Coastal Engineering 2000

Three paradigm shifts in coastal engineering are overviewed. The paradigm shift in evaluation of wave pressures exerted upon vertical breakwaters have been completed: from the discontinuous, dual formula system to the continuous single formula system. The paradigm shift in wave transformation analysis has been taking place from the significant wave approach to the random wave approach. The paradigm shift in sediment transport problems will occur soon with a shift of attention from bedload motions to sediment suspension by breaking waves. The author is proposing a new power model for estimation of local sediment pickup rate.

Coastal problems are complex and coastal processes are often not clearly understood. Our design tools are sometimes inadequate and the data used in design is usually incomplete or of insufficient quality. The resulting designs therefore contain substantial uncertainties. To reduce these uncertainties, designs normally incorporate results of model studies. This modelling essentially provides an opportunity to reduce uncertainty through trial and error. The models themselves are not perfect and hence model results also contain uncertainties. It is encouraging, however, that there are many opportunities to improve the art of coastal design. This paper addresses various ways to reduce uncertainties in model results and design. These range from proper model validation to better interpretation of model results, to improvements in models and people operating those models. (Technical) symbiosis can also be achieved through careful integration of field measurement and modelling techniques.

There is a compelling urge for humans to live by the sea. The urge is there despite the risks of catastrophic storm surges wiping out the lives of thousands within a few hours, together with the demolition of property and ruination of valuable farmlands, and the presence of disease lurking within insect vectors or through cruel water-borne pathogens of coastal waters. To reinforce this nastiness, recently Australian immigration authorities sent video images of our muddy inhospitable coast, infested with crocodiles, mangroves and mosquitoes, to countries from where illegal immigrants are emanating.

The velocity field is modeled for sea waves propagating over a sloping bottom covered by megaripples. The flow is assumed to be irrotational, and long waves of small amplitude are considered. The analysis has been carried out to investigate whether an appropriate rotation of the coordinate system exists such that the cross-correlation of the velocity components due to waves vanishes, allowing an estimate of turbulent Reynolds stresses from the correlation between tilt corrected vertical and horizontal velocity components. The results show that such a system exists, and that the tilting angle depends on the bottom profile and on the characteristics of the wave field. As suggested by Stanton and Thornton (1996), the angle can be computed by minimizing the measured cross-correlation. However the present analysis suggests that the procedure should consider different wave components separately and should be applied sequentially at different heights from the bottom.

A model is developed for the turbulent eddy viscosity induced by wave breaking in the surf zone, which is based on the concept of a roller momentum-thickness and established theory for free turbulent wakes. The model is then tested in comparison to laboratory measurements of residual turbulence reported in Nadaoka and Kondoh. Without introducing any empirical coefficients, the ability to predict turbulence intensities for both spilling and plunging breakers is demonstrated.

As waves shoal and break across the surf zone, much of their kinetic and potential energy is dissipated by turbulence and entrainment of bubbles into the water column. This surface injected turbulence advects down through the water column, modifying the eddy viscosity profile. Under strong breaking waves in shallow water, the surface breaking turbulence extends down to alter the structure of the bottom boundary layer, and in turn significantly effects sediment suspension and transport. As the effective eddy viscosity of the water column is determined by the effects of both bottom and surface generated turbulence, understanding these sources of turbulence and distribution through the water column has important implications in modeling momentum transfer in the nearshore. In this paper, measurements of void fraction profiles under breaking waves and concurrent turbulent shear estimates allow the depth of influence of bubbles and wave-breaking induced shear to be estimated in the nearshore.

In this paper, a two-dimensional multi-scale turbulence model is proposed to study breaking waves. The purpose of developing the two-dimensional multi-scale turbulence model was to produce a relatively accurate model with moderate computer requirements. The free surface was tracked by the VOF technique, the log-law profile for the mean velocity was applied at the bottom. Compared to RANS models, the present model showed better agreement with experiments in terms of predicting breaking wave surface elevations, especially near the breaking point. The undertow predicted by the present model is reasonable. The SGS turbulent transport mechanism was also discussed in the paper.

Theoretical solutions for the wave bottom boundary layer (WBL) are obtained using a viscoelastic turbulent closure model including sloping bed effects. The overlying free stream velocity is given by nonlinear Stokes wave theory for a sloping bottom. The viscoelastic closure scheme extends conventional eddy viscosity models by incorporating the effects of eddy relaxation and diffusion on vertical momentum exchange in the WBL, and gives improved predictions of observed velocity profiles. Field measurements of nearbed velocity profiles are then compared with theoretical solutions for a 2° bed slope. Field measurements were obtained in the lower 50 cm of the water column in 3.7 m depth with a coherent Doppler profiler. Results are presented from a storm event for flat bed. Within the region 8 cm above the bed, the observed velocity profiles change rapidly in amplitude and phase relative to potential flow theory, indicating the presence of the wave boundary layer. Furthermore, the observed vertical velocity profile in this region deviates significantly from the WBL theory for a horizontal flat bottom, but compares well with the sloping bottom theory presented here.

Laboratory measurements of free surface elevations and fluid velocities were made to investigate the inner surf and swash zone hydrodynamics for one case of irregular waves on a rough, fixed, impermeable bed. The vertical profiles of the tangential velocity near the bed were measured at seven locations in the surf and swash zone using a laser-Doppler velocimeter and precision traverse. The temporal variation of the bed stress was estimated from an assumed logarithmic velocity distribution. The logarithmic velocity profile was established in the inner surf and swash zone for many phases of each runup and rundown event. The average of the absolute bottom stress was largest just below the still water shoreline and was dominated by the rundown bed stress at that location. The quadratic drag law with the friction factor fitted for each wave at each location gave good estimates of the measured bed stress. The friction factor averaged over all waves at each location was not constant across the inner surf and swash zone. The use of separate friction factors for the runup and rundown cycles improved the bed stress estimates above the still water shoreline.

This paper presents a unified numerical model for the bottom boundary layer and the upper layer in the surf zone. The model is based on the 2-DV Reynolds equations for turbulent flows with free surface boundary. At each time step of computation, the numerical mesh generated for the physical domain is obtained by applying an algebraic mapping technique, in which grid points are clustered close to the sea bed to resolve the high velocity gradients expected in the bottom boundary layer.

The paper deals with a mathematical and numerical model for simulating the sediment transport within bottom boundary layer. The mathematical model uses Reynolds equations for the hydrodynamic model and the two-dimensional convection-diffusion equation for the sediment transport model. Results of the numerical model are compared with laboratory data of Ribberink et al. and Katopodi et al.. Based on the analysis of comparisons, the validity of the model is discussed.

There are numerous ways to derive a system of 2D Boussinesq-type wave equations from the 3D potential flow equation with free-surface boundary conditions. This freedom in design is exploited here to derive a Boussinesq-type model that has a number of unique properties. It describes the depth-integrated transport of mass and momentum in strictly conservative form. Its compact formulation is independent of the vertical reference level and allows for an efficient implementation. The model is complemented with absorbing boundary conditions that dynamically take into account the average celerity and direction of both the incoming and the outgoing wave. The model is validated by means of a number of standard test cases.

Nwogu's equations are transformed to the frequency domain, retaining all terms with the purpose of obtaining reference solutions in the frequency domain. These equations constitute a boundary value problem which is solved numerically. It is shown that simple forward spatial integration cannot be applied without reducing the equations in some way. Three approximate models allowing spatial integration are derived, and the influence of the approximations is investigated using the results of the boundary value problem formulation. One of the approximate models are applied to varying depth, showing some problems with discontinuities in the bed slope.

A new set of highly accurate Boussinesq-type equations are presented. The equations are formulated in six variables, counting vectors as one: The surface elevation, the horizontal gradient of the velocity potential at the free surface, the horizontal and vertical velocities at the free surface and the horizontal and vertical velocities at an arbitrary z-level. The arbitrary z-level is determined by optimizing the vertical distribution of the horizontal and vertical velocity components compared to linear fully dispersive wave theory. A Stokes type analysis is performed and the new formulation is found to retain high accuracy in the linear and nonlinear characteristics for wave numbers as high as kh=30. A numerical model is developed in one horizontal dimension and results are presented for the case of a highly nonlinear solitary wave propagating over a constant depth. The numerical results are shown to be in excellent agreement with exact solutions.

A model for solving the two-dimensional Boussinesq type equations is presented. The model equations are discretised in space using unstructured finite element technique. The standard Galekin method with mixed interpolation is applied. The time discretisation is performed using a predictor-corrector method (a 4th-order Adams-Bashforth-Moulton method). The model is verified using three test cases and the results are compared with experimental data and results determined by an existing Boussinesq model. The application of the model for large coastal areas is illustrated with a simple case study. Based on the present work, it is concluded that the new model using unstructured meshes can provide a cost-efficient tool for prediction of waves in large coastal areas, which includes the surf zone.

Results of large-scale laboratory tests are used to evaluate breaking criteria for waves in intermediate depth with and without favorable or in-line currents. The laboratory tests simulated design waves for the near-shore Gulf of Mexico, where breaking waves with heights of up to 12.2 m (40 ft) are expected in a water depth of 15.2 m (50 ft), and where wind-driven currents are expected. This paper compares the observed breaking wave heights to those predicted using three breaking criteria of Miche, Battjes and Janssen, and Goda. Results show that all three work reasonably well for the zero-current conditions. All three also work well when a current is present, provided the Doppler-shifted wave period is used. In addition, the paper shows that the breaking criteria work best when the wavelength is computed using Stokes 3^rd-order wave theory.

The accurate prediction of shear stresses at the seabed forms an essential element in modelling of the coastal environment. Flows which induce bed friction generally include a mean component (from wind-induced currents or tides) and an oscillatory component (from waves), and this paper describes an investigation into seabed friction under such combined wave-current flow. In particular, it presents new laboratory measurements of the shear stress exerted by waves or wave-like flows on a rough boundary and how that oscillatory component is modified by the addition of a current. The effect of the waves on the current is reported, and the results compared with predictions from wave-current models, including some being developed as part of the present project.

Laboratory experiments of wave blocking have been performed with periodic and random waves including partial and complete wave blocking in a novel experimental arrangement with a constant cross-section in the region where the longitudinal current velocity varies in the longitudinal direction. Observations have been made of reflected waves with downstream group velocity and upstream phase velocity. Analysis in frequency-wave number space has successfully identified these two wave components. State-of-the-art model results of the amplitude evolution show significant discrepancies with the observations.

It is well known that water waves tend to be higher or lower as they propagate onto an opposing or following current, respectively. This is also true for wind waves generated on currents. In the equilibrium range of wind waves, however, the spectral densities of the waves generated on a following or opposing current are larger and smaller, respectively, than those for the waves generated on quiescent water. To see this, a series of laboratory experiments was carried out in a wind-wave and current flume for various conditions of water depth, current and wind. The experimental results qualitatively confirm the theoretical equations proposed by Gadzhiyev et al. in 1978 and Suh et al. in 1994 with the former performing marginally better for following currents.

This paper presents the contents as well as examples of the hydrodynamic part of our time and depth-dependent 1DV solver using a Poisson solver for pressure for explicitly simulating various wave-current-turbulence interactions of periodic nonbreaking surface waves propagating on horizontally uniform currents and horizontal beds. The accompanying paper (Bosboom and Klopman, 2000) presents the sand transport module interacting with this hydrodynamic solver. The reduction in spatial dimensions excludes the simulation of some intriguing wave-current interactions such as Langmuir cells. These circulations augment the vertical exchange of horizontal momentum and of matter. Radder, see (Dingemans, 1999), proposes a cell-averaged model that will be added to our 1DV code. Progress is also made of implementing our hydrodynamic 1DV solver into a 3D free-surface hydrostatic solver, as an interface for depth-averaged wave-forecasting models such as HISWA and SWAN, see (Groeneweg & Uittenbogaard, 2000).

This study investigates the impact of a new formulation for the dissipation source term S_ds on the numerical simulation of fetch-limited wind-wave evolution. This new form of S_ds, featuring a nonlinear dependence of spectral dissipation rates on the azimuthally integrated saturation parameter B(k) = k⁴F(k), is implemented in the AUSWAM model, a version of the WAM model used by the Australian Bureau of Meteorology. When compared to results obtained with the standard operational AUSWAM source-term configuration, experiments made with the new saturation-dependent S_ds produced evolution curves of integral spectral parameters that agreed more closely with fetch-limited observations. The new form of S_ds also provided more flexibility in terms of model tuning. Overall, these results closely follow the trends of exact-nonlinear fetch-limited simulations described in previous studies.

The Atlantic Ocean shoreline of New Jersey is bordered by Long Island, NY, to the north and the Delaware Bay to the south. The coastline is generally oriented north to south for 80 km from Sandy Hook to Barnegat Inlet and northeast to southwest for 120 km from Barnegat Inlet to Cape May. The northernmost portion of the shoreline is characterized as a coastal headland, and the central and southern portions are composed of barrier islands. A total of 11 tidal inlets line the ocean shoreline of the state. The nearshore area within 5 km of the coast contains numerous shoals and sand waves. As shown in Figure 1, the southern portion of the coastline is characterized by a broad shallow nearshore area as compared to the more steeply-sloped nearshore in the north. The region also contains the Hudson Canyon, which extends southeastward from the entrance of New York Harbor to the edge of the continental shelf. The Hudson Canyon is as much as 30 m deeper than the surrounding ocean bottom at the western end, and reaches depths of nearly 1000 m near the eastern edge.

Miles (1997) recently presented a short review of the progress in theoretical modelling of wave generation by wind during the period since his own pioneering work and that of Benjamin in the late fifties. With minor analytical elaborations and the major advances in computational capabilities, the original Miles-Benjamin model is still widely applied in linear instability analysis of this important practical phenomenon with very useful results. It appears likely, however, that further significant advances in predictive modelling will require improved understanding of the highly complex physics of the interaction process between the turbulent wind flow at the interface and the deforming water surface. At present, this knowledge can only come from direct numerical simulation and advanced physical experimentation, paralleling similar studies of solid wall layer turbulence. On the other hand, a laminar flow is a simple and fixed model. The classic experiment of Schubauer and Skramstad and the later numerical calculation of Kaplan have proved that, on a solid plate, the initial growth rate of some selected frequencies of artificial two-dimensional air waves inside the laminar boundary layer can be explained by linear instability theory. It is, therefore, interesting to know, for the coupled flow at an air-water interface, if the physical processes of the initial formation of water waves under the action of laminar air flow will be dominated by linear instability theory. Following this reasoning, the present wind tunnel study has been designed to provide information on the basic mechanics and physics of initial formation and growth of waves on a flat water surface under the action of laminar air flow. Primary objectives of the study therefore include measurement of the wave growth rate and phase velocity as a function of wave frequency and space under the fundamentally driving laminar flow conditions. A numerical calculation to solve the coupled Orr-Sommerfeld equations in the space-amplified growth rate was also developed for comparison with observed results.

Using long-term wind and wave data from five of the National Data Buoy Center (NDBC) buoy stations in the Pacific Ocean, this study examined the validity and accuracy of estimating the wave height distribution from the corresponding wind speed distribution. Both the log-normal and the Gamma distributions were used as the conditional probability distribution of significant wave height with known wind speed. The results show that the wave height distribution can be satisfactorily estimated from the wind speed distribution from both conditional distributions. Fitting of the wave height distribution from the log-normal distribution is slightly better than that from the Gamma distribution.

The horizontal momentum exchange due to the organised motion in combined waves and current is analysed in an Eulerian framework. The interaction between the waves and a vertically sheared current causes small time-varying velocities due to the time-varying deformation of the current velocity profile by the wave motion. These velocities are — in combination with the wave orbital velocities — of importance for the momentum exchange, and they are included in the analysis. Their significance is illustrated by examples, considering a situation with a steady uniform longshore current.

This paper aims to propose a widely applicable numerical method for the computation of longshore current on the basis of Boussinesq equations. Laboratory data of longshore current of Visser are used to be compare with the numerical results. The effects of side boundary conditions to the longshore current are discussed. A so-called ‘numerical pump' method is proposed in handling the side boundaries for the purpose to obtain a relatively uniform longshore distribution of longshore current and to diminish the circulation of flow outside the surf zone.

Swell enhances wind-induced wave growth in the third-generation wave models of the WAM family (e.g., WAM, SWAN, TOMAWAC). This is contrary to observations in laboratory conditions where swell reduces wind-induced wave growth. To improve the performance of these models, it is hypothesized here that high-frequency whitecapping is increased by surface-straining near the crests of low-frequency waves. The pulse-based parameterization of whitecapping in these models is accordingly scaled at every frequency with the ratio of high-frequency steepness over total wave steepness (in an experimental version of SWAN). A generic laboratory experiment which illustrates the phenomenon can now be reproduced. The growth of young wind sea in idealized conditions is not affected. Moreover, the spectral shape (both in frequency and direction) improves. However, in the one field case that is considered here, the effects are marginal.

Measurements of the kinematics of three cases of breaking waves have been conducted using the Particle Image Velocimetry (PIV) method. A set of four parameters are used do describe the kinematics, and the development of the waves as they approach breaking is studied using these parameters. The parameters reveal significant features in the temporal development of the internal kinematics of steep, asymmetric transient waves.

The prediction of wave breaking onset and accurate estimates of the associated wave energy dissipation rates are crucial for improving wave prediction models in regions of high wave energy, such as along the coastline, wind-forced seas and ship wakes. A useful parameterisation of breaking strength is the energy dissipation rate per length of breaking front, normalised by the fifth power of the wave speed, gravity and water density. The strength parameter b appears as a proportionality constant. We reprocessed the data from the hydrofoil-induced, continuous wave breaking experiments of Duncan. This yields a consistent behaviour for the parameter b that correlates strongly with increasing wave steepness. In addition, values of b can be derived from the freely-propagating breaking wave data of Rapp and Melville that also increases systematically with wave steepness. Also, our recent measurements of small-scale, wind-forced laboratory waves provided dissipation rates that are consistent with measurements obtained at much larger scales in the absence of wind. For the case of short wind-forced waves, the direct input from the wind must also be included. Our analyses show that: 1)The threshold wave steepness for transition between incipient and spilling breaking is very similar for a variety of wave conditions, 2)Significantly higher dissipation rates due to wave breaking are observed for quasi-steady breaking waves generated by subsurface obstacles compared with freely-propagating waves, 3)The dissipation rates of short wind waves are comparable with those of larger-scale, freely-propagating wave packets in the absence of wind, and 4)Consistent values of the dissipation per unit crest length coefficient b can be derived for all cases as a function of wave steepness.

Wave breaking inception is investigated under laboratory conditions for regular and irregular wave trains breaking over 1D and 2D bathymetries. New breaking criteria incorporating the spatial wave slope "just before" breaking as a parameter are formulated and existing breaking criteria are assessed. The distortion of phase velocity of regular wave trains propagating over a shoal bathymetry is also investigated. The new wave breaking criteria are introduced into a novel, mild-slope equation based, finite volume numerical model. Non-linear amplitude dispersion and energy dissipation due to wave breaking and bottom friction are also taken into account. The numerical predictions are in good agreement with the collected and other existing experimental data.

In the coastal zone ripples are formed under flow conditions ranging from the onset of grain motion until the occurrence of sheet flow. The ripples significantly alter the flow near the bed, and they have a strong influence on the friction, the dissipation of energy, and on the net sediment transport. For the operation of large models in the coastal zone it is important to parameterize the effect of the ripples under different flow regimes. This is usually done by using period-averaged quantities, i.e., the effective roughness, the wave-current friction factor and the dissipation factor. The aim of this work is to calculate the dissipation factor under wave plus current conditions, in the case where the current is in the same direction of (or opposite to) the waves. Recently, a calculation of the friction and the roughness of the wave plus current flow over a rippled bed was carried out. Here detailed measurements of the flow over fixed ripples were conducted. The measurements were used to validate a computational model, which was used to calculate the friction factors for ratios of the current velocity and the maximum oscillatory velocity between 0 < U_c/U_w < 2. It was assumed that the ripples in this regime were not affected by the current, such that they were symmetric. In this work the same computational model is used to calculate the dissipation. An analysis of the results shows that, for most regimes, one can use the friction factor to calculate the dissipation.

An statistical approach for analysing the probability of local water surface breaking event is proposed by defining a new variable, the safety margin described in terms of the water column. Under some assumptions, the probability of water surface breaking event at a given location of the beach profile has a simple expression in terms of the mean and the variance of the safety margin. The model is validated for some specific cases with experimental results from the SUPERTANK, obtaining a fairly good agreement.

An accurate three-dimensional (3D) Numerical Wave Tank (NWT) solving the full nonlinear potential flow equations is proposed for modeling wave propagation up to overturning over arbitrary bottom topography. The model combines a high-order 3D Boundary Element Method (BEM) and a Mixed Eulerian-Lagrangian (MEL) time updating of the free surface, based on explicit second-order Taylor series expansions with adaptive time steps. The spatial discretization is third-order and imposes continuity of the inter-element slopes. Discretized boundary conditions at intersections between domain boundary sections (corner/edges) are well-posed in all cases of mixed Dirichlet-Neumann problems. Waves can be generated in the tank by wavemakers or directly specified on the free surface. If required, absorbing layers can be simulated on lateral boundaries. Node regridding to a finer resolution can be applied at any time step over selected areas of the free surface. Applications to wave overturning over a ridge and wave impact on a vertical wall are presented.

The free-fall condition proposed by Nadaoka et al. as a general wave breaking criterion is examined for its applicability to multi-directional breaking waves. The depth-integrated breaking wave model proposed by Nadaoka and Ono is applied to directional breaking wave simulation in which the free-fall condition is employed as a wave-breaking criterion. Comparison of the numerical results for simple directional breaking waves with the laboratory data obtained by experiments conducted in a multi-directional wave basin show good agreements in the breaking points, validating the free-fall condition as a useful breaking criterion for directional waves.

The morphological evolution of a rip channel system has been investigated using two different numerical approaches. The first approach is a state-of-the-art commercial 2DH Coastal Area model whereas the second approach is a linear stability analysis. The results of the two different approaches have been compared and both models predict rip channels spacings of similar magnitudes.

Two years of daily time exposure video images were analysed to examine the effect of incident wave conditions on the spacing and persistence of rip channels along a swell dominated, microtidal beach (Palm Beach, Sydney, Australia). The results indicated that rip channels do not have any preferred locations along the beach. Rip spacing did not increase or decrease with likewise variations in wave height. Once formed, rip channels migrated longshore under obliquely incident waves, while they were fixed in location under normal wave incidence. Gradients in longshore sediment transport caused by longshore currents due to obliquely incident waves appear to govern longshore migration of rip channels. A two-dimensional depth averaged hydrodynamic model (2DBEACH) was applied to idealised bathymetry to examine processes governing rip strength. The model results indicated that both rip velocity and transport increased with increasing wave height. Rip velocity also increased with falling tide levels, while rip transport initially increased and then decreased with falling tide levels.

The superposition of normally incident wave groups and an edge wave at the same frequency on a plane beach produces rip currents with a longshore spacing determined by the edge wave dispersion relationship. The model differs from Bowen in two ways. Firstly, the edge wave slowly modulates the total water depth instead of the incident wave height. Secondly, the lower infragravity frequency results in longshore scales one to two orders of magnitude larger than Bowen's model. Solutions for both tanding and progressive edge waves have been obtained. For the progressive edge wave case the location of the rip currents depends on the relative phase (θ) between the incident wave groups and the edge wave while the magnitude of the currents depends on the mean incident wave height, the modulation of the wave group and the edge wave amplitude. In the standing edge wave case the location of the rip currents is independent of the phase and, with θ = 0, the solutions are identical to the progressive edge wave case. However, as θ → п/2 the magnitude of the rip circulation decreases to zero.

Fully nonlinear wave equations over general topography (GWE) are derived to simulate surface wave propagation over coastal regions. The variational principle is used to derive the GWE. The new equations are extension of the nonlinear mild slope equations (NMSE) which was derived by Isobe. The GWE are capable of studying propagation of highly nonlinear water waves over steep slopes or at points of slope discontinuity. The GWE can be used to derive both mild slope and Boussinesq type equations of different order. The physical interpretation of the GWE proves that it satisfies Laplace equation and all boundary conditions. A numerical algorithm is given for solving the GWE. Results are presented to illustrate the main features of the theory.

We invert for the bathymetry under random shoaling waves using two different inverse techniques: direct inversion using Levenberg-Marquardt method and a variational inverse method. For both methods, we parameterize the bathymetry using the Bruun-Dean's profile. For the direct inversion, we first show that bathymetric parameters can be obtained with synthetic random wave data. Next, we perform the inversion to show that the bathymetry is obtained exactly using both the adjoint model and direct inversion methods.

The implementation and performance of a new active wave generating-absorbing boundary condition for a numerical model based on the Volume Of Fluid (VOF) method for tracking free surfaces is presented. This numerical boundary condition AWAVOF is based on an active wave absorption system that was first developed in the context of physical wave flume experiments, using a wave paddle. The method applies to regular and irregular waves. Velocities are measured at one location inside the computational domain. The reflected wave train is separated from the incident wave field in front of a structure by means of digital filtering and subsequent superposition of the measured velocity signals. The incident wave signal is corrected, so that the reflected wave is effectively absorbed at the boundary. The effectiveness of the active wave generating-absorbing boundary condition is proved using numerical simulations with VOFbreak².

A numerical model is developed for the extended Boussinesq equations expressed in the generalized curvilinear coordinate system. The model is applied to the study of solitary wave propagation through circular channels. The general features of solitary wave propagation are described and the effects of channel width and incident wave height on the transmission and reflection properties are examined. It is shown that the wave transformation becomes significant in wide channels. The maximum crest height at the outer wall of channel is then investigated in detail. The maximum crest height can reach almost twice as large as the incident wave amplitude in wide channels. The numerical results indicate that the maximum crest height can be correlated fairy well with a single dimensionless parameter.

This paper presents the development of the probability density function applicable for wave heights (peak-to-trough excursions) in finite water depth including shallow water depth. The probability distribution applicable to wave heights of a non-Gaussian random process is developed using the maximum entropy method. When wave heights are limited by breaking wave heights (or water depth) and only first and second moments of wave heights are given, the probability density function developed is expressed in terms of wave parameters such as H_m (mean wave height), H_rms (root-mean-square wave height), H_b (breaking wave height). When third and higher moments of wave heights are given, it is necessary to solve a system of nonlinear integral equations numerically using the Newton-Raphson method to obtain the parameters of the probability density function which maximizes the entropy function. The probability density function thus derived agrees well with the histogram of wave heights in finite water depth obtained during storm.

In this paper two parametric models for the joint distribution of wave height and wave steepness is presented. The wave steepness parameters considered here are the crest front steepness and the crest front velocity. The models are fitted to field data and compared with laboratory data and data obtained by linear and non-linear simulations.

The New South Wales Department of Public Works and Services' Manly Hydraulics Laboratory operates a network of Waverider buoys and water level recorders along the New South Wales east coast. The network comprises seven long-term Waverider stations and 14 ocean tide gauges, providing one of the most comprehensive data sets available anywhere in the world. The network was installed in response to storms in 1974 that resulted in severe damage all along the NSW coast. The MHL wave database now includes 25 years of measured data, with the oldest established water level site at Fort Denison within Sydney Harbour recording data since 1888. This paper presents an update of the wave data for various stations along the coast. In particular, the more recent analyses of the wave height recurrence data in terms of storm duration are presented and discussed. Recent trends in data collection have seen the installation of directional buoys at two locations, with a third to be installed shortly. The directional data is presented and discussed with comparisons to the previously observed and hindcast wave directions. Variations in the directional distribution from year to year are discussed. The definitive design storm event in NSW is taken as the 1974 storms, which are generally considered to have a recurrence of l-in-100 years. The available data from that storm event is considered in terms of the measured wave record to more accurately assess the recurrence for this event. Some comments on the adequacy of the longer-term records are provided.

The evaluation of design waves for coastal protection structures in Wadden Sea areas can be improved essentially by applying advanced mathematical wave models like the third-generation SWAN. Nevertheless the remaining problems require enormous further efforts.

The aim of this paper is to find a model to be used for the bivariate description of extreme wave heights and wave periods representing relatively deep-water sea states. To achieve this, four statistical models taken from literature and a model based on the physical behaviour of waves have been tested on wave data at two sites. The models have been compared with regard to their ability to correctly describe the data, their behaviour when used for extrapolation to extreme events, and the transparency of the methods.

Measurements of uprush and backwash velocities, the shape of the swash lens, pore water pressures in the beach and hydraulic gradients were obtained on a sand beach and a gravel beach on the south coast of the UK. Detailed time histories of a single swash event on both the sand beach and the gravel beach are shown. On the sand beach, large upward-acting hydraulic gradients which exceed the potential for sediment fluidisation are frequently observed. In some cases, these large upward-acting hydraulic gradients occurred under a falling head of water with offshore-directed velocities of 0.7 to 1.4 ms^–1. In other cases, the upward-acting hydraulic gradients occurred when the head of water at the surface was zero. The phasing between these destabilising hydraulic gradients and uprush/backwash velocity is critical to the potential for sediment transport. On the gravel beach, downward-acting hydraulic gradients (infiltration) existed for most of the uprush and backwash cycle. The hydraulic gradients for the infiltration events on the gravel beach were an order of magnitude greater than infiltration events measured on sand beaches.

Swash zone is the final leg of wave propagation where wave energy dissipation occurs, accompanying by potential sediment accretion or removal from the beach surface. A full understanding in the complex swash-groundwater-sediment interaction has gradually emerged, promoted by some geographers and coastal scientists in more recent time from undertaking detailed field measurements in the swash zone. From the measured swash velocities and pore-pressure gradients below the beach surface, it helps verify the assumptions of infiltration and exfiltration as possible mechanisms for accretion and erosion from the beach surface, respectively. This paper compliments these findings, by presenting the laboratory results of pressure distribution induced by internal waves on a smooth slope. Regions of fluctuating but persistent positive and negative pressures were found along the swash plane. This could explain why the rippled bed profile occurs after breaking reported elsewhere.

A 1-D phase resolving numerical wave model, based on the Boussinesq equations is coupled to a sediment transport module and a morphodynamic module. The wave model incorporates the effects of breaking waves by a roller formulation. The sediment transport module is designed to calculate the bed load motion of a coarse grained sediment. The morphodynamic module integrates the sediment flow rate to model an evolving bed. Results for a 1:20 slope beach evolving for a 2 hour simulation are shown, and validation and further application of the model are discussed.

Rapid video measurements of foreshore morphology and velocity were collected at Duck, NC in 1997 to investigate sediment transport processes in the swash zone. Estimates of foreshore evolution over a roughly 30 m cross-shore by 80 m alongshore study area were determined using a stereogrammetric technique. During the passage of a small storm (offshore wave heights increased from 1.4 to 2.5 m), the foreshore eroded nearly 40 cm in less than 4 hours. Dense, horizontal surface velocities were measured over a sub-region (roughly 30 m by 40 m) of the study area using a new particle image velocimetry technique. This technique was able to quantify velocities across the bore front approaching 5 m s^–1 as well as the rapid velocities in the very shallow backwash flows. The velocity and foreshore topography measurements were used to test a three-dimensional energetics-based sediment transport model. Even though these data represent the most extensive and highly resolved swash measurements to date, the results showed that while the model could predict some of the qualitative trends in the observed foreshore change, it was a poor predictor of the observed magnitudes of foreshore change. Model — data comparisons differed by roughly an order of magnitude with observed foreshore changes on the order of 10's of centimeters and model predictions on the order of meters. This poor comparison suggests that future models of swash-zone sediment transport may require the inclusion of other physical processes such as bore turbulence, fluid accelerations and skewness, infiltration/exfiltration, water depth variations, and variable friction factors (to name a few).

In this study, a time-domain Boussinesq model for nearshore hydrodynamics is improved to obtain the conservation of vertical vorticity correct to the second order. This model is then utilized to simulate surface waves and longshore currents under field conditions. Satisfactory agreement is found between the numerical results and the measurements, including wave height and the longshore velocity component. The model results give insight into the spatial and temporal variabilities of the wave-driven longshore currents and the associated vertical vorticity field. One striking result of the simulations is the prediction of the strong longshore current in the trough shorewards of the bar as observed during the DELILAH field campaign.

A highly nonlinear Boussinesq model is utilized to study the wave transformation in surf and swash zones. The model considers the time-dependency of the breaking process. An extrapolation for mass and velocity is used to determine the location of the last wet point. The model results are compared with experimental before and after breaking to check its accuracy.

In this paper, simple but effective techniques are used to improve the performance of two commonly-used sets of Boussinesq-type equations. The O(μ²) equations of Wei et al.are extended through a redefinition of the reference velocity variable, which allows both linear shoaling and nonlinear properties to be improved significantly. Computational examples of nonlinear shoaling waves demonstrating this improvement are presented. The enhanced equations of Madsen and Schäffer are improved through a comparison with the higher-order Boussinesq equations of Gobbi and Kirby Through the selective cancellation of higher-order terms, equations result that are linearly of O(μ⁴) for a flat bed and for mild slopes in two dimensions. Properties on a flat bed are identical to Madsen and Schäffer, but performance on a sloping bed is significantly improved.

A new wave absorbing system, called the liquefied sandbed wave barrier (LSWB) system, is currently under development at the Port and Harbour Research Institute (PHRI) of Japan. The wave damping effect by the LSWB system is substantial as confirmed by small-scale experiments and FEM numerical calculations, i.e., the wave transmission coefficient of the system is less than 0.2. Here, the results of large-scale experiments are discussed in view of practical application. Although the LSWB system provides high wave damping nearly equal to theoretical values, difficulty exists in obtaining a homogeneously liquefied sandbed due to the occurrence of liquefied sandbed compaction by cyclic wave loading, which in turn reduces excess pore pressure and the wave damping effect. These two phenomena primarily occur when the sandbed is made of fine sand having small permeability. Based on experimental results, we propose a design method including countermeasures against such problems and a prototype LSWB system is constructed in a very large wave flume at PHRI. Wave damping by the prototype LSWB system is confirmed to be quite stable and high as predicted by theoretical calculations.

Undertow, mean water level fluctuations and turbulence are studied in a wave flume for waves breaking on a 1/20 sloped bottom covered with thin porous layers of different characteristics. Free surface has been measured using capacitance wave gauges at different locations. Several velocity profiles were obtained using Laser-Doppler-velocimeter (LDA). The study indicates the differences in the dynamics of the mean flows and turbulence between the impermeable and porous bottoms. Furthermore, the differences between spilling and plunging breakers are shown.

An experimental technique is used in conjunction with a numerical model to produce Forchheimer coefficients for flow in any porous material. The results show that to model oscillatory flow in a porous material not only do the the viscous and inertial drag coefficients need to be satisfactorily determined but also the added mass coefficient. A series of steady flow experimental results which yield Forchheimer coefficients for a porous media are used in conjunction with oscillatory experiments to determine appropriate values of the added mass coefficient.

The nonlinear shallow water equations can be used to model broken waves within the surf and swash zone. Here we detail the development of several numerical schemes that have been taken from gas dynamics and adapted for use in the surf zone. The numerical schemes can be applied in one or two horizontal dimensions, they have the advantage over shallow water models used at present that they are faster and more accurate.

A numerical model based on a high order non-oscillatory MacCormack TVD scheme is presented for the solution of the nonlinear Saint Venant equations in the inner surf zone. A comparison with measurements of surface elevations on a beach (Truc Vert Beach, France), shows that the model is capable of predicting the transformation of irregular waves in the inner surf zone and in particular the merging of broken waves.

A new numerical scheme based on the C-CUP method with a subgrid-scale approach using the Dynamic SGS model is developed to solve the complicated air-water mixing flow problems and is applied to the air-water interface with air bubbles and aerosol excited by wave breaking. The numerical model succeeds in simulating not only wave breaking but also the complicated turbulent air-water mixing flows after breaking, and is useful for the proper consideration of highly nonlinear motions including free-surface turbulence, air-entrainment, and splash-up cycles. On the basis of the present simulated results, the turbulent flow structures and a physical role of the entrained air bubbles during splash-up cycles in the surf-zone are discussed.

A flow model is developed to predict the fluid velocity in the nearshore zone. The model is a combination of 1-D horizontal wave model with 1-D vertical model. A new combination is suggested at the trough level. A comparison with the experimental data is made to check the validity of the flow model. The model is used to study the orbital velocity variation for spilling and plunging breakers.

The present generation of spectral models for wave generation, propagation and dissipation are based on explicit numerical representations of each of the physical processes involved. As a result, such models provide a valuable framework within which we can relate our understanding of wave processes to measurements made under complex environmental conditions. This is particularly the case in shallow estuarine and coastal environments. In this paper we report on the use of spectral modelling in conjunction with a measurement programme to examine wave growth in a large intertidal estuary. We use the results to examine the role of nonlinear four- wave interactions, and to seek improvements in the way nonlinear energy transfer is computed in spectral wave models.

The aim of this paper is to examine deficiencies of the widely used Discrete Interaction Approximation (DIA) for the computation of non-linear quadruplet wave-wave interactions in operational wave prediction models. Its sensitivity to the frequency resolution of the wave spectrum is illustrated by means of a simple wave growth experiment. An improved DIA is presented in which a second wave number configuration is added to the existing DIA.

In this paper, we present an analysis of a phase-averaged wind-wave model using a hindcast simulation of a moderate wave growth event that occurred during the SandyDuck '97 field experiment. We observe the activity of various source/sink terms in the model, with special attention to the deep-water dissipation term. We note shortcomings with this term and discuss possible improvements.

The wave transformation model STWAVE was applied to calculate wave heights and directions at the entrance to Willapa Bay. The model was driven with input waves from an offshore buoy and compared to nearshore pressure gauge measurements. Including current in the bottom pressure gauge analysis for Willapa had a significant impact on wave height estimates (neglecting current resulted in up to 20% overestimates of wave height during flood current). Verification results showed reasonable agreement between calculations and measurements (root-mean-square (RMS) errors in wave height of 0.1–0.3 m and RMS errors in direction of 7–15 deg). The dominant transformation process for waves in the bay was wave breaking over the Willapa bar. The dissipation is controlled by the tide elevation over the bar. Wave-current interaction is significant only in the outer Willapa entrance channel where currents reached 2 m/sec. Wave heights on ebb increased up to 80 percent and on flood decreased up to 20 percent.

An analytical model based on Bowen and Holman is used to investigate the existence of instabilities due to the presence of a second extremum of the background orticity at the front side of the longshore current. The growth rate of the so-called frontshear waves depends primarily upon the frontshear but also upon the backshear and the maximum and the width of the current. Depending on the values of these parameters, either the frontshear or the backshear instabilities may dominate. Both types of waves have a cross-shore extension of the order of the width of the current but the frontshear modes are localized closer to the coast than the backshear modes. Moreover, under certain conditions, both unstable waves have similar growth rates with close wave numbers and angular frequencies, leading to the possibility of having modulated shear waves in the alongshore direction.

Effect of submerged vegetation upon wave damping and run-up on beaches have been studied using laboratory experiments. The study has focused on the kelpLaminaria hyperborea. The reason is that this kelp is commercially harvested along the Norwegian coast and there is a need to obtain better knowledge on the possible consequences of this harvesting. The majority of the laboratory experiments were run with an experimental setup intended to represent conditions along sandy beaches along the Jæren coast in southwestern Norway. Two experimental setups were used. One with fixed sloping concrete bottom and one with sand shaped to represent the cross-shore area from offshore of breaking to somewhat beyond the dune top. A kelp field was simulated by 5000 artificial kelp plants in scale 1:10. When sand was present in the flume the kelp forest was put in the deeper part of the surf zone, giving a kelp-free area near the shoreline. The experiments confirmed that kelp reduces wave heights, and they also showed that the wave damping due to the kelp reduces wave breaking. It was also found that the breaking process reduces wave heights more rapidly than kelp. For a situation with kelp growing in less shallow water (water depth > about 2.5 m) a lot of the wave breaking takes place inshore of the kelp field for the wave conditions tested (H_m0 <~ 2.5 m). The difference in wave heights with or without kelp was found to be minor in very shallow water. When the kelp grows in very shallow water (< about 2 m), run-up on a beach was also reduced with kelp in the flume.

Though there is agreement that shoreline and aquatic plants are an integral part of more environmentally compatible shore protection techniques, there is little data or design information available to ensure successful implementation. The value of shoreline wetlands has become increasingly recognized. One of the important functions of shoreline wetland vegetation is its ability to absorb wave energy; however, considerable questions regarding the magnitude and importance of this process exist. In order to address these concerns, a research study was undertaken to assess, qualitatively and quantitatively, wave attenuation by emergent wetland plants. A Lake Ontario shoreline wetland was monitored over a 3 year period and an extensive series of complementary laboratory flume tests were performed. The laboratory experiments were conducted using irregular waves and live vegetation taken from the field site. Several key parameters and trends, with respect to wave attenuation and emergent wetland vegetation, were identified. A pair of empirically based equations was developed that predicted wave attenuation through the emergent, freshwater, wetland plants.

The effect of seagrass on coastal hydrodynamics results in the reduction of water velocities within the seagrass meadow, re-direction of flow above the canopy of the meadow, together with a region of increased turbulence generated at the canopy-water interface. This turbulence enhancement process is apparent under both unidirectional and orbital flow. The inflection point in the velocity profiles, a result of the drag exerted by the seagrass meadow on the flowing fluid under current action, leads to instability and the generation of organised intermittent turbulent structures. This large-scale turbulence retains its coherency over length scales in the order of the bent canopy height and dominates exchange between scalars above and below the canopy. The changes in water flow due to the presence of seagrass affects many processes such as mixing and particle transport, and other important biological behaviour such as oxygen exchange and pollen dispersal are probably driven by energetic bursts of turbulence.

The mechanics of a surf-zone plunging breaker are studied from Particle Image Velocimetry (PIV) measurements and a numerical model based on the Navier-Stokes equations, using a Volume of Fluid (VOF) method. An additional numerical model using a Boundary-Integral Method (BIM) is also used in order to generate input conditions for the main numerical model. The PIV measurements were performed at the University of Edinburgh and then compared against the results found by the numerical model developed at DHI Water and Environment. Good agreement is found, throughout the breaking process, between the velocity fields of the plunging breaker measured using PIV and those predicted by the numerical model.

A velocity adjusting method using the mass consistent (MASCON) model is proposed in order to satisfy the mass-conservation law when Particle Image Velocimetery (PIV) analysis is used. It is confirmed that this method is very effective in PIV analysis. The internal characteristics of various breaker types are investigated using this method. It is clarified experimentally that the shear distribution in the wave crest plays an important role in breaker transformation.

A three-dimensional numerical model based on the complete Navier-Stokes equations is developed for wave breaking. A model based on the Navier-Stokes equations is valid over entire range of the water depth and can be used to simulate linear or nonlinear water wave propagation with or without energy dissipation. To include the wave breaking the concept of the surface roller is applied. It is assumed that the surface roller is essentially a passive bulk of water, being transported with the wave celerity c. The model has been tested against existing experiment data and good agreement has been achieved.

A Navier-Stokes solver with a k — w turbulence model is used for simulating spilling breakers in the surf zone. Two different numerical techniques for describing the free surface are investigated. First, a surface tracking approach is applied, using a height function description of the free surface and a time-depending curvilinear grid being adapted to the free surface at every time step. Secondly, a VOF method is employed where a scalar field is introduced to divide grid cells into fluid and void cells and the grid is fixed in time. The time evolution of the turbulence model quantities being subject to the straining motion of wave orbital motion is analysed, and an unstable parameter region is found. After having removed the instability by an ad-hoc modification of the turbulence model, the VOF-method shows good agreement with measurements with respect to the elevation statistics and flow kinematics, while agreement of the turbulence intensities with measured values is reasonable. The present moving grid approach does not describe correctly the flow kinematics in spilling wave breaking, and consequently this approach fails in predicting wave elevation profiles on-shore of the breaking point.

It can be supposed that fluid motion before wave breaking is two-dimensional in each wave direction. However, wave breaking makes it complex three-dimensional turbulent flow. In this paper, it is discussed what in going on just after wave breaking and how this transition from 2D to 3D happens, based on the numerical results of the Large Eddy Simulation (LES). It is pointed out that, just after the plunging point, the instability associated with vorticity occurs in the high shear flow under breaking waves, and then the 3D velocity field significantly appears and evolves during the wave breaking process. It is also suggested that three-dimensional simulation has to be carried out to estimate the local fluid velocity, which is important factor in terms of sediment transport, in the surf zone, because three-dimensionality of velocity field is significant.

The development of a dual frequency, Differential Global Positioning System (DGPS) technology, giving centimetre accuracy on the movement of a mobile receiver, has resulted in high accurate measurements of the surface of the sea by means of a three dimensional (3D) wave buoy. With this technology the buoy is not affected by a transducer transfer function, particularly in the long wave domain. This paper shows the advantages of being able to monitor long period waves viz. the forewarning of approaching storms, the ability to predict long period surging in bays and harbours, and the more accurate monitoring of wave energy.

In order to exploit marginal gas fields off the South African south coast a large unmanned buoy will be moored in the vicinity of the fields to control the flow of gas from a number of wellheads to an offshore platform. The control buoy (CB) is a taut moored facility, and comprises a floating buoyant structure moored by multiple tethers to a gravity base on the seabed. The tethers are of such a length that the net buoyant upthrust is resisted by the tether tension. The surface piercing buoyant structure comprises a series of stiffened steel tubular sections, with an access tube at the water surface, widening to a large buoyant equipment chamber below the trough of the 100 year wave. The gravity base structure (GBS) consists of a cellular ballastable reinforced concrete structure. The structure was built in a dry-dock and towed to site prior to being lowered to the seabed in a controlled manner. The design of the structure provides a square with sides of 15.5 metres length and a height of 11.5 metres. This structure comprises reinforcing steel of approximately 210 tonnes and around 1000 cubic metres of concrete. The dry weight of this complete GBS is approximately 2700 tonnes. The design of the GBS provided interesting challenges to the design team. The tender for the design and construction of the GBS was awarded to a team consisting of Civil and Coastal Construction and Entech Consultants, with Australian specialists, Advanced Geomechanics, responsible for the geotechnical aspects. Subsequently the CSIR Environmentek was involved in physical and numerical modelling of the GBS during towing and lowering in various sea states. The GBS design philosophy was as follows: 1) No subsea preparation of the founding area to take place. The GBS must have sufficient structural strength to accommodate seabed undulations of up to 250mm, 2) Construction to take place within one of the dry-docks around Cape Town, 3) Maximise less costly ‘on land' operations and thus minimise ‘offshore' operations, 4) Obviate the use of additional piling offshore, 5) Obviate the use of slurries as ballast i.e. preferably use only seawater to minimise offshore costs, and 6) Robust design principles backed up by detailed analytical and structural modelling. This paper will cover four primary areas of design of the GBS namely, geotechnical analysis, hydrodynamic analysis of CB and GBS, structural analysis of GBS and attachments as well as naval analysis of towing and installation.

A new, segmented wavemaker is under construction at DHI Water & Environment. At the time of writing, an archetype has been tested and the installation of the full-length wavemaker near completion. Despite of DHI's long experience with wavemaking technology, almost every aspect of the wavemaker has been developed anew and a number of features are unique. In every respect, an effort was made to comply with future demands for precision, stability and performance, while retaining a simple and durable mechanical design.

The present paper gives the complete 2^nd order wavemaker theory for generation of multidirectional waves in a semi-infinite basin. The theory includes superharmonics and subharmonics and is valid for rotational as well as translatory wave board motion. The primary goal is to obtain the 2^nd order motion of the wave paddles required in order to get a multidirectional irregular wave field correct to second order, ie in order to suppress spurious free-wave generation. The wavemaker theory is an extension of the full 2^nd order wavemaker theory for wave flumes by Schäffer.

Wave induced pore pressure and instantaneous liquefaction are known to occur and cause loss of bearing capacity of sand. The possible pressure fluctuation due to a series of plunging breakers is anticipated to yield liquefaction that will influence the conditions for erosion and the supporting capacity for structures. Wave bottom pressure forms the boundary condition for the wave induced pore pressure. It is believed that not only variation of the pressure itself, but also the variations of its first and second order spatial derivative play an important role in the formation of liquefaction. Experimental studies on water wave propagation over impermeable slopes have been carried out to provide important insight to the topic. In this investigation focus is on plunging breakers as these are expected to give the maximum pressure variability.

A time-averaged model that is based on the finite-amplitude shallow-water equations was developed to predict the root-mean-square wave height, wave setup, and free surface skewness and kurtosis from outside the surf zone to the inner swash zone. Initially, this model was calibrated and compared with data from three laboratory tests on a relatively steep slope(1:16) and two tests with equilibrium beach profiles. The model is verified herein using new laboratory tests on a 1:30 slope that included runup measurements. Additionally, the model predictions are compared to field data collected at Duck, North Carolina. The model is shown to effectively predict the cross-shore variations of the skewness and kurtosis as well as the root-mean-square wave height and setup on laboratory and natural beaches. The exponential gamma distribution is shown to be capable of describing the measured probability distributions of the shoreline elevation as well as the free surface elevation in the field.

The measurement of mean water levels, roller geometries and the phase averaged velocity and turbulence intensity fields under spilling and plunging waves breaking in a 2D laboratory surf zone is presented. The paper further describes the analysis of measured parameters and their comparison against predictions from numerical models, demonstrating the value of the technique for model validation purposes. The velocities were measured using digital correlation image velocimetry (DCIV) whilst water levels and roller geometries were determined through grey scale filtering of video images. The phase ensemble-averaged horizontal and vertical components of velocity and turbulence intensities are measured throughout the entire flow domain, including the aerated wave roller.

The theory and implementation of the dominant wave effects in a 3D mean flow model are described. The effects considered are the wave-induced mass flux, wave-induced turbulence, the effects of streaming and forcing due to wave breaking. To model the wave-induced mass flux we have used the GLM method. This method is a hybrid Eulerian-Langrangian approach that also enables the inclusion of a vertically non-uniform mass flux distribution. The model shows good agreement with measurements. It was found that the application of a vertically non-uniform mass flux improves the model predictions considerably. An important conclusion is that with minor modifications any Eulerian-based 2DV, 2DH or 3D flow model can be upgraded to a more physically correct GLM-based model.

Global estimates of extreme significant wave heights H_s are made from altimeter data collected by three Earth orbiting satellites: Geosat, ERS-1 and TOPEX/Poseidon. Data are collapsed into a 2° latitude by 2° longitude rectangular mesh element data base. Practical methods of estimating extreme H_s are described and limitations of their application to altimeter data are highlighted. A well documented procedure for extreme H_s analysis, based on the Fisher-Tippett type 1 extreme value distribution, is applied to the combined satellite data base, providing useful information where estimates of extreme H_s are presently unavailable.

Instrumental wave data at 31 stations around Japan with the record lengths from 6 to 29 years were analyzed for extreme wave heights. Rejection tests for candidate distribution functions were made by means of the DOL (deviation of outliers) and REC (residue of correlation coefficient) criteria by Goda. The distribution that was least frequently rejected in a particular region was selected as the most probable population distribution. The Weibull distributions with the shape parameter k =1.4, the same with k = 1.0, and the Fisher-Tippett type I distribution were found to be the population distributions of the Japan Sea region, and the northern and southern Pacific regions around Japan, respectively.

This paper presents a wavelet transform analysis of continuous wave recordings in the Sea of Japan during 1986 – 1990. The analysis is carried out to study the incidents of freak waves. The results show that a well-defined freak wave can be readily identified from the wavelet spectrum where strong energy density in the spectrum is instantly surged and seemingly carried over to the high frequency components at the instant the freak wave occurs. Thus for a given freak wave, there appears a clear corresponding signature shown in the time-frequency wavelet spectrum. Since freak waves are primarily transient events occurring unexpectedly, wavelet transform analysis on continuous, long duration wave measurements clearly represents the most ideal approach to discern the localized characteristics of freak waves for further exploration.

In this paper a regional frequency analysis is suggested in order to obtain more accurate estimations for the tails of wave height distribution functions. A case study with wave height data on the Norts Sea is presented.

The present paper describes the 3-D variation of rip currents through the use of physical and numerical models. Experimental measurements of rip currents are made in a directional wave basin. The vertical profile of the rip current is found to vary from depth uniform inside the channel to depth varying further offshore. Offshore from the channel the rip current has much stronger velocities at the surface than near the bottom. A nearshore circulation numerical modeling system is applied to the wave basin. The results from the model show qualitative and quantitative agreement with the laboratory measurements.

Numerical experiments using the SHORECIRC model are conducted for rip currents on a barred beach to explore the effect of particularly the rip spacing and the bar distance from the shoreline. The results show that essentially rip currents are local flow patterns that are not influenced by neighboring rips if their longshore spacing is larger than 4 – 8 times the width of the rip channel. Consequently the velocities in the rip are also independent of the rip spacing and much of the water brought over the bar by the breaking waves returns back to sea through the local undertow. It is also found that the rip is almost entirely forced in the rip channel itself though a system of circulation cells behind the bar plays an important role in the volume exchange.

Ship waves in a shallow and narrow channel such as a canal are greatly different from those in a deep open sea. In the present paper, ship waves in the channel restricted by vertical walls have been studied by numerical calculations together with data measured in laboratories and fields. A remarkable feature of the ship waves is the appearance of solitons ahead of the sailing ship. The calculated heights of soliton agree well with laboratory data by Ertekin et al. The maximum wave heights in the train of ship waves are also investigated and compared with laboratory data by Kurata and Oda and field data observed newly in the Shingashi river. The height of ship waves is greatly varied by the depth Froude number, the blockage coefficient and the river currents. The numerical model has been confirmed to be able to predict such ship waves in a shallow and narrow channel with satisfactory accuracy.

The probability density function of the surface elevation of a non-Gaussian random wave field is obtained. The derivation is based on the maximum entropy (information) principle with the first four statistical moments of the surface elevation used as constraints. The density function is found by the use of the Lagrangian multipliers method and it is shown that only two of four Lagrangian multipliers are independent. The applied method of numerical solution is described in detail and the useful nomograms that give the Lagrangian multipliers as functions of skewness and kurtosis are calculated and incorporated in the paper. For slightly nonlinear waves the approximate maximum-entropy probability distribution is developed. The condition of the existence of this approximate distribution agrees with the empirical criterion for small deviations from the Gaussian distribution of random water waves. The theoretical results compare well with field experiment data even in the strongly non-Gaussian case.

In this paper, we shall study wind-waves and air-sea interaction parameters in two fetch-restricted coastal areas using DHI's third-generation wind-wave model, MIKE21 OSW3G. The wave model is originally based on WAM physics and has been improved for shallow water applications as described in Johnson and Kofoed Hansen. Model results are compared with selected subsets of field data collected in water depth of approximately 5m (at Ro/dsand, Femer Belt, Denmark) and 7–10m (in O/resund, Denmark), respectively. It is found that for wind speeds u₁₀ higher than, say, 13m/s the sea-state dependent roughness model (as also used in WAM Cycle 4) overpredicts the momentum transfer resulting in too large wave heights and periods in high-resolution coastal area models. This result supports previous findings. It is also found that a conventional drag formula improves the agreement between simulated and measured stress at Ro/dsand, but results in poorer agreement with wave measurements. In O/resund, however, the drag formula results in very good prediction of wave conditions for large wind speeds (u₁₀>15m/s). The effect of using spatial varying winds compared to homogeneous conditions is found to be marginal. Riso/'s WAsP Engineering model has been used to calculate the spatial varying winds in the area of O/resund.

This paper presents a system for estimating extremes of winds and waves over more than one hundred years on the Northwestern Pacific Ocean including the Japan Sea, which consists of a probabilistic generation model of a parametric low pressure system, and wind and wave models. The stochastic low model is established on the basis of a statistical analysis for the data sets of parameterized low pressure systems gathered from weather charts over the Northwestern Pacific Ocean in the past 32 years. A Monte-Carlo simulation over 2000 years confirms that the stochastic model reasonably produces not only overall properties of low pressure systems but also their space-time variation with a northeastward movement. Then, the distributions of sea-level pressure, wind speed and wave height for the return periods of 50 and 500 or 1000 years are estimated using the system. The distributions of their 50-year return values are in gross agreement with those evaluated using the analysis data for recent historical lows. This suggests that the system may be reasonably applicable to the estimation of their extremes for longer return periods of more than several hundred years.

The present paper describes a 1-D depth inversion method to determine water depths from surface images using extended Boussinesq equations. Synthetic input data from a time-dependent Boussinesq model is used as input. A least squares method is used to estimate local wave phase speed from the time-lagged images. The inversion model predicts underlying water depths and water particle kinematics for various wave conditions to reasonable accuracy. For irregular wave conditions, the inversion results from several images have to be averaged to estimate the actual depth.

Measuring devices that are fixed to definite points are employed in the usual surf zone observation which provide accurate time records. The deployment of the instruments, however, is limited in most field experiments, which restricts the spatial understanding of the surf zone dynamics. In this context, a moored video system is developed to obtain spatial images of the surf zone. Field experiments were conducted at HORS, a research pier located in Hazaki, Japan. Results of the video record processing demonstrate the potential of the system. There are some foregoing studies existent in coastal studies using video techniques which are mainly concentrating on inferring the sea bottom profiles by image analyses. This study is a new approach, which tries to reveal spatial and temporal variation of the surf zone hydrodynamics.

Directional spectra sometimes have two peak directions due either to waves from two generation areas, or to incident and reflected waves. In the present study, a method for estimating standardized bimodal directional spectra for a three-component array which measures the water surface elevation and two components of the water particle velocity is applied to field and laboratory data. Furthermore, a method for estimating directional spectra in a field of incident and reflected waves is also developed and applied to the data. The validity of these methods is confirmed through the applications.

A combined probability density function (pdf) of the irregular wave amplitudes and the directions of propagation of 3-D irregular waves is developed theoretically. The normal direction to the wave crest line when the wave crest passes a fixed point, is used for the direction of wave propagation. The only parameter involved in the pdf is the long crestedness parameter.

During the early 1980's a data analysis system was developed in South Africa to automatically analyse digital data from the system of wave buoys along the coast. This system, unique at the time, provided an unbiased assessment of the quality of the data through built-in statistical tests based on the assumptions of the standard model of ocean waves. With the advent of directional measurements the basis of this data quality system had to be reassessed since the number of sensors and the complexity of the measurements had increased from the initial one-dimensional system. This paper reviews a system of quality control for directional wave measurement with specific focus on the implementation thereof, for a directional wave buoy using differential GPS technology. Various statistical tests are assessed. The influence of missing data points in a record as a result of the GPS recording procedure receives particular attention.

Recent results of numerical wave models have shown that the presence of a bimodal directional spreading is a robust feature at wavenumbers above the spectral peak. This directional bimodality is controlled mainly by directional transfer of energy through nonlinear wave-wave interactions. In this study, we carry out a comprehensive data analysis on the evolution of the wave directional distribution during two active wave growth periods in the Lake Michigan. The wind and wave measurements are acquired by a heave-pitch-roll buoy moored at an offshore station. An empirical method(EMP) averaging the results of the maximum likelihood method (MLM) and maximum entropy method (MEM) is used to estimate the directional distribution from buoy measurements. The study shows that the bimodal distribution is a distinctive and persistent feature over a broad frequency range throughout the wave growth process. The characteristics of directional bimodality are quantified by parameters related to the separation angles and the amplitudes of the sidelobes. In general, the values of the parameters are smallest near the peak frequency and increase toward both lower and higher frequencies. This frequency-dependent pattern appears to be invariant to the change of wave age throughout the wave growth process. The persistent nature of the directional bimodality indicates that the nonlinear wave-wave interaction mechanism not only actively moves wave energy away from the peak frequency into both higher and lower frequency components but also constantly redistributes wave energy into directions oblique to the wind direction.

The prediction of coastal sediment transport depends mainly on the turbulence model used in the oscillatory boundary layer. In this paper, two time-dependent eddy viscosity models are presented. The first is based on turbulence measurements over fixed bed and the second corresponds to measurements over mobile bed. We introduced into these models the entropy correction function at flow reversal. In order to provide simple models for practical uses in coastal engineering, we have parameterized the friction velocity and the boundary layer thickness.

A new method is proposed for evaluating the cross-sectional distributions of the undertow (return flow) velocity in a surf zone over arbitrary bottom-forms in a fairly simple manner. It is based on an energy budget concept, a surface roller model and a Boussinesq-type wave equation set including a breaker-induced momentum diffusion term. Validity and applicability of this method for various wave and beach conditions are examined by comparing computed undertow velocity distributions with laboratory measurements.

Boussinesq-type equations are used to model waves breaking in shallow water by including the effect of vorticity generated in the surf zone. The terms that describe breaking appear as corrections to the momentum equation. The model reproduces most of the dynamics in the surf zone. Non-linearity is important for wave height and set-up predictions close to breaking, both in the shoaling region and in the surf zone. The magnitude and the profile of the undertow, especially in the surf zone, is predicted accurately by the model. Magnitude of eddy viscosity, which is used in the formulation for vorticity transport, is not critical except for undertow predictions. Comparisons to wave group data show that the predictions of the wave shape and the wave height are very good. The model predicts a larger phase speed for the waves in the shoaling region, which is related to the assumption of weak dispersiveness of the waves. The model also predicts the generation of long waves in the surf zone.

This paper deals with the applicability of Boussinesq models in coastal areas in the direct vicinity of beaches and dykes. The improvement of an eddy viscosity concept with regard to modelling of the wave shape in surf zones is discussed. Furthermore the modelling of wave runup based on a newly developed Wet Slope is presented. It allows to determine the water volume associated with wave overtopping. Model calculations of laboratory tests and natural foreshore situations are carried out with the new strategies, and related issues are discussed.

We show that Boussinesq models derived from potential flow theory or using Euler's equation evaluated at different locations are not equivalent when vertical vorticity is present. We show that models such as Wei et al. have an inconsistency in their advective term once vorticity is present. We also derive two models based on Euler's equations, which should be more consistent with the level of dispersive approximations. We then compare numerical solutions of these two models with Wei et al.'s model and with the model derived assuming full irrotationality. Results are presented for two cases of rip currents formed in narrow rip channels by waves breaking on an idealized bar.

This paper describes the application of two third-generation wave models to typical coastal engineering studies. Two very different coastal sites were considered and model runs for Case Study 1 were carried out based on measured wave data recorded at an offshore location. For Case Study 1 the model results are compared with wave data recorded at an inshore location. Three storm conditions were considered in detail, but model runs were also carried out for the complete set of measured data. The application of third generation wave models to a second site, Case Study 2, is also demonstrated.

A new method for estimating directional wave spectra from the Doppler spectra by HF/VHF radar is proposed. This method is developed by introducing a Bayesian approach, previously proposed by one of the authors, as one of the most accurate and reliable methods for estimating directional wave spectra for in-situ measurements. The principal advantage of the new method is that it can be applied without introducing empirical weighting coefficients. Applicability, validity and accuracy of the proposed method are demonstrated with numerically simulated data as well as field data measured by VHF radar.

It has been accepted as a truth that under a steady wind forcing condition, the wind generated waves travel in the direction of the wind vector. Based on field measurements, the directional beamwidth is narrowest near the spectral peak, and increases toward both higher and lower frequency components. Over the last several decades, such scenario is the basis for the design of the directional distribution function of any spectral model for engineering and scientific applications. We present results from a spectral analysis of 3D topography of random surface waves generated by a quasi-steady wind field. The directional spectra display clear bimodal pattern in the wavenumber region just above the spectral peak. The generation mechanism of the bimodal directional distribution in the short wave region is identified to be nonlinear wave-wave interaction. Quantitative comparisons of measured and simulated directional distribution functions are in very good agreement.

Most of the Ryukyu islands are surrounded by coral reefs. Transformations of the waves approaching the island's reef coasts have been studied by many researchers through field observations and model experiments. An estimating formula for wave height on reef seas was suggested by Takayama et al., and is now used in practical applications. However, it seems that the tests of this formula by past field observations are not sufficient. This is because the conditions of the experiment from which the formula was derived, were different from field conditions, especially in the case of coral reef seas, when the incident wave height is so great as to be accompanied by surf beats. Long period components of incident waves cannot be accurately reproduced in models for effects of multi-reflecting waves in wave channels. Furthermore, previous field observation data used in the testing, could not adequately cover the whole range of periods of waves consisting of incidents wave groups, because not enough wave meters were used. In our study, nine wave meters were used in field observations simultaneously, to observe the incident waves and transmitted waves on reef flats. We succeeded in obtaining field data corresponding to very large incident waves, having significant wave heights of over 10m. Based on our field observations, we have tried to clarify the characteristics of wave transformations and test the coefficients contained in the estimating formula for wave height as mentioned above.

Skewness of the near-bed cross-shore orbital velocity plays a central part in many beach equilibrium and sediment transport models. Although Boussinesq models can be used to predict the velocity skewness of shoaling and breaking waves, these models are computationally quite intensive. Herein, a large collection of data from a number of field environments are used to derive via genetic programming an analytical expression for velocity skewness under shoaling and breaking waves. The resulting expression provides a good fit to the data.The inclusion of skewness in a sediment transport model demonstrates its importance in predicting the shoreward transport of sediment during periods of beach recovery.

New experimental data on 2-D surf beat generation by a time-varying breakpoint are presented. Surface elevation and velocity data obtained from bichromatic wave groups are found to be consistent with theory, with surf beat generation linearly dependent on incident short wave amplitude. A comparison of the cross-shore structure of the long wave motion with a numerical solution describing the interaction of the incident bound long wave and the outgoing free wave additionally suggests that the bound long wave is not reflected at the shoreline. This is also consistent with data showing that the dominant swash oscillations do not necessarily occur at the group (bound wave) frequency, rather the swash may be directly forced at longer time-scales by the slow variation of short wave phase between sequential wave groups.

Near-bottom pressure and velocity, measured along a cross-shore transect extending from the shore to about 8-m water depth on a barred beach, are used to study the cross-shore propagation of surf beat and the associated cross-shore flux of surf beat energy. The dominant Empirical Orthogonal Functions (EOF's) of pressure fluctuations measured in less than 5 m depth at relatively low beat frequencies (0.005–0.025 Hz) had well developed nodes and antinodes, with ±п phase jumps at the nodes, suggestive of standing wave motions. The dominant EOF's of relatively high frequency surf beat (0.03–0.05 Hz) showed some nodal structure, but their phase increased approximately linearly with distance from the shore indicating net shoreward propagation. EOF's of combined pressure and cross-shore velocity fluctuations at beat frequencies showed a similar mixture of standing and progressive waves. Furthermore, phases between pressure and velocity components were close to ±п/2 at relatively low beat frequencies (< 0.25 Hz), as predicted by standing waves theories, but at higher beat frequencies (0.3–0.05 Hz) phases usually had magnitudes less than п/2, but significantly greater than zero, suggestive of mixed standing and shoreward progressive waves. Shoreward propagating surf beat carried a shoreward energy flux. During a storm, this shoreward flux was about half the flux that could have been carried if all surf beat propagated directly shorewards. The energy carried shoreward by propagating surf beat was lost either at the shoreface (for moderate waves) or on the offshore side of the bar (during a storm). On one occasion surf beat carried energy seawards outside the surf zone and shorewards inside the surf zone, consistent with theoretical models that predict surf beat forcing at the outer edge of the surf zone.

Waves of period a few minutes to a few hours are frequently observed in coastal bays and harbours and often cause harbour seiching. This paper describes analyses of water level records from two bays in south-eastern Australia, in both the time and frequency domains, to characterise waves of periods greater than about 3 minutes and to identify their forcing mechanisms. Port Phillip Bay has a constricted entrance while Port Kembla has an open entrance, giving rise to different dominant wave modes and generation mechanisms. These differences are discussed, and the Miles and Munk paradox is (again) refuted.

Long waves in shallow water affect the design of structures in that they modulate nearshore water levels. This permits larger waves to impact the structure and increases the maximum levels of runup and rundown. Physical model tests show that long wave height at a structure in shallow water is primarily a function of significant breaking wave height and to some extent of breaking wave steepness. Further analysis presents a description of the long wave profile with distance offshore by combining absorbed and standing wave expressions. The amplitudes of these long wave profiles were found to be closely related to significant breaking wave height and to breaking wave steepness.

The interaction of free long waves and free short waves inside and outside the surf zone is investigated and new experimental data are presented. A simple conceptual model of the interaction process suggests that the modulation of the short wave breakpoint by the long wave motion will lead to additional long wave generation, thereby modifying the apparent long wave reflection coefficient. This change in reflectivity appears dependent on the relative position of the short wave breakpoint and the long wave nodal/antinodal points, and hence the short wave amplitude. The experimental data largely confirms this hypothesis, and also suggests that non-linear interactions may become significant offshore of the breakpoint.

This paper describes the development of infragravity waves on the basis of field data obtained at five locations with the depths of 8–20m. The data included several storms due to winter monsoon and three typhoons. The analysis of the field data as well as numerical experiments based on the second order interaction theory revealed various characteristics of infragravity waves, such as the development in the amplitude, the correlation with the envelope of short waves and the ratio of forced and free waves.

A new method for estimating infragravity wave properties from a two-dimensional horizontal array of pressure and current meters is developed. At each frequency the mix of progressive and standing (in the cross-shore direction) waves is determined by a least squares fit to the observed cross-spectral matrix. The method yields estimates of edge wave shoreline amplitudes and of the propagation directions and cross-shore structure of progressive waves. Observations from an array spanning depths between 1–5 m are used to illustrate the method, and preliminary results suggest that progressive and standing (both trapped and leaky) waves both contribute substantially to the infragravity wave field.

Recent modelling of tides over a large tract of the SW Pacific has provided improved knowledge of the trapped tidal wave around New Zealand. An amphidrome in the semidiurnal solar tide (S₂) off the east coast produces a marked contrast in spring-neap tides between east and west coasts. The interannual and decadal variability in sea level around New Zealand (up to a range of 0.2 m) confirms that the Pacific-wide ENSO system and the effect of the Interdecadal Pacific Oscillation (IPO) are not confined to tropical and sub-tropical, latitudes, but are clearly, but not simply, linked to the southern mid-latitude region straddled by New Zealand. The confounding behaviour of interannual and decadal variability and its non-stationary link with ENSO effects masks the ongoing global sea-level rise. Further advances are now possible with the completion of networks of open-coast sea-level gauges in Australia, Pacific Islands and New Zealand, complemented with satellite altimetry and robust tidal models.

Hydrodynamic pressure of a bore on a vertical barrier have been investigated numerically and experimentally. The bore is produced by the broken solitary wave, after shoaling the breaking shows plunging type breaker. The bore impact on the vertical wall is identified and correlated with the incident wave kinematics.

Sediment transports due to tsunamis have caused serious damages. On the other hand, they can be used to analyze historical tsunamis. A model to evaluate erosion, deposition and sand movement of tsunamis is proposed in this study. A hydraulic experiment was carried out to develop the model and it is applied to the 1960 Chilean Tsunami in Kesennuma Bay in Japan.

Subsequently deepenings of the waterway in the inner part of the Ems estuary at the southern North Sea coast changed not only the tidal regime but also that of storm surge water levels. Therefore a thorough going review of the existing coastal protection masterplan became necessary. Moreover the design procedures for the estuarine dykes had to be adapted to the state of the art in tune with existing legal requirements. A statistical model for the computation of storm surge set-ups in estuaries was introduced and verified. Design waves were evaluated by application of the third-generation mathematical model SWAN and the design wave run-up was determined by using relationships derived from results of large scale model tests.

A large number of physical model tests have been conducted for the proposed Coega harbour in South Africa. The study entailed a thorough investigation into the stability of a dolos armoured breakwater subjected to breaking wave forces in water depths of up to 19 m. Dolos stability was optimised in terms of size, shape (waist-to-height ratio and fillet/chamfer sizes), packing density and armour slope angle. Trends used for steering the optimisation were based on extensive historic research tests together with model test results as they became available in the present study. Both two and three-dimensional tests were conducted in which a total of more than 7 000 dolos movements were recorded with a new PC based digital imagery method. To interpret these movements, a comparison with previous work was required, both with regard to dolos movements recorded in physical model studies and with respect to both physical model results and recorded prototype damage.

Most breakwater design formulae are based on the results of extensive physical model testing, however there exist a number of basic discrepancies between the behaviour of model and prototype breakwater armour units, and the way in which breakwater damage occurs and is assessed. These discrepancies are often overlooked. This paper intends to highlight the discrepancies, improve understanding of the variables and propose ways to achieve a closer correlation between the interpretation of model and prototype damage of concrete breakwater armouring in general, and of dolos armouring in particular.

This paper describes the use of the US Army Corps of Engineers CORE-LOC® concrete armor unit for the repair of dolos-armored jetties at Manasquan, NJ. The prototype repair was based on successful generic two-dimensional and three-dimensional physical model investigations of this repair concept conducted at the Waterways Experiment Station. These first proof-of-concept experiments showed qualitatively, the core-loc repaired test section was more hydraulically stable than the original dolos-armored slope. Heather-Clark et al, at the Council Scientific and Industrial Research, Stellenbosch, South Africa found similar results when testing the core-loc for the repair of dolos-armored slopes. The repair at Manasquan was the first use of core-loc to repair a prototype dolos-armored slope. This paper discusses the design aspects of core-loc unit when used with dolosse. It will cover construction and placement techniques used for the repair. It will discuss how the core-loc units were integrated with the dolos matrix. And finally, it will include some lessons learned from the project.

In a series of papers, the authors have described a new method for analyzing and predicting damage progression on rubble mound structures. Empirical equations with coefficients determined with data from a series of small-scale physical model stability tests using depth limited waves, with each test consisting of a sequence of storms, are described. These equations provide a method for predicting eroded area and its alongshore variability, and the eroded profile extent, depth, and alongshore variability for breakwater and revetment trunks. The equations apply to both sequences of storms and constant wave conditions. These papers are summarized herein for use in design.

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

Rubble mound (and sometimes also other coastal) structures on a sandy bottom usually need a filter between the sand and the structure, in order to prevent scouring through the relatively large stones, and hence, large settlements of the structure. This is specifically the case for aprons in front of breakwaters and under toe berms.

The paper describes the ongoing development of design philosophy of stable berm breakwaters, which aims at minimum movement of armour rocks on the berm, taking into account the armour rock quality. The general method for designing an Icelandic type berm breakwater is to tailor-make the structure around design wave load, possible quarry yield, available equipment and required functions. The present authors design many breakwaters each year and for low design wave height, Hs< 2.5 to 3 m, usually conventional design is chosen, but berm breakwaters for heigher wave heights. The availability of large rock is examined with the aim of finding a quarry giving over 15 to 20% of produced rock with stability parameter, Ho, below 3.0.

The hydraulic performance and wave loads of single screens and chamber systems were investigated within an extensive test programme at the Large Wave Flume (GWK) in Hannover, which is part of the "Forschungszentrum Küste (FZK)", a joint coastal engineering research centre of both Universities Hannover and Braunschweig. In cases where wave transmission has to be completely avoided (e.g. to achieve sufficient operating time of sea ports) single permeable walls do not provide sufficient protection, hence structures with an impermeable wall have to be considered. A comparison of One- and Multi-Chamber-Systems in terms of the reflection properties and the wave loads demonstrates the advantages of systems with more than one wave chamber. The phase lag analysed between front wall and rear wall of One-Chamber-Systems is particularly investigated and discussed. This paper is mainly dealing with wave forces acting on such structures. Due to strong interrelations between wave forces, wave reflection and surface elevation, the two latter aspects will also be considered.

Probabilistic analysis, based on the final outcomes of the European research project PROVERBS, is applied to two example cases: Genoa Voltri main breakwater (Italy) and Easchel breakwater, a fictitious case combining Eastern Scheldt Storm Surge Barrier (the Netherlands) for the subsoil and Gela breakwater (Italy) for the rest. Sliding induced by non-breaking, impact or broken waves is the discussed failure mechanism. A calibrated 1 degree of freedom dynamic model, easy to use in a probability based design process, is adopted for the evaluation of the force transferred to the foundation by impacts. For both example cases, realistic results were obtained also thanks to some attention on the choice of congruous statistics.

A study has been conducted to investigate the stability of a caisson-type breakwater constructed over a multi-layered base in a nonlinear wave field. The nonlinear interactions among waves, caisson-type breakwater and the multi-layered high base have been considered. The problem has been simulated numerically by two models, BEM-FEM model and poro-elastic FEM model. The latter models are developed to simulate the nonlinear wave field and its interactions with the porous media. Modifications have been made in the models to account for the multi-layered base and applications have been made to various configurations and properties of the breakwater. It has been found that the nonlinear effects become more significant in case of a high base and the fine material of the base may suffer from tensile stresses. The base may also fail at smaller wave heights than that needed for causing failure in the caisson.

Probabilistic design tools for vertical breakwaters (PROVERBS) was a major European research project within the 4^th framework programme of the European Union and was finished in 1999. The overall objective of the project was to develop and implement a reliability based framework and associated probabilistic tools for the design of vertical breakwaters. 23 research organisations from 8 European countries and from disciplines such as fluid and soil mechanics, structural dynamics, applied mathematics, coastal and harbour engineering have contributed to the project. The paper discusses PROVERBS results and shows applications to representative breakwaters as well as their implementation within a risk analysis framework. The advantages and restrictions of probabilistic design will be summarised and conclusions will be drawn towards extending future research to risk analysis approaches.

The breakwater at Cherbourg, France, was constructed over nearly a century, although the conception began with the desire of Louis XIV to provide a strategic position in the English Channel for the French Navy in 1750. The original concept employed a caisson-type structure filled with stone. Problems with materials, labor and finances proved this not to be constructable and the long-term solution of a rubble mound detached breakwater was developed. The structure was competed in 1850. No significant changes to the final design have been made and only limited maintenance is required.

The rubble mound coastal structure covered with artificial armor units has been accepted worldwide. However, since it is hard to obtain big stones in the field, the stones placed under the upper layer of Tetrapod, Dolos, Accropode, Core-loc etc. do not usually satisfy the design requirement of weight in the case of large waves. This circumstance has required the development of a middle armor block. In this study, a new shape of block, which can replace the stone as a filter layer, has been developed firstly in the world.

Evaluation of scale effects in lab tests are one of the topics of interest for breakwater designers. In this case, the study is focused on rubble mound breakwater crown walls. The case structure selected was the crown wall in the top of the Principe de Asturias breakwater, Port of Gijon (Spain). Three tests were carried out on this breakwater cross section with different scales: field measurements at the prototype breakwater (scale 1:1), lab tests at 1:18.4 and 1:90 scales. The wave-induced horizontal forces from the three data sets were compared and differences were found. Force distributions were non-dimensionalized with wave distributions showing that no differences were noticeable between the lab tests while an 18% of smaller forces were measured at the prototype.

The wave induced forces constitute the main load variable in the probabilistic design of vertical breakwaters and the evaluation of their probability distribution is necessary to achieve an optimal design of the structure without compromising reliability and without resulting in seriously overdesigned constructions. This paper discusses results of model tests performed in the CRF wave basin at HR Wallingford, in order to verify the influence of 3d effects on the shape and the parameters of wave forces distribution under impact conditions.

Innovative structures like horizontally composite breakwaters or so-called ‘Japanese-type' are increasingly used to reduce loading on and hydraulic responses from vertical breakwaters leading to a reduction of the dimensions and costs of the structure. Horizontally composite breakwaters consist of a protective layer in front of the vertical breakwater which is made of armour blocks. Large-scale hydraulic model tests were conducted to measure wave-induced horizontal and uplift forces on a vertical model breakwater. Comparisons of these force time series were performed for a structure with and without a protective layer made of tetrapods. Tentative formulae to calculate damping ratios of wave forces were then derived and compared to standard design formulae.

The present design procedures design same size of a caisson, if the extreme wave with required return period is same each other in a predominant wave direction but even if it is different in the direction other than the predominant one. It is doubtful whether the actual stability is same. Therefore the estimation procedures of the expected sliding distance are proposed to check the stability of a caisson, when the directional occurrence distribution of extreme waves is considered. In the results of sensitivity analysis the friction factor and wave force estimation are major among uncertain factors. It has become clear that the directional occurrence distribution of extreme waves largely affects the stability of a concrete caisson.

Older coastal structures are frequently built from brick- or blockwork and suffer from a particular type of damage: individual blocks are thrown out of their position into the sea, creating weak spots in the structure which the sea can immediately exploit. Such damage may be attributable to wave impact pressures travelling into water filled cracks in the structure and creating bursting pressures inside the structure. Model studies showed the possibility of impact-generated pressure pulses travelling into water filled cracks. Based on these observations, concepts for a numerical model of pressure pulse propagation in water were developed and implemented. It was found that the numerical model approximates the model test results well, including the comparatively large energy losses without fluid flow which were observed in the model tests and the development of a steady, soliton-like shape of the pressure pulse. The effect of different geometries, such as the infinitely long crack or the crack with a semi-reflective corner, were analysed. A non-linear version of the numerical model was developed to model pressure propagation at full scale.

Large pipelines and mattress stabilization systems were modeled in the field at scales of 1:4.81 and 1:6.35. The physical models were installed in 12 metres depth of water. Significant wave heights of over 3 metres and tidal currents in excess of 2 m/s occurred during 8 months of modeling. At the prototype scale, these severe conditions represented storm events with average recurrence intervals in excess of 10,000 years. The paper focuses on the logistics of undertaking physical model studies in the field. It is concluded that a well designed and planned testing program can result in physical models constructed in the field being less expensive than conventional large scale modelling in a wave flume.

In this study, a numerical model for the easy estimation of the total wave forces acting on a vertical slender plate installed in waves is presented. For the numerical modeling, first, a discrete vortex method combined with BEM is developed on the basis of the strip method, in order to simulate the vortex formation around the plate. Furthermore, a wave force equation is newly derived that is independent of Morison's equation and that describes the effect of vortex shedding explicitly. The total wave forces are estimated by integrating the results from the wave force equation along the vertical direction. The validity of the numerical model for the flow field was verified by experiments using. PIV (Particle Image Velocimetry). Subsequently, the validity of the model for the estimation of the total wave forces acting on the plate was finally verified by experimental measurements.

Large scale experiments have been conducted in the LARGE WAVE CHANNEL of the Forschungszentrum Küste (Coastal Research Centre) in Hannover to investigate the loads acting on a slender circular cylinder attacked by a breaking wave. The wave kinematics, the impact and the cylinder's response were measured simultaneously. For the load measurement two independent methods were used. On the one side pressures were measured and on the other side forces were determined at the bearings. Analysing the data a theoretical description for the two-dimensional impact is confirmed and peak values for the three-dimensional impact are obtained. It is shown that the commonly used calculation method for the impact force fails because the duration of impact is overestimated.

Submerged wave filters for coastal protection- integrated in multi-layer systems of permeable vertical walls — are very efficient, as the advantages of such structures are obvious in terms of wave damping performance, reduction of wave transmission, reflection and forces. This paper presents the hydrodynamic behaviour of submerged filter systems, i.e. wave loads, transmission and reflection. Firstly a new approach of transient viscous free surface flow computation (RANSE/VOF solver) for such filters is presented. For validation and further analysis — with regard to their non-linear characteristics — wave filters are additionally investigated and optimised experimentally in wave flumes of different scale. The influence parameters — porosity, height and number of filters and filter distances as well as wave height and period — are particularly evaluated and quantified. Together with the numerical and experimental results efficient artificial reefs can be designed.

The use of offshore reefs for coast defence has been questioned by several authors in recent years, predominantly due to concerns over the effects on adjacent beaches. Other concerns that are expressed in relation to offshore reef schemes are listed below : 1)The impacts on downdrift beaches are unpredictable and large; 2)Environmental impacts are adverse; and 3)Whole-life costs are high relative to the alternative defence options. This paper demonstrates the level of confidence that may be placed in generic outline design criteria, by reference to the Happisburgh to Winterton Sea Defence Strategy on the east coast of the United Kingdom. In addition, the paper presents the successful development of an outline design of reef geometry to detailed scheme design, using computational models to predict downdrift erosion effects. Observations of the actual downdrift beach response over a period of nine years are compared to model predictions. Given the nature of the Conference, no discussion of environmental impacts is presented, although increases in biodiversity and fish catches have been recorded in the vicinity of the reef scheme.

This paper deals with the functional design of submerged breakwaters and the associated hydro-morphodynamic impact. After presenting the advantages and difficulties of submerged structures it summarises the state of art on the hydrodynamic impact/effect for such a type of structure. The next pages describe the experimental set-up used to construct a number of large-scale mobile bed tests to further advance the knowledge on the hydrodynamics and morphodynamics associated to this structural type. The next section presents the corresponding numerical analyses, which supplement the findings of the laboratory work. The final section presents on-going work on the effect of these structures on beach profile dynamics.

One-line numerical modelling and three-dimensional scale physical model studies were completed to predict the extent of shoreline widening that could be anticipated at the Gold Coast in response to extensive sand nourishment (completed June 2000) and construction of a submerged reef structure (completion anticipated December, 2000). A coastal imaging system is currently being used to continuously monitor and quantify regional-scale coastal change. These data will provide the all-too-rare opportunity to compare and contrast predicted and prototype coastline adjustment to the implementation of major coastal engineering works.

The scour process around a vertical cylinder due to tsunami runup was investigated experimentally using a large-scale laboratory facility. Temporal variations of scouring around the cylinder were optically observed with the multiple CCD cameras that were installed inside of the cylinder. All the other necessary data, e.g. water depth, flow velocity and pore pressure, were obtained by the conventional electronic sensors. In addition, we measured the topography changes before and after the tsunami runup. The temporal variations of the scour process were clarified. It was found that the pore pressure field around the cylinder is one of the key factors to understand scouring mechanism associated with tsunami runup.

This paper reports the results of an experimental study on the scour around a vertical pile and in groups of piles submitted to wave forcing. In particular, the influence of the wave non-linearity on local scour around single piles has been studied. In fact, as the characteristics of non-linear waves evolves in the domain the scour processes shall depend on the position of the piles, i.e., on the local characteristics of the waves. The scour processes around vertical piles located in the surf zone are also discussed in this paper.

Seawalls in deep-sea areas with severe wave conditions are quite expensive to construct. In order to reduce the costs for the construction of such structures, the authors devised three types of composite-type seawalls, and evaluated their performance through hydraulic model tests. Of these three, one type of sea wall (what the authors call Block Armored Caisson-type Seawall) showed the most favorable results in terms of overtopping prevention and cost-effectiveness. Furthermore, in order to establish design methods for this type of seawall, hydraulic model tests and numerical analysis were conducted. The tests and analysis also yielded useful results for establishing wave overtopping estimation method and wave force evaluation method. Through these tests and analysis, it was founded that the Block Armored Caisson-type Seawall has better performance than conventional composite-type ones, and is one of the most practical structures for deep-sea areas subject to severe wave conditions.

Estimating the probability distribution of deformation is essential in the future design of composite breakwaters. In this paper, characteristics of the sliding phenomena and a method to calculate the sliding distance are described, and the deformation-based reliability design, named the expected sliding distance method, is proposed. This new design gives a more economical cross section of the breakwater than that by the current design especially in a shallow water area.

The most popular type of breakwater in Japan is the composite breakwater consisting of a vertical wall installed on a rubble mound foundation. To resist the enormous power of storm waves, especially in deep and rough seas, concrete caissons are usually employed as the vertical wall. While the development of adequate design and construction methods has generally prevented composite breakwaters from suffering total failure, heavy storms have occasionally caused substantial damage to the breakwaters. The present paper introduces and discusses composite breakwater failures in Japan over the past two decades in Japan.

Practically, all stability relations in use for the design of slopes with rubble or rip-rap protections are of an empirical nature. Based on experimental data, they have been obtained by curve fitting. One of their limitations therefore is that they can only be used within the range of the experiments executed. Two widely used stability relations are those by Hudson and Van der Meer. Iribarren started already 60 years ago with a model based on a, although simple, physical concept. Hudson tried to establish proportionality constants for this concept with tests in a wave flume with regular waves, but did not completely succeed. He finally came with the well-known equation that can be used for preliminary design of breakwaters. For gentle and very steep slopes, the influence of the slope angle is not represented correctly, due to the empirical nature of the equation. The same is true for revetments where the Hudson equation underestimates the wave attack. Moreover, the Hudson equation does not take into account the wave period and some other parameters that influence the stability. Van der Meer established a relation, based on many tests with irregular waves, which takes more parameters into account, making it therefore more generally applicable. So, although the results of Van der Meer's relation are quite acceptable for practical use, it is rather unsatisfactory that, despite spectacular breakthroughs in fluid dynamics and hydraulic engineering, we still do not have a stability relation based on insight into the physical processes. The search for a stability relation with a more sound physical basis is therefore still justified, e.g. for geometries differing from simple slopes, and also from an educational point of view. Two completely different pilot projects at Delft University of Technology indicate that efforts to establish such a relation are promising.

Rubble mound breakwaters are by far the most common type of breakwater, the importance of which is clearly reflected in the vast amount of published research. Especially, the hydraulic stability of the main armour layer has been studied in order to obtain reliable design equations. It should be straight forward to assume, that a relation between the exerted wave loads and the stability of the armour layer would be of major interest, but the normal approach to the problem has simply been to relate easy accessible wave parameters, e.g. wave height and period, directly to the single unit weight, thus leaving the wave loading in a black box. This approach is observed in all formulae including the well-known Hudson-type formulae and the Van der Meer formulae. All shown formulae are modified from their original form to include the equivalent cube length D_n50 = (W₅₀/ρ_m)^1/3 instead of unit mass W₅₀. Taking a closer look on the stability formulae large differences in the influence of the different parameters are observed although several points of resemblance are observed. Despite the major efforts in obtaining a reliable stability equation a large scatter between damage predicted by the stability equations and model test results still exists. When turning toward prototype the situation is even worse. With the objective to reduce some of the variability an alternative approach based on force considerations is presented. The paper will describe a new stability equation for rock armoured slopes derived on the basis of the recorded wave induced forces and the resistance forces. The work is based on a study carried out at Aalborg University in the period 1995 to 1998, Hald.

The present paper discusses the effect of mass density on stability of rubble mound breakwaters. A short literature review of existing knowledge is give to establish a background for the ongoing research. Furthermore, several model tests are described in which the stability of rubble mound breakwaters with armour stones of different densities are investigated. The results from the model test are discussed with respect to application and further research.

This study gain the assessment referring to the stability weight of armour stones for the breakwater head and trunk under multidirectional waves through the series of laboratory experiments in the multidirectional wave basin and the numerical calculations of the stone weight using the velocity measurements and the static stability formula for the armour stone on the heads and trunk. Furthermore, in order to support more comprehensive understanding of the stability weight of armour stones on the head and trunk under multidirectional waves, the dynamic stability formula for the armour stone, which is taken the rolling motion of stones on the slope of breakwaters at every moment into consideration, is developed.

Coastal structures have been constructed of blockwork since ancient times. Although there exists a very large number of more modern blockwork seawalls and breakwaters, some of which are of very great commercial importance, there is little or no guidance available for the monitoring of the condition of such structures, nor for their maintenance and repair. This paper begins by presenting an overview of a range of blockwork seawalls and breakwaters. Evidence of damage is presented, and loading / damage initiation mechanisms are reviewed. The possibility of new methods of stability analysis based upon block revetment experience is noted. It is concluded that progress will rest upon both the further analysis of historical records, and progress in methods of assessing the internal state of blockwork seawalls and breakwaters.

Recently a series of large scale model tests were performed in the Deltaflume of Delft Hydraulics to investigate two important aspects of the stability of block revetments: 1) Influence of ageing: Three test series, one with a revetment of rough natural stone (granite blocks) and two with rectangular concrete blocks and 2) Influence of the spectrum of the wave attack. A revetment with rectangular blocks. The most important aspect of ageing of block revetments is the washing in of silt and sand. This leads to a considerable reduction of the permeability of both the cover layer and filter layer. For the periodic safety assessment of the revetments in the Netherlands it is necessary to be able to calculate the stability of these structures.

Flood defences in the Netherlands are mainly covered with grass. Hard revetments are applied in places where the grass can't provide sufficient resistance against the attack of waves and current. Since centuries these revetments consist of placed block revetments. In the old days natural stones such as basalt were used. Initially the basalt was placed directly on the clay, but this clay appeared to erode beneath the blocks. Consequently, a filter layer beneath the basalt was applied: a straw mattress with above that a layer of rubble. After the flooding disaster of 1953, natural material was scarce, so it was replaced by concrete blocks, which were placed directly on the clay. The idea was, that these concrete blocks could be placed close to each other, resulting in a relatively impermeable layer, through which the clay would not erode. The very neatly look was another advantage of this type of structure. The height of the concrete blocks was dimensioned based on experience. The design criterion was "not too much damage during yearly circumstances". If the damage appeared to be too much, the concrete elements were being replaced by heavier ones.

In this paper a model is developed which describes the mechanical behaviour of block revetments on dikes under wave loading.

An experiment was conducted to examine the probability distributions of the waterline elevation on a stone revetment with a 1:2 slope located in the surf zone on a gently sloping beach. The experiment consisted of 27 tests for three spectral peak periods and nine water depths at the toe of the revetment. For each test, 10 wave gauges were utilized to measure the irregular wave transformation from outside the surf zone to the revetment. A runup wire was placed parallel to the revetment to measure the waterline oscillations. An acoustic Doppler velocimeter was also utilized to measure the fluid velocities at the toe of the revetment. The wave reflection coefficients, estimated using a three-gauge array placed just seaward of the surf zone, were less than 0.4. The measured time series and spectra indicate the dissipation of incident waves and the generation of low-frequency waves as the water depth was decreased at the toe of the revetment. The exponential gamma distribution, with measured mean, standard deviation, and skewness, can describe all of the measured probability distributions adequately for all of the tests. The time-averaged model CSHORE predicts the measured cross-shore variations of the mean, standard deviation, and skewness fairly well, although CSHORE underpredicts the standard deviation of the waterline elevation noticeably as the toe depth is increased.

Wave run-up measurements at the rubble mound breakwater of Zeebrugge were analysed to obtain wave run-up and wave run-down velocities at prototype scale. A simple energy equation was applied to predict wave run-up and wave run-down velocities and calibrated by using field data. In addition, existing methods to calculate wave-run-up velocities were reviewed and discussed.

Prototype measurements, physical model tests and numerical model computations have been performed and combined to study wave run-up on dikes with shallow foreshores. For instance shallow foreshores considerably affect the evolution of wave height distributions and wave energy spectra between deep water and the toe of coastal structures. The numerical model investigations were performed to study the influence of wave energy spectra on wave run-up and wave overtopping. This resulted in a characteristic wave period for wave run-up and wave overtopping, which essentially takes the effects of arbitrarily shaped wave energy spectra into account. This was confirmed in a series of physical model tests with different types of foreshores and different types of structures. Also, results from physical model tests were compared with results from measurements in prototype. The six storm conditions that were measured in prototype were accurately reproduced in the physical model tests. The results of each of the three data-sources were combined and led to a prediction method which is rather generic and can be used for conditions with deep water and also for conditions with shallow foreshores.

The paper deals the estimation of wave run-up on dykes and revetments. The well known wave run-up formula, derived by Hunt, and already supplemented for some influences from irregular waves as described in previous publications was used for further supplementation and verification with special respect to the real sea state conditions and the complex dyke profile cross-sections, which often exist in field.

Spatial coherence of wave impact pressures at a vertical breakwater in multidirectional seas is studied as part of an EU project under the LSF-TMR programme. The lay out and programme of tests are shortly described. A method for the identification of breaking waves is presented. The percentage of breaking waves for increasing wave height are estimated and compared with existing empirical formulae. The horizontal dimension of the breaker is investigated using two different methodologies: the first analyses the decreasing of the highest 1/250 force with increasing horizontal dimension of the caisson, with special attention to the effects of wave spreading, and the second analyses the spatial correlation of impulsive force per unit length along the breakwater.

An optimal design of vertical breakwaters subject to breaking and non-breaking waves requires 3D-effects such as short-crestedness and wave obliquity to be taken into account. For design purposes the potential load reduction of these effects should be properly considered to enable a more economic design of these structures. 3D-model tests have been conducted by a European research team coordinated by University of Bologna (Italy) and composed of Aalborg (Denmark) and Braunschweig Universities (Germany) in the Coastal Research Facility (CRF) at HR Wallingford. In this paper, these tests and first results are described and compared to standard design methods available suggesting that there is an even higher decrease of forces and pressures with increasing obliquity of the waves than assumed by present design.

Developments in computational modelling of storm waves propagating in the coastal surf zone and overtopping at sea walls and related structures is reported. The AMA-ZON suite of 1D and 2D Plan shallow water models are used for the calculations. The models employ a modern Riemann-based upwind scheme in a finite volume form for use on boundary-conforming meshes. Sea wall structures are approximately represented using a steep bed slope. Breaking waves are modelled as steep moving fronts represented by bore waves. Comparisons with measured data show good agreement for sloping sea walls. Results are presented for the effects of wave obliquity on overtopping discharges including cases involving Mach stem formation. For vertical and recurved sea walls, an accurate model of wave breaking is required.

A wave breaking and an overtopping at an upright seawall are simulated based on the particle method, which is the Lagrangian gridless model completely different form the ordinary Eulerian ones. The behavior of a wave breaking and an overtopping has been well simulated by the MPS (Moving Particle Semi-implicit) method, which is categorized as the Lagrangian particle method. Especially, the existence of splash, which was difficult to be simulated by the former Eulerian methods such as the VOF, is clearly simulated by the MPS method. The difference of velocity fields for the different hydraulic conditions and the geometrical conditions of a crown of seawall has been numerically investigated. The overtopping quantities estimated by the MPS method show good agreement with the Goda's experimental curve.

Sometimes dike sections or seawalls are partially protected by low-crested structures up to one kilometre in front of these coastal defences and more than one kilometre in length. Wave energy may be transmitted over these low-crested structures or dams and waves can penetrate through various openings. These waves have periods similar to the wave periods of the incident waves. Local wave growth of shorter period waves may become important if some fetch is present between dam and coastal defence. Wave spectra in front of the dike sections are often therefore bi-modal. Also sea and swell and/or irregularly shaped wave generation areas may give rise to these bi-modal or double peaked spectra. Until now, little was known about their influence on required dike heights. A series of physical model studies (conducted at a nominal scale of 1:20) were undertaken by HR Wallingford for the Flood and Coastal Defence with Emergencies Division of the UK Ministry of Agriculture, Fisheries and Food (MAFF). The intention was to provide information on wave breaking behaviour and the impact of bi-modal wave conditions on beaches and coastal structures. This research was described by Coates et al. and by Hawkes et al. Wave conditions and wave overtopping were measured for two or three water levels over different bed slopes of 1:50, 1:20 and 1:10. During a project for the Dutch Public Works Department — IJsselmeer District, Alkyon and Infram studied wave-structure behaviour over low-crested dams and the effect of bi-modal seas on required dike heights. As a part of this project Infram visited HR Wallingford and used above research to establish a method for predicting wave overtopping with bi-modal seas for Dutch applications. The research was described (partly) by Van der Meer et al. At that time it was recognised that the wave and wave overtopping data measured by HR Wallingford would be interesting to the Dutch Public Works Department for several reasons as they are responsible for establishment of wave boundary conditions and guidelines for safety assessment of the Dutch coastal defences. The actual work consisted of four parts and was described in full depth in Van der Meer et al. 1) re-analysis ot approximately 200 wave flume runs to obtain various time and frequency domain parameters. This work was performed by HR Wallingford 2) validation of the SWAN-model and analysis of wave breaking formulations. This work was performed by Alkyon and Delft Hydraulics 3) validation ot a model on shallow wave height statistics by Delft Hydraulics and 4) further analysis on wave overtopping by uni- and bi-modal seas, performed by Infram in co-operation with Delft Hydraulics Only the latter part, the wave overtopping analysis, is the subject of this paper.

This study deals with both the investigation of the splash-up and overtopping of a seawall at a particular coastal site by storm waves and the more fundamental investigation of the splash-up of solitary waves on a vertical wall located on a plane slope. The former showed the effects on the overtopping rate of the nearshore bathymetry and of modifications to an existing structure. The latter study was directed at tsunami mitigation measures in a combined experimental and numerical investigation. It also demonstrated the effect of nearshore bathymetry on wall splash-up, and it was found that for a given wave height the position of the wall on the plane slope was of critical importance to the maximum splash-up. A numerical model predicted the splash-up-time history for non-breaking and broken solitary waves reasonably well. The maximum splash-up was found to be a unique function of the maximum slope of the front face of the waves which in turn is dependent on offshore wave height, depth, offshore bathymetry, and wall location relative to the shoreline.

If a sea bottom slope is gentler than about 1/20, influence of wave groups on wave overtopping becomes large. In this case, wave overtopping rates can be satisfactorily evaluated by a Boussinesq approximation model, and the danger of wave overtopping on coastal structures should be evaluated using the largest overtopping rate or an overtopping rate averaged only over total overtopping time. Even when wind speed does not exceed 30m/s, influence of wind speed on wave overtopping should be considered. In this case, there is high possibility that relationship between an increase rate of run-up height and wind speed obtained at a physical model can be applied directly to a prototype.

Most research work on wave transmission over low-crested structures has been concentrated on establishing the wave transmission coefficient, i.e. the ratio between transmitted and incident significant wave height. It is clear that such structures decrease the wave height, but there is more! Goda, Tanimoto et al. Raichlen et al. and Van. der Meer all conclude that also the mean period reduces to 0.4–1.0 of the incident mean period. The conclusion is that overtopping generates more waves. Further, Raichlen et al. and Lee give examples of measured spectra of transmitted waves. Both examples show the peak of the spectrum similar to the incident spectrum, but with much more energy at the higher frequencies. A good estimation of the wave height in front of a structure is required for design or assessment of such a structure. But also wave period and sometimes spectral shape may have influence on the design. Wave run-up, for example, depends largely on the wave period. In order to establish the required dike height for acceptable run-up, both wave height and period should be known. In situations where a low-crested structure in front of such a dike gives some protection, wave period and spectral changes should be studied. A local situation in the Netherlands was the reason for the research presented in this paper. Figure 1 gives a schematised layout. A large lake is situated on the west side (left side in the figure) and NW wind may generate waves up to a significant wave height of over 2 m. The dikes on the eastern side are partly protected by a system of various low-crested structures or dams, including some openings. The figure shows the results of a calculation on wave penetration. Such calculations were performed by Alkyon. Besides wave penetration, wave transmission is generated over the low-crested dams. The area is about 1 km by 2.5 km. This means that with a fetch of more than 1 km also locally generated (short) waves will be present during extreme conditions. The wave climate in front of the dikes can be described as a combination of wave penetration, wave transmission and locally generated wind waves. This paper deals with wave transmission only, but the effect on the total wave climate is discussed at the end.

This paper presents a particle image velocimetry (PIV) based measurement technique for flow acceleration. Based on the illumination of seeding particles three times over two frames and continuously tracking an individual particle over the three distinct illuminations, two velocity fields and a Lagrangian acceleration are obtained. Subsequently, the dynamic pressure can be calculated by integrating the Lagrangian acceleration through the Euler equation, provided that the fluid is incompressible and the flow is inviscid. The technique not only provides a method for acceleration measurement but also reduces the constraint on the time separation between adjacent illumination pulses imposed by the camera framing rate in a single pulsed triple-frame technique to a much shorter camera specific frame transfer time. Monte Carlo simulations are used to test the technique for a deep water wave.

The wave transformation on a foreshore has been studied experimentally in a wave flume using both regular and irregular waves. Different models for the wave height prediction before and after breaking have been compared taking into account wave shoaling, wave breaking, wave set-up and frictional losses. The uncertainties of these models are quantified.

Laboratory experiments were conducted with irregular waves on a uniform 1:50 slope with a breakwater. The objective of the research was to gain understanding of the relation between the short wave groups and the low frequency motion. Peak frequency, wave height, water depth, structure length and angle of wave incidence were varied. The relation between the short wave groups and low frequency motion is investigated qualitatively by visualising the spatial evolution of the cross-correlation function between the short wave groups and low frequency motion.

Coastal engineering works being influenced by the action of the uncertain sea, of tides, currents and waves, are subject to the highest levels of risk. This paper describes how a better identification and management of the hydraulically related risks, will allow for a Latent Defects Insurance. This insurance covers the decennial liability of contractors, designers and consulting engineers in addition to the contractor's All Risk insurance before completion and handover of the works. The client's choice for an insurance as part of a risk control strategy is highlighted by means of some important projects in marine environment.

A new type of seawall (non-wave overtopping type seawall) having a deep circular cross section is proposed in this study. The basic characteristics of this seawall are investigated through wave tank experiments and numerical simulations. In the experiments, measurements are made on the minimum crest height which satisfies non-wave-overtopping condition, wave pressure and water spray transported behind the seawall. The optimum dimension of wave dissipating blocks setting in front of the seawall is investigated for checking wave overtopping as well as securing stability. The fluid motion near the seawall is reproduced by numerical simulation based on SOLA-VOF method. These hydraulic factors of non-wave overtopping type seawall are compared with the conventional upright seawall and advantages of non-wave overtopping type seawall in control of wave overtopping are discussed.

A large number of coastal and port structures have been constructed in order to prevent wave overtopping beach erosion and so on. Some of them are sometimes damaged by storm waves generated by strong monsoons and huge typhoons. Therefore, it is important to clarify the damage characteristics of coastal structures for the safety design in future. The reports of damaged structures from 1992 to 1996 are selected from the annual books of damaged facilities edited by Port Bureau of Ministry of Transport in order to investigate the characteristics and causes of their damages. Seabed scouring at the foot of coastal structures such as sea walls is one of the main causes of damage and more than 50% of damage is caused by it. Also the scouring damage takes place even in mild wave conditions. Once the seabed has been scoured, wave breaking point moves closer to the sea walls due to the deepened depth. Consequently, incident waves are increased, and wave forces or wave overtopping become more severe. The prediction model of the scouring with high accuracy should be developed. The deformation or change of sea bottom is one of urgent problems to be solved in near future.

The paper elaborates upon the fundamental controls of rock armour packing and the financial consequences of errors in void porosity assumptions. Results from detailed case studies and numerous contracts are summarized in order to compile a data source from which up-to-date guidance on void porosity and layer thickness coefficients can be drawn. A new rapid survey method to assess in-situ packing density is introduced.

The U.S. Army Engineer Research and Development Center successfully field-tested a new floating breakwater offshore Cape Canaveral, FL in May 1999. This paper describes this new hybrid construction concept, analytical and numerical models of the transmission coefficient, and results from the measured performance.

This paper describes experimental tests on a series of floating breakwaters which have various vertical plates attached to improve their efficiency. The breakwaters are moored using conventional mooring systems and the horizontal forces in these have been measured . Results of typical tests are given.

In this paper, a series of experiments were conducted to study the wave-induced vortex behavior around a submerged obstacle by applying FLDV (Fiber Laser Doppler Velocimetry) and PIV (Particle Image Velocimetry) techniques. The evolution of vortex generation and shedding in a wave cycle had been clearly visualized in the process of PIV. More precise message about a flow field around a submerged breakwater was measured by FLDV and vorticity and vortex energy were further calculated from the flow field.

The response of a breakwater and the underlying seabed to waves has been recognized as an important design problem in the field of harbor and coastal engineering. In this research, a model is proposed on the basis of an analytical method for the response of a composite-type breakwater and seabed to sinusoidal standing waves. In the proposed analytical model, the problem of the response is decomposed into the wave mode, called a scattering problem, and the caisson motion mode, called a radiation problem. The model is characterized by solving each decomposed problem using a complex Fourier series technique.

This study investigates the Mach reflection of random waves by numerical simulations and with experimental observations, especially for the difference and similarity between periodic waves and random waves. As the incident angle becomes large, the normalized significant wave height in front of a reflecting wall becomes large. This tendency is the same as the Mach reflection due to the Stokes wave or the cnoidal wave. The wave height distribution in the normal direction to the wall, that is, the width of stem wave is almost the same even if the nonlinearity of incident waves becomes large. This is a different point between the periodic waves and random waves.

A single solitary wave interacting at normal incidence with a semi-infinite vertical breakwater results in the formation of a single vortex which is subsequently shed from the structure. In this paper, we describe experiments which were conducted using a solitary wave propagating along a uniform depth wave flume past a vertical wall. Both surface elevations and strength of the vortex were measured in the experiments. A fully nonlinear Boussinesq model with Smagorinsky subgrid mixing is then employed to simulate the experiments. Comparisons are made between the numerical results and experimental data. It is shown that the present numerical model is capable of simulating wave-induced vortices. It is also shown that the model predicts wave height better than the potential flow models do.

Various loading situations for a gecontainer during placement are distinguished. Critical loading situations are the moment the geocontainer slips through the opening of the split barge and the impact on the bottom. Calculation methods for these two situations are presented. According to the theory developed, the impact on the bottom is influenced by the degree of saturation of the fill material in the geocontainer. The theory developed is used in the design of a geocontainer dam projected in a canal in Amsterdam.

The idea of containing soil materials in geotextile units made of nonwoven needle-punched geotextiles have lead to highly visible projects in coastal and hydraulic engineering considering the soft coastal protection philosophy. The completion of the Australian Gold Coast artificial (surfing) reef made of individually installed geotextile sand containers (up to 400 tonnes weight each) shows a pioneering coastal protection solution without use of any traditional construction elements like rock, steel or concrete. Economic geotextile construction elements for groynes, erosion control, dune revetments and scour stabilization demonstrate that geotextile sand containers with a minimum impact on the environment can provide an flexible alternative to traditional materials.

The generation of groundwater movement in beaches at wave and surf-beat frequencies is not a trivial process. Measurements of beachface porewater pressures beneath the swash zone show a clear spectral peak that coincides with the spectrum for the horizontal movement of the watertable exit point across the beachface, rather than the "usual suspects" of surf zone water-level or wave runup. The generation of beach groundwater waves at these frequencies is determined by a combination of the movement of the swash front and the characteristics of meniscus drainage within the upper layer of the beachface. Based on experimental data, recommendations are provided for describing the propagation of watertable waves which are influenced by the capillary fringe above the watertable. With respect to small amplitude waves, this is easily done by incorporating experimentally based effective porosities n_e in the dispersion relations. The effective porosity corresponding to time-periodic waves is complex because of the phase lag of the total moisture relative to the watertable. To a great degree of accuracy n_e has been found to depend on a single dimensionless variable: n_e=n_e(ωH_c/K) where ω is the angular frequency, H_c is the capillary height and K the hydraulic conductivity. Incorporating the experimental n_e-information into non-linear wave equations is challenging: By analogy with the hysteresis free model of Parlange & Brutsaert, the experimental n_e-values suggest the use of fractional (2/3) order derivatives.

A field experiment using the Beach Management System (BMS), in which porous pipes that collect groundwater are buried parallel to the shoreline to reduce the groundwater level, was carried out at the Chigasaki Beach on the Shonan coast in Japan. The change in groundwater level under various tide and wave conditions was measured. Pore-pressure gages were buried below the foreshore surface. Comparison of data sets obtained using pore- pressure gages buried in the cross-shore direction showed that short-period variation of the groundwater level corresponding to the incident waves was measured near the shoreline and this short-period variation attenuated landward with an increase in groundwater level. Also, the change in groundwater level with tidal mode was measured. A linear relationship was obtained between the absolute wave run-up height and the groundwater level, where the absolute wave run-up height was calculated using Hunt' formula, taking account of the tide level. The lowering effect of the groundwater level by the BMS was observed under the condition that the absolute wave run-up height was less than 2m above the Mean Sea Level.

In the period from November 29 till December 15, 1999 a team of scientists from the Institute of Oceanology, Russian Academy of Sciences, carried out the field experiment at the coast section of the Black Sea. The basic purpose of the experiment was to study spatio — temporal variability of suspending and sand sediments transporting processes in a zone of deformation and breaking of random storm waves. During the experiment it was managed to record changes of vertical profile of suspended particles in different phases of a density peak passing through a measuring position. It was revealed that separate waves in groups of high waves make the largest contribution into the process of sediment suspension. Changes of suspended sand concentration profiles were measured in different phases of concentration peak passing. The obtained profiles confirm a hypothesis of Nielsen about convectional nature of sand suspending process by vortexes from the bottom.

In this paper, results of field observations of vertical distribution of suspended sediments by size, shape and density carried out in the nearshore zone of a large man-made lake are presented and discussed. It is customary believed that such a distribution of suspended sediment demonstrates quasi-steady decrease of all parameters in the direction from the sand bed towards the water surface. However, the field observations conducted revealed the. profiles with other character of change of suspended sediment concentration, sediment grain size heavy minerals and rolled particles content. It was found that the monotone decrease of those sediment parameters is just a particular case of vertical sorting of the suspended sands.

This paper presents the approach taken to model and predict decadal scale shoreline change in the Columbia River littoral cell along the coast of southwest Washington and northwest Oregon. This work is a principal component of the Southwest Washington Coastal Erosion Study, a research program directed by the Washington Department of Ecology and the US Geological Survey. A primary goal of the study is understanding and predicting coastal change at a management scale of tens of kilometers and decades. Historical morphological changes are viewed in context with coastal change over several centuries prior to human influence as well as with recent data collected by beach monitoring that quantifies morphologic response to forcing conditions. These multi-scale data sets are being used to inform process-based modeling that simulates historical changes and predicts the evolution of the coast several decades into the future. The initial shoreline change predictions mostly depend on extrapolation of historical sediment budgets. The example predictions of shoreline change to 2020 presented in this paper suggest the sensitivity of the present shoreline configuration to potential reductions in sediment supply. The results emphasize the significance of the sediment budget estimates used to predict the shoreline position in future decades.

Extensive erosion occurred along the Oregon and Washington coasts in the Northwest USA during the El Niño winter of 1997–98, followed by additional impacts from the La Niña storms of 1998–99. Analyses have been undertaken of the processes, including a detailed documentation of wave conditions and mean water levels that affect the elevations of tides. Generally there is a reversal in the relative importance of these processes during El Niño versus La Niña events, with tides being elevated throughout the El Niño winter, while the largest storms occurred during the La Niña. However, the high wave conditions of both years have been found to be part of a progressive long-term increase in wave heights and periods, that has been greatest in the Pacific Northwest. The major storms of both winters were analyzed through calculations of the runup of the waves on beaches, which when added to the measured tides yields the total elevation achieved by the water during the storm. Surveys of eroded beaches and foredunes show good agreement with the calculated total water levels and elevations of the eroded dunes. The major erosion also provided the opportunity to test models to estimate the potential horizontal distance of dune retreat during major storms, models that can be used to establish setback distances.

Coastal profile steepening on the Danish North Sea coast because of groynes has been known for more than 50 years. In this paper, profile steepening as a result of more than 20 years of intensive nourishment in the inner part of the profile has been documented. A first estimate of the long-term effect of steepening on the need for nourishment is presented. Besides, a comprehensive monitoring and analysis programme initiated in 1998 by the Danish Coastal Authority is presented as well as the first results. The main purpose of the programme is to increase the understanding of the processes in the outer part of the profile so that the estimate of the long-term effect of steepening on future nourishment volumes can be improved.

Narrabeen Beach is exposed to waves averaging 1.5 m and is very responsive to changes in both wave height and direction. In order to assess the nature and scale of beach change, the following data were analysed. Twenty-three years of monthly beach profiles taken at 5 locations along the 3.6 km long beach, daily directional deepwater wave conditions, together with the monthly Southern Oscillation Index, both for the same period comprise the data set. The maximum scale of shore-normal beach oscillation was 96 m (mean 73 m), while maximum volume changes (storm demand) was 243 m³/m (mean 193 m³/m). Longshore time series of profile deviations from the ensemble beach volume highlighted a relationship, whereby the northern profiles were out of phase (–0.8 correlation) with the southern profiles, suggesting a beach rotation around a neutral central profile. Principle component analysis (PCA) revealed that the 2^nd component displayed a linear trend from a positive northern profile to a negative southern profile around the central fulcrum, and explained 60% of the variance, verifying the observed rotation. The rotation accounts for up to 15 m and 30 m³/m of the shore-normal beach change. Analysis of directional wave data and the Southern Oscillation Index (SOI) suggests beach change is driven both by changes in wave height (power) and subtle change in wave direction, both of which are positively related to the SOI.

This paper investigates the effect of wave-induced streaming on sediment transport by applying a newly developed numerical sediment transport model. The transport model solves the intra-wave oscillatory motion and sediment concentrations. The wave-induced streaming in the wave boundary layer, as occurs in propagating waves, is an integral part of the computed flow field. Comparison of the computed flow field with wave-current flume experiments gives good results. The model can also describe the horizontally uniform situation in an oscillating water tunnel, in which vertical orbital velocities and wave-induced streaming are absent. The model is successfully tested against measurements of sediment concentrations and net transport rates performed in a large-scale oscillating water tunnel. The importance of streaming is assessed by comparing model results for the case with wave-induced streaming and the case of the oscillating water tunnel. For a typical water tunnel condition, the effect of the absence of vertical velocities and streaming is found to be a 40% lower net transport rate than the corresponding situation under propagating waves. These differences result not only from the net transport by the streaming velocity, but are also due to an increased asymmetry in the model of near-bed velocity, bed shear-stress and resulting sediment concentrations. This result suggests that the differences in transport rates between water tunnel and propagating waves may not be insignificant.

The sediment transport in the surf zone is modelled by combining a Navier-Stokes solver, a free surface model, a turbulence model, and a sediment transport model. The flow solver is based on the finite volume technique for non-orthogonal grids. The model is capable of simulating the turbulence generated at the surface where the wave breaks as well as the turbulence generated near the bed due to the wave-motion and the undertow. In general, the levels of turbulent kinetic energy are found to be higher than experiments show. This results in an over prediction of the sediment transport. Nevertheless, some qualitative features have been modelled with success such as the onshore transport under plunging breakers and offshore transport under spilling breakers.

This paper concerns work being undertaken as part of the EU MAST3 SEDMOC project (1998–2001). One of the main aims of this project has been to improve our ability to predict sediment transport rates throughout the physical parameter ranges of importance in coastal engineering practice. Here the transport predictions of a local, one-dimensional (vertical), numerical research model, and also Bijker's practical sand transport model, are compared with data from two field sites. The importance of the wave-related component of sediment transport is also assessed.

The possibility of sand supply from the shoreface to beaches was evaluated based on a variety of methods involving field data and modeling results obtained from five coasts on three continents representing a wide range of coastal environments. The field data include wave-current measurements, historical seabed soundings and geological surveys. Cross-shore transport estimates from modeling on the annual time scale were compared against scaled-down inferences from the seabed-change and geological data. The results are all consistent with there being net onshore transport over the long term from the lower shoreface to beaches in each of the environments. These environments typify settings that occur commonly (probably predominantly) along the world's coasts. So net shoreface sand supply to beaches may be a widespread and common but little appreciated factor in coastal stability. The effect of this net supply is to offset other factors causing shoreline recession, such as positive gradients in littoral transport Moreover, shoreline progradation occurs if sand supply from the shoreface dominates over littoral sediment losses. Implications are clearly significant for coastal engineering and coastal management, despite the processes not being immediately apparent: long-term shoreface sand supply to beaches is masked by more rapid cyclical changes. Rates of shoreface sand supply to beaches indicated from various lines of evidence are typically on the order of 10⁰ m³ a^–1 per meter of shoreline. This volume corresponds to a lowering of the shoreface by only a few grain diameters per year.

In this paper the existence of an equilibrium grain size distribution is examined by means of the analysis of the spatial and temporal variations of crossshore grain size distributions from several beaches along the Spanish coast. Over 3,000 sand samples from 31 beaches, covering a wide spectrum of wave climate conditions and grain sizes, are analyzed. A relationship between the wave climate and the standard deviation of the grain size distribution is proposed.

A cross-shore process-based model was used to simulate the sediment transport rates near Egmond aan Zee, The Netherlands, and the morphological changes near Duck, NC, USA. Driven by the locally measured hydrodynamics and using a fixed bed roughness height of r_w = 0.02 m, the model predicted the current-related suspended transport rates near Egmond aan Zee within a factor 2 of the measured values, except for the very calm conditions. The wave-related transport rates were on an average a factor 4 smaller than the current-related components. The model was used to simulate calm weather waves with onshore bar migration and storm waves with offshore bar migration near Duck, NC. The morphological changes in the nearshore were primarily driven by cross-shore gradients in the current-related transport rate.

The estimation of sediment transport rate in swash zone has a great influence on offshore beach profile evolution. However, the method to estimate it has not been established, because the phenomenon is complex and numerical analysis is difficult. In this paper we apply nonlinear long wave theory to analyze sediment transport in swash zone. It is found that the characteristics of water particle velocity and undertow influence the rate of sediment transport in the cross-shore direction and sediment transport rate becomes very large in swash zone. And the characteristics of sediment transport in swash zone are different from those in the offshore region.

To evaluate the sand volume blown from the beach to the inland, a field study was carried out using a sand fence installed at the inland side edge of beach. Field data showed that 1) the sand volume accumulated around 2 m high fence was about 30 m³ / m which was about half of that estimated assuming a dry sand surface condition, 2) the vertical distribution of the sand transport rate on the beach surface obeyed a predictive formula below a height of about 50 cm, 3) it is possible to control the wind-blown sand by employing suitable fencing works.

This paper concerns work carried out as part of the EU MAST3 SEDMOC project. One of the main aims of this project has been to improve our understanding of detailed sediment transport processes and, hence, our ability to predict sediment transport rates throughout the physical parameter ranges of importance in coastal engineering practice. Here a two-phase flow model has been used to predict sand transport rates under equilibrium bed, steady flow conditions. This model gives a complete description of the flow both near the bed and also up in the dilute suspension layer.

The solid-gas two-phase flow model is combined with the granular material model to simulate the detailed mechanics of sediment transport in wind-blown sand layer. The physical characteristics of the wind-blown sand layer is investigated from the viewpoint of computational mechanics of sediment transport by taking into account the sediment-flow interaction and the interparticle collision. Changes in the wind-velocity profile and the Reynolds stress profile due to the load of sediment are calculated. The velocity and the existing probability density of moving particles, and the distribution of colliding frequency of particles are estimated to consider the physical structure of the wind-blown sand layer.

In this paper a new beach equilibrium formulation, that treats the shoaling portion of the profile independently from that of the breaking portion, is proposed. The two portions are matched at the breaking point. The formulation considers wave reflection from the beach and the tidal variation of the sea level. Both profiles are represented by a similar expression that depends on two parameters: A and C, which account for wave dissipation and B and D, which account for beach reflection. The parameters are then calibrated using over 50 profiles from 13 beaches along the Spanish Coast.

A Laboratory study, on beach stabilization by using artificial compaction control, has been conducted. Erosional and accretional waves were applied to uncompacted, moderately compacted, and densely compacted sandy beaches. Changes in beach profile and cross-shore distribution of compaction were measured, then the net cross-shore sediment transport, the shoreline change, the average size of ripples, and the volumetric change were calculated. The results generally show that the higher the compaction, the lesser the net offshore sediment transport and erosion volume. On the other hand, the effect on the decrease of accretion volume was relatively small. This paper also presents a methodology to estimate a cross-shore distribution of local porosity based on the measured local compaction.

This paper investigates a wind-wave-current system and the sea-bottom change characteristics near the surf zone under the stormy condition. About two-month observation of current profiles measured by ADCP, sea-bottom level changes measured by both ultra-sonic and photocell type level meters, and waves and beach profiles along the pier, was conducted in Ogata Coast by using TOP(T-shaped Observation Pier), in the period of January–March, 1999. The following results were obtained, (1) there are two types of sea-bottom changes, "recovery" and "non-recovery" types, (2) sediments eroded from the shore-face clearly move offshore storm by storm, (3) sea-bottom changes measured by two types of level meter have no significant difference, (4) ripple movement and concentration of suspended sediment near the sea bed may be detected by analyzing echo intensity of ultra-sonic type sea-bottom level meters.

An idealized cross-shore transport model was used to investigate the interaction between equilibrium beach profiles and bathymetric perturbations that were triggered by an infinitesimally small change in the incident wave height. A low tide terrace shape characterized the computed equilibrium profiles. This shape resulted from the assumed, nonlinear dependence of the equilibrium slope on the equilibrium value of the relative wave height (the latter was defined as the ratio of the rms wave height and water depth). We found that a small modification of the incident wave conditions resulted in the formation of bar-like perturbations on the equilibrium profile's terrace edge. Strong transport gradients associated with changes in the location of initial wave breaking caused the localization of the bar-like perturbations. This analysis did not resolve the potential for the bar-like perturbations to grow as free instabilities.

A numerical model based on a new sediment transport formula is presented to predict overwashed dune profile evolution. This model can also compute the cross-shore variation of the depth-averaged suspend sediment concentration. The computed sediment concentrations are high over the dune and low below the still water level. The computed profile evolution and sediment transport rate are compared with the representative data from small-scale dune overwash experiments. This model can reproduce the overall dune profile evolution and cross-shore sediment trasport rate at least qualitatively but tends to underestimate the erosion of the dune crest due to the error of an empirical formula for overtopping rates. To predict overtopping rates more accurately, a probablistic model is developed together with the time-averaged wave statistics predicted by the nonlinear time-averaged wave model CSHORE. The predicted overtopping rates are in fair agreement with the measured overtoping rates.

This paper relates nearshore ripple behaviour to cyclic changes in hydrodynamic conditions due to a sea breeze. Simultaneous time series measurements of waves, currents, and ripple crest positions were obtained from the nearshore of a micro-tidal low energy beach in southwestern Australia during two diurnal sea breeze cycles. Large parallel ripples with wavelengths of 0.3m–1.2m and heights of 0.05m–0.15m were present in coarse sand for the duration of observations. Mean ripple migration rates were calculated every half hour. During the sea breeze, wave height increased and wave period decreased with the addition of locally generated, short period wind waves on the incident swell waves. As a result, mean offshore flow (undertow) increased and cross-shore velocity skewness and asymmetry decreased. Ripples migrated onshore during the swell-dominated period and offshore during the sea breeze. It is proposed that the ripple migration direction is a function of the balance between onshore cross-shore velocity asymmetry and skewness and offshore mean flow.

To optimise the dredging of sand waves in navigation channels, it is important to predict the regeneration of the sand waves. For this purpose, the authors combine a morphodynamic evolution model, based on the Landau equation, with data measured in a field experiment in the Bisanseto sea in Japan. A good agreement is found between the measurements and the model result. Therefore, the combination of the Landau model and a genetic algorithm, proves to be a useful tool for the maintenance of navigation channels through a sand wave field.

A programme of field experiments has been conducted to ascertain the effect of small-scale bedforms (ripples) on nearshore sediment transport. The deployments used pressure transducer, electromagnetic current meter and optical backscatter sensors for high frequency measurement of hydrodynamics and suspended sediment concentrations alongside two acoustic instruments; a 1.2 MHz rotating side-scan sonar and 2 MHz sonar altimeter. The two instruments respectively provide details of ripple presence, orientation and wavelength, and height. Bed behaviours are described tor a range of hydrodynamic conditions in the saturated inner surf zone and can be related to a mobility number parameter (Ψ) derived from the total (incident and infragravity) wave energy. For Ψ less than 10, the bed remains static and as wave energy increases (10<Ψ<40) ripples are present and migrate. Further increases in wave energy (20<Ψ<60) cause suppression of ripple heights. The bed appears clear of small-scale bedforms for Ψ>80. As bed characteristics change with increased forcing, a change is also observed in the phase between high concentration sediment suspension events and instantaneous velocity. Visual analysis of the data suggests that a vortex shedding mechanism for suspension acts when the bed is rippled. High suspension concentrations in phase with the forcing velocity were only observed under extremely energetic conditions (150<Ψ<240).

A numerical model is developed to investigate the formation of ripples at high sediment transport rates in oscillatory flow. Allowance is made for the movement of the crest during the course of the cycle and for the difference in shear stress on mobile beds compared with fixed beds. Equilibrium ripple height and length are computed for a range of conditions. The curves obtained for ripple wavelength, ripple height-to-length ratio and bed planation show satisfactory agreement with experimental data. Empirical formulae are proposed in the light of the computed results

This paper discusses the practical applicability of NLINE, a new contour line model. The model follows a pragmatic approach to provide practical and accurate simulations for a wide range of spatial and temporal scales of beach changes. The model provides full, time-dependent simulations of wave transformation over irregular bathymetry and calculates the corresponding sediment transport and the 3-D morphological changes. NLINE can simulate short-term changes in profile shape in addition to long-term morphology changes and beach response to coastal structures. The paper demonstrates the model capabilities through a case study for a barrier island beach along the south west coast of Florida.

In the framework of the Coast3D Project a measurement campaign was conducted at Egmond, The Netherlands, during the spring of 1998. The site has been selected as representative for an alongshore relatively uniform coast. The instrumental lay-out was chosen to allow for validation of numerical models for the nearshore. Not only a dense spatial coverage of the modelling area is available, but also detailed measurements of boundary conditions, like wind field, deep water wave height and water levels. In this study, the Coast3D dataset is used to validate the hydrodynamic performance of Delft3D. Evaluation of the model results, acquired by using default process parameter settings, shows a good approximation of measured longshore and cross-shore currents.

In this study, a numerical model for three-dimensional beach evolution has been developed. The model for waves and current is based on the extended Boussinesq-type equations derived by Nwogu with a breaker-induced energy dissipation term introducing the eddy viscosity. Beach deformation is computed with an improved model using the sand transport rate formula proposed by Dibajnia and Watanabe, which is capable of estimating the net transport rate under nonlinear asymmetric irregular waves. The validity of the model is confirmed by comparing computed results with laboratory measurements under multi-directional irregular waves.

This study uses three-dimensional data to analyze storm response of a U.S. east coast barrier island. Ground-controlled aerial surveys are used to develop digital terrain models (DTMs) for Topsail Island, North Carolina before and after hurricane Fran (landfall September 5, 1996). We use these terrain models to calculate pre- and post- storm volume, look at spatial distribution of volume change, and extract two-dimensional cross-sections for subaerial profile study. We compare two sections of Topsail Island where dune response differs—in one, severe overwash removed a large portion of the primary dune field, in the other, dunes remained relatively undisturbed. Pre- and post-storm dune crest elevations in the areas differed by 1 m on average. Pre-storm dune reservoir volumes were determined using cross-sections and using the spatially continuous DTM. Dunes overwashed in Fran had reservoir volumes less than 20 m³/m; surviving dunes, more than 40 m³/m. We also consider the shoreline position from a three-dimensional perspective. The wet-dry line, often used to measure shoreline change, is projected onto the surface of the DTM and interpolated elevations assigned to each vertex point. Pre-storm wet-dry line elevation averaged 1.2 m; post-storm 0.8 m. A 1 m contour position is chosen as an alternative ‘shoreline.' Short-term shoreline change measured using the wet-dry line and 1 m contour are compared.

In order to obtain more insight into the selective transport phenomenon of graded sand, experiments were conducted on the transport of bimodal sand in sheet flow conditions under nonlinear oscillations. Transport mechanism was observed and moving layer thickness and transport rate were measured. A relation for the moving layer thickness was proposed for coarse sand. It was found that the transport rates of fine sand are considerably mitigated when percentage of coarse sand in the mixture is about 50% or more.

The vertical grading of the mixed-size sediment in sheetflow regime under the oscillatory flow is experimentally investigated. The velocity profile and the concentration distribution of the sediment are found by the video film analysis. The trajectories of large-size sediment show the existence of the reverse grading, which is the mechanism of armoring. Some features of the developing process of armoring are shown by the time series of the vertical sediment-size distribution.

To verify the diffusion concept for the description of time-averaged sediment concentration profiles in a fractional approach, suspended sediment concentrations and grain size distributions were measured for the same hydraulic conditions, using a ‘uniform' (D₉₀/D₁₀ approx. 2) and a graded (D₉₀/D₁₀ approx. 5) type of sediment. From the measurements, it was found that suspended sediment concentrations are larger for the graded sediment. Further, a very strong vertical sorting was measured close to the bed, especially for the graded sediment. Finally, it was found that the time-averaged sediment concentrations and the grain size distributions (including the strong vertical sorting) of the suspended sediment are described well, using the diffusion concept.

Understanding coastal evolution requires an approach that provides a thorough understanding of sediment movements and influences upon them. It is essential to identify the link between the geomorphology/sedimentology and the hydrodynamic process and the controls they impose upon one another. This paper presents the approach being adopted by Halcrow on studies in the UK. This brings together two disciplines in a model, which can be used to test coastal defence options and assist in the determination of appropriate future coastal management.

This paper introduces an N-line model for predicting long- as well as short-term beach changes. Previous N-line models have not yet been very successful, mainly because they were not based on realistic relations for cross-shore sediment transport and for the cross-shore distribution of the longshore transport. The model is formulated as a classical N-line model using an arbitrary number of layers. The cross-shore sediment transport rate is calculated as a product of potential transport rate and the actual local bottom slope relative to the local equilibrium slope. This transport is divided between the layers based on a transport distribution across the surf zone. In the longshore direction the transport rate is based on the CERC equation, again with a division between layers according to an across-shore transport distribution function. A calibration/validation application of the model to a data set from the US Army Field Research Facility at Duck, North Carolina, showed that the model results agreed quite well with measured long-term field data. In addition, the applicability of the model to predict short-term beach evolution is demonstrated through an illustrative example.

In order to assess the effect of future developments to Cape Town harbour on the sedimentary shoreline of Table Bay, a shoreline model is established. This model is founded on an assessment of the sediment budget and dynamics of the bay together with the calculated nearshore refracted wave field. The model is successfully validated against the measured long-term trends of erosion in the region. Since future erosion to the southern Table Bay shoreline is predicted, a beach nourishment solution is explored. In response to concern that a specific proposed extension to Cape Town harbour may affect the already eroded nearby beaches, an analysis of nearshore wave height and angle changes due to the extension is carried out. This analysis is found to be sufficient to conclude that no effect due to the extension will occur on the sedimentary shoreline situated 2 km north at the end of a seawall. However, indications are that effects on surfing waves adjacent to the development may occur.

This paper presents results of an experimental and theoretical study on wave-related suspended sand transport under irregular waves in the ripple regime. Experimental data were analysed to determine the mean and oscillating suspended transport components. The analysis results clearly show the influence of the particle diameter on the wave-related transport. The second part of the study is related to a 1DV model, which simulates the instantaneous velocity and sand concentrations from close to the bed up to higher in the water column. The model is based on the classical diffusion approach taking both the turbulence-related and the effective wave-related diffusion into account. It shows that the time-averaged sand concentrations can be simulated reasonably well in the ripple regime using the calibrated equations.

Field observations of near-bottom suspended sediment under random non-breaking waves have been used to derive a conceptual model to characterise the pulsing response of the sediment under the pass of wave groups. The model links the pulse characteristics -generation of the pulse, lag in the response, duration, period between consecutive pulses and intensity of the pulse- with the groups one. To do this, the run length method was found to be a good predictor provided the threshold velocity to define a group be properly selected. This threshold velocity depends on the energy of the wave-state in such a way that as larger the velocities are, the larger the threshold to generate a pulse will be. In addition to the mean run length and the total run, a new parameter using the envelope of the velocities was introduced to characterise "how big a group is", which was is linearly related to the intensity of the pulses.

An empirical formula for the pickup rate of sediment suspended by random breaking waves is derived, based on the CERC formula for longshore sediment transport and a power model of the work rate of sediment suspension being proportional to the spatial rate of change of the wave energy flux. Prediction of the cross-shore variation of the depth-averaged sediment concentration agrees with the data of several field measurements and large-scale flume tests. The cross-shore distribution of longshore sediment transport rate is also predicted with the newly-proposed sediment pickup formula and the longshore current model for random waves by Goda and Watanabe. Results of prediction are in good agreement with the field data of SandyDuck experiment.

An existing numerical model system for the flow field and suspended sediment concentration for oscillatory flow has been applied to a laboratory condition involving regular waves. The flow field was obtained from an existing model proposed by Kim et al., which is a modified CFD package SOLA based on SMAC scheme. The flow sub-model solves the continuity and Reynolds momentum equations in the x-z plane. Wave orbital velocities, shear stresses, and pressures were all reasonably reproduced by the sub-model. The model results for the vertical velocity component show good agreement with Williams et al.'s measurements. The suspended sediment transport sub-model solves the advection-diffusion equation for suspended sediment concentration using a splitting method, and involves a shear entrainment over the length of ripple. The calculated wave-period average ripple-length average suspended sediment concentration profile shows reasonable agreement with measurements in the Deltaflume

Results of field research of time variations of suspended sediment concentration above the rippled bottom under irregular waves are discussed in this paper. A simple method of its prediction is proposed on the basis of convection-diffusion model and field data.

Short term morphological changes have been analysed by means of a fractal technique based on the evaluation of the local and global Hurst exponent. Field measurements collected during beach cusp formation and development and time series obtained through simulations by a numerical model have been considered and compared. Results indicate the possibility that beach morphology might self-organise as a response to the hydrodynamic forcing at least at certain time-scales and at locations inside the swash zone where the forcing is less effective.

This paper presents a numerical model for predicting the bottom topographical changes around coastal structures using quasi-3D nearshore current model. The present model is abbreviated as Q3D-ISE (Initial Sedimentation/Erosion) model. The computations of the present model don't feed back into the computation of hydrodynamics and sediment transport. First, in order to calibrate and verify the present model, the computed results were compared with the results of movable bed laboratory tests with the detached breakwater. Secondly, the applicability of the present Q3D-ISE model to nearhshore currents and bottom topographical change under storm in the field was investigated. Finally, the applicability of the present model was discussed and the availability of the present model was confirmed.

This paper presents a new modelling paradigm justifying the application of small-scale basin models using mobile bed sediments for predicting medium-term wave-generated plan form beach response to nearshore structures.

For national decisions regarding coastal management it is important to understand the long-term effects and large-scale implications of both natural processes such as climate-change sea-level rise and major coastal engineering projects such as large-scale land reclamations. To this purpose, within the framework of the national Dutch research program "COAST*2000", a behaviour-oriented model is being developed that is basically capable of quantifying the long-term (50 to 100 years) and large-scale (1–100 km) morphological evolution of the Dutch coast. The set-up of this so-called PONTOS-model is discussed in this paper, focusing on the definition of the model, its validation and the results of application of the model for the Holland coast.

This paper investigates seabed sediment suspension due to the presence of waves and currents at the Mouth of the Columbia River (MCR). Relevant data were measured at a location 6 km offshore the MCR in a water depth of 19 meters with seabed sediment composed of fine to medium sand. The analyses described in this paper address the following question: When waves and currents interact along the seabed of an ebb tidal shoal, what is the effect on bottom sediment (sand) suspension? Special considerations included: assessing the modification of waves by current, describing the spectral relationship between bottom current and peak sediment suspension, and investigating wave group effects. Results indicate that: Currents influence the pressure signal for PUV measurements which can result in erroneous results for calculated wave height and period; The coherence between waves and response of suspended sediment is high yet complex due to multiple spectral peaks from waves, wave grouping, higher order effects; The RMS value of wave-induced bottom current can be used to identify grouping frequency which impacts suspended sediment response.

Among many sediment transport phenomena, coherent structures, bursts and sweeps have been identified as important mechanisms for entraining sediment into the flow near the bed. Large eddy simulation allows the reproduction of unsteady, intermittent and spatially non-uniform fluid motions and sediment concentration fields. This paper has two main foci: (1) to illustrate that these flow structures and their resultant sediment transport patterns are strongly influenced by the bottom geometry and (2) to illustrate that this coupling between bottom geometry and fluid motion may not be dependent on scale. A comparison is drawn between the transport over straight-crested and three-dimensional ripple geometries at laboratory scale and it is found that although similar structures are responsible for suspension of sediment over the two boundaries, incipient suspension of sediment is confined to regions between lines of zero streamwise curvature over the three-dimensional ripples whereas this effect is absent over the straight-crested ripples. Field-scale flow (Re ~660,000) is solved for over straight-crested ripples to investigate the influence of scale on the flow and similar coherent structures are observed. Future work will implement sediment transport in this field-scale flow.

Several empirical relations exist to calculate the concentration and transport of sand above rippled beds. Since these relations are based on physical experiments that only make use of a limited range of hydro-dynamical parameters and sediment characteristics, they often fail in predicting transports for other situations. E.g. the grain size of sand is difficult to vary. Numerical experiments however can form an interesting additional tool to examine the concentration field, and hence the transport of sands. It is not only possible to vary wave conditions easily, it is also possible to ‘measure' at each place over the ripple velocities and concentrations. This allows interpreting real measurements, which typically measure in a few verticals only.

The velocity and sediment-concentration distributions in the case of irregular waves and currents are studied by using the theoretical model developed by means of a mixing-length concept for sediment-laden flow, and by improving the sediment-concentration formula based on the same hypothesis. The predicted results are compared with a set of velocity and sediment-concentration data collected previously in a recirculating wave flume. The time-averaging procedure is adopted, since it eliminates the random scatter of the instantaneous components of velocities and concentration. The general characteristic of the time-averaged velocity is greatly affected by the significant-wave height and the flow direction to the generated waves, although the mixing length is a function of the sediment concentration. To compute the time-averaged vertical distribution of suspended sediment, two different formulae are proposed. The agreement between the simulated velocity and concentration profiles and the measured ones is satisfactory for the flow containing fine sands.

The steps required to assess the scour potential and bed stability around coastal structures are discussed. The influences of enhanced turbulence levels on the bed shear stress are assessed with a numerical model and with field data.

A coastal profile consisting of sand is continuously being modified by the action of the incoming waves, particularly in the surf and breaker zone, where bars can be built up, shifted about or leveled out by the wave-induced cross-shore sediment transport. Prediction of the profile development is important because its shape determines the wave decay and because its development is an integral part of the coastal erosion process. Further, the shape of the profile is important for the distribution and the magnitude of the longshore current and sediment transport, which is also a key factor in the coastal erosion or accretion. A considerable research effort has been made on the processes of cross-shore transport, but it has proven to be difficult to quantify because the mean cross-shore discharge is zero and the transport is composed of several opposing contributions that may be of the same order of magnitude. Outside the surf zone many contributions related to non-linear effects in the wave boundary layer have been identified, such as: streaming in the boundary layer, drift of suspended sediment, effects of higher harmonics in the wave orbital motion and effects related to wave groups and bound or free long waves.

The recent availability of spatially-dense airborne lidar data makes assessment of the vulnerability of beaches and dunes to storm impacts practical over long reaches of coast. As an initial test, elevations of the tops (D_high) and bases (D_low) of foredune ridges along a 55-km reach on the northern Outer Banks, NC were found to have considerable spatial variability suggesting that different parts of the barrier island would respond differently to storms. Comparing statistics of storm wave runup to D_high and D_low, we found that net erosion due to overwash and dune retreat should be greatest at the northern and southern ends of the study area and least in the central section. This predicted spatial pattern of storm-induced erosion is similar to the spatial pattern of long-term erosion of the shoreline which may be controlled by additional processes (such as gradients in longshore transport) as well as the cross-shore processes considered here. However, consider feedback where at erosional hot spots there is a deficit of sand (caused by gradients in longshore transport) which lead to lower dunes and enhanced erosional cross-shore processes, such as overwash. Hence, the erosional hot spots would be exacerbated, further increasing the vulnerability of the beach and dunes to net erosion.

This study presents the applicability of an artificial neural network for predicting some major parameters of a storm-built beach profile. The prediction model is derived based upon learning the bar profiles obtained from previous large wave tank tests. Back-propagation neural network — a supervised learning model, is used in which the interconnection weights in the network are repeatedly adjusted in the learning process in order to achieve the best performance. Base on the proposed neural network model, five major geometric parameters for a storm-built bar profile are predicted for a given wave condition. The results from the neural network model are found to be much accurate than the empirical relationships given by Silvester and Hsu and Hsu and Wang.

Measurements of profile topography, waves and tides from Victoria Beach (Spain) are used in order to analyze the relationship between beach profile changes and neap-to-spring variation in tidal range. The principal component analysis (PCA) method is used to objectively separate the spatial and temporal modes of variability of the beach profile data. It is shown that the most important mode of profile variability at Victoria Beach during the period of analysis corresponds to the fortnightly variation of the tidal range. The point of maximum variability is shown to be located between the neap and the spring high water levels. The maximum difference of levelling at that particular profile point was 0.65 m. Based on previous works, a preliminary conceptual model is presented in which the fortnightly profile variations for reflective beaches are related to the RTR parameter defined by Masselink and Short. It is concluded that, although these changes involve only a small amount of sand, the difference of vertical level at some particular points can be important as in the case of Victoria Beach.

The beach volume in two sets of morphological surveys at the coast of Egmond aan Zee was related to the depth of crest of a subtidal bar and the incident wave height. It is shown that the beach volume and the depth of crest of the first set were negatively related with r² = 0.46. A much lower skill in the second set was due to the response time of the beach which was O[10²hour]. Beach volume changes related negatively to the wave height on the inner bar crest though the skill was low (0.29). The results are interpreted as a profile change model which is compared to the traditional bar-berm model.

One of the methods to estimate sediment transport modes over a wide coastal area is proposed in this study. Lots of methods to estimate sediment transport modes have been carried out so far, however, clear indication is obtained in a limited case. In this paper the contents of heavy minerals that is the result of mineralogical analysis are used as a natural tracer indicating sediment transport modes. In order to get more clear view of sediment transport modes, the results of mineralogical analysis were processed by a statistical analysis. The method using the natural tracers is considered as one of the most effective methods in estimation of sediment transport over wide coastal area.

Many managers and owners of land situated behind eroding cliffs need to know how rapidly that land will recede. Recession predictions have traditionally been made through regression analysis of data obtained from historic maps. The historic rate has usually been considered to provide a reasonable prediction of future conditions. More recent models have represented the processes involved in the eroding cliff system. These are more powerful because they can predict the results of conditions that have not prevailed in the past. A weakness of this approach is that the models have been used to make deterministic predictions. This paper introduces a new type of process based model that is applied in a probabilistic way to provide a probability distribution of predicted recession distance. The model captures the involved processes in a relatively simple way so that multiple realisations can be performed within a manageable time. The current form of the model is described and examples of its output are given. It has been developed using data obtained from a specific site. This site and the data that is being collected from it are also described. The model is in the process of being rewritten and extended to capture a larger system of processes and some of these ongoing developments are described. The advantages of probabilistic process models of soft cliff recession are then discussed.

The skill of six well-known formulas developed for calculating the longshore sediment transport rate was evaluated in this study. Formulas proposed by Bijker, Engelund-Hansen, Ackers-White, Bailard-Inman, Van Rijn and Watanabe (1992) were investigated because they are commonly employed to calculate the time-averaged net sediment transport rate in the surf zone. Detailed, high-quality data on hydrodynamics and sediment transport from Duck, NC, collected during the DUCK85, SUPERDUCK, and SANDYDUCK field experiments were utilized to assess the predictive capability of these six formulas. Overall, the Van Rijn formula was found to yield the most reliable predictions over the range of swell and storm conditions that the field data covered. The Engelund-Hansen formula worked reasonably well, although with large scatter for the storm cases, whereas the Bailard-Inman formula systematically overestimated the swell cases and underestimated the storm cases. The formulas by Watanabe and Ackers-White produced satisfactory results for most cases, although the former overestimated the transport rates for swell cases and the latter yielded considerable scatter for storm cases. Finally, the Bijker formula systematically overestimated the transport rates for all cases.

A method is presented for evaluating nearshore waves and currents as well as cross-shore distributions of longshore sand transport rate under conditions of obliquely incident regular waves. A set of Boussinesq-type wave equations is used for the computation of waves and currents in surf and swash zones. The longshore sand transport rate is computed using formulas proposed by Dibajnia and Watanabe. The validity of the present method is examined through comparisons of computed results for the waves, currents and longshore sand transport rates with laboratory experimental data.

In this paper we report on the development and performance of an engineering model, STRAND which has the aim of predicting longshore movement of coarse sediment above the still water line of steep beaches. The model assumes that this transport is driven by swash run-up at the edge of an unsaturated inner surfzone and uses Nielsen's formulation for sediment transport rate. The hydrodynamic sub-model is shown to agree well with field measurements of swash run-up and swash period. We argue that consideration of interactions between subsequent swash events implies that a monotonic relationship between transport rate and incident wave period is inappropriate. Bulk longshore transport rates are shown to compare reasonably with previous estimates from field studies in the UK and accounts for up to 50% of the net longshore flux. Agreement of this simplified model with one of the best available laboratory data sets, Kamphuis, is very good indeed. However, new laboratory and field data are required before stronger conclusions can be drawn.

The coastal barriers of the NSW Central Coast, SE Australia were formed in the Holocene, during and immediately following the last postglacial marine transgression. They were fed by sediments winnowed from what is now the inner shelf. Barrier growth continued for some 5000 years after the sea reached its present level indicating the potential for present day morphodynamic coupling of the nearshore and inner shelf. It is likely this coupling is responsible for some observed long-term, large-scale coastal changes. Current meter and other measurements taken at MacMasters Beach on the NSW Central Coast provide evidence of this coupling and demonstrate significant cross-shore sediment transport potential beyond the nearshore zone.

The cross-shore sediment transport in surf zones on beaches is analyzed on the basis of the time-dependent, depth-integrated sediment continuity equation including sediment suspension, storage, advection and settling. The energetics approach by Bagnold is shown to correspond to the special case of local equilibrium between sediment suspension and settling. The corresponding time-averaged model together with the simplified assumptions of Dean yields a uniform suspension rate for the standard equilibrium profile with the scale parameter A as a function of the sediment fall velocity. The simplified time-averaged model with new moving boundary conditions at the shoreline and breaker point is shown to predict both erosional and accretional beach profile evolutions under regular waves in a large tank. The sediment suspension rate estimated for the equilibrium terraced and barred beaches under irregular waves is found to be roughly uniform in the surf zone but increase significantly in the swash zone.

A quasi-2DV sediment transport model is used to demonstrate the importance of the wave skewness on the on/offshore sediment transport calculations. The model combines a phase-averaged and a phase-resolving wave module with an intra-wave sediment transport module. A simple method to generate time series with a prescribed skewness is suggested. This method was shown to provide good results provided a reasonable estimate for the actual skewness is available. This study also showed that the skewness of the oscillatory currents is more important than the asymmetry of the oscillatory current.

The determination of predictive indices for the direction of cross-shore sediment transport is of significant interest in several aspects of coastal engineering analysis. Such indices may be used qualitatively to analyze large scale morphological evolution of beach profiles, or may be used more quantitatively to determine the local transport direction at a particular point in space and time in a number of conventional coastal sediment transport models. Johnson first indicated that the deep water wave steepness H_o/L_o was an indicator of the direction of cross-shore sediment transport: in laboratory experiments, values of H_o/L_o > 0.03 were observed to cause beach erosion, while values of H_o/L_o < 0.025 produced accretive conditions (here H_o and L_o represent wave height and wave length, respectively, in deepwater). Since these observations did not account for effects of sediment size, Dean used heuristic arguments concerning the hypothetical suspension and settling of sand grains under a breaking wave to introduce an additional dimensionless "fall velocity parameter", such that the dividing line between erosive and accretive conditions was determined to be: H_o (over) L_o gT (over) пw = 1.7 where g is gravitational acceleration, T is wave period, and w is sediment velocity. The resulting index has been used extensively since that time. More recently Ahrens and Hand used the wave orbital velocity under the trough from nonlinear wave theory U_t non-dimensionalized by the critical velocity for sediment motion U_c to obtain a predictive index U_t/U_c which described much of the accretive and erosive behavior of the data set of Kraus and Mason.

A numerical morphological model has been applied to investigate the initiation and development of along-shore variations in a long-shore bar (morphological instability). Two cases have been studied: a case where bar generating effects are included starting with an initially plane bed (Q3D) and a case where an otherwise stationary bar — uniform in the alongshore direction — is used as the initial topography (2DH). In both cases the morphological evolution of the slightly perturbed initial states is simulated beyond the initially linear stage. In the Q3D case a long-shore bar was formed with the bar crest significantly meandering down the coast. The bar crest did not seem to develop any (rip) channel like features. In the 2DH case on the other hand the bar tended to break up forming channels.