the Hydraulic & Coastal Engineering Laboratory of Aalborg University (AAU). This paper describes the influence of wave obliquity on the profile shape, on the initiation of longshore transport and on the longshore transport rate at the trunk section both during and after the profile reshaping, whereas the roundhead stability is described in Juhl et al (1996). Furthermore, tests were made for studying the influence of storm duration and of short crested waves. Equations for calculation of profile development and longshore transport rate under oblique wave attack are introduced.

Wave flume tests were carried out aiming to describe and quantify the interaction between main armour and toe-berm damage up to failure. Experiments are described in brief, as well as the qualitative combined damaging process. An interaction scheme is formulated; data and formulae are provided for the quantification of the risk implied in the combined failure.

Smooth concrete slope protection structures are an interesting alternative to rip-rap slopes for areas with a mild wave climate (up to H_s = 3 m), especially where the accessibility and the aesthetic appearance of the slope is of great importance. The smooth surface makes the water line accessible to bathers and fishermen and it also enables an integrated design in the scenery.

Unfortunately the smooth surface gives a much higher wave run-up, leading to a higher structure. To tackle this problem one can use a smooth surface with artificial roughness elements.

The present research leads to the conclusion that relatively small roughness elements reduce wave run-up considerable, but don't effect the stability of the cover layer.

An experimental study has been carried out concerning horizontal velocities induced by a regular wave acting on a rough permeable steep slope. Time-histories of vertical distributions of the horizontal component of local velocity observed for all the considered wave conditions have been compared with results from 1st and 2nd order wave theories. Further analysis has concerned water surface elevation, depth-averaged velocity and uniformity level of velocity profiles. For both local and global characteristics of velocity field, results from wave theories expected to apply are not in good agreement with experimental data. 1st order theory appears satisfactory for the shorter waves but departs significantly from data as the Ursell number increases.

Results of a laboratory investigation were analyzed to determine the response of quarrystone armor units to particular wave periods. Results indicate that individual stones appear to respond to particular wave periods depending on the stone’s mass, shape, and placement in the structure’s armor layer. Results also indicate that the wave period critical for design may not be the longest wave period in the incident waves, and investigations must be carefully conducted to determine the critical design conditions.

Reliability based design of monolithic vertical breakwaters is considered. Probabilistic models of important failure modes such as sliding and rupture failure in the rubble mound and the subsoil are described. Characterisation of the relevant stochastic parameters are presented, and relevant design variables are identified and an optimal system reliability formulation is presented. An illustrative example is given.

In this paper a “semi-dynamic approach for the slope stability analysis of rubble mound breakwaters” is presented. The principles of the method are described. Tide and wave action are taken into account in the slope stability analysis of deep slip-surfaces. For these slip-surfaces the moment of maximum wave run-up is most critical.

Pore water pressure variations at the seabottom are also measured below the seabottom but attenuated and approximately up to the so called influence depth h_ID. The fact that the pore pressure variation is attenuated leads to “overpressures” at the moment of low water and below the wave trough. The attenuation depends mainly on the wave period T and soil characteristics k (permeability) and E_oed (oedometric compression modulus).

This experimental study is concerned with one particular aspect of possible failure modes for a rubble-mound breakwater: the interactions between the toe-berm and the main-armour of the breakwater. Through a series of laboratory tests in a wave basin under long-crested and short-crested waves, we investigate the mutual influence of both these component parts of the breakwater on its general stability. The effects of several wave parameters are examined for four sizes of toe-berm stones. For the trunk section, experimental results are found to compare quite satisfactorily with existing design formulas both for the main-armour and the toe-berm. As a general trend from the tests results, the interaction processes appear to have only moderate effect. Their major feature is an increase of damage to the armour when the toe-berm is unstable. On the opposite, minor effects of main-armour on toe-berm stability were observed. In particular, the “toe-berm armouring process” (by units falling from the armour) appears to occur only marginally and under precise conditions.

Engineers and scientists at the U.S. Army Engineer Waterways Experiment Station (WES) are developing a Rapidly Installed Breakwater (RIB) System specifically designed to address problems associated with the military’s efforts to offload ships during Logistics Over The Shore (LOTS) operations. Problems arise with these operations when seas become energetic and limit capabilities of crane operators and stevedore crews. The RIB System is designed to solve this problem by creating a 'pool' of calmer water where these operations occur so that crews can continue to function. A series of small-scale laboratory experiments conducted in 1995 and 1996 at WES’s facilities in Vicksburg, Miss., and at the O. H. Hinsdale Wave Research Laboratory at Oregon State University in Corvallis, laid the groundwork for the RIB System development and yielded an optimum RIB System configuration known as the “Double Delta”. Laboratory results, obtained with the Double Delta configuration, showed that wave heights could be reduced by more than 80 percent. During the spring and summer of 1996, a mid-scale RIB System successfully demonstrated its capabilities during a field deployment, with wave height reduction on the order of 75 percent. Based on these results, it is believed that the RIB System will be integrated into the Army’s LOTS asset inventory and become a key part of the solution to the military’s LOTS problems.

A model for calculating the accumulated travelled stone distance is given based on the easy accessible parameters such H_s, T_p, θ, number of waves and Dn₅₀. A comparison with selected prototype structures is presented showing the relation between breakwater damage and armour stone motion. The comparison also signifies that only little transport should be allowed to avoid severe damage. The best possible design of the berm breakwater with maximum utilization of the quarry when possible is suggested by Sigurdarson et al.

The failures experienced in Japan by wave-dissipating concrete blocks (WDCB) covering vertical wall breakwaters are investigated, and the deformation characteristics such as failure features and factors are examined.

Typical examples for failures are illustrated, and two main types for failures are suggested: (a) scattering of WDCB due to shortage of their weight, (b) settlement of WDCB following deformation of the toe area. These types are analyzed and then the latter is discussed with some preliminary experiments. The results suggested that both stability of WDCB and applicability of the Hudson formula depend on the location and their cross-sectional shape, and that a weakening of sand bed due to wave action, especially wave-induced liquefaction, is an important factor of settlement deformation as well as scouring.

From these results and additional field surveys, finally, two parameters are suggested which can explain the effect of stability of WDCB and toe area on both scattering and settlement behavior, and a classification of resultant failure characteristics and a conceptualized diagram of failure behavior of WDCB are presented.

A new stability formula for wave-dissipating concrete blocks covering horizontally composite breakwaters is proposed after reviewing the existing stability formulae and verified using experimental data. A method for estimating the expected value of the accumulated damage to wave-dissipating concrete blocks within their lifetime using the Monte Carlo simulation follows thereafter and the practicability of this method for reliability based design of wave-dissipating concrete blocks is shown.

The main objective of the present study was to compare the damage to a rubble mound breakwater under regular and irregular wave attack, and thereby identify an irregular wave height parameter that corresponds to the wave height of a regular wave in terms of inducing a similar degree of damage to the structure. The 1984 edition of the Shore Protection Manual recommends this irregular wave height parameter to be H_1/10 (the average of the highest one-10th of the waves in a sea state), but other researchers recommend H_1/30 (e.g. Vidal et al., 1995). For the present study, H_1/20 is the irregular wave height parameter that yields the best correspondence between irregular and regular waves. However, this result is dependent on the length of the time series and on the number of times this time series is recycled to achieve a given damage level. The new wave height parameter H_n (the average of the n highest waves in a sea state) proposed by Vidal et al. (1995) takes into account the statistics of the large waves contained in the time series as well as the number of times this time series is recycled. The present study indicates that H₂₅₀ (the average of the highest 250 waves in the sea state) is a suitable wave height parameter for characterizing breakwater stability under irregular waves.

Three-dimensional (3D) model tests were carried out for studying the stability of a berm breakwater roundhead and the adjacent trunk section. The present paper describes the influence of the wave incidence angle and wave steepness on the roundhead stability. The test results are described in terms of profile development, recession of the berm, eroded and deposited volumes and the transport of stones during reshaping. Results from analysis of the influence of wave obliquity on profile shape, initiation of longshore transport and longshore transport rate at the trunk section are presented in Alikhani et al (1996).

Composite breakwaters are increasingly becoming popular as port structures to cope with enlargement of ports and the weak ground of coastal areas. To determine their effectiveness in withstanding tsunamis, model experiments are performed. Results show that damage to composite breakwaters can be reduced considerably by strengthening the mound surface around the heel of the structures.

The hydraulic stability of armor units on the leeside slope of an overtopped breakwater is analyzed using the velocity and depth of overtopping water on the crest computed by an existing numerical model. The stability analysis is carried out considering the hydrodynamic forces of the overtopping jet impinging on a leeside armor unit. A traditional force balance method is used to predict the stability number N_s for initiation of armor movement. The computed critical stability numbers N_sc for stones compare well with the observed stability numbers, provided that the hydrodynamic force coefficients are calibrated once for the stone stability on leeside slopes. The computed results indicate that the minimum stability of the leeside armor units occur at intermediate crest heights. The stability of leeside armor improves as the seaward slope is made flatter. The leeside slope of a breakwater in relatively deeper water is more stable. The leeside stability of a breakwater in shallower water with its crest height near still water level (SWL) can be improved by increasing the the back slope angle. A wider crest also improves the leeside stability.

Further studies are required to refine the developed stability model. The influence of tailwater in reducing the water velocity of overtopping jet needs to be included which has not been considered in the present analysis. The developed model would be very useful in designing the geometry of an overtopped breakwater and the size of leeside armor units because of a large number of design parameters.

An experimental study has been carried out to investigate the concept of extending the core into the berm of a berm breakwater. Five different core configurations were tested. The reshaped profiles were not significantly influenced by the core configuration. The core configuration should be such that the core material is not directly exposed to the waves during the reshaping.

The concept of extending the core into the berm will lead to cheaper berm breakwater structures since the core material is cheaper than the armour stones.

A series of large scale (1:15) experiments have been undertaken to assist the Societe d'Energie de la Baie James (SEBJ) in the development of new design guidelines for riprap. The stability of revetments resting on 1:1.8 and 1:2.25 (V:H) slopes is considered. In an attempt to quantify the relative roles of stone size, gradation and armour layer thickness, these tests were undertaken with stone gradations varying from (M_max/M_min ranging from 1 to 10) and with armour layers both 2.2D_n50 and 2.7D_n50 thick.

The results of a field campaign of measurements of pressures on a prototype wave screen are analyzed and compared to the results of laboratory tests and to the calculation methods proposed by Jensen, 1984, Günbak et al., 1984, and Martin et al. 1995. Both the field campaign data and the lab tests results seem to fit quantitatively better to the method of Martin et al. than to other proposed formulae. Moreover, the proposed modelization and description of the process employed to develop the method of Martin et al., 1995, are consistent to the measured pressure profiles and time-pressure series.

The measurements of wave kinematics over the breakwater heads under uni and multidirectional waves attack were undertaken to achieve an improved understanding of the influence of wave directionality on the stability of heads. The characteristics of the magnitudes and directions of velocity vectors under 3D waves were assessed by comparing with those measured under 2D waves. The sensitive zones of the initial damage in the head sections were evaluated by linking the measurements of velocity components with a stability formula for armour stones on the heads, which was derived in this study.

The nonstationarity of the sea waves is usually significant for periods longer than 3 hours (1,000 waves) with a correlation coefficent r_HH(3) below 95% on most coasts of the world. Therefore, the actual engineering problem is to define an appropriate armor damage model applicable for nonstationary processes and not only for stationary sea states with a given storm duration. In deep water, five conditions are identified for any rational armor damage model to properly take into consideration the storm duration. A new exponential model applied on individual waves is shown to accomplish the five necessary conditions identified, and is compared with the Teisson’s and Vidal’s models based on totally different assumptions, but accomplishing most of the conditions. The three models provide similar results for a wide range of values if the parameters are n63% = 30 and N_W = 50 for the exponential and Vidal’s models respectively. An example of the application of the exponential model to nonstationary processes is given, applying the new method to the case of the partial failure of the Zierbana breakwater (Port of Bilbao, Spain) under construction in February 1996.

This paper describes observations made of incipient motion on both stone and sphere armor layers. Velocity measurements were made during these experiments both inside and just outside the armor layer. It is shown that the vertical convective acceleration across the armor layer is proportional to the square of the vertical velocity. An incipient lifting motion criterion is derived based on Morison forcing for the dominant mode of motion: vertical lift under the steep breaking-wave face. The experimental observations and measurements are used to validate the incipient motion criterion for breakwater armor.

This study for overtopping reduction in crownwall design presents several results of 2D (wave flume) and 3D (wave basin) tests on irregular wave overtopping of different configurations for breakwater sections were obtained by the Applied Hydrodynamics Institute (INHA) in order to improve the design of the small-craft harbour at San Sebastian in the North of Spain(fig. 1).

San Sebastian is one of the most well-known and beautiful tourist cities in Europe and for that reason aesthetic as well as environmental aspects of construction had to be taken into account.

An experimental study of breakwaters with an initially horizontal berm below the SWL was conducted in a wave flume. The study aimed at defining the shape and geometrical features of the adjusted stable profiles and at confirming the existence of a zone of non-significant profile adjustment below the initially flat and horizontal slope.

A new type of seawall is proposed in this study. The seawall has a deep circular arc cross section and allows no wave overtopping any more. The critical crest elevation of the seawall, which defined as the minimum crest elevation on which the wave overtopping dose not occur at all, is investigated through the wave tank experiments. The wave pressures and wave forces acting on the seawall are also measured, and the characteristics of the wave pressure distribution and wave forces are examined.

This paper describes one aspect of a series of projects which the U. S. Army Corps of Engineers has undertaken to improve maintenance management of coastal and navigational structures. At the core of these projects is the development of procedures for more uniformly evaluating and describing the physical condition and functional performance of structures, and further, the development of methods where the condition and performance of structures, and their parts, can be expressed numerically to take best advantage of the benefits available from the use of microcomputers in maintenance management. These procedures are designed to allow the condition and performance of different structures to be more easily compared and more uniformly tracked over long time periods and to aid the repair budgeting prioritization process. This paper briefly describes the performance-based assessment method for breakwaters and jetties, primarily of rubble construction.

This paper describes the wave overtopping along a seawall of a man-made island where nuclear power plants are projected to construct and the stability of armor units at the concave section of seawall. Effects of the wave directionality on them were investigated by using multidirectional wave basin not only for a design wave but also larger waves than the design one to ascertain the durability and margin of the safety of seawall.

On October 7, 1994 a full scale breach growth experiment has been carried out at the Dutch- Belgium border, in the Zwin at the west-end of the Dutch-Belgian border. A small breach was initiated in a sanddike with a height of 3.25 m and the breaching process was monitored. The present paper focusses on the numerical modeling (hindcasting) of the breach growth process.

Since the early 1980’s fundamental research on the behaviour of placed block revetments has been carried out in the Netherlands. This research has focussed on understanding the physics of this particular revetment type, which has resulted in empirical (Pilarczyk, 1985), analytical (Burger et al, 1990) and numerical (Bezuijen et al, 1987) design methods. These methods have been tested extensively in large and small scale model tests. (for instance Klein Breteler, 1988, den Boer et al, 1983).

During the last years extensive field research has been carried out (Stoutjesdijk, 1992). This research has shown that a large difference in physical behaviour can exist between newly placed revetments or large scale models, and older ('aged') revetments in the field. To investigate this phenomenom further, field work, laboratory tests and modelling efforts have been carried out. This paper describes the current state of affairs. Purpose of this research is to quantify the net effect of aging on the stability of placed block revetments. If the net effect proves to be positive, it may prove possible to upgrade the stability of revetments by artificial simulation of aging effects.

We conducted a series of model in a wave flume measuring pore pressures in the reclaimed soil (sand) to investigate the settlement failure mechanisms of caisson type seawalls. Settlement of reclaimed soil was reporduced by considering that the geotextile sheet, which separates the backfill and reclaimed soil regions, had an opening ripped in it such that soil rapidly leaks out. Also reproduced were the phenomenon of sand boiling (liquefaction), the presence of saturated reclaimed soil above the backfill stones, seawall construction with no backfill stones, and impulsive pressures acting on the joint plate connecting two caissons. Experiment results further clarified the fundamental mechanisms of the settlement failures.

At the Zeebrugge harbour (Belgium) a cross-section of the N.W.-breakwater has been instrumented for the study of physical processes related to the behaviour of a prototype rubble mound breakwater in random wave conditions. Within the EC MAST programme (project MAS02-CT92-0023) this monitoring system has been reengineered and extended to a high-quality full scale data acquisition centre (Troch et al., 1995).

The development of the prototype monitoring system to a world-wide unique system with respect to the infrastructure available at Zeebrugge, the instrumentation installed on site, and the data management developed, is briefly summarised.

Filed measurements of wave attack in front of the breakwater, and pore pressure response inside the breakwater core, have been analysed in order to determine the hydraulic response of the full scale breakwater. Analysis results on wave run-up/run-down measurements, phreatic set-up calculations, and pore pressure wave attenuation are presented here in more detail.

Wave interaction with dynamically stable structures is simulated by means of a numerical model based on finite-amplitude shallow-water wave equations. The model can simulate wave motion on and inside permeable structures. For dynamically stable structures, including berm breakwaters, reef-type structures and gravel beaches, a procedure is developed to simulate the natural response to wave attack. This procedure is extended, for instance by implementing effects of grading and effects of seawalls, to increase the applicability for practical applications.

From the moment they are constructed, rubble-mound breakwaters are due to be damaged someway. Accepting damage is one of the basic principles of mound breakwaters design. Damage can take place either gradually in time or catastrophically after a major storm. Gradual deterioration of the armour layers or foundation may be unnoticed without the aid of a monitoring program and may ultimately result in the failure of the armour layer, in slope instability or in unacceptable large settlements. By comparison of measurements of the state of the structure at a number of points in time, a monitoring program allows these changes to be identified at an early stage, thus enabling the appropriate maintenance action to be carried out.

The stability of low-crested rubble mound structures has been treated before by various researchers. In the first phase of this study two data sets from different laboratories were combined to one homogeneous data set. Re-analysis of these data resulted in a design diagramme for the stability of the seaward side, the crest, the rear and the total armour layer of the structure. Secondly, model tests were performed on carefully selected rock with different rock shapes (angular, flat and rounded) and different gradings, all for a low-crested structure. Results show that the differences between the various rock types were small, especially for the start of damage. The influence of the length/thickness ratio showed even no infuence at all which means that the sometimes strict requirements in construction may be released.

At the Congress on Coastal Structures and Breakwaters, a stability relation for toe structures of rubble mound breakwaters was presented, see Van der Meer et al., 1995. In that relation the relative stone density, Δ, was used in the stability parameter H_s/ΔD_n50. In the tests on which the relation was based, however, Δ was not varied, so some uncertainty remained on the influence of this parameter. Additional tests were therefore carried out with different stone densities, leading to the conclusion that there is no influence of the stone density, other than represented in the stability parameter H_s/ΔD_n50. Computations were done, coupling the orbital velocities in the waves in front of the breakwater to the stability of the stones of the toe structure leading to encouraging results. Both computations and tests show an influence of the waterdepth in front of the breakwater which is not yet included in the stability relation.

This paper presents the results of a study using 15 years of beach profile data to determine how the presence of seawalls influences the existing erosional trends of the beach at Sandbridge, Virginia (USA). Three analysis methods using historic and seasonal time scales were used to answer three questions about the possible effects seawalls may have on adjacent nonwalled beaches. The results show that, statistically, there is no difference in the erosion rates of walled and nonwalled beaches. Seasonal variability of volume is greater for walled profiles. Seasonal recovery rates for both profile types are similar. Finally, the claim that the erosion of landward volumes at nonwalled beaches is increasing due to the presence of nearby seawalls is not supported by the evidence at Sandbridge beach.

A new type of submerged breakwater with a triangular plane form which modifies the wave propagation angle is proposed. Its performance is demonstrated and assessed analytically. Preliminary movable bed experiments were conducted. The breakwater was installed in front of the beach to modify the wave propagation angle in the offshore zone. Longshore current and littoral drift were driven through the effect of wave angle modification.

An extensive 3-D model test program has been performed to study the effects of wave obliquity and multidirectionality on the hydraulic response of vertical (caisson) breakwaters. In this paper the results of the wave forces and pressures are shown. The measurements are compared with the Goda’s formula with some divergences. The tests show that multidirectional wave loads do not reduce with increasing obliquity of the mean direction, whereas a reduction occurs for oblique long-crested waves. Three-dimensional effects on the uplift forces are better described by Goda formulations and smaller scatter is observed when comparing with measurements. The analysis of the longitudinal distribution of the horizontal pressures confirmed that the global wave load decays with increasing multidirectionality and obliquity, with clear advantages for the design of long monolithic breakwaters.

Detached breakwaters alter the nearshore wave climate and hence the wave-driven current and sediment transport patterns. They obstruct a part or all of the long shore sediment transport and because of this, they play a role in the large-scale sediment budget of the coasts where they are applied. Their local effect on the coast is to form single or double salients or tombolos. The most common tools applied for modelling the impact of detached breakwaters are the coastline models. They assume that the coastal profile is more or less constant in shape, and that the long shore sediment transport is related to the local angle of incident waves.

This paper presents an evaluation of current design formulae for beach response to multiple breakwaters, comparing the predictions of the design guidelines with observations of beach response made during the large scale field experiment carried out at Elmer, on the UK south coast. The introduction describes typical shoreline response to breakwaters, the forcing mechanisms responsible and the characteristics of macro-tidal beaches. The remainder of the paper presents the empirical design tools, and the results of the evaluation.

The sedimentological impact of waves on a sandy beach with a detached breakwater is simulated using a compound system of models. The results are satisfying since a salient could be generated behind the structure. They are in agreement with bed evolutions surveyed in experimental facilities and in nature. A quantitative analysis of the results performed in the framework of the working group 'Coastal Area Modelling' of the project MAST G8M shows that the volume of accretion computed here is in good agreement with the volumes obtained by other models and empirical formula.

An analytic method for the combined diffraction and transmission around a porous breakwater gap is presented. The method can be summarized as follows. First of all, it is necessary to decompose the incident wave into two components, according to the incidence angle and the permeability of the two breakwaters that form the gap. Then, let the breakwaters be completely transparent to the relevant component of the incident wave and ascertain the transmission field. Next, treat the breakwaters as solid to the other component of the incident wave and solve the diffraction field. Finally, superpose the transmission and the diffraction to give the objective wave motion. The available analytic methods for the diffraction by an aperture on solid wall are comparatively studied since they play the central role in working out the final solution of a real problem with combined diffraction and transmission. Sample computations are carried out for typical cases with both regular and irregular incidence. The computational results show that the phase effects of the porosity of the breakwaters on a combined wave field can be significant.

An empirical predictive scheme for wave reflection from rock island breakwaters is derived from a multiple regression analysis of a large data set (780 data points) which includes both laboratory and full-scale measurements. The large parameter space embraced due to the inclusion of both laboratory and field data leads to a robust solution for the prediction of wave reflection. The resulting equation expresses the reflection coefficient as a function of a number of dimensionless parameters which can be identified with specific physical processes. These include wave breaking, dissipation due friction and turbulence induced by structural roughness, and transmission into and through the breakwater.

The interaction of water waves with a tensioned, inextensible, vertical flexible membrane hinged at the sea floor and attached to a solid cylindrical buoy at its top, was investigated in the context of two-dimensional linear wave-body interaction theory. A two-domain boundary element program was developed based on a discrete-membrane dynamic model and simple-source distribution over the entire fluid boundaries. To verify the numerical results, a series of experiments were conducted with two different models in the two-dimensional wave tank. For each model, both surface-piercing and submerged cases were tested. The numerical prediction was generally in good agreement with experimental results except resonance regions. The comparison was improved after including viscous or material damping effects. It is shown that the buoy/membrane system can be a very effective wave barrier if it is properly designed.

Since impounding of the various reservoirs of the La Grande Complex in northern Québec, the riprap of several dams and dykes suffered some damage during the fifteen-year period which followed. A mandate was given to the Société d'énergie de la Baie James (SEBJ) in January 1992 to review the riprap design and evaluate the necessary repairs. The paper focuses on this work. An improved design method, for the riprap of earthfill dams of large reservoirs, is proposed based on four years of intensive studies and fifteen years of field data. Large scale model tests with irregular waves completed the studies.

Geosystems has gained popularity in recent years because of their simplicity in placement and constructability, cost effectiveness and their minimum impact on the environment. An overview is given on application of the existing geosynthetic systems in hydraulic and coastal engineering.

Groynes can be a valuable shore-protection structure. An example for this fact are the ’Strombuhnen’ (’stream groynes’) which have been constructed on most of the East Frisian islands throughout the last hundred years. These groynes are integrated in an engineering coastal protection system, which includes seawalls, dune revetments, ’Strandbuhnen’ (’beach groynes’) and artificial beach-restoration. The modern approach of society in Germany (and many other countries) towards nature preservation and integrated management of the coastal zone discourages use of ’hard’ constructions. However, there are several demands of society, for which we have to concede, that properly designed ’stream groynes' can function effectively and economically; under certain conditions; this can also be the case for 'beach groynes'. According to the stated demands, these constructions have, more or less, the target to govern natural processes; hence they are principally objectable from an environmental point of view.

Permeable pile groins have been built on the southern shores of the Baltic Sea in large numbers for the past century and a half, yet no detailed literature has been written on how these structures function. The study of the groin system at Warnemüende, has shown that this type of groin causes a reduction of the littoral current and elimination of the local rip currents. This, in turn, causes underwater profiles to raise, a widening of the beach and a seaward movement of the shoreline.

A previously unreported mechanism which is believed to be a key process in the formation of shingle beaches is identified. It is proposed that this mechanism be called “winnowing”.

Several new considerations relating to the selection of appropriate model sediments for shingle beach models are discussed. It is shown that lightweight sediments are subject to a significant scale effect and a compromise solution is suggested.

The results of some experiments, never previously performed, of beach scour in front of sea walls resulting from various combinations of wave attack and groundwater flow in the beach are presented. These show that the presence of groundwater flow in the beach has a significant impact on the amount of toe scour to be expected.

In the outer coastal zones, where wave conditions are severe, steel-pipe piles often undergo abrasion due to the collision of sand particles. The abrasion characteristics of steel-pipe piles were clarified from the results of full-scale experiments. The abrasion rate of steel-pipe piles was found to be approximately proportional to the second power of the amplitude of flow velocity. The larger the ratio of sand particle diameter to pile diameter was, the higher was the abrasion rate. As the collision energy of sand particles obtained by numerical analysis was nearly proportional to the measured abrasion rate, it was considered that the abrasion rate can be estimated from the collision energy.

Wave overtopping problems continue to require more attention due to the complexity of the physical process and the lack of available predictive models. In a recent experimental study on the kinematics of wave overtopping on marine structure by Lee, Zhuang and Chang (1993), it was found that the overtopping wave constitutes a jet-like water mass impacting the shoreward region of the breakwater. This jet-like water mass induces strong vortices and large water particle velocities in both the horizontal and vertical direction in the shoreward region behind the marine structure. The large rotational velocity field is capable of removing the armor units of the breakwater and scouring the bed in the shoreward region of the breakwater. In the study of Zhuang, Chang and Lee (1994), a numerical model capable of generating the rotational velocity field in the vicinity of the shoreward face of the breakwater was proposed. This paper presents the computation results from a refined viscous rotational model and their comparisons with newly acquired experimental data.

The flow of water due to the overtopping of a vertical wall by waves is modelled. The waves are computed with an accurate irrotational flow solver. The case where a jet of water is projected up the face of the wall is considered. A simple estimation is made from the computation of the amount of water that can pass over the crest of a wall of finite height. The results for overtopping volume per wave show a roughly exponential decaying dependence on the height of the wall above the still water level. Results are given for waves of differing height and also for various sizes of berm in front of the wall. The effects of surface tension are included to investigate the possibility of errors in scaling experimental results to prototype scale. These are larger than expected.

Effects of strong onshore winds on runup and overtopping of coastal revetments were studied in a wave flume with wind-generating capabilities. Runup and overtopping were measured during tests with onshore wind blowing over mechanically-generated waves. The addition of a constant wind over monochromatic waves added substantial energy to the wave field but the energy spectrum remained single peaked if the generated wave period was short (one second). These single-peaked incident spectra of the combined wind/wave tests were then reproduced mechanically using just the mechanical wave generator, with runup or overtopping again being measured. Runup and overtopping were both found to be considerably higher with similar incident spectra under the influence of onshore winds. Results are presented for a range of structure slopes, wind speeds, wave periods, and wave heights. Both smooth and rough revetments were tested.

The influence of both wave breaking and wind on the wave overtopping discharge of vertical sea-walls were assessed. In a qualitative way the influences of wave breaking agreed with the trends as pointed out by Goda (1985). The influence of wind on overtopping appears to be only relevant in specific conditions related to wave breaking. Even in these conditions the influence appeared to be smaller than expected.

In 1997, the Northumberland Strait Crossing will form a 13 km fixed link (bridge) between New Brunswick and Prince Edward Island in the Canadian Maritimes. This $800 million project has presented many engineering challenges, one of which has been the assessment of scour protection requirements for the 65 bridge piers. A multi-faceted coastal engineering investigation was undertaken by Baird & Associates to assess the potential for scour, and, where required, to design scour protection. Key activities included geotechnical investigations to define the seabed characteristics, numerical modelling to define the wave, current and water level conditions at the crossing site, physical modelling of wave-current interaction with the bridge piers, and the development of a new methodology to estimate the erosion potential of the seabed under extreme wave and current conditions.

The direct application of standard scour prediction techniques was not possible for this project due to the combination of complex flow conditions (waves and currents), complex pier geometry (conical base, with some piers located in dredged pits), and complex seabed conditions (highly weathered and fractured bedrock). A new methodology to estimate the potential for scour, considering these complex conditions, was developed using the empirical erodibility approach of Annandale (1995). Measurements of actual scour around one of the first four bridge piers installed early in the project were used to calibrate/verify the methodology. Using this new methodology, scour protection was recommended at approximately onequarter of the bridge piers. The protection system consists of a 10 m wide band of either armour stone or tremie concrete placed around the base of the piers.

Detailed mean water level measurements from the Brunswick River on the NSW North Coast have, to date, suggested that the contribution of wave setup to the super-elevation of river entrance water levels is quite small. Data indicate that the over heights inside the area of wave breaking in rivers are typically smaller than at the same depth in a beach surf zone with the same waves. It is thought that difference between beach surf zones and river mouths is due to the momentum flux of the river current and the current’s influence on the wave breaking process. Nevertheless, tidal anomalies of the order 0.5m are measured once or twice a year by tide gauges just inside river entrances along the east coast of New South Wales. These anomalies are thought to be mainly due to freshwater outflow and/or oceanic phenomena.

Scour at inlet navigation structures was investigated using a series of movable-bed physical models. Experiments included ebb and flood flows, sometimes combined with wave action. A new and potentially important scour mechanism was identified for situations where the ebb-flow discharge is redirected by a navigation structure. As ebb flow is deflected, flow velocities increase and a scour trench forms adjacent to the jetty.

In this paper formulations from inviscid jet theory are used to develop an easily-applied, but crude, prediction capability for maximum flow velocity in terms of entrance channel velocity and inlet geometry. A simplified scour prediction method is also provided, but much needs to be done to make it more realistic. Preliminary conclusions are given about scour produced by flood flow combined with waves.

A probability distribution of the simultaneous maximum wave amplitude within a finite width along a virtual vertical plane placed in a 3-dim. irregular sea state is studied theoretically. The probability distribution differs considerably from the Rayleigh distribution even when the width of the structure is an order of 1/10 significant wave length. The difference increases with the interval width. Especially, appearant probability of large amplitude is considerably larger than that expected from the Rayleigh distribution. Coastal structures which were designed with sufficient safety margin have sometimes failes. There are possibilities that the structures were not attacked by “unexpectedly large waves” but large waves which could have been possibly expected if we had taken the width effect into account.

The results of an experimental study of beach response in front of wave-reflecting structures are presented. The particular beach response problem is the so-called “N-type” response where sand is eroded in the area between the node and antinode and is transported towards the node. The characteristics of the equilibrium beach profile are presented and an equation describing the profile is proposed. The beach response is fundamentally dependent on the interaction between the flow and the ripples superimposed on the larger bedforms. Particle image velocimetry (PIV) has been used to look closely at the ripples and the flow. It is found that the sand transport towards the node results from larger vortex growth on the antinodal side of ripples than on the nodal side caused by the asymmetry in the main flow velocity time history which itself is a result of the superposition of the non-linear incident and reflected waves.

The fundamental characteristics of the wave field around an existing artificial reef in Japan are studied based on field measurements and wave simulations using a nonlinear wave model that takes reef porosity into account. Results of two-dimensional simulations and comparison with field data of significant wave heights and reef velocities indicate characteristic wave evolution of nonbreaking and breaking waves and confirm the damping effect of the reef.

A summary is presented of the results from a 3-year monitoring study of a submerged breakwater placed alongshore for shore protection. The experimental breakwater project, located in Palm Beach, Florida, USA, was concluded in August, 1995. The monitoring program was instituted to determine changes in wave climate and bathymetry, and to assess the shoreline response relative to pre-project conditions. The Palm Beach breakwater consisted of 330 interlocking concrete units, each 1.8 meters in height, 3.7 m long, and 4.6 m wide, which formed a 1,260 m-long shore parallel barrier. The breakwater, termed the Prefabricated Erosion Prevention (P.E.P.) Reef was placed in approximately 3 m of water roughly 73 m from the shoreline. The project was intended to increase shore protection against storm waves and to create a wider beach in the lee of the Reef. Wave transmission measurements indicated a 5 to 15% reduction in incident wave heights due to the Reef. The results of the monitoring program at the end of two years indicated erosion throughout the project area, primarily in the lee of the Reef, where the annual volumetric erosion rate was measured to be 2.3 times higher than the pre-project rate. The submerged breakwater is interpreted to have increased the longshore currents via ponding of water trapped behind the breakwater, which was then diverted alongshore. Laboratory experiments were conducted to investigate this ponding phenomenon and to test the performance of various segmented and repositioned breakwater arrangements. Shoreline erosion in the lee of the Reef was sufficiently severe to warrant removal of the structure in August, 1995.

This study deals with wave transformation over a submerged triangular breakwater that is composed of a series of elements with a triangular horizontal cross-section. The idea of such a triangular breakwater is founded on the use of the wave refraction due to peculiar spatial change in water depth around it.

A numerical model is developed to predict nonlinear wave transformation over and around the breakwater on the basis of fully nonlinear wave equations proposed by Isobe (1994). Laboratory experiment has also been conducted in a wave basin. The validity of the numerical model is examined by comparing the computations with the measurements.

The aim of this paper is to investigate experimentally and numerically the breaking limit, breaking and post-breaking wave deformation due to three different types of submerged structures such as bottom-seated, non-bottom-seated fixed and tautly-moored structures. Based on laboratory experiments, the breaking limits have been formulated for three different types of the submerged structures. Moreover, a modified SOLA-VOF method with the non-reflective wave generation method has been proposed and found to be very effective in evaluating the wave breaking process and post-breaking wave characteristics.

The use of submerged barriers in Italy is rather new starting in the first 80’s. Since that time more than 50 submerged barrier defence system were constructed and this type of structure is progressively complementing and substituting the traditional use of parallel emerging breakwaters.

The paper presents documentation about the experience gained on the topic and describes and compares to prototype experience the design criterion suggested by the authors, based essentially on the selection of a proper wave attenuation necessary to obtain to desire profile modifications.

A wave equation, taking account of the effects of porous medium, is transformed into coupled parabolic equations. It is assumed in the theory that the mean water depth and the thickness of porous layer are slowly varying and the bottom undulation is rapidly varying compared to the wavelength of surface waves. Though we can utilize the Bragg reflection to reduce transmitted waves behind breakwaters in one-dimensional case, wave heights behind breakwaters do not always decrease due to wave refraction-diffraction in horizontal two-dimensional case. By adding a dissipation term to the coupled parabolic equations, we can calculate the wave breaking deformation.

A combined BEM-FEM model has been developed to study the nonlinear dynamic interaction between a submerged breakwater and waves. The resistance coefficients in the equations of motion inside the porous media have been experimentally determined based on measured values of the wave forces on spherical armor units in a submerged breakwater. Comparisons of the numerical model results with the experimental measurements indicate that this modification has improved the model accuracy in simulating the wave deformation and the energy dissipation due to a submerged breakwater. Results also show that the model gives good estimates for the wave kinematics inside and around the breakwater which are necessary to compute the stable armor stone weight.

A submerged breakwater induces a circulation with onshore currents over the structure and offshore currents through gaps, resulting in sediment loss to the offshore region. A new submerged breakwater with inclined multiple blades is tested by laboratory experiments and numerical simulations. This breakwater can generate offshore currents over the structure and onshore currents through gaps suggesting onshore sediment supply.

An important study case with different defence structures and the results of the monitoring data of are reported. Field éxperiences are specially usefull to compare two soft structures used to defend the Lido of Ostia, i.e. the coastline of Rome at the mouth of river Tevere (Tiber)².

Existing data on wave transmission have been critically examined to obtain a homogenous data base. These data have been re-analyzed, and an expression has been derived relating the transmission coefficient to structural parameters and wave parameters.

The project “Dynamics of Beaches” is carried out by a network of six European Universities within the framework of the Human Capital and Mobility Program of the European Union. The aim of the project is to improve the existing knowledge on physical processes governing the nearshore zone due to effects of submerged breakwaters. Within the project hydrodynamic and morphological experiments have been carried out.

This paper discusses the results of the experiments that took place in a wave flume and the large wave basin at Delft University of Technology. The experiments were carried out with movable beds and varying wave conditions.

Detailed measurements of spilling and plunging wave pressures on a vertical wall are carried out to identify and compare their characteristics. Kinematical differences between the spilling and plunging breakers enable us to investigate better the generation mechanism and characteristics of the impact pressure. Further, the reliability of numerically computed breaking wave pressure is investigated through the comparisons with the experimental results. It is made clear that the impact pressure can be well expressed in terms of internal kinematics of breaking waves.

Experiments were focused on deflection responses of the wall member of upright structures to impulsive wave forces. The experiments revealed that the wall deflection response depends on wave loading modes as well as on natural frequency of the wall member system, f_NW. Single degree-of-freedom model of transient impact shows that the peak wall deflection is given as a function of the ratio between rise time of wave force τ_F and f_NW, representing characteristics of the wave load and the wall member. The measured peak deflection agrees well with the predicted by the model. In addition, the model indicates that with decreasing natural frequencies of the wall system, the wave load mode brought about greater peak deflections changes from the mode of short duration force to that of long-lasting force.

Three theories for predicting regular wave transmission past vertical wave barriers are evaluated using three sets of experimental data. The three theories are: (1) the power transmission theory of Wiegel (1960), (2) and modified power transmission theory that includes effects of wave reflection, and (3) the eigenfunction expansion theory of Losada et al. (1992). Under deep and near-deep water conditions – which are typical of most design conditions – the theory of Wiegel is found to over predict wave transmission under most circumstances. The modified power transmission theory provides better agreement with the data. The eigenfunction method provides good agreement for deep wave barrier drafts but overestimates transmission for shallow drafts.

In order to investigate the generation mechanism of high peak wave pressures on vertical/steep walls two physical experiments are carried out on a specially constructed research apparatus. It is found from present experiments that the enclosed air volume as a physical medium under compression could not be a cause for the high peak short-period wave pressures. The wave breaking on a vertical wall is accompanied by cumulating of the wave energy and its redistribution on the smaller area of the wall and conditions for shock wave are created after the collision of the streams.

Fenton’s short-crested wave force approximations were modified for designing a vertical breakwater in deep water regions. The theoretical water surface profiles and depth-distributions of hydrodynamic pressure in front of a vertical breakwater were first evaluated with field wave conditions of height H_D = 10m and period T = 9.6s at depths d from 20m to 40m. The calculations immediately illustrated characteristics of residual pressures at wave crest and exponentially decreasing profiles under design water level. As d increased, wave crest height decreased as well and the crest pressure deviations became negligible while overestimated pressure force by assuming linear under-water pressure distributions became more significant. Through appropriate modifications, a design wave force model were proposed and compared with Goda’s design formulae for standing waves. Results clearly displayed that 45° incident short-crested waves could induce greater total wave forces on a vertical breakwater than those by Goda’s formulae at the same depth. Differences became greater at d = 40m by about 12% ~ 17% for T = 10s and 17% ~ 29% for T = 18s based on Fenton’s 2nd and 3rd-order approximations.

This paper discusses wave impacts on vertical and composite breakwaters and related coastal structures. It describes types of vertical walls in use, with particular reference to older walls that may be much more influenced by wave impacts. Methods to estimate wave forces are identified. Analysis of performance suggests that these under-predict wave impact loads, and cannot identify combinations of geometry and wave conditions which lead to impacts.

Comprehensive 2-dimensional hydraulic model tests have been conducted using random waves to measure wave pressures (and other responses) on a wide range of simple and composite vertical walls. The test results have been used here to:

Analysis of % of impacts has defined a new design diagram to identify wave conditions and wall/mound geometries which cause impacts. These results are intended for engineers analysing vertical or composite walls in deep water, in harbours, or along the shoreline.

Froudian scaling laws are often used to convert model wave impact pressures to prototype scale. However, although many model studies have been performed in the past, the effects of scale on the magnitude and duration of wave impact pressures have yet to be determined.

Wave impact pressures were monitored on a Cob armoured breakwater at LaCollette Harbour, Jersey, UK, throughout the Winter of 1993/94. In addition, a 1:32 scale model of the prototype breakwater was constructed at the University of Bristol and subjected to a similar wave climate as was measured at prototype scale. A comparison of the pressures measured at the 2 scales has allowed the scale effects present in the wave impact process to be determined.

Based on impulse theory and experimental investigations on breaking wave kinematics and impact loads, prediction formulae for impact forces have been derived for vertical face breakwaters and further monolithic structures where wave effects dominate design considerations. Hydraulic model tests have been performed to obtain the water mass involved in the impact process and to verify the theoretical results obtained from theory.

A numerical method is developed to analyze the dynamic responses of large-scale floating structures to waves. A boundary element method is applied to evaluate the fluid motion and a finite element method to analyze the response of structure. The BEM and FEM are combined to solve the wave-structure interaction problem by satisfying the continuity of the pressure and displacement on the fluid-structure interface. The unknown time-dependent boundary conditions on the free surface and the interface are evaluated by a time-stepping procedure, which gives a time domain solution. An implicit scheme ensures the calculation precision.

The determination of the design wave height (often given as the significant wave height) is usually based on statistical analysis of long-term extreme wave height measurement or hindcast. The result of such extreme wave height analysis is often given as the design wave height corresponding to a chosen return period. Sometimes confidence band of the design wave height is also given in order to include various sources of uncertainties.

In this paper the First Order Reliability Method (FORM) is used to determine the design wave height corresponding to a certain exceedence probability within the structure lifetime. This includes the statistical vagrancy of nature, sample variability and the uncertainty due to measurement or hindcast error. Moreover, based on the discussion on the statistical vagrancy of nature, a formula for the calculation of encounter probability is presented.

Many coastal structures and natural coasts have openings, overhangs and projections which are open to impact by incident water waves. The sudden impact of a wave on a rigid surface leads to a rapid rise of pressure and consequent violent water motions. We consider the wave impact on the underside of a projecting surface. The example discussed is that of a flat deck close to the mean water level. A pressure-impulse approach is used, which has the advantage that given a solution for one problem it is possible to select pressure-impulse contours which give the solution to related problems. The pressure gradient on the underside of the deck is especially strong near the seaward edge of the impact region, so this is a region where any projections on the structure’s surface may be subject to strong shearing forces. On the other hand the maximum pressure-impulse is at the landward end of the impact zone, it is here that the deck is most likely to be ‘blown’ upward.

Problems associated with the measurement of wave impact pressures are described and the poor comparison between the results of previous studies is outlined. It is argued that the force impulse form and magnitude are more relevant parameters for caisson design than maximum impact pressures. Data from small and large scale laboratory measurements are used to develop a simplified design approach for caisson breakwaters based on the limited magnitude of the force impulse. Comparison between large scale data and predictions based on small scale results show reasonable agreement.

Recently, wave overtopping over a vertical wall for normal incidence were treated analytically on the basis of the wave energy flux concept (Mizuguchi, 1993). In this study, the Mizuguchi’s model for normal incidence is extended to oblique incidence. Incident wave angle effect on the wave overtopping rate is investigated. Validity of the extended model is checked experimentally. Satisfactory agreement between the extended model and the experimental results was found for the wave overtopping rate.

This paper describes results of a field experiment to examine the effect of wave reflection on suspended sediment transport in front of a seawall. High frequency measurements of wave elevation, velocity and suspended sediment concentrations were made simultaneously on a natural beach and in front of a seawall at Teignmouth in South Devon (U.K.) in June 1995. Wave reflection at the natural beach was found to be dependent on frequency; low frequency waves being preferentially reflected while incident waves were dissipated. At the seawall the incident wave reflection coefficient was 0.9 indicating only a small amount of dissipation. The doubling of energy over the sea bed was found to greatly increase the suspended sediment concentrations in the water column, although the amount of this increase depended on the water depth. A data analysis technique was developed which allowed the incoming and outgoing wave contributions to the sediment transport to be analysed. In these accretionary conditions incoming waves transported sediment onshore in both wall and beach cases, while in the wall case sediment transported offshore by the outgoing waves balanced the onshore transport. Sediment build up which was observed at the top of the natural beach was not observed in front of the wall. Sediment maintained in suspension in front of the wall was available for longshore transport, and this was enhanced by the presence of the wall.

A laboratory experiment was carried out to investigate wave energy dissipation in a coastal kelp field of Laminaria hyperborea with a purpose of finding the damping rate. Parameters measured were wave heights at 8 locations along the direction of wave propagation, forces on artificial kelp plants, and velocities in between the plants in 4 different water depths. It was found that in 4, 6, 8 and 10 meter water depths, the damping coefficient was 0.0094, 0.0032, 0.0014 and 0.0005m^-1 respectively. Results show that the damping rate varies with population density, size of plant, water ¹depth and wave period.

In order to develop a new beach preservation technique which has two functions of protecting the beach in a storm and enabling utilization of beach during calm sea, we consider the system of controlling a groundwater level by burying a permeable layer under the foreshore. Since most of the components are buried underground, people on the beach do not notice the presence of the system, enabling preservation of the beach in its most natural state. The greatest challenge of the system is, however, whether installation of the permeable layer alone will fully prevent erosion. Authors therefore conducted an experiment to evaluate beach stabilization effect of the present system. The result indicates that the permeable layer buried in the sand can prevent rise in the groundwater level and the wave set-up. The critical wave height for the foreshore erosion is 1.66 times higher than that on the beach without the permeable layer.

To have a coastal protection work of high quality, we are developing a new beach protection system, that is a beach drainage system, in which the groundwater is naturally drained to the offshore through a permeable layer setting up under the beach. To examine the drainage function of the permeable layer and its effect on the beach stabilization, a field experiments have been conducted during storms. As a result, it is confirmed that the permeable layer drain the groundwater gravitationally into the surf zone and has a function of decreasing a speed of erosion in a storm, and the eroded foreshore is recovered quickly in a calm.

It is essential to understand the details of the mechanisms by which a coastal drain works in order to build up the method which enables us to estimate discharge requirement for effective operation in field conditions. Some measurements on the changes of quantities which may be relevant to the function of coastal drain are discussed. Then, an attempt to implicate the current components produced by drainage in a numerical model of beach profile evolution is discussed.

A commercial multi-segmented beach dewatering system became operational December 1994 on the eastern shoreline of Nantucket Island, Massachusetts, USA. The objective of the installation was to cost-effectively stabilize a critically eroding reach of shoreline with minimal environmental impact. To assess the potential for wider use of beach dewatering in coastal erosion management, a comprehensive and independent monitoring program was developed and implemented to objectively evaluate the beach dewatering project. Observational methods and analyses are discussed relative to the ability to differentiate between the influence of the dewatering segments on beach response, in contrast to 'natural' shoreline response to coastal processes. Economics, measurement needs, measurement accuracy, and temporal and spatial resolution of data acquisition are discussed and evaluated.

The extent and causes of shoreline variability at Ocean Beach are studied. Sediment transport processes and directions are identified utilizing available information of the following: geographic description of vicinity; sediment characteristics; detailed data regarding tidal currents; and wave behavior. The net alongshore transport rate at Ocean Beach is estimated to be northward. The rate decreases with distance north, with sand accumulating in the beach and dunes. The sand that passes Point Lobos is believed to continue alongshore through the Golden Gate. Some is lost to maintenance dredging and dunes. The remainder is speculated to return to Ocean Beach by ebb tide currents.

This investigation addresses empirical evidence on wave action and shore erosion during extreme floods on Great Lakes coasts. Historical information shows that record coastal floods on the Great Lakes usually involve moderately extreme storms during relatively brief intervals with overall lake level much above the long-term average. The 100-year flood on U.S. lakeshores appears most likely to be accompanied by coastal wave heights with recurrence interval of about: three years on the four upper Great Lakes; or one-half year on Lake Ontario. Shore changes during the 100-year flood seem susceptible only to a coarse statistical estimate because available studies reveal Great Lakes erosion to be extremely variable in onset and amount. Two simplified erosion treatments are outlined here, one applying average annual recession rate for a locality, and the second, an empirical relationship originally developed for seacoast storm effects. The latter treatment appears verified by evidence from a Lake Michigan study, and such estimates of episodic erosion cross section are much lower than for extreme events on U.S. seacoasts.

Increased development along the Oregon coast has led to heightened concern over beach erosion. As a result, more shore stabilization structures have been erected in recent years. A long-term field monitoring program, involving seven typical structures located on the central Oregon coast, was initiated in the spring of 1986 to quantify the effects of shore stabilization structures on the surrounding beach and adjacent properties. All structures are rip-rap revetments or seawalls. Volumetric changes of the subaerial beach at each site were examined at scales ranging from the entire beach surrounding the structure to the beach in the immediate vicinity of the structure. When the data coverage and site geometry permitted, a far field control section was utilized to compare the volumetric response of a portion of beach relatively uninfluenced by the presence of the structure with that of the beach on the two structure flanks. Measurements are presented for the seven structures over the observation period of ten years to document the long-term effects the structures are having on the fronting beach and adjacent unprotected properties. Ten years of monitoring has revealed that the structures at these seven sites are having no adverse impacts on the surrounding beach or adjacent properties. This can be attributed to the limited amount of wave attack that the structures have experienced. The structures are built high on the profile, and experience wave attack only during the most severe storms.

Profile volumes provide an indication of the condition of barrier islands and beaches. While site specific, they can be used along any littoral shoreline as a measure of the relative “health” of one section compared with another. Assuming shorelines develop an equilibrium profile around which the beach cycle and cross shore changes occur, profile volumes integrate small scale perturbations and provide a target sediment volume for the site between reference contours. Profile volumes may be considered for various parts of the profile as follows:

• Dune volume above storm surge levels (after FEMA) as a measure of the reservoir of sand required to prevent over topping.
• Mean sea level (MSL) barrier cross-section — the section that must be fully scoured to produce a full breach channel.
• Inner beach profile — the section that represents the condition of the recreational beach.
• Inshore profile — the section that represents the core “base” of the barrier island.

By comparing versions of these sections from site to site, especially where there have been known breaches and variations in beach erosion rates it is possible to develop systematic criteria for the health of the shoreline in question. Profile volumes provide a straight-forward technique for diagnosing barrier erosion problems. A case study from Westhampton Beach and Fire Island (New York) illustrate the application.

Since 1989 research has been contucted in the Netherlands on the issue of breach growth. This contribution describes the set-up and results of wave basin experiments which had the aim to obtain insight into the process of growth of the width of a breach. From analysis of the recorded data (flow characteristics in the breach and the development of the breach) an empirical relation for breach width growth has been derived. This relation has been implemented into a (conceptual) numerical model which is briefly described in this document also.

This paper examines the influence of Hurricane Andrew on the sediment budget of an 80-kilometer section of the Louisiana barrier islands west of the modern Mississippi delta. Because long-term bathymetric change has been extensively studied in this area, excellent baseline data are available for evaluating the impact of Hurricane Andrew. Results show that despite the high intensity of the storm and a storm track optimally positioned to impact the study area, the storm did not have an overwhelming influence on the sediment budget when compared to the changes occurring over the previous 50 years. For the Louisiana barrier islands, a 50-year record appears to be adequate for averaging the long-term contributions of both major and minor storm events to the sediment budget.

This paper describes the morphological and economical evaluation of the beach nourishment maintenance strategy of an eroding recreational beach at the Dutch coast. In addition to the results of this evaluation two alternative strategies were analysed. In order to assess the economical feasibility of the alternatives appeared to be essential to estimate the morphological effectiveness of the alternative strategies. Therefore, an extensive numerical modelling scheme was set up. The numerical modelling played a key role in the understanding of the existing morphological system and subsequently in the assessment of the effectiveness of the alternatives on a long term basis. The morphological effectiveness of the alternatives, being offshore breakwaters and a 450 m long groin, was calculated in terms of reduction of required beach nourishments. The objective of the study was not only to find an optimal coastal morphology strategy but also to find the best strategy which combines a sound beach protection with effects valuable for the specific recreational function of the beach, including an effective way to deal with eventual lee-side erosion. Possibilities were studied to shift the erosion to the dune area in the north which would allow a more flexible and dynamic way of maintenance.

Ocean City Inlet, Maryland presents a data-rich site for evaluating the total littoral impact of an inlet system with a significant adjacent beach response. Analysis of adjacent beach and bay shoreline data, adjacent beach profiles, ebb and flood shoal evolution, and dredge/fill history provided a database with which the inlet’s littoral impact to adjacent beaches was quantified. The even/odd method, which decomposes shoreline changes into their symmetric (even) and antisymmetric (odd) components about a point of significance, was applied to the volume change dataset. This analysis indicated a present-day (1996) alongshore impact distance of 8 to 13 km from the centerline of the inlet. A second method, which relates the total “inlet sink” volume to adjacent island (ocean and bay) volume change, was also applied. The total inlet sink volume ranged from 10.8 to 15.6 million m³, and reflects the volume of material captured by the inlet which is assumed to have been derived from adjacent beaches. The inlet sink method indicated that, at most, 10.8 million m³ can be realized within ±14.2 km (data limit). The paper concludes that the alongshore impact of Ocean City Inlet most likely extends beyond ±14.2 km.

A probabilistic model has been developed to analyze the susceptibilities of coastal properties to wave attack. Using an empirical model for wave runup, long term data of measured tides and waves are combined with beach morphology characteristics to determine the frequency of occurrence of sea cliff and dune erosion along the Oregon coast. Extreme runup statistics have been characterized for the high energy dissipative conditions common in Oregon, and have been found to depend simply on the deep-water significant wave height. Utilizing this relationship, an extreme-value probability distribution has been constructed for a 15 year total water elevation time series, and recurrence intervals of potential erosion events are calculated. The model has been applied to several sites along the Oregon coast, and the results compare well with observations of erosional impacts.

A conceptual model to explain and simulate the long-term (decadal) Ebro delta coast evolution is presented as well as the approach to be followed to convert this conceptual model into a numerical one able to quantitatively predict the deltaic coast behaviour. Moreover, a first running sub-model which simulates most of the changes suffered by the outer coast is described in details. This sub-model is a long-term scale version of a one-line coastal model in curvilinear coordinates. The developed model has been verified and predictions of coastline evolution under different scenarios are also presented.

Nam Ha Province is situated on the coast of the Red River Delta, immediately east of the mouth of the Red River. The coast of the delta is very dynamic in which large quantities of sediment are supplied by wet season run-off. However, in Nam Ha province the coast is retreating such that successive lines of dikes have been abandoned and a unique 'managed retreat' strategy is underway with double lines of dikes along large parts of the province’s coast. This paper reviews and describes the possible causes of the erosion problem and highlights the unique way in which the local coastal engineers are adopting, out of necessity, the classical retreat strategy. Other impacts of the problem such as environmental and socio-economic impacts are also reviewed. Based on the qualitative first order analyses a strategy has been defined towards a sustainable development of this coastal area.

The purpose of this study is to examine the recent shoreline history at Indian River Inlet, Delaware using beach profile data. Indian River Inlet was stabilized in the late 1930’s with two parallel rubble mound jetties. The stabilization resulted in considerable modifications to the surrounding beach environment, leading to the construction of a sand bypassing system in 1990. The profiles adjacent to the inlet are first examined with the standard tools, such as shoreline change, volume change, and sand budget. Then, details are given on the use of Principal Component Analysis (PCA) in the coastal field, an explanation of its function, and the differences between the complex and non-complex versions. Results are presented for areas north and south of the inlet in both 2-mode and 3-mode versions of Complex Principal Component Analysis (CPCA). The results illustrate the ability of CPCA to detect moving features within the profile data, including its direction and speed, as bypassed sand is seen moving to the north.

An improved 3-D beach evolution model coupled with the shore-line model, named “3D-SHORE”, was newly developed to estimate both the spatial bottom topography change and the shoreline change. In calculation of the shoreline change, the total longshore sediment transport rate is estimated by integrating the local sediment transport rate in the direction parallel to the shoreline from the breaking point to the run-up point. The applicabilities of the model were verified through comparisons with both the results of the movable bed laboratory experiment and the actual beach evolution.

Shoreface nourishments are sometimes used as an alternative for ordinary beach nourishments. Many aspects of the behaviour of shoreface nourishments are still unknown. Shoreface nourishments affect the morphological behaviour of a coast. Line modelling might be used to study and to predict the behaviour of shoreface nourishments after execution. Although not every detail of the real behaviour can be dealt with, line modelling is still a rather simple but powerful tool. The recent application is discussed of the line modelling technique to study several shoreface nourishments carried out in the NOURTEC framework.

The littoral processes and long-term shore protection plans are analysed for the coast of Valencia (Spain). The breakwaters built during this century by the Port Authorities have greatly affected the most Southern beaches by interrupting the natural longshore sand transport. The monitoring program of the beaches of Valencia (Spain) has been established for a precise estimation of the evolution in time of the beaches to the North and South by the Port of Valencia. Periodic topographic surveys provide the basic time-dependent beach description of the area. The two main objectives are the following: a) 3-D description of the beach surface, including estimation of reliability and measurement errors of bathymetrics, and b) stochastic description of wave climate.

High precision and cost-efficient beach surveying techniques have been developed during the monitoring program of the beaches of Valencia (Spain). Beach profiles and zero-shorelines have been obtained with systems and errors similar to the terestrial topography. The methods are simple enough to be applied by general land surveyors with a minimum training and may be extended to a variety of beaches for systematic and low-cost monitoring programs.

While structural erosion or accretion of a coastal stretch is of primary concern to coastal management, knowledge of coastline oscillations on larger time scales relative to the erosional or accretional trend would allow for a more efficient management practice. Our analysis of more than thirty years of observations of dune, beach and nearshore evolution reveals some of the typical oscillatory behaviour in time and space on a decadal scale. We have focused on the behaviour of the duneface and analyzed the possible relation between the duneface behaviour and that of the nearshore morphology. Amongst our results are the findings that the demeaned oscillatory duneface evolution on a decadal scale is not only correlated with the recurrence frequency of the migratory bar system, but also with a cumulative measure of episodic wave events.

The Terschelling shoreface nourishment was studied over a period of about 2.5 years. The nourishment was originally designed to act as a feeder berm. Since its implementation, the nourishment has completely satisfied the design objectives. However, the nourishment only partly acts as a feeder berm and the actual success of the nourishment is also based on its breaker berm function. The creation of a wave shadow zone leads to an interception of part of the longshore drift and the development of a salient effect.

Sand balance of the littoral system determines whether erosion or recession will occur. Adding sand to the system is the only engineered way to restore the balance and prevent erosion or recession. Justification of beach nourishment as a shore protection measure depends on the benefits criteria used in the analysis, and societal goals will decide the criteria.

The problem of coastal erosion in Russia became especially urgent in 50th-60th during the extensive river damming, taking place mainly in the regions valuable for society. To prevent erosion, which spanned thousands of kilometres of new shoreline different shore protection techniques were used, including hard structures, shoreface and beach nourishment as well as hybrid methods. Most if not all of these techniques were previously applied on Novosibirsk Reservoir, one of the first Russian large man-made lakes. Long-term observations of structures state and recent studying of response of the coastal environment on the projects emplacing testify the greater efficiency of coastal stabilization by beach nourishment programs and hybrid structures.

Within the framework of the EU-sponsored programme Marine Science and Technology (MAST), a full-scale test was implemented in 1993 in Denmark, Germany and the Netherlands with the aim of evaluating the use of shoreface nourishment.

In this paper the background, the set-up and the results of the Danish part of the NOURTEC project are presented.

This paper evaluates the utility of mathematical models for prediction of the planform movement of beach nourishment projects. The results of one-line models (analytical and numerical) are compared to the evolution of nine laboratory-scale model beachfills. Several methods of planform modeling are evaluated, varying in complexity. Comparison of planform modeling suggests that, in some circumstances, using a simple analytical treatment of refraction may be a feasible alternative to using more rigorous numerical wave modeling for shoreline modeling purposes. The relative ability with which different equations for net longshore sediment transport rate reproduce observed beachfill evolution is discussed. Information on the effect of wave climate and beachfill geometry on beachfill lifetime is extracted from the laboratory study. The observed effect of lower wave height, greater beachfill length, and the tapering of a beachfill is a greater beachfill lifetime, in agreement with conventional wisdom. Increasing beach slope and decreasing wave period are both observed to cause a slight decrease in beachfill lifetime.

The nearshore zone of the Hel Peninsula has a hydro-geomorphological system which, together with the influence of the port at Wladyslawowo, causes permanent erosion of the basal and central part of the peninsula’s sea coast. After a period during which traditional methods of coastal defence (seawalls, groynes) were used, a massive artificial nourishment of the dune and beach was realised in the years 1989-1995. The borrow material used was of lagoon and marine origin. The progress of morpho- and lithodynamic processes was evaluated basing on quantitative analyses of changes in topography and granulometry. In the land part of the coastal zone, accretion of deposits resulted in rebuilding of the dunes and beaches. In the nearshore zone, accretion occured on the beach slope, and resulted in the development of shore terraces and breaker bars (especially the outer breaker bars). This was accompanied, by related with the accretion, processes of erosion in the form of U-shaped troughs. These processes proceeded at small changes in the erosion/accretion (e/a) system of the nearshore zone in the whole region. Smaller input of sandy material into the nearshore zone resulted in gradual return of the e/a system to initial state. If the safety of the peninsula is to be maintained, artificial nourishment must be executed every year. Frequency and volumes of renourishment will depend on the quality of used material. Therefore new sources of borrow material must be seeked.

A beach profile numerical model is employed to calculate the change in dune cross-section for a wide range of increased, water level events. The volume loss in dune cross-section increases with relative increase in storm surge elevation above the design water level. These “damage curves” for dunes are analogous to rubble mound damage curves created by excessive wave energy above the design wave height.

The results are applied in the design of a protective, beach-dune structure (with buried seawall as a safety factor) at Dam Neck, Virginia for the US Navy. The damage curves are used to estimate annual dune maintenance costs and hence, total life-cycle costs for this “soft” alternative to shore protection. Interestingly, the dune-beach-buried seawall alternative costs less than a concrete structure using artifical units for armor.

Construction is complete and a three year monitoring project begun so that actual versus theoretical dune damage curves can be determined in the future.

Twenty-six beach profiles were surveyed immediately after the passage of storm conditions and were compared with pre-storm situations. They include 1) eleven locations spread throughout the entire 60 km reach of the Pinellas County coast including wide, narrow, natural and nourished sites, with and without seawalls; and 2) 15 locations confined to three adjacent nourishment projects along 14 km of Sand Key.

The overall behavior of the nourished and natural beaches along the 60 km reach of coast was similar, displaying a general trend of 1) shoreline erosion ranging from 2 to 10 m, 2) upward and landward migration of the nearshore bar, and 3) backbeach accumulation and increase in the berm height. Shoreline orientation and beach sand composition played no significant role in beach performance during the storm. The technique of dry beach replenishment using a dragline and conveyer belt may contribute to the more severe shoreline erosion at the Indian Shores nourishment project as compared to the traditional pumping technique used at Indian Rocks Beach and Redington Beach.

Temporary berm accumulation and shoreline accretion were recorded at two chronically eroding locations downdrift of structures. The shoreline accretion was caused by the landward sand transport induced by the storm waves. The storm accumulation was eroded by the normal-weather longshore sediment transport within three months after the storm.

The current version of SBEACH model (Larson and Kraus 1989) failed to reproduce the Opal-induced beach changes in the surf zone. The unsuccessful prediction was attributed to the uncertainties in offshore wave measurement, and morphological and computational complications caused by the exposure of hard bottom in the nearshore region.

An empirical model is presented which simulates the effect of tidal translation of cross-shore sediment flux patterns, in support of a hypothesis that wave height and tidal range are the key influences in the formation of characteristic macrotidal beach profiles. The energetics-based model is based upon field observations of cross shore currents and sediment fluxes from three high-energy macrotidal (tide range>4 m) locations around the U.K, chosen as representations of dissipative, intermediate and reflective environments (after Wright and Short, 1984). The observed depth-dependant flux patterns are translated across linear beach profiles, with gradients modelled from sediment characteristics (Dean 1977, Kriebel et al 1991), the evolution of characteristic macrotidal beach profiles and the development of attendant features such as break-point bars, low tide terraces, and steepened foreshores are observed.

This paper considers the evolution of steep mobile sediment beaches under random waves and results from a new experimental investigation are presented. Both hydrodynamic data obtained over fixed beds and the resulting profile evolution of fine, coarse and bimodal sediment beaches are discussed. Wave heights and undertow in the inner surf zone are found to be poorly predicted by commonly used numerical solutions. In addition, the undertow appears to be strongly influenced by wave grouping in the nearshore. The behaviour of the fine, coarse and bimodal sediment beaches are compared and contrasted. The fine sand beaches tend to erode in the inner surf and swash zones, with the sediment moving predominantly offshore to form a bar. In contrast, onshore sediment transport dominates over the coarse sand beaches, resulting in the formation of a berm above the initial still water level. The bimodal beaches show a similar evolution to the fine sand beaches. However, considerable sediment sorting occurs, with the swash zone largely denuded of fines and the coarser sediment deposited between the still water line and the bar. The data suggests that the stability of the coarse material is significantly reduced by the presence of fines, with little evidence of armouring effects under high incident energy conditions.

The Wave Project at the University of California at Berkeley was established in 1944 to develop a relationship between nearshore waves and the underlying topography for supporting amphibious military landings. The project was continued for scientific purposes until 1952 under the more general name of “Wave Observation and Beach Surveys,” including the Amphibious Oceanography Project. These early field observations are a central part of the genesis of coastal engineering in the United States. Beach profiles were surveyed by stadia and by amphibious vehicle along the coasts of Washington, Oregon, and California, and the results were documented in University of California, Fluid Mechanics Laboratory, reports in the HE-116 series. The profile survey measurements, now 50 years old, are still the only such data available for many beaches along the U.S. Pacific Coast. The data set thus comprises a valuable baseline for documenting change in the coast, and it is a resource on the morphology and grain size for high-energy beaches that are extremely difficult to survey. The profile survey plots in the limited-circulation reports have been digitized and are available for general access in the present study. This paper reviews the early measurement program and the available data set.

Dunes constitute a central element in shore-protection designs aimed at preventing inundation and erosion of the upland by storms. In the present study, the dune-erosion mechanism is investigated through field observations of the performance of sand dunes under storm action in Japan and in the United States. The observations are quantified by analysis of three test series carried out in the SUPERTANK project. The SUPERTANK data set includes tests on erosion of an uncompacted and a compacted near-vertical dune by random waves. The SBEACH numerical model of dune erosion and profile change is modified to erode dunes by the force of incident waves. This sediment can then supply the profile change model that demands offshore movement of sand in response to the occurrence of storm waves and elevated water level. The simulations show good agreement with the erosion measured at SUPERTANK for the uncompacted and the compacted dunes.

A phase-resolving wave transformation module is combined with an intra-wave sediment transport module to calculate the on/offshore sediment transport rates. The wave module is based on the Boussinesq equations extended into the surf zone. The vertical variation of the instantaneous currents and concentrations are calculated. The net sediment transport rates are calculated, and the equation for conservation of sediment is solved to predict the beach profile evolution. The results of the present paper showed that the undertow contribution to the sediment transport rates dominated only at local areas even for eroding beaches, suggesting that other contributions should not be neglected.

Based on a large amount of published laboratory results, reliable model is developed for computing beach profiles under regular wave actions. The sediment transport is separated into suspended load and bed load. The suspended load is computed as the product of the time-averaged suspended concentration and the time-averaged velocity. The bed load is developed following the similar step as Watanabe (1983) but the applied area is different. The wave model of Dally et al. (1985) is modified and used to compute wave height transformation. The beach profile change is computed from the conservation of sediment mass. The beach deformation model is verified with small scale and large scale experiments. Reasonably good agreement is obtained between measured and computed beach profiles.

In the present study, experiments were conducted using CRIEPI’s Large Wave Flume (205m long, 3.4m wide and 6m deep) to investigate cross-shore hydrodynamics, sediment transport and beach change processes. On the experiments, suspended sediment transport in the surf and swash zones was directly measured under the condition of random waves. Moreover, the long wave effect to sediment transport was also investigated.

The aim of the following paper is to demonstrate that standing long waves can generate intertidal morphological features in a dissipative macrotidal setting. In this environment the tidal excursion can exceed the length scales associated with long waves. This extends the work of Simmonds et al (1995) in which it was shown that monochromatic long waves could generate sediment convergence patterns that bore a good similarity to observed topographic features, namely ridges and runnels from a field site on the Belgian coast. The simulation is modified to include a band of long waves and it is found that a good correspondence with real topography can still be achieved on a tidally averaged basis by allowing for a degree of uncertainty in the breaking criterion. It is also argued why the observed scales are more likely to correspond with the shorter end of the long wave spectrum. The simulation helps to shed light on the conditions in which such features are known to form.

The paper presents mathematical models for wave deformation and for beach profile change in the surf and swash zones. Boussinesq-type equations including a breaker-induced energy dissipation term (Watanabe et al., 1994) is extended to the swash zone by introducing a periodically moving shoreward boundary. Computation is made on the wave deformation on constant slope beaches, particularly on the runup and run-down heights as well as the wave heights at the still water shoreline, which are compared with existing formulas. Beach profile change is computed with the sediment transport rate formula proposed by Dibajnia and Watanabe (1992) after a further generalization, together with Lagrangian treatment for the sediment motion in the swash zone, using the near-bottom velocity obtained from the wave computation. The validity of the models is examined through comparisons with measurement data obtained in large wave flume experiments.

A new non-linear cross-shore sediment transport model called CROSS is developed based on equilibrium beach profile concepts and scaling relationships. CROSS and three other existing models, CCCL, (Chiu and Dean 1984), EDUNE (Kriebel 1989) and two versions of SBEACH (version 2.0, Larson and Kraus 1989, and version 3.0, undocumented) are investigated by comparing erosion occurring from November 1991 to January 1992, at Ocean City, Maryland, the site of a major beach fill placed by the State of Maryland and Federal Government in 1988, 1990 and 1991. Among the four models, CCCL is the only one which overpredicts average dune erosion; the other three underpredict it. Overall CROSS and EDUNE yield better predictions than the other two models.

A 5 MHz multiple transducer array was used to measure wave generated bedforms near Duck, NC. The transducer array consists of 37 transducers with a center to center spacing of 1.2 centimeters. Seabed measurements were made with approximately 1 millimeter vertical and 2 centimeter horizontal resolution. Measured ripple dimensions are compared to three popular ripple prediction models. It is shown that errors of over 100 percent were found between measured and predicted ripple heights and lengths for all ripple models compared. Errors in predicting ripple steepness ranged from 37 to 55 percent.

This paper takes advantage of fortuitous, near ideal conditions which existed for a subset of field data, to obtain the hydraulic roughness of the surface of a coral reef platform. This was accomplished by observing the transformation of natural, unbroken, oscillatory wave trains, propagating over the reef top in water of constant depth, where wave bed friction damping was the only active wave transformation process. The paper also demonstrates that while coral reefs may be perceived as being much rougher than sandy beds, they may in fact be no rougher in hydraulic terms, than many sandy beds experiencing the same wave and water depth conditions.

In almost all of the previous studies on the seabed configuration, the seabed configuration is classified based on the bottom shear stress, or Shields number. While, in the wave field, the wave-induced-water-pressure change can have a secondary effect on the sediment transport. The laboratory experiment on the seabed configuration under the coexistence of the oscillatory flow and the water-pressure change is conducted in this study, to investigate the effect of water-pressure change on the seabed regime classification.

The existing region of various bed configurations, such as no-motion, bed-lad, suspension over ripple and sheet flow, changes with the change of the amplitude of water-pressure change. The ripple geometry, or flatness of ripple, are also affected by the water-pressure change. The mechanism of theses changes are discussed related to the lift force due to the porewater-pressure distribution in sand layer.

Mobile bed hydraulic models have been used in the laboratory for a very long time. Attempts to predict the consequences of river engineering works, dams and barrages, flood protection schemes and dredging methods have led to wide ranging scientific research in material scaling. The design of breakwaters, beach protection systems and sea walls have long been studied in physical models. All of these require a method for measuring the effects of water movements and the resultant erosion, deposition and scouring of materials. This paper reviews some methods that have been used on laboratory models, and attempts to suggest ways forward in the future.

Boundary layer flow above sand ripples under both oscillatory flow and progressive waves is examined by two dimensional numerical simulation. The simulation shows the difference of the flow between under an oscillatory flow and progressive waves. The boundary layer flow under oscillatory flow is symmetric, on the other hand, the flow under progressive waves is asymmetric. The mechanism of the asymmetric flow is explained by the convection effects of progressive waves.

The vertical distribution of the mean shear stress inside the surf zone is compared to the terms in the time-averaged horizontal momentum equation using one set of laboratory measurements of the free surface elevations and fluid velocities u and w induced by regular waves spilling on a plane slope. The vertical distribution of the eddy viscosity is estimated directly from the measured mean shear stress and velocity. The shear stress distribution in the surf zone is shown to vary linearly with depth until the bottom boundary layer where it reached a nearly constant, negative value. The shear stress variation in the transition region differs distinctly from the inner surf zone. The vertical variation of $\overline{uw}$ is shown to be small outside the surf zone except near the bottom. Inside the surf zone, it is shown that the $\overline{uw}$ term of the horizontal momentum equation is likely to be important in the transition region and that its importance diminishes in the inner surf zone. The vertical distribution of the eddy viscosity has a form which is small near trough level, increases to a maximum value about one-third of the depth below trough level, and then decreases toward the bottom. The eddy viscosity in the middle of the bottom boundary layer is two orders of magnitude less than the eddy viscosity in the interior.

Field observations of near-bed high frequency velocity fluctuations and suspended sediment are compared with predictions of momentary flow stability by a quasi-steady linear instability model. Field observations were made as part of the Duck94 cooperative field experiment and consisted of a vertical array of four hot-film anemometers and 19 fiber-optic backscatter sensors located within the wave bottom boundary layer. Predicted instabilities for the quasi-steady model occur over length scales ranging from 2 cm to 1 m and therefore may be assumed to be a plausible mechanism for the generation of turbulence and suspension of sediment. However with the quasi-steady model, the instabilities are at the same phase as the sediment suspension events, but are occurring too late in the wave phase for them to be generating the observed turbulence.

The boundary layer flows and wave-induced pore pressures inside porous beds are both investigated in wave tank. Two kinds of porous beds are composed of two different grades of quartz sands which the porosities are 0.437 and 0.472 respectively. According to the experimental results, it is found that the larger pore pressure in permeable bed is induced by the longer wave period, and the pore pressure has an exponential attenuation with the wave steepness increasing.

From the elaborate measurements in the boundary layer, the overshooting induced by wave motion is effected by bed porosity and it becomes smooth. In the experimental cases, the maximum horizontal overshooting occurs at $\tilde{Z}/\Delta \approx 1.2$, which is lower than the impermeable case of $\tilde{Z}/\Delta \approx 2.7$ obtained by Hwung and Lin (1989). Furthermore, the vertical overshooting has also been found in our experiments.

This paper treats the numerical prediction of initial and long-term morphology of small pipeline trenches. For this purpose a refined flow and sediment transport description is applied such that the entire mathematical problem is formulated and solved on a curvilinear grid using a k – ε turbulence-closure.

The backfilling process of trenches exposed to either waves or a steady current is of importance in relation to the implementation of pipelines in the marine environment. With respect to the sedimentation of trenches, the non-dimensional Trench-Keulegan-Carpenter number, KC = a/L, where a is the excursion length of a particle in waves and L the trench length, is investigated in detail, and an optimal KC-number for the backfilling rate is found. Coherent structures in the non-uniform unsteady trench-flow are shown to dominate the deposition rate when present.

The importance of a detailed description of the flow is further justified by comparing predictions of a very simple flow-model neglecting convective terms with the sophisticated flow-model.

A general, closed-form solution is presented to the linearized equation describing the velocity in a turbulent boundary layer. The solution is valid for any type of time-varying free-stream velocity, although the focus of the paper is on oscillatory flows generated by surface waves propagating over the sea bottom. A primary objective is to employ the solution for waves with an asymmetric velocity field, where nonlinear effects are small enough to be neglected in the linearized turbulent boundary layer equation. The general solution is developed to more convenient forms for a few special cases, including a sinusoidally varying free-stream velocity and a velocity given by stream function theory. The solution is tested against two different data sets from oscillatory tunnels; one set involves a sinusoidal and the other set a cnoidal free-stream velocity.

High resolution synchronous measurements of turbulence, waves and vertical suspended sediment (S_sed) concentration profiles have been obtained during a storm above a rippled bed comprising coarse/medium sand located close to the end of a large offshore sand bank in a water depth of approximately 20 m. These data are utilized to study the temporal characteristics of sediments in suspension. Sediment resuspension ‘events’, exhibiting vertical coherence up to approximately 30 cm above the sea bed, are observed to span a range of temporal scales encompassing half wave, wave and wave group periods. The vertical concentration of S_sed is shown to be enhanced significantly by wave groups. Average S_sed profiles are described using a simple Rouse-type and an new ‘convective’ model.

Previous investigations have established the dependence of ebb delta volumes on wave energy and tidal energy at sandy inlets. In this study, this dependence was examined with respect to the rate of delta growth and the final equilibrium delta volume starting with the opening of a new inlet when no delta is present. A diagnostic model was developed for examining the influence of the ratio of wave energy to tidal energy on delta growth. Model sensitivity tests showed that increasing the suspended sediment concentration in the littoral zone caused the delta to approach equilibrium faster, but did not affect the equilibrium volume. Increasing the wave height increased the time of approach to equilibrium but decreased the volume. Finally, increasing the sand size increased the growth rate as well as the equilibrium volume. The model was applied to five Florida inlets. It was shown that the delta may never attain a true equilibrium volume, and the actual volume may fluctuate about a “quasi”-equilibrium volume consistent a wave energy to tidal energy ratio representative of the long-term wave and tidal conditions at the entrance.

The Port of Tauranga is located within a tidal inlet estuarine lagoon system which has been dredged to improve navigation for shipping since 1968. In 1992 a major dredging program deepened the entrance navigation channel through the ebb-tidal delta from 10 to 14 m, and the inner harbor channels to ~13 m. As a condition of the consent to dredge a detailed monitoring program was required which included annual hydrographic surveys over the flood and ebb-tidal delta as well as recording current meter records from morphodynamically sensitive locations to compare with records taken before the dredging. Results of the hydrographic surveys showed significant morphodynamic change of the flood-tidal delta had occurred essentially by the time the 6 month dredging program was completed. Comparison of the S4 current meter recordings showed current changes consistent with expectations of the EIA. Changes on the ebb-tidal delta were not expected but have occurred although not as rapidly, and seem to be ongoing.