Coastal Engineering 1994

Similarity relationship among non-dimensional significant wave parameters are discussed which is based upon the 3/2 power law. The characteristics of the wind wave spectra in deep water are investigated by using the parameters of JONSWAP spectrum and the 3/2 power law. From theoretical and empirical arguments, it is confirmed that a f^-4 power law exists at high frequency range, that JONSWAP spectrum parameter γ and σ are varied with fetch, and that parameter α and γ satisfied a -1/3 power law. In shallow water region, spectral form of wind waves is varied with the shoaling coefficient. Through the analysis of the wind wave spectra, a new spectral formula is obtained.

A numerical model is developed to predict the flow characteristics in a swash zone for obliquely incident wave trains. The two-dimensional shallow water equations are de-coupled into independent equations each for on-off shore motion and for longshore motion. A front of swash wave train is treated as a moving boundary which makes the solution predictable for landward zone of the still water level. The results show non-vanishing longshore velocities and volume flux at the still water shoreline. These quantities are found to increase with the beach slope. The two-dimensional uprush and downrush motion near the front of swash waves shows skew figures, which may cause zig-zag longshore sediment transport inherent in swash zone.

In order to define a directional wave sensor for laboratory experiments, three measuring systems as well as seven directional analysis methods are combined, applied and compared on three different tests performed in a directional wave basin. "Single-point" gauges are found to accurately analyse unimodal spectra when associated to advanced methods (Fit to bimodal model, Iterative Maximum Likelihood Method, Maximum Entropy Method, Bayesian Method). The heave-pitch-roll gauge used in this study is in particular very simple and shows promising capabilities. For bimodal spectra (two directional peaks at same frequency) however, only the wave probe array combined with the Maximum Entropy Method or the Bayesian Method appears to be able to produce reliable estimates.

We have made a critical analysis of the processes and the parameters that affect the accuracy with which wind and waves can be evaluated close to coast. For each process we quantify the possible error, whenever possible complementing this with numerical tests and practical cases.

The present paper describes the second phase in the development of a fully spectral wave model for the near shore zone (SWAN). Third-generation formulations of wave generation by wind, dissipation due to whitecapping and quadruplet wave-wave interactions are added to the processes of (refractive) propagation, bottom friction and depth-induced wave breaking that were implemented in the first phase (Holthuijsen et al., 1993). The performance and the behaviour of the SWAN model are shown in two observed cases in which waves are regenerated by the wind after a considerable decrease due to shallow water effects. In the case of the Haringvliet (a closed branch of the Rhine estuary, the Netherlands) reasonable results in terms of significant wave heights were obtained. In the case of Saginaw Bay (Lake Huron, USA), the SWAN model underestimates the significant wave height deep inside the bay (as did two other models). Due to the absence of triad wave-wave interactions in the model the mean period is not properly shifted to the higher frequencies in shallow water. Adding these triads is planned for the next phase of developing the SWAN model.

Continuous records of wind speed and direction show a high variability both in the high and low frequency ranges. This variability is usually not considered in the numerical hindcast of a storm. We discuss the related implications for the maximum wave heights and for the values from the statistics of extremes.

This paper presents some results of research relating to the theoretical predictions of mass-transport velocity within the free surface zone of water waves in intermediate water depth. The theoretical results are compared with measurements made in a wave flume.

The theoretical estimate of a mean drift has allowed for a better estimation of the return flow in the wave flume. Examples of such estimation are given and graphically presented in the paper. Finally, the stability of the obtained mean velocity profiles throught the experiments is examined.

Detailed laboratory measurements are made of the velocity fluctuations to investigate the processes of the turbulence generation, advection, diffusion and dissipation in the surf zone. An order of magnitude analysis of the transport equation of the turbulent kinetic energy using the normalization adopted by Kobayashi and Wurjanto (1992) indicates an approximate local equilibrium of turbulence for shallow water waves in the surf zone. Estimates are found for common surf zone turbulence parameters. The calibrated values are used to show that the eddy viscosity varies gradually over depth and is nearly time-invariant and that the local equilibrium of turbulence is a reasonable approximation for spilling waves in the inner surf zone.

This paper concerns the interaction of waves and currents, and in particular the effect of the time-averaged vorticity distribution associated with a sheared current. Laboratory data describing both the "initial interaction" of waves and currents, and the "equilibrium" conditions arising within an established wave-current combination are presented. These results are compared to both the existing irrotational solutions and a multi-layered numerical model capable of describing an arbitrary current profile. The interaction of regular waves and sheared currents is shown to be in good agreement with this latter solution. However, a similar description of random waves on sheared currents is limited by the wave-induced changes in both the mean current profile and the associated turbulent structure.

Waves propagating in a curved channel are examined analytically and with a variety of parabolic and spectral models. The results show that the wide angle parabolic method is reasonably robust, but not exact, while a spectral method based on trigonometric functions is superior to a Chebyshev polynomial method. Angular spectrum models are discussed and shown to be equivalent to an eigenfunction expansion in the cross-channel direction.

Aquatic vegetation, such as seagrasses, macroalgae and trees whether submerged or subaerial are an important feature of a coastal ecosystem. For the past years, the dissipative character of large stands of kelp has been the subject by several studies. In the present work, a new analysis is developed for the flow model and the vegetation motion using field and experimental results carried out on kelp fronds and kelp plant models. A comparison is also made between the theoretical model and experimental results. Basing from this, an analytical solution for water waves propagating over submerged vegetation is developed.

The degree of nonlinear coupling in a random wavefield propagating over and beyond a bar is examined using a physical wave flume as well as numerical simulations based on time-domain extended Boussinesq equations and their frequency-domain counter-part. The nonlinear phase speed is computed from the evolution of the nonlinear part of the phase function inherent in the frequency-domain model. Over the bar, the phase speeds of the higher harmonics are larger than the linear estimates due to the nonlinear couplings, resulting in virtually dispersionless propagation, while beyond the bar crest, nonlinear effects on the phase speed vanish rapidly, implying full release of bound harmonics. Quantitative measures of nonlinearity such as the skewness and asymmetry have also been determined. They have near-zero values in the deep-water region on either side of the bar and a pronounced peak over the bar. On the downwave side, the random wave field is found to be spatially homogeneous. This implies that it can be fully described by the energy density spectrum without additional phase information related to the bar location.

An absorbing wave maker operated by means of on-line signals from digital FIR filters is presented.

Surface elevations are measured in two positions in front of the wave maker. The reflected wave train is separated from the sum of the incident and rereflected wave trains by means of digital filtering and subsequent superposition of the measured surface elevations. The motion of the wave paddle required to absorb reflected waves is determined and added to the original wave paddle control signal.

Irregular wave tests involving test structures with different degrees of reflection show that excellent absorption characteristics have been achieved with the system.

Significant features on Wadden Sea wave climate are evaluated in respect of the state of the art. Main emphasis was laid on an analysis of the governing boundary conditions of local wave climate in island sheltered Wadden Sea areas with extensions being sufficient for local wind wave growth. Explanatory for significant wave heights a reliable parametrization of local wave climate has been evaluated by using generally available data of water level and wind measurements.

It is common practice to consider the random waves as a succession of discrete waves characterized by individual amplitudes and periods. The zero-up-crossing criterion isolates some discrete waves that are not physical waves. The orbital criterion avoids these "false waves". As a result, the orbital criterion proves to be more consistent and robust, and to have a less variability. The selection of the discretization criterion results in some significant differences in the wave statistics, which are analyzed. As an example, while the mean period for the zero-up-crossing criterion is T₀₂, the mean period for the orbital criterion is T₀₁.

A new type of wave gauge has been developed for the measurement of waves near a beach or near an existing coastal structure. It consists of a nylon tube with diameter between 0.5 and 1cm and length up to 500m. The seaward end of the tube is open so that the wave induced pressure fluctuations can be transmitted through the water in the tube. The landward end, which is conveniently above the water, is fitted with a pressure transducer. This is simple and reliable technology well suited for use in developing countries. Maintenance and running coasts are also very low. The frequency response function of the system is somewhat complicated but a workable formula is presented and "once and for all" calibration of the system can be done very easily.

The quantity of spray transported by strong wind has been measured experimentally when the wind blows over waves propagating on a sloping bed. The leeward variation of spray concentration is much smaller than that in the vertical direction because of the quasi uniform supply of spray from the water surface. In the theoretical development, therefore, the balance has been analyzed between the upward flux of the concentration by turbulent diffusion and the downward flux due to the spray precipitation. Three characteristic quantities introduced in the analysis have been obtained by superposing the experimental data on the theoretical solutions. They are related to the wave and wind parameters to predict quantitatively the spray concentration supplied from sea to shore.

This paper presents an extension of the maximum entropy principle method (MEP), named the extended MEP (EMEP), as a general and practical method for estimating directional wave spectra. Since the EMEP is formulated to consider errors in the cross-power spectra, it proves to be an accurate, reliable, and robust method against such errors. In addition, we also examine the EMEP using numerical simulation and field wave data, with its validity being subsequently discussed.

This paper deals with regression models for estimating probability distributions of long term wave height, sea state persistence above a wave height threshold and peak wave height during a storm, and yearly-averaged occurrence rate of peak wave height event. The models, in which input condition is the variance of long term wave height at a concerned sea area, were constructed on the basis of statistical analysis of the long term wave height data obtained around the Japanese coast. First, the effect of observation interval on the above-mentioned wave climate statistics was investigated and a method to remove the effect by use of FFT was proposed. Second, Applicability of each regression model was confirmed from close agreement between estimation and observation for the wave climate statistics. Finally, return periods of extreme wave height with prescribed sea state persistence and wave height threshold at wave observation points around the Japanese coast were estimated with a combination of the present regression models.

The maximum possible wave conditions in the southern North Sea are estimated with synthetic storms and a third-generation wave model. The storms and the physics in the wave model have been chosen within the uncertainty of the state-of-the-art to have maximum effect. The wave conditions appear to be limited by the presence of the bottom and to some extent by the assumed maximum wind speed of 50 m/s. The maximum significant wave height thus determined for the southern North Sea is about 0.4 times the local water depth.

The offshore and side boundary conditions to a time—dependent mild slope equation for random waves are improved to introduce given incident waves into and extract reflected waves from the computational domain with reduced computational time and storage size. The resulting numerical model is applied to calculate the wave field, nearshore current, and bottom topography change around a detached breakwater.

Linear and nonlinear governing equations are derived to calculate the time evolution of random waves subject to refraction and diffraction.

In the linear theory, the frequency-dependent coefficients in the mild-slope equation (Berkhoff, 1972) are approximated by a rational function of the frequency, and then a time-dependent and frequency-independent expression of the mild-slope equation is derived. The resulting equation is applicable to simulate the transformation of random waves in the nearshore zone. Results of numerical calculation agree well with experimental results for random wave shoaling in the offshore zone.

A set of nonlinear governing equations is also derived to simulate the nonlinear wave transformation. The velocity potential for the wave motion is expressed as a series in terms of a given set of vertical distribution functions. Then, the Lagrangian is integrated vertically and the variational principle is applied to yield a set of nonlinear, time-dependent, two-dimensional governing equations for the nonlinear random wave tranformation. Comparison between the results of numerical calculation and flume experiment shows good agreement for the random wave shoaling near the breaking point and for wave disintegration due to a submerged breakwater. .

The present paper is concerned with the simulation of turbulent boundary layer dynamics over a moveable seabed in random waves. A new theoretical approach for the evaluation of moveable bed roughness in spectral waves based on the grain-grain interaction idea is presented and tested against data from the laboratory and field. The new approach is combined with the methodology which assumes that the spectral wave condition can be represented by a monochromatic representative wave. Good results have been obtained, although further testing against data gathered in the North Sea is required.

The physical difference of beach erosions between on the steep and on the gentle beaches has been discussed, based on the field data and the theory of generation of the infragravity waves. As a result, it is shown that the incident waves are predominant in the wave run-up phenomena on the steeper beach, while on the gentler beach the infragravity waves are predominant.

The effects of strong wind on wave breaking were discussed with the field data. At around U =23m/s the maximum wave steepness of 0.034 was obtained. At the wind velocity of more than 23m/s, the wave steepness becomes small once because reformed waves which were already broken at the offshore were measured. This corresponds with the changes of the ratio of wave breaking. The relationship between the mean period of SIWEH and significant wave period was made clear. It was found that pulsating behavior of undertow influences wave breaking in a shallow water.

Two different versions of maximum entropy methods(MEM) were compared with two conventional methods for analyzing directional ocean wave spectra. The two MEMs were originally proposed by Lygre and Krogstad (1986) and Kobune and Hashimoto (1986), respectively, and the two conventional methods are the truncated Fourier series method(TFS) and Longuet-Higgins parametric model(LHM). The comparisons included hypothetical idealized cases and actual measured data. For the hypothetical cases, the MEM by Kobune and Hashimoto clearly performed better, particularly for dual-peaked spectra. As for the comparisons from measured data, the MEM generally yielded narrower directional spreading than the two conventional methods but all methods gave nearly identical main direction information. However, this MEM does have occasional convergence problem in real sea data analysis. The problem is removed with the aid of an approximation scheme. This modified scheme is employed in the automated directional spectral analysis of measured sea data.

In this study, the appearance probability of the freak waves is theoretically introduced applying the definitions by Klinting and Sand (1987). Their three conditions are formulated theoretically applying the probability distributions for the run of wave heights (Kimura, 1980) and the distance of a mean point of the zero-crossing wave crest and trough from mean water level (Kimura and Ohta, 1992b). Its appearance probability in a uni-directional irregular wave condition is studied first, the theory is extended then to the 3-dimensional wave condition, and the definition is discussed in terms of the probability in the last.

A theoretical expression for the joint distribution of wave height, period and direction is derived based on the hypothesis that sea surface is a Gaussian stochastic process and that a band-width of energy spectra is sufficiently narrow. The derived joint distribution is found to be an effective measure to investigate characteristics of three-dimensional random wave fields in shallow water through field measurements.

Based on the linearized governing equations, a bottom roughness specified by the equivalent Nikuradse sand grain roughness, k_N, and a time-invariant eddy viscosity analogous to that of Grant and Madsen (1979 and 1986) the solution is obtained for combined wave-current turbulent bottom boundary layer flows with the wave motion specified by its near-bottom orbital velocity directional spectrum. The solution depends on an a priori unknown shear velocity, u_*r, used to scale the eddy viscosity inside the wave boundary layer. Closure is achieved by requiring the spectral wavecurrent model to reduce to the Grant-Madsen model in the limit of simple periodic plane waves. To facilitate application of the spectral wave-current model it is used to define the characteristics (near-bottom orbital velocity amplitude, u_br, radian frequency, ω_r, and direction of propagation, ϕ_ωr) of a representative periodic wave which, in the context of combined wavecurrent bottom boundary layer flows, is equivalent to the wave specified by its directional spectrum. Pertinent formulas needed for application of the model are derived and their use is illustrated by outlining efficient computational procedures for the solution of wave-current interaction for typical specifications of the current.

In this paper we study wave breaking and runup of regular and irregular waves, and the generation of surf beats. These phenomena are investigated numerically by using a time-domain primary-wave resolving model based on Boussinesq type equations. As compared with the classical Boussinesq equations the ones adopted here allow for improved linear dispersion characteristics, and wave breaking is incorporated by using a roller concept for spilling breakers. The swash zone is represented by incorporating a moving shoreline boundary condition and radiation of short and long period waves from the offshore boundary is allowed by the use of absorbing sponge layers. The model results presented include wave height decay, mean water setup, depth-averaged undertow, shoreline oscillations and the generation and release of low frequency waves.

This study aims to develop a method using wavelet transform to detect wave breaking event from temporal water surface elevation data. Sudden surface jump associated with breaking wave is regarded as shock wave and shock wavelet spectrum is defined to detect the occurrence of the surface jump. The visual observation of breaking wave crest shows that this method can almost completely detect the occurrence of breaking wave in random wave trains.

A set of fully-dispersive nonlinear wave equations is derived by introducing a velocity expression with a few vertical-dependence functions and then applying the Galerkin method, which provides an optimum combination of the vertical-dependence functions to express an arbitrary velocity field under wave motion. The obtained equations can describe nonlinear non-breaking waves under general conditions, such as nonlinear random waves with a wide-banded spectrum at an arbitrary depth including very shallow and far deep water depths. The single component forms of the new wave equations, one of which is referred to here as "time-dependent nonlinear mild-slope equation", are shown to produce various existing wave equations such as Boussinesq and mild-slope equations as their degenerate forms. Numerical examples with comparison to experimental data are given to demonstrate the validity of the present wave equations and their high performance in expressing not only wave profiles but also velocity fields.

The Green-function method for analyzing wave refraction, diffraction and reflection is improved by deriving rational explicit formulations of boundary conditions. Possibilities and limitations of the method are discussed. Trial computations and their comparisons with experiments demonstrate the validity and usefulness of the numerical model.

A new system of equations is proposed for calculating wave deformation of irregular waves under the assumption of small amplitude wave and of mild slope of bottom configuration. The system is composed of a vibration equation for water surface elevation and three elliptic equations defined in horizontal plane. These equations are coupled each other. The coupled vibration equations are capable of calculating water surface elevation of irregular waves in a time domain.

Nonlinear aspects of the transformation of a multidirectional wave field in shallow water are investigated using Boussinesq-type equations. Second-order interactions between different frequency components in an irregular sea state produce lower and higher harmonic components at the sum and difference frequencies of the primary waves. For water of constant depth, expressions are derived from the Boussinesq equations for the magnitude of the second-order waves induced by bidirectional, bichromatic waves. These are used to investigate the effect of the direction of wave propagation on the near-resonant interactions that occur in shallow water. For waves propagating in water of variable depth, a numerical model based on a time-domain solution of the governing equations is used to the predict the spatial evolution of the directional wave spectrum. The results of the numerical model are compared to experimental results for the propagation of bidirectional, bichromatic waves and irregular, multidirectional waves on a constant slope beach.

This paper presents the development of a probability density function applicable to waves in finite water depth (which can be considered to be a nonlinear, non-Gaussian random process) in closed form. The derivation of the density function is based on the Kac-Siegert solution developed for a nonlinear mechanical system, but the parameters involved in the solution are evaluated from the wave record only. Further, the probability density function is asymptotically expressed in closed form. Comparisons between the presently developed probability density function and histograms constructed from wave records show good agreement.

This study deals with the probability distribution of zero-crossing wave height applying the definition of the zero-up(down)-cross method faithfully. In this study, gap between wave crest or trough and the envelope at the same location, which has been neglected in the ordinary studies is taken into account in the wave height definition. Its probability distribution is approximated with the Weibull distribution. The probability distribution of the zero-crossing wave height is, then, introduced theoretically together with the theory by modified Tayfun Method and the statistical properties of the gaps. The numerically simulated irregular wave height distributions agree well with the theoretical distribution.

The numerical model SKYLLA, developed for simulation of breaking waves on coastal structures is described. The model is based on the Volume Of Fluid method and solves the two-dimensional (2DV) Navier-Stokes equations. Weakly reflecting boundary conditions allow waves to enter and leave the computational domain. Impermeable boundaries can be introduced to simulate a structure. A two-model approach can be used to simulate overtopping over a low crested structure. Results obtained with the model are compared with those obtained with physical model tests for waves on a 1:20 slope of a submerged structure.

The main focus of the experiment was to observe and measure large-scale vortices generated by breaking waves over a submerged breakwater. These flow structures are important in sediment transport due to their ability to trap sediment particles negating their normal settling velocity. The technique of Particle Image Velocimetry (PIV) was used to measure the spatial distribution of velocities at an instant; an approach which is essential for measuring coherent structures in the flow. Experiments were conducted in the 50m flume at The University of Florence which was fitted with a 1:100 beach, wave elevations, as well as velocity fields, were measured.

The paper deals with the experimental details and a display of the velocity and vorticity maps obtained using PIV.

The way in which the Boussinesq and Serre models deal with the internal kinematics of waves on mildly sloping beaches is examined. The equation normally used on the depth-averaged horizontal velocity to impose a parabolic profile vertically up through the wave is studied using experimentally and theoretically obtained values. In general, it is found that for near-bed regions the equation provides satisfactory comparisons, however, as one approaches the surface the theoretical values can substantially exceed the experimental ones, particularly in the crest of the wave.

Wave run-up, wave set-up and wave run-down are determined by using the residence time in the form of a duration curve. This method introduced by FÜHRBÖTER and WITTE (1991) considers the totality of a run-up series without considering individual run-up events separately. By using the residence time concept, wave run-up is not any more a timeless event but can be described as a time dependent variable. The results obtained by using this concept are in good agreement with previous studies based on other methods for defining wave run-up, wave set-up and wave run-down. The residence time concept has been used for regular and random waves. This concept is particularly useful for random waves, because there is no need to count the number of waves loading a dike.

This paper describes experiments performed with the UCL shear plate device to make direct measurements of the bottom shear stress vector under the action of combined waves and currents. The three corresponding velocity components have also been recorded simultaneously, enabling the results to be expressed in terms of a friction factor. The scope of the work extends that of earlier tests on regular waves, and includes three sequences of random waves propagating above a fixed rough bed in still water and over two orthogonal currents.

The results show that, for the range of conditions considered, the addition of an orthogonal current has no discernable effect on the amplitude of the shear stress time series or on the friction factors used to characterize the complete sequence. If a single friction factor is used to describe the shear stress throughout a sequence of random waves, and if that factor is calculated from the RMS of the shear stress during the sequence scaled on an equivalent regular wave with a bottom orbital velocity amplitude of u_rms √2, then the results agree well with earlier observations from tests on regular waves, and f_w can be predicted from standard formulae.

The non-linear nature of the largest waves in random wave trains is studied. Experimental wave elevation records from measurements in a large wave basin are analysed. Longcrested as well as shortcrested wave conditions, with various spectral shapes, are included. The spatial development of spectral and statistical properties of the wave trains are analysed. The results indicate that closer than 10-15 wavelengths, observed deviations from linear theory may be explained by 2nd order effects. Further away, higher-order modulational instabilities may lead to a stronger increase of extreme waves. This is especially observed in narrow-banded long-crested waves, while observations in short-crested sea show very little content of these space-dependent modulational effects.

We investigate the vertical, wave averaged distributions of shear stresses and Eulerian flow in normally incident, shoaling and breaking waves. It is found that shear stresses are solely due to wave amplitude variations, which can be caused by shoaling, boundary layer dissipation and/or breaking wave dissipation. The resulting shear stress and mean flow distributions for these cases are derived, and compared with earlier work.

The attractive, now frequently used modelling choice of specifying a shear stress at the mean surface level is discussed in the context of the constituent equations and related boundary conditions and constraints. A derivation of the shear stress at the mean surface level is given both by using the momentum balance and energy balance equations, which is shown to lead to the same result, if the effects of a changing roller are incorporated correctly.³⁾

Finally, matching solutions for the shoaling and breaking wave cases between the boundary layer and the middle layer for the shear stresses and the wave averaged flow are derived.

Beach erosion has become a major problem at coral-sand beaches in Bali, Indonesia, due to the rapid changes in natural environment and utilization of coastal areas. An observation of waves was carried out at Sanur beach in Bali to know what waves are effective for beach processes. The representative waves are predicted by use of the mild-slope and KdV equations with evaluation of the coefficient of bottom friction. Empirical formulae of wave energy dissipation are proposed for taking into account of wave height damping due to breaking on the coral flat. The maximum wave on the coral flat, occurring in the reforming region of waves after breaking near the reef edge, can be decided by the theoretical results of the highest wave of permanent-type on water of uniform depth. Sanur beach has observed swells with a period longer than 15 sec, being incident onto the coral flat without breaking. This maximum wave of non-breaking progressive-type is, therefore, evaluated by the experimental wave height criteria.

This paper presents a newly developed type of submerged directional wave meter having the capability to measure water surface elevation and multiple current velocity components. These components are determined from Doppler frequency shifts using the complex covariance method. The developed system was demonstrated to be capable of successfully obtaining directional wave data, as well as adequately estimating directional wave spectra.

A time-dependent and a time-independent wave equations are developed for waves propagating over porous rippled beds taking account of the effects of porous medium. The mean water depth and the thickness of porous layer are assumed to be slowly varying compared to the wavelength of surface gravity waves, and the spatial scale of ripples is assumed to be the same as the wavelength of surface waves. By using the time-independent equation, the Bragg scattering is examined in one-dimensional case. The results show that the reflected and transmitted waves become smaller than those in the case of impermeable rigid rippled bed due to energy dissipation in porous medium.

A new wave-generation system, composed of a source and an absorber, is proposed to realize a non-reflective wave field in a laboratory basin as an advanced alternative to conventional methods. Theoretical studies based on the linear potential theory were carried out to investigate the characteristics of wave fields generated by the proposed method. Performance of the new system was compared to that of conventional serpent-type wave-makers. The proposed system was founded to provide a significantly larger effective area for multi-directional waves than does the serpent-type wave makers.

Experimental studies using a two-dimensional wave tank were also conducted to verify the performance and practicality of the new system. The results showed that the new devised equipment can produce a nearly non-reflective wave field and can generate waves efficiently even in deep water.

The field experiment at Lake George has brought valuable data that was not yet available. The analyses done to the data has shown new insights into shallow water waves. Already from the first analyses we can derive some interesting things. The one-dimensional shallow water spectra seem to have a clear peak enhancement and tail that is proportional to f^-4.5. The directional spread with two-dimensional spectra shows at the higher frequencies (twice the peak frequency) the waves move symmetrically at an angle with the wind. More analysis needs to be done to fit different kind of spectra and to find a function for the directional spread.

Wave hindcastings in the West Pacific Ocean and at selected locations along the Pacific coast of Japan by the use of two wave prediction models are conducted for 118 typhoons which occurred from 1940 to 1991 to estimate maximum wave height at each point during a typhoon. Combination with maximum wave height data in the concerned area for 125 typhoons from 1934 to 1983 obtained by Yamaguchi et al. (1987a, 1987c) results in data sets of maximum wave heights caused by 243 typhoons from 1934 to 1991. Spatial distribution of the most extreme wave height and wave height for return period of 100 years, and their variation along the Pacific coast of Japan are re-examined on the basis of statistical analysis of the data and compared with the Yamaguchi et al. results (1987a, 1987c), in which case there is little change in the distribution except for the Western Kyushu coast. In addition, maximum wave height along the coast of the Japan Sea is evaluated in a similar manner.

Irregular wave run-up on beaches has been studied on the basis of laboratory and field data, which confirmed that long-term wave run-up corresponding to surf beat (or infragravity waves) appears in case of a sea bottom slope gentler than about 1/20. Moreover analytical and numerical models to calculate surf beat caused by wave groups are investigated, and empirical and numerical models to predict the long period wave run-up are proposed.

A theory of wavemaker system for coastal waves (nonlinear random waves in very shallow water) having the desired statistics is developed under the assumption that they are treated as random trains of the KdV solitons and further its applicability is examined experimentally. This wavemaker system is shown usefull to generate accurately nonlinear waves having the desired water surface profiles of which nonlinearity is specified by the Ursell number U_r ≥ 15 for regular waves (cnoidal waves) and U_r ≥ 8 for random ones (coastal waves).

A method for estimating the directional spectrum as well as the reflection coefficient in a incident and reflected wave field is developed for practical uses. In the method, the directional spectrum is assumed to be expressed by a circular normal distribution which includes several parameters, Then the parameters are estimated by the maximum likelihood method. The validity of the method is verified by numerical simulation.

The directional spectrum is one of the basic characteristics of sea waves. The observations of directional spectrum of sea waves are successfully conducted at platform Bohai 8 during 1991 and 1992 using a wave gage array and it is the first time in China. Based on the field data, the directional spectrum which depends on the wave growth is given in this paper. Before observations, the effects of the figure of gage array, the distance between the gages and the platform itself on the measured results and the precision of some methods for estimating the directional spectrum were investigated and compared with the methods of numerical simulations and model tests of multi-directional irregular waves. This ensures the quality of the observations and estimations of the directional spectrum.

A numerical model for the transformation of narrow-banded irregular waves over gradually varying bottom topography is presented. The model is based on the mild slope wave equation for component waves. Perturbation of the mild slope wave equation with respect to the deviation of the angular frequency of any component wave from that of a principal wave, which is a small quantity for waves of narrow-banded spectra, is carried out. The mild slope wave equation, which depends on the frequency of the component wave, can thus be replaced by the perturbation equations in terms of the principal wave parameters. The finite element method is considered for numerical solutions of the perturbation equations. Since the matrix of the linear algebraic finite element equations depends on neither the component wave properties nor the order of the perturbation, numerical solution of an irregular wave field can be efficiently obtained. The model is applied to the computation of the wave motion over an elliptic shoal. The computed wave height distribution shows satisfactory agreement with the available experimental data.

A full spectral third-generation wave prediction model has been extended with formulations for surf breaking and nonlinear triad interactions and a first assessment of its performance against shallow water wave data has been examined. The formulation for wave energy loss by surf-breaking in shallow water is based on the expression of Battjes and Janssen (1978), which has heuristically been modified to predict the energy loss per spectral component. The source term for nonlinear triad interactions was taken from Abreu et al. (1992). Results of the extended model have been compared against laboratory and field data. The results of the model computations indicate that surf breaking and triad interactions are important processes in the coastal zone. Surf breaking is mainly responsible for the decay of wave energy, whereas triad interactions are mainly responsible for changes in the mean wave period. The applicability of the Abreu formulation is limited and needs further attention.

The generation of a single low-frequency wave (LFW) pulse by a single group of waves incident on a beach is investigated by means of laboratory experiments and a numerical model. This simplified case allows the LFW to be measured in isolation, after the incident group has passed and before there is any reflection from the wavemaker. A beach consisting of two different slopes (1:100 and 1:20) was used, and runs were made with the water level on each slope. The results were simulated using a composite numerical model, with Boussinesq equations in the deeper water and nonlinear shallow water equations in the surf zone. For some calculations, a friction term was included. For the 1:20 slope, the outgoing LFW is well predicted even without the friction term. With a 1:100 slope, a friction factor of 0.01 gave a good result, in this case reducing the amplitude of the outgoing LFW by a factor of about 2 compared with the frictionless result. The nondimensional equations show that the friction term is insignificant if the beach slope is large compared with the friction factor. Runs of the surf zone part of the model show the outgoing LFW to be correlated with the swash motion. Its amplitude is largest if the duration of the wave group is similar to the swash period of the largest wave in the group. The model also showed a slightly stronger than linear dependence of LFW amplitude on incident wave amplitude.

A physical model study of a vessel moored inside a lagoon harbour was undertaken in order to optimize a breakwater layout that best reduces the penetration of long wave energy inside the lagoon. The longer the breakwater at the entrance: the smaller the surge motion inside the lagoon. A combination of a short breakwater at the entrance channel and a pair of groynes in front and in the rear of the vessel also led to an efficient reduction of the surge motion. However, cost estimates and evaluation of vessel manoeuvrability are required to make an optimal choice of the breakwater layout. The use of a deterministic approach in wave generation led to a quicker testing procedure.

An extensive study of Barbers Point Harbor, including field wave gaging and numerical and physical modeling, was conducted to analyze the harbors response to infragravity wave energy. Infragravity waves have been defined as waves whose periods are greater than 25 sec. Field data collected over a 4-year period were used to calibrate the numerical model while eight extreme events were simulated in the physical model. Agreement between the numerical model, physical model, and the prototype data is good. The importance of spectral shape in the frequency domain also was analyzed by comparing the results from broad and narrow spectra.

Tsunami source model is disscused by numerical analysis for the 1992 Flores Island, Indonesia. Computed results with the composite fault model with two different slip values show good agreements with the measured run-up heights in the northeastern part of Flores Island, except for those in the southern shore of Hading Bay and at Riangkroko. The landslides in the southern part of Hading Bay could generate local tsunamis of more than 10 m, which could be the reason of discrepancy between the measured and computed one. The circular-arc slip model proposed in this study for wave generations due to landslides shows better results than the subsidence model. It is, however, difficult to reproduce the tsunami run-up height of 26.2 m at Riangkroko, which was extraordinarily high compared to other places. Two villages located on the southern coast of Babi Island, back side of the tsunami source region, received severe damages. The simulation model shows that the reflected wave along the northeastern shore of Flores Island, accompanying a high hydraulic pressure, could be the main cause of huge damages in the southern coast of Babi Island.

This paper describes the limitations associated with some of the wave grouping measures that are currently available in the literature. A brief review of the new concepts that have been proposed recently to overcome these limitations is also included in it.

Extensive analysis of prototype waves is carried out worldwide to establish a relationship between the degree of grouping in waves and their variance spectral density. But some of these analyses have been unable to identify any relationship because of the statistical variability inherent to records of finite length. A brief discussion of this variability is included in this paper.

Loading operations failed at a berth in Sendai New Harbour in 1992. The vessels continuously moved along the berth, in spite of small wave heights and weak winds, which were much less than the criteria for loading operation at the berth. To clarify the cause of the failures, the authors analyzed the observed wave data. The phenomenon related to the time characteristics of wave groupiness. The vessels' motions were caused by the long waves that were bounded by wave groups. Mean Wave Group Period (${\overline{T}}_g$ ) proposed here, can explain the phenomenon.

Coherent structures dominating in the tidal turbulence field inside the Osaka-Bay were detected by flow visualization through satellite image sensors. To obtain the hydrodynamical characteristics, scale down model experiments were done with the Froude/Rossby similarity law. The tidal residual circulations were reproduced on the ensemble mean turbulence field, which is made very similar to each instantaneous turbulence owing to the robustness of the coherent structure interlocked inside a closed vessel. The earth rotation effects were verified to dominate the turbulence processes in this closed vessel, and a hysteresis due to the moon aging was revealed.

A numerical method has been developed for the analysis of ship motions in a harbor with arbitrary bathymetry. A BEM-based 3-D model, applied partially to a near-field surrounding a ship, is combined with a FEM-based 2-D model, utilized in the remainder of harbor domain. This combination may achieve an efficient computation of the ship motions with taking into account of wave deformation in a harbor. Preliminary examinations have been performed to investigate appropriate location of a matching boundary where these two models are coupled. It is found that, for reliable prediction, (2 ~ 3)h (h: water depth) is required for the distance between the matching boundary and a body. The numerical results of added mass and damping coefficients for a rectangular floating body in a rectangular basin are then compared with those obtained from a conventional numerical model. Favorable agreement between the results verifies the present numerical method. Ship motions in a harbor with slowly varying depth are also demonstrated.

The linear long-wave theory is used in the first stage to find the tsunami initial profile. The perfect reflection is assumed at the land boundary. On comparing the computed with the measured overall runup distribution, the best fault model is found among 24 models. It consists of three sub-faults dipping westward. It satisfies the measured land subsidence and overall distribution of runup heights in Okushiri Island.

Then, the shallow-water theory with bottom friction is used to simulate runup. The runup condition is used as the land boundary condition. The arrival time and runup heights agree well with the measured.

Three-dimensional model for storm surges was developed, in which momentum equations first were solved in the vertical direction together with mass conservation and turbulence model, then mass conservation in the horizontally two-dimensional coordinates was solved by the finite difference method. Several fundamental tests concerning swing and wind-induced current, were performed to examine the model properties. Finally the hindcasting of the current profile in the Tanabe bay was conducted to test model applicability.

This paper describes results from an unusual research project completed under Topic 3R2 of the European Union's MAST research project G6-S Coastal Structures. In this project, data were collected from the major European hydraulics laboratories on the hydraulic and structural responses of example rubble mound breakwaters and sea walls that each laboratory had previously studied in wave flume or wave basin tests. The main responses considered here are:

The paper describes some of the analysis of armour stability and hydraulic performance of these structures, and explores the potential to develop general conclusions from ad hoc studies. This paper develops some of the analysis described initially within the G6-S project by Allsop & Franco (1992), but also re-considers and revises some of the early analysis and initial conclusions.

A calculation method is presented to determine the strength of a block revetment against wave loading. The critical loading on such a revetment is present during wave run-down when still relatively high pore pressures exist in the filter layer and the blocks can be pushed out of the revetment. The strength of placed block revetments against this loading is not only composed of the weight of the blocks, but also of the friction and clamping forces. Friction and clamping forces are incorporated in a calculation method, using a simplified model that takes into account the horizontal and vertical forces separately. Example calculations show the forces that can be expected in such a cover layer.

A special reflecting wall 12 m long and 2.1 m high was built off the beach at Reggio Calabria, and 30 wave gauges were assembled before the wall and were connected to an electronic station on land. It was possible to observe the reflection of wind waves generated by a very stable wind over a fetch of 10 Km. The experiment aimed to verify the general closed solution for the wave group mechanics (Boccotti, 1988, 1989), for the special case of the wave reflection.

The slender, complex types of armour units, such as Tetrapods and Dolosse are widely used for rubble mound breakwaters. Many of the recent failures of such structures were caused by unforeseen early breakage of the units, thus revealing an inbalance between the strength (structural integrity) of the units and the hydraulic stability (resistance to displacements) of the armour layers. Breakage is caused by stresses from static, pulsating and impact loads. Impact load generated stresses are difficult to investigate due to non-linear scaling laws. The paper describes a method by which impact loads on slender armour units can be studied by load-cell technique. Moreover, the paper presents Dolos design diagrams for the prediction of both breakage and hydraulic stability.

The steep wave diffraction by a fixed circular submerged cylinder is numerically simmulated as a completely nonlinear time domain evolution from an initial condition. Attention is focused on two aspects of the problem. The first is a study of the perturbation introduced by the cylinder on the wave field; the second is a study of the hydrodynamic forces on the cylinder due to the waves.

In this study, physical experiments are used to investigate the relationship between fluid velocities on the surface of two rubble-mounds and the shear stresses τ and normal stresses σ acting on the surface layer of rock armour. Results presented herein indicate that the peak magnitude of slope-parallel hydrodynamic forces on rubble-mound armour located below the still waterline can be reasonably well estimated using wave friction factors originally developed for rough turbulent oscillatory flow over impermeable horizontal beds. Stresses on rubble-mound armour are also compared to the prevailing surf similarity (Iribarren) parameter. The largest stresses are found to result from waves that form collapsing breakers.

Storm damage to rubble-mound structures can range from the piece-wise removal of individual armour stones to the large-scale sliding of the entire armour layer. This paper presents an overview of qualitative and quantitative descriptions of various types of armour layer damage due to wave action. This work is based on a series of large-scale physical models of revetment stability. The discussion includes methods for measuring the change in profile and the use of the normalized area eroded, S. A new parameter, d_c is introduced as a measure of the minimum depth of cover remaining on the structure. An analysis method is presented which predicts the armour layer's factor of safety against sliding.

Prototype experiments were carried out to quantify when personnel on top of a promenade breakwater will lose their balance due to overtopping waves. The danger of being carried out into the sea was also investigated using model experiments. Based on our results, we developed an empirical formula for calculating the wave height at which personnel danger occurs.

After an extensive series of 2-D model tests on the overtopping response of various caisson breakwaters, general conceptual design formulae and graphs have been derived which relate the mean discharge with the relative freeboard. The influence of geometrical changes is described by reduction factors with reference to the pure vertical structure. A simple correlation has been made with the overtopping performance of sloping structures. Overtopping volumes per wave were also measured and fitted with a universal probability function; their effects on model persons and cars behind the crownwall were statistically evaluated, thus allowing an upgrading of the existing criteria for the admissible overtopping on breakwaters.

We carried out model experiments to quantitatively elucidate the motion of overtopping waves on a caisson breakwater, with results leading to the development of an empirical model that can evaluate the maximum current velocity and depth of such waves on a breakwater. In addition, we developed a formula for calculating the wave forces acting on breakwater handrails, then confirmed its validity using field experiments.

A series of model tests was carried out in a wave basin at LNH to quantify the effect of long-crested, oblique waves on rubble mound breakwaters. Four types of armouring units (quarry stone, Antifer cube, tetrapod and ACCROPODE^®) were tested, under six angles of wave attack (0°, 15°, 30°, 45°, 60°, and 75°). Overtopping, toe berm and main armour stability were studied as functions of wave obliquity. A method is proposed to reduced the results obtained under oblique waves to those obtained under normal waves, allowing thus for the use of formulae derived under normal waves for the design of a breakwater under oblique wave attack.

This paper deals with investigations on loads from wave-induced shock pressures on seadykes with composite slopes and berms. The investigations have been done with large scale laboratory tests, using different wave climate characteristics (regular waves, PM – spectra and field spectra). Two different types of dyke cross-sections have been investigated: one with an upper slope 1:6 and a berm in front, and the other one with composite slopes 1:3 in the lower part and 1:6 in the upper part. The presented results were discussed with respect to the influences of wave climate, of absolute waveheights and of geometrical conditions.

The damage of rubble mound breakwater is a basic interest in the field of design and realisation of coastal works. The individuation of formulations to associate this element with the geometrical characteristics of structures and wave climate conditions is carried out using physical model tests. It is therefore necessary to implement an objective damage valuation method able to point out armour units movements on the layer from the settlement phase to the collapse.

A methodology able to permit an exact measurement of the external layer armour units movements and its damage has been carried out by ESTRAMED S.p.A.; it consists on a computerised analysis of armour units movements in order to give an objective valuation of the damage.

Such methodology is based on photographic images analysis of the armour taken from a fixed point. The procedure permits to determine the position of each armour unit on the images relative to the subsequential damage stages and the movement of each armour unit.

A laboratory experiment was carried out in a wave tank to examine significant features of wave breaking over permeable submerged breakwaters and to determine the breaker height and depth indices. Submerged trapezoidal-shaped breakwaters were place on a 1/20 steel slope, and permeability of the breakwaters was varied.

The experiment showed that the breaker height and depth change with the breakwater permeability governing the strength of return flow over the breakwater. Breaker height index was developed in terms of the integrated parameter ξ_s" proposed by Hara et al. (1992), which consists of the geometrical and structure properties of the breakwater as well as properties of incident waves. To determine the breaking position or depth, additional indices were also proposed. Validity of the computation scheme of the breaker height and position were confirmed by comparisons with the experiments.

An experimental investigations into the wave forces acting on the vortex-excited vibrating vertical circular cylinder in regular waves have been performed with emphasis being placed on the amplification of the wave forces caused by the fluid-structure interaction. The cylinder is vibrating only in the transverse, cross-flow, direction by means of the restriction of the vibration of the in-line direction. The results indicate that the existence of amplification of the lift forces acting on the vortex-excited vibrating cylinder in comparison with the stationary cylinder is a function of the ratio of wave frequency f_w to the natural frequency of the cylinder in water f_nw and Keulegan-Carpenter number at still water level CKC. The in-line forces are also amplified in the range of CKC where large amplitude of oscillation in the transverse direction occurs.

Over the last fifteen years a long running research programme has been undertaken at HR Wallingford to investigate the overtopping discharge performance of a wide range of sea walls. The research, which is funded by the Ministry of Agriculture, Fisheries and Food, is principally aimed at deriving methods to enable design engineers to determine the overtopping performance of a particular sea wall cross-section under a range of wave and water level conditions. The studies have generally used random wave physical model tests in order to collect data which can then be employed to derive empirical equations that describe the level of overtopping discharge.

The stability coefficient of the well-known the Hudson formula, KD, has been established by many laboratory tests for various types of armor blocks with a range of specific gravity 2.16~2.47 representative of normal concrete. Design manuals for coastal structures do not describe the adoption of high-specific gravity armor blocks for use in field construction. To examine the effect of specific gravity on stability of Tetrapods, then a laboratory test was conducted by using Tetrapod models of different weights which are composed of five values of specific gravities. Temporal changes of damage ratio arranged test conditions that satisfy the Hudson formula do not coincide among each other, depending on wave period and specific gravity. The effect of the specific gravity on their stability is discussed. As a result, it is found that the relationship between the stability and the specific gravity is considerably affected by the surf similarity parameter and Reynolds number.

This paper presents the results of a research study to quantify the stability of rock armoured groynes on steep shingle beaches. The research was needed to identify why significant numbers of rock revetments and groynes have suffered greater damage than would be predicted by conventional design methods. The paper describes the design and execution of tests in a large wave basin, at notional scales of 1:10-20, on four types of typical beach control structures. The test structures were constructed on a model shingle beach of slope 1:7, and were subjected to random waves of steepnesses s_m=0.02 or 0.04.

The tests confirmed that armour damage may be substantially greater than predicted by existing methods, even on simple slopes under normal wave attack. The results of the damage analysis have been used to suggest modified coefficients to van der Meer's plunging wave formulae.

A study of the irregular wave runup and rundown phenomenon on rough impermeable slope is conducted in order to investigate the effects of various surface roughness to the wave runup-rundown activities based on various kind of dyke and incident wave conditions. The roughness of dyke surface was defined as f_r which is functions of shape of the slender rectangular obstacles and its displacement distance. Results shows that the correlation between the relative significant runup height (R_us/H_s) and the incident wave steepness (H_s/L) have the same tendency either in regular or in irregular waves. The relative runup height has its maximum value when the dyke slope (cot θ) near 2. Next, the runup characteristics in regular wave was agree well with the Rayleigh distribution but it is a little bit smaller than that the Rayleigh's in irregular wave. Besides, the strong correlation between the wave runup and the surf similarity parameter ξ was found. The decrease of the relative runup height with the increase of the surface roughness was got also. It may be useful to applied into the design work of the seawall.

A series of hydraulic model tests has been carried out in a wave basin with the aim of studying the effect of oblique waves on the wave overtopping of traditional rubble mound breakwaters without superstructure. The model tests concentrated on measuring the mean overtopping discharge for wave attacks varying from 0° (perpendicular to the structure) up to 50°. Analyses of the overtopping results were made with respect to the significant wave height, wave steepness, crest free board, crest width and angle of wave attack. The paper describes the influence of these parameters on the mean overtopping discharge for a traditional rubble mound breakwaters with an armour layer slope of 1:2.0.

When constructing a small fishing port along sandy beach, the most important considerations are how to prevent sand deposition at the port entrance and beach erosion along the down-drift side of the port. To solve these problems, an offshore fishing port connected to the shore by a bridge was planned at Kunnui, Hokkaido Prefecture. The port was designed to allow littoral drift to pass between the port and the shore. The appropriate shape and offshore distance of the port to restrict the development of tombolo was determined by hydraulic model tests and numerical simulations of wave-induced current near the port. Bottom sounding was carried out in parallel with the construction work. As a result, development of tombolo was restricted to some extent and no serious beach erosion occurred. This port seems to have generated unexpected strong cell-like circular currents on both sides, and sand deposits deposited by these currents. There are, however, no problems at present concerning the shape, offshore distance and location of the port entrance.

This paper is aimed to investigate theoretically and experimentally the topographical change and the local scouring around multiple large cylindrical structures under wave actions. It is revealed from laboratory experiments that the bottom configuration, the local scouring area and its depth around the cylindrical structures are changed largely according to the number of cylindrical structures, the structure's diameter, the incident wave angle and the sediment size. The theoretical model which developed newly is shown to predict well the topographical change around the structures.

The armor stability of composite breakwaters has been investigated by large 3-D model experiments using oblique irregular waves. The characteristics of wave-induced flow near the mound, which directly affect the armor stability, are disclosed theoretically and numerically. The stability number of armor units in breakwater trunk, head and tail sections is formulated for oblique wave angles less than 60°. The applicability of the proposed methods is confirmed by prototype failure data, and the analyses of case studies are shown for some practical conditions.

A mathematical model for nonlinear wave propagation over a rectangular step is formulated based on the boundary element method. The wave profile computed by this model gives a more realistic wave profile than that of linear wave theory. The calculation of the height of nonlinear waves is studied, and as a results of the study the reflection and transmission coefficients are computed based on the technique which considerd the higher harmonic components in the computation of wave height. The solutions of these coefficients are presented and compared with laboratory experiments.

Small-scale model tests were recently conducted in a wave flume at the University of Hannover in order to study in more detail the relationship between impulsive loading induced by waves breaking on a caisson breakwater and subsequent displacements of the latter. These experiments are briefly described and some first results are discussed. Thereby, particular emphasis is put on the relationships between (i) oscillatory motions and permanent displacements, (ii) wave loading and oscillatory motions and (iii) wave loading and permanent displacements.

The findings presented in this paper are intended to improve the understanding of the stability of caisson breakwaters subject to impulsive breaking wave loads and to help developing proper tools for the dynamic analysis of such structures.

More than 30,000 pcs. of the ACCROPODE blocks have been applied for the wave dissipator of the breakwaters and the revetments at the Haramachi thermal power station where construction works of the harbor started about four years ago.

Since the ACCROPODE has not been used in Japan before-hand, hydraulic model tests were needed to examine its characteristics and to confirm the feasibility to the project, although extensive tests have been made in the world.

This paper describes the results of tests on the stability, reflection and transmission coefficients of the ACCROPODE blocks and the field experience at the Haramachi power station. Much reduction of the construction costs and good stability against storm waves attacked were obtained which showed its super usage as the wave dissipator.

Time evolution of scoured seabed profiles around a vertical slender cylinder under waves has been investigated by means of laboratory experiments. The characteristics of the scoured bed profiles on the developing process is discussed considering the flow features. The local scoured bed profiles are classified with the location of the maximum scoured point. And the developing scouring process of each classified type is discussed. We found that for each scour type, the scoured bed retains a similar profile during its whole developing process. The ultimate scour depth on the vicinity of the cylinder surface is related to the Keulegan-Carpenter number, and it is independent of the sand bed condition.

Wave induced uplift pressures and forces have been investigated by small- and large-scale model tests. Detailed analyses of waves at the structure, forces and structure motions showed that conventional design formulae neglect details of pressure development which contribute to the total uplift force. Direct comparison between quasi-static, dynamic forces and the commonly used formulae show that dynamic effects exhibit a significantly different behaviour in comparison to those observed during quasi-static wave attack. The most relevant of the effects which may be useful for setting up a numerical model for the prediction of uplift pressures are described.

Linear and nonlinear wave forces exerted on a submerged horizontal plate are studied using the method of matched eigenfunction expansions for velocity potential together with the perturbation technique up to second order. Energy damping coefficients are introduced in the formulation to incorporate the effects of vortices and wave breaking. The theoretical results are compared with experimental data to obtain validity and limits of the second-order solution. The theory with proper energy damping coefficients can well simulate the wave forces even when wave breaking occurs over the plate. The second-order oscillatory wave force is relatively small as compared to the first-order one, while time-independent, steady wave force becomes comparable with the first-order one at small relative water depth and its direction is always upward.

Coastal zone management policy in the United States and many other countries discourages use of groins for shore protection, even though properly designed groins can maintain beach width, increase longevity of beach fills, and prevent loss of sand into inlets, navigation channels, and submarine canyons. A lack of a systematic approach to groin functional design and a poor image from incorrect applications are probably responsible for the aversion to groins. In this study, a modern approach to groin functional design is demonstrated by applying the shoreline response model GENESIS to simulate the action of single and multiple groins. Groin bypassing and permeability, evolution of the shoreline in a groin field, and groin tapering are discussed. The balance between net and gross sand longshore transport rates emerges as an important factor controlling groin functioning. A criterion is introduced for judging groin success, and an example design diagram is developed based on this criterion to demonstrate the feasibility of developing a general and rational functional design procedure. Predictions are tested in reproducing shoreline change observed at the 15 groins at Westhampton, Long Island, New York.

In order to investigate the influence of water depth on the profile of reshaping breakwaters, model tests have been performed in deep, intermediate and shallow water conditions. The results show that the reduction factor for the dimensions of a reshaped profile in intermediate and shallow water conditions does not depend only on the wave height reduction. Other influencing factors are identified as breaking depth, wave steepness and foreshore slope. Moreover, at any water depth condition, the characteristic wave height corresponding to the frequency of stone movements on a reshaped profile is larger than the significant wave height. In the present tests, good results are obtained using the 1/50 wave height. Finally, whereas the offshore evaluated reflection coefficient increases with the water depth at the structure, the same coefficient evaluated in front of the structure shows an opposite trend.

The subject of this paper is to compare the design forecast and the actual performance of a coastal protection scheme combining segmented near shore breakwaters and beach nourishment.

A new type of breakwater caisson is presented for improving water quality in a harbor. Circular resonance channels connected with flow conduits in the caisson cause clear sea water inflow into a harbor through the conduits. The hydraulic characteristics of this caisson with respect to wave reflection, overtopping and transmission appear excellent compared with those of conventional caissons. The potential of water quality improvement is great due to its high efficiency in normal wave conditions. A simple resonance model is developed to identify an important dimensionless parameter. Experimental results show that the new concept of circular channel breakwater is promising in terms of its hydraulic performance.

A survey of prototype dolos breakages was performed to determine the distribution of failure modes. The results showed that 89% of the failures originate near the fluke-shank intersection. A series of static and dynamic finite element analyses was subsequently performed with the aim of improving the resistance of the dolos against the most commonly observed modes of failure. Of the six dolos shapes analysed, a large fillet extending from the fluke to the centre of the shank was found to be the most effective in reducing the stress in the critical fluke-shank intersection. Compared to a sharp intersection, the large fillet reduces the stress by more than 60%.

An experimental investigation was undertaken to investigate the stability of breakwater heads under uni and multidirectional wave attacks. Waves of normal and oblique incidence were used in the investigations and the stability results were assessed along with relevant measurements of wave surface elevation, measured in the proximity of breakwater heads.

The cost-effectiveness of conventional and D-armor breakwaters are compared. Initial cost and capitalized anticipated damage during the lifetime of the structure are the basic elements to be considered in the economic optimization problem. A four level structural response function and a linear initial construction cost estimation are used to define the economic function. An exponential approximation to the return period of the design wave storm with an uncertainty factor is used to estimate the economic impact of the wave climate uncertainty. Finally, the adaptative design concept is introduced considering the advantages of designing for repairing and monitoring breakwaters after construction.

This paper outlines the development and initial testing of a new optimized armor shape, called CORE-LOC, that balances and optimizes engineering performance features such as hydraulic stability, strength, and layer porosity. The new shape has significantly reduced design stresses over many existing shapes, yet has superior interlocking and therefore greater stability. The unit has internal maximum tensile stress levels of approximately half that of dolosse and, therefore, should not need reinforcement. For over 1000 flume tests, the core-loc has demonstrated two-dimensional no-damage stability numbers over 7 and Hudson stability coefficients over 250. In nearly all tests, the core-loc layer could not be damaged up to the wave height-period capacities of the flumes. A site-specific three-dimensional stability test of the proposed Noyo, California, offshore breakwater showed a stable no-damage stability number of 2.7 for H_s or a Hudson stability coefficient of 13 when the core-loc armor layer was exposed to repeated attack of a very severe design-level storm. The unit has been designed to be used alone or as a repair unit for dolosse. Core-loc-repaired dolos model slopes showed improved stability over the original dolos slopes. Finally, through reduced volumes, the core-loc layer is substantially more economical than all other commonly-used randomly-placed armor.

The stable weight of armor rubbles of a submerged wide-crown breakwater was analyzed in relation to the wave force acting. At first, stability models for armor rubble were derived based on the idealized spherical armor unit; then, the shape effect of armor stones on acting wave forces and stability was investigated experimentally. Based on the results, the proper modification of the stability models for spherical armor unit gives good estimate of the stable weight of armor rubbles. Furthermore, the shape effect on wave forces and stability is significant; whereas, the shape effect of armor rubble on the stable weight is relatively small.

This paper deals with the hydraulic characteristics of two kinds of submerged plate type breakwaters. One is a plate with a gradual upward slope, the other is with a downward slope. The characteristics of the temporal and spatial wave induced flow and turbulence around a plate are discussed in detail on the basis of the result of the water particle velocity measured by the Laser Doppler Velocimeter. In addition, the effects of the plate length, the submerged depth of the crown and the inclination angle of a plate on the wave transmission, reflection and wave energy dissipation are discussed.

Finally it is suggested that a plate with a gradual upward slope is effective not only for the control of wave absorption but also for water purification.

This paper proposes an approximate calculation method for the second-order wave interactions with arrays of vertical cylinders of arbitrary cross section. In mathematical formulations, the first- and the second-order boundary value problems are derived by perturbation method, and Green's Identity Formula is used to express the distribution of the velocity potentials on horizontal plane. Second-order water surface elevations near the cylinders and wave forces acting on the cylinders are computed, and the results are verified by comparing with wave tank experiments in the valid range of the Stokes second-order wave theory.

The characteristics of hydrodynamic forces acting on a bottom-seated hemisphere in waves only, in currents only and in waves & currents are presented from the viewpoint of the design of an artificial reef. A large number of regular wave experiments were conducted in order to find the empirical formulas of the hydrodynamic coefficients for the bottom-seated hemisphere. It is shown that the proposed empirical formulas are sufficiently accurate for predicting the hydrodynamic forces. The effects of the normalized water depth and hemisphere spacing relative to its diameter are also elucidated experimentally.

The entrained air present when a wave impacts upon a vertical wall is modelled. A numerical boundary-integral method is applied, with appropriate initial conditions giving a prescribed surface profile and corresponding velocity potential, to model an overturning wave trapping a single air pocket between the oncoming wave front and the vertical wall. The resulting detailed computations provide suitable initial parameters for a simple theoretical model of the trapped air pocket as described in Topliss, Cooker & Peregrine (1992). The fundamental frequencies, and pressures on the impact wall due to the bubble can thus be estimated from the numerical computations. Video frames of small-scale experiments by Hattori & Arami (1992 and private communications) are also examined in detail and similar use of the model provides further pressure estimates. The resulting frequencies and maximum pressures are compared with the measured values. The peak pressures on the impact wall are within 30% of those measured and the frequencies are generally closer. Scaling with wave size is also discussed.

The entrances to most of the ports in South Africa are protected by rubble mound breakwaters which have dolos armouring. As part of their maintenance programme, Portnet, the local Port Authority, has commissioned the CSIR to annually monitor the main breakwaters. A minimum of five years of photographic and other monitoring data have now been accumulated. This paper presents a brief description of the dolos breakwaters in South Africa, and the field monitoring techniques used to record the annual damage to the armouring. The results and analysis of the photographic monitoring are given in more detail. The application of these results are also presented, and some exciting new developments in breakwater monitoring are discussed.

Failure mechanism and destruction processes of rubble mound structures under the irregular wave attack are discussed in considering with the effects of wave grouping, storm duration, and structural conditions using the model test results. In the analysis of the stability, a new irregular force parameter that affect the failure of rubble mound structures is defined by combining wave grouping characteristics, storm duration effects and wave-structure interaction mechanisms. Using the external force parameter, a modified rubble mound design formula is suggested, and its applicability is proved by the results of comparative studies with the conventional results.

The block subsides gradually into sandy bed under water pressure fluctuation. In actual coast the oscillatory flow also acts on the block. The block subsidence is reproduced qualitatively in a laboratory. The subsidence occurs even under the oscillatory flow. Under some combinations of water pressure fluctuation and oscillatory flow, the subsidence is larger than any of the subsidence under the pressure fluctuation only and the subsidence under the oscillatory flow only.

Stability relations for rock on a mild slope are derived and compared with experimental results. It appears that for non-breaking waves the stability on a mild slope can be described with existing relations for stability on a horizontal bottom in oscillatory flow. For breaking waves, no existing relation can be used and a provisional empirical design rule was established. The results can be applied in designing outfall protections.

The characteristics of short term over topping rate for a deepsea block armored seawall are investigated experimentally. Two series of experiments were conducted. One is a series that seawall has low crown height and a wave grouping effect is investigated. Another experiment is a series that it has a high crown height and slope effect of armor unit is studied. From these experiments, we have to consider the short term wave overtopping rate for the design of drainage facilities of deepsea structure such as an artificial island.

Estimating the sliding distance is essential in the future probabilistic design of caisson breakwaters. In this paper, characteristics of the sliding phenomena are described, and a method based on the equivalent sliding forces to calculate the sliding distance is proposed. This calculation method is applicable for both impulsive and ordinary wave forces considering the shear force at the bottom of the caisson.

Two kinds of experiments were made: 1) Rigid-bed experiments and 2) erodible-bed experiments. In the former experiments, bed shear stresses were measured around three kinds of structures: 1) a vertical circular cylinder, 2) a cone-shaped structure and 3) the head of a breakwater (with and without side slopes). The results are presented in terms of amplification in the bed shear stress for the structures considered.

In the erodible-bed experiments, actual scour tests were carried out with the aforementioned structures. The results regarding the scour tests are related to the measured bed shear stress.

The present work aims to improve our knowledge of reflection coefficient of waves on a breakwater through a programme of laboratory tests. The experiments are conducted on a linear rubble-mound breakwater under random long-crested wave conditions. The wave signals are recorded through an array of 8 wave probes. Three wave reflection analysis approaches are applied and compared on the laboratory recorded data : Least-Squares Methods, Directional Analysis Methods, Modified Directional Analysis Methods. These methods are briefly presented, their assumptions are highlighted and their characteristics are discussed on numerical tests. The Directional Analysis Methods appear to be unable to properly model the superimposition of incident and reflected wave fields. When applied to laboratory experiments, the Least-Squares Methods and the Modified Directional Methods show concordant results, but nevertheless exhibit some differences. The effect of oblique incidence on reflection coefficient is then tentatively analysed.

Physical model tests were carried out aiming to provide information on armor stone movements in a berm breakwaters. The following items were examined: displacement threshold, frequency and length of stone displacements. Data were obtained from the observation of cumulative displacements at the end of each wave attack and from video records during the attacks; basic statistical analysis was performed. Threshold conditions, moving frequency and cumulative displacements are expressed as function of a modified mobility number, as stone mobility increases with both wave height and wave period.

Information on mobility and displacement is eventually used to estimate longshore transport and abrasion. The longshore model is based on the assumption that stones move during up- and down-rush in the direction of incident and reflected waves; the model compares favourably with experimental existing results. The abrasion model is based on a proportionality assumption between abrasion volume and abrasion work; the proportionality coefficient characterizing the stone material resistance to abrasion is derived from Latham and Poole mill abrasion tests.

In 1993, the U.S. Army Corps of Engineers, Waterways Experiment Station, Coastal Engineer Research Center conducted the Large Scale Dolos Flume Study (LSDFS) in order to investigate the structural response of concrete armor units. The study was primarily carried out in the large wave flume at the O.H. Hinsdale Wave Research Laboratory, Oregon State University. Over 300 model dolos units with a mass of 26 kg and a waist ratio of 0.32 were used. The units were cast from concrete. The instrumented dolosse were fitted with surfacemounted strain gages then subjected to a wide range of wave loading conditions. This strain gaging and the state-of-the-art data acquisition system increased the signal-to-noise ratio so that accurate measurements of static, quasi-static, wave-induced hydrodynamic, and unit-to-unit impact loading could be recorded. The LSDFS included a standard calibration series, static ramp tests, dry-land impact tests, and regular and irregular wave flume tests. Hydrodynamic instrumentation in the flume tests consisted of a very dense array of wave gages, current meters, runup-rundown gages, pore pressure transducers, hydrophones, digital video, and still photography in the nearshore zone. This paper presents previously unpublished details of the LSDFS specifically pertaining to instrumentation, calibration, dry-land impact tests, and some preliminary results of impact response captured in the flume tests.

H\d₀ Parameter for Preliminary Design of Conventional Breakwater Structural Head. Data Analysis of Spanish North Coast Harbours

The impact processes on a vertical wall resulting from breaking waves are numerical simulated. Two dimensional incompressible viscous flow which is governed by the Navier-Stokes Equations and the continuity equation is solved by a finite difference scheme based on the Volume of Fluid(VOF) concept. Some comparisons with experimental results reveal that the present model is able to simulate the impact process with negligible air entrappment not only qualitatively but also quantitatively well. Although the impact pressure of a plunging breaker with non-negligible air entrapment can not be quantitatively well simulated by this model due to the restriction of the incompressible flow, the wave kinematics is still well simulated.

The maximum distance a wave may travel up the face of a coastal structure, or rate of overtopping if runup exceeds structure crest elevation, are critical parameters in planning and design of a coastal structure. Runup and overtopping are usually estimated by empirical equations based on physical model studies that do not include the effects of strong onshore winds that are typically present during design storm conditions. While it is generally assumed that onshore winds will increase runup and overtopping over no-wind conditions, there is currently no means of accurately calculating effects of these winds on runup and overtopping.

A joint research project by US Army Corps of Engineers and Texas A&M University (TAMU) is currently investigating wind effects on runup and overtopping of revetments and vertical walls through a series of physical model studies conducted in a combined wind/wave flume at TAMU. Initial tests measured runup and overtopping rates on a 1:3 smooth revetment for a range of incident monochromatic wave conditions, with wind speeds varying from no wind to maximum blower output. With the addition of wind, large increases in runup and overtopping were recorded over the no wind condition. The combined wind/wave spectrum recorded during tests with wind was then reproduced mechanically. Runup and overtopping were significantly higher during tests with wind than during no-wind tests that reproduced the combined wind/wave spectrum.

The tests indicate that runup and overtopping estimates that do not include wind effects are underpredicting runup and overtopping on coastal structures. Continuing efforts in this study are aimed at quantifying prototype wind effects on runup and overtopping based on physical model results.

From a recent experimental study on the kinematics of wave overtopping on marine structure by Lee, Zhuang and Chang (1993) it was found that the overtopping wave generates a strong rotational velocity field in the shoreward region of the breakwater. The present study focuses on the development and the implementation of a numerical model for the generated velocity field in the vicinity of the shoreward face of the breakwater. The numerical model consists of two basic elements: The velocity field generated by using the potential flow theory utilizing boundary element method and the rotational velocity field generated by the separated flow of the overtopping waves as they leave the breakwater site using vorticity stream function formulation. The computational results at a region far away from the separation zone based on the potential flow theory (boundary element method) are used as specified boundary conditions for simulation in the vorticity stream function model. The numerical results have been compared with the experimental data revealing the rotational feature of the velocity field in the separated zone (shoreward region of the breakwater). The generated vortical motion remains in the separation region even when the wave has travelled to the region far away from the breakwater.

An extensive research program has been set up under the name of "Rubble mound breakwater failure modes". This research is part of the European MAST II project, (MArine Science and Technology) in which a number of universities and hydraulic institutes, from various countries in Europe, are participating.

Economic breakwater design requires knowledge of the wave induced pore pressures in the rockfill in view of sliding stability, filter requirements, wave transmission, wave overtopping and internal set-up. A mathematical model for the prediction of these pressures and the associated pore water flow has been developed. The model gives an integrated description of both external flow and internal flow. The sensitivity of the output to several input parameters and the validation of the external flow to model tests is discussed.

A numerical model that can simulate plunging waves on permeable structures is described. The 'Volume Of Fluid' method is used to solve the two-dimensional (2D-V) incompressible Navier-Stokes equations. After implementation of porous media flow for applications with permeable structures, the model has been verified by using several analytical solutions and by comparisons with physical model tests to study breaking waves on and inside permeable structures.

In the past wave forces on vertical structures have been measured in a number of site specific projects at the Danish Hydraulic Institute and Delft Hydraulics. For nine selected cases, the data on forces and moments were re-analyzed, leading to an expression for reliability of Goda's formula for calculation of forces and moments on vertical breakwaters. Secondly, probabilistic level II design calculations were made using Goda's formula with the found reliability. It appears that the reliability of this formula has by far the largest influence on the probability of failure. Finally the influence of model tests on the probability of failure was studied. In that case the wave height has the largest influence on stability, which is usual for most coastal structures designs.

Effect of permeability on pressure distribution over the permeable surface of a porous medium is investigated. Measured pressure distributions comparing impervious and permeable cases are presented. Flow of the free fluid over the permeable boundary and flow of the fluid in the porous medium are computed numerically, maintaining the interaction of the two flow fields through the boundary conditions at the permeable surface. Turbulence is modeled by a low Reynolds number k-ε model including a novel technique to model surface roughness effect eliminating the need for wall functions.

Physical mobile bed models were used to study the morphological effects of groins on an initially straight beach that was exposed to obliquely incident irregular waves. The tests were carried out at two different wave basins with the beach length of 8 and 28 m. A straight beach in the absence of groins was tested for each set of variables, then one or two impermeable surface piercing groins with different lengths were installed and tested. A detailed morphological and hydrodynamic data base was acquired which can be used for calibration and verification of numerical morphology models. Testing procedure and conditions are explained and typical results are presented along with a preliminary analysis which reveals the significant features of the evolution of beach bathymetry.

Using line modeling, in the scope of the NOURTEC project a prediction is made concerning the behavior of the shoreface nourishment of Terschelling and an evaluation concerning the behavior of the combined supply on beach and shoreface at Norderney. Computations suggest smaller longshore diffusitivity on the upper beach than on the zone between NAP-1 m to -3 m for Terschelling and the inverse for Norderney (groynes↓). Cross-shore diffusitivity at Norderney appears to be much larger than at Terschelling. If further investigations substantiate those results, these lead to the conclusion, that shoreface nourishment at Norderney is still more preferable than at Terschelling.

It has been argued that seawalls have a detrimental effect on the adjacent beach. These effects may only be noticeable over a period of years or may be short-term effects associated with storms or with seasonal transitions of the beach. Many theories on beach and seawall interaction have been speculative and have lacked actual field or laboratory evidence for their basis. This study uses four years of monthly and post-storm beach profile data to examine what influences the seawalls at Sandbridge, Virginia (USA) have on the adjacent beaches. Long-term effects of the seawalls are analyzed using fourteen years of profile data. Five parameters are defined to describe the subaerial beach profiles. Changes in the profile parameters in time are quantified using three methods of analysis.

A field experiment measured in situ sediment resuspension in the bottom boundary layer. Spatially and temporally dense suspended sediment concentration profiles, three-dimensional velocities and pressures were obtained from a location with a flat, fine-sand bottom in Lake Erie in 1992. By use of a conceptual model, ten minute averaged near bottom sediment concentration is found to be proportional to significant wave orbital velocity and group wave parameters. The result attempts to clarify the ambiguity of using a monochromatic wave parameterization for bottom boundary layer model comparisons with measured data containing spectral wave conditions.

At Yunlin county a major development of over 10,000 ha of reclamation is being planned for port related industries. The development is taking place along a coast that bordered by Choshui river and the Wai-San-Ting sandbar. Detailed modeling using MIKE21 package with wave, flow and sediment transport modules were used to assess the morphological changes. Four such "relict" deltas were identified according to its ancient river courses. The decay of the sandbars was mostly independent due to the major discontinuities at sandbar headlands and tidal channels. The analysis of the complex morphological processes has provided an important insight into the probable impacts of coastal developments and guided the expensive and time-consuming model operations.

The paper presents a simple model for the prediction of longshore and crosshore suspended sediment transport rates outside the surf zone in water depths less than 20 m or so. The model consists of a depth-resolving hydrodynamic component, which considers wind-induced currents in the presence of waves and includes the Coriolis effect. The hydrodynamic model component is coupled with a model for the mean suspended sediment concentration to produce a prediction of the depth-varying mean suspended sediment flux vector. In addition to specification of environmental conditions, i.e. waves and sediment characteristics as well as current driving forces (wind velocity and pressure gradient), the model requires three parameters: C_a, the wind-drag coefficient; k_N, the movable bed bottom roughness; and γ0, the resuspension parameter. These three model parameters were determined (Madsen et al., 1993) from a subset of field data obtained in 13 m depth off Duck, North Carolina, during the severe "Halloween Storm" of 1991 and are used to perform a limited comparison between predicted and observed current velocity vectors and mean suspended sediment concentrations. The agreement is very encouraging and model prediction of an offshore loss of 22 m³ sediment per m beach compares favorably with the loss of 27 to 54 m³ obtained from beach profile surveys.

A stability analysis is used to investigate the development of large-scale periodic bottom topographies on a straight uniform coast. The work is an extension of the work by Hino (1974) and (1976), and special attention is paid to improve and refine the description of the sediment transport. The effect of the bed slope on the bed load sediment transport turns out to be very important. Further, the behaviour of suspended sediment is described by introducing lag effects that modify the predictions of the wave length considerably.

Much of the research on beach control structure concentrates on sand beaches. Relatively little work has been done on gravel beaches though they are important features along temperate and sub-arctic coastlines, particularly in the UK. Until recently attempts to manage these beaches and to control erosion have relied on traditional approaches such as timber groynes, designed by past experience and engineering judgement. To improve this situation HR Wallingford have undertaken a programme of flume and wave basin physical model studies followed by the development of numerical models and design guidelines.

The most recent phase of this programme has been an investigation of beach response to detached breakwaters. This work was undertaken at a scale of 1:50 in a mobile bed, random wave basin. The breakwaters varied in length, crest elevation and distance offshore. The sea conditions varied in wave period and water level. Measurements were taken of wave heights around the structure, beach planshape development and longshore transport rates. For each breakwater configuration and sea condition an efficiency value has been derived which relates the longshore transport rate in the presence of the structure to the potential open beach rate. These efficiency values can be used to tune breakwater dimensions to the actual long term drift rates of a specific beach, thereby providing a stable beach.

This paper briefly reviews some of the previously published work, then discusses the major findings of the recent model tests and suggests methods for applying the results. The results are, at present, only applicable to a limited range of sea and beach conditions, but it is anticipated that the approach will be developed for general application. The findings are also related to a recently completed detached breakwaters and beach recharge scheme on the UK south coast.

Employing a recently developed model for the creation and evolution of the aerated region of breaking waves, the relative importance of the roller in driving and mixing cross-shore and longshore currents is explored. Modeling results using linear wave theory confirm that in the mean balances of mass, momentum, and energy, the roller plays a role comparable to (and sometimes greater than) the underlying organized wave motion. It also appears that the roller is responsible for the landward shift of the peak cross-shore and longshore current observed in laboratory and field measurements, and is as important as the net convective acceleration in cross-shore mixing of the longshore current.

Results are described from movable and fixed bed wave tank tests to examine the characteristics and causes of three dimensional beach profiles occurring in a narrow wave tank. The movable bed tests demonstrated a strongly repeatable sequence in which both the hydrodynamics and sediment transport patterns were two-dimensional over the initial stages of testing; however, after approximately 200 to 240 minutes, a horizontal circulation appeared and strengthened and resulted in a narrow channel incised adjacent to one of the tank walls. This circulation was reminiscent of a rip current system and resulted in a net landward transport of sediment. During the later stages of profile evolution, an equilibrium was reached in which the profile was steeper and the channel adjacent to the wall persisted. The fixed bed tests were conducted to examine, under controlled conditions, the mechanisms and causes of the horizontal circulation. Tests were carried out specifically to examine generation and maintenance mechanisms for rip currents and edge waves. One set of the fixed bed tests induced a jet into the surf zone and examined its interaction with incident waves. The interaction was found to exert a torque which was counter to that of the induced jet and thus would reduce its circulation. Edge wave mechanisms were examined in the second set of fixed bed tests by generating incident waves with the wave period corresponding to the edge wave length equal to twice the width of the tank for various edge wave modes. No indication of edge waves were found in the experiments. It is concluded that the sequence of profile evolution documented in the movable bed model tests is most likely caused by a long term instability and is reminiscent of and may be representative of the beach recovery stages from a storm profile.

The shear instability of a uniform longshore current and the fully developed shear waves are studied in the numerical hydrodynamic model MIKE-21. The effect of the shear waves on the sediment transport, the cross-shore momentum transfer and mean velocity profile and the dispersion of suspended or dissolved matter is studied. The strength of the shear waves is calculated for a varying flow resistance and a varying momentum exchange coefficient. The formation of shear waves can be suppressed by modest rip channels in a longshore bar.

The environmentally favoured method of beach maintenance by nourishment with sand raises the question of minimization of the average annual sand requirement. In the following sand loss estimation models are compared to field data. A concept for protection of the dry beach and dune areas against erosion during stormtides is discussed as a means of reducing the required sand volumes for the beach maintenance.

A new and detailed model for predicting the profile change of a real beach is presented. The model is based on the sediment transport formula of Dibajnia and Watanabe (1992) and therefore incorporates, explicitly, the asymmetry of the near-bottom orbital velocity and the undertow into the transport of bottom sediment. Its applicability is examined by using the data of beach profile change obtained from prototype scale laboratory experiments as well as field measurements. It is shown that quite accurate profile simulation is possible when the details of the flow field and transport mechanism are considered.

A nonlinear, short-wave-averaged (surf beat) model is presented. The model is based on that of Roelvink (1993), but the numerical techniques used in the solution are based on the so-called weighted-averaged flux (WAF) method (eg Watson et al, 1992), with time-operator splitting used for the treatment of some of the source terms. This method allows a small number of computational points to be used, and is particularly efficient in modelling breaking long waves. The short-wave (or primary-wave) energy equation is solved using a more traditional Lax-Wendroff technique. Results of validation indicate that the model performs satisfactorily in most respects.

This paper presents results of a study of the kinematics of planar oscillatory flow over a rippled sea bed. The flows are mapped using Particle Image Velocimetry (PIV), a flow measurement technique yielding accurate, full field maps of an instantaneous velocity field. The practical implementation of the PIV method for this study is described, and flow maps presented for amplitude of oscillation to ripple length ratios of 0.8, 1.2 and 1.8. The generation of vortices at the ripples and their subsequent trajectories is described. Finally, the vortex strengths for the three flow regimes are investigated.

The effect of bottom friction and turbulent lateral mixing on shear instability of the longshore current is investigated. Transition conditions for this instability as a function of non-dimensional parameters related to the basic current, topography, bottom friction and lateral mixing are found. A direct nonlinear numerical simulation of shear instability is presented. The basic flow is found to be supercritical and the amplitude of shear waves can reach at least 20% of the basic flow. A small increase in the period due to non-linearity is also found. Preliminary results suggest that far from criticality there is an important contribution of the instability to the mean flow. Some applications to field and laboratory experiments are discussed.

A review of some of the potential sources of error associated with the use of aerial photographs to map shoreline change is presented. The influence of both tides and waves in the estimation of the position of the wet sand line on the subaerial beach is included. The use of the relatively new digital photogrammetry as applied to shoreline mapping is discussed and suggested as having the potential for being a superior method for this application.

This paper presents a set of devices and a study both experimental and original in order to determine the influence of various parameters on the sedimentation-consolidation process of soft soils. We use this system to investigate the behaviour of a natural estuarine mud. A series of tests is performed, in which each test differs from the reference test in the value of only one parameter. We give a synthesis allowing the comparison of the action of each parameter on the mud behaviour. This systematic parametric experimental study builds an original data base, which is obviously necessary to validate theoretical modelization.

Sediment cloud, which is released periodically from the crest of ripples, plays a very important role in suspension over a ripple bed under the wave action. By considering the special role of the sediment cloud, suspension is divided into two subprocesses: (i) the transition process from bed-load motion to suspension as the entrainment of the sediment cloud; and (ii) the diffusion process of suspended sediment released from the sediment cloud. The trajectory of the sediment cloud is calculated by Lagrangian approach in the flow field solved by k-ε model of turbulence. The suspended sediment concentration is simulated by solving a diffusion equation which has the source term due to sediment cloud.

Experiments were conducted on a sand beach to represent occurrences of minor to major dune overtopping by varying the spectral peak period of incident irregular waves. Both water overtopping and sand overwash rates were measured. The experimental results were compared to existing empirical formulas for equilibrium beach slopes (Kriebel, Kraus, and Larson, 1991), cross-shore sediment transport (Kraus and Mason, 1993), and irregular wave reflection (Seelig, 1983) from sand beaches. Scale and non-equilibrium effects were found to be important causes of discrepancies between predicted and measured values. Additionally, an empirical formula for the overtopping of coastal structures (De Waal and Van der Meer, 1992) was compared with overtopping measurements for the experimental dune. The empirical formula of De Waal and Van der Meer gave order-of-magnitude estimates, but could not account for the effects of the profile evolution within each test. The measured average volumetric sediment concentration was found to be independent of the normalized overtopping rate and varied by only a factor of two.

Numerical simulations are presented for the flow and the dynamics of non-cohesive sediment over 2D ripples in waves and current. For this purpose, a model based on a discrete vortex approach using the "cloud-in-cell" concept has been applied. The hydrodynamic model drives a Lagrangian model for the suspended sediment.

The characteristic vorticity structures prevailing in the vicinity of ripples are accurately replicated and sediment suspension mechanisms are successfully described. Thus, the sediment transport resulting from asymmetrical waves and combined waves and current can be predicted. Especially, the wave-related component of the transport opposes the maximum free stream velocity and contributes significantly to the total transport. In the present work, the effect of the wave-induced drift is not included.

A new in-situ erosion meter has been developed to measure the in-situ bed-shear strength of cohesive beds. It is assumed that the current velocity, at initiation of motion of the toplayer of the bed, can be used to compute the critical bed-shear stress. This critical shear stress is the characteristic parameter which can define different types of sediment beds.

The in-situ measurements show that the test results are determined by the prevailing hydrodynamic conditions in the field (wave activity) and recent depositions rather than by physical and biological parameters.

A method to control cross-shore sediment transport by a distorted ripple mat which is the artificial ripples of distorted cross section has been studied through hydraulic experiments and numerical simulation. First of all, the relative importance of factors affecting cross-shore sediment transport on fixed bed ripples and the condition on which sediment is definitely transported on-shoreward are obtained. Based on this condition, experiments with movable bed are carried out to see how efficiently the distorted ripple mat can be utilized in stabilizing natural/artificial beaches. Furthermore, a numerical model of beach profile change in which effects of ripple distortion are considered has been developed and beach stabilizing effects of the mat are also reproduced numerically.

The time-dependent response of sediment suspension to water velocity was explored by modeling field measurements collected in the surf zone during a large storm. Both linear and nonlinear input-output models were formulated with water velocity as input and suspended-sediment concentration as output. A sequence of past velocities (velocity history), in addition to velocity from the same instant as the measurement of suspended-sediment concentration, were used as input. The velocity-history length was allowed to vary. The models also incorporated a lag between input (instantaneous velocity or velocity history) and output (suspended-sediment concentration).

Instantaneous horizontal water velocity, or velocity to a power, does not contain enough information to predict suspension in the surf zone. Unlike steady uniform flow, more than one velocity is necessary to parameterize pick-up and mixing of sediment into the water column. Using a velocity history improves predictions of suspension by more fully specifying flow conditions (including accelerations and changes in accelerations) responsible for suspension.

Suspension in the future is better predicted than suspension at the same instant as velocity measurements. Incorporating such a lag between velocity and concentration improved predictions, with optimum lag time increasing with elevation above the sea bed (from 1.5 seconds at 13 cm to 8.5 seconds at 60 cm for linear models). These lags are largely due to the time for an observed flow event to effect the bed and mix sediment upward.

Nonlinear models relating suspension to velocity do better than linear models using the same velocity history. Nonlinear models are able to exploit changing relationships between suspension and velocity history for different wave shapes. For the environmental conditions of our study, the optimal model (correlation coefficient of 0.58) used 3 seconds of velocity history (approximately one-quarter wave period) and a 1.5 second lag to predict suspension.

A search of the literature shows there are no established standards for the spacing of profiles for postnourishment monitoring. One standard that appears to apply in the United States relates to construction surveys. Most recent nourishment projects use prefill and postfill profiles at 100-foot (ft) [ ~ 30 meter (m)] spacing for payment purposes. Rarely is this close spacing duplicated in subsequent monitoring surveys. How accurately does such spacing reflect the actual volume of fill remaining?

Four sets of closely spaced profile surveys to closure were performed over a two-year period following the 1991 Hunting Island, South Carolina, nourishment project. Fill volumes remaining within the project area were computed to closure depth using the average-end-area method. The complete dataset at 100-ft (30 m) spacing provided the basis of comparison. Volume calculations were performed for the possible combinations of profiles at greater spacings up to 1,200 ft (365 m). The normalized results show the expected increase in error as profile spacing increases. However, the variation was generally less than ±3 percent up to spacings of 500 ft (~ 150 m). At 1,000 ft (~ 365 m), the error band spanned 20 percent of the project volume. The Hunting Island dataset provides guidance for minimum profile spacing for nourishment projects with highly varying fill sections or irregular shoreline morphology. Spacings of 400-500 ft (120-150 m) provided a reasonably accurate result. Accuracy was greatly reduced at longer spacings. Longer nourishment projects, involving less variable fill volumes, likely can be evaluated at somewhat longer spacing with comparable accuracy. However, a disadvantage of surveying only the minimum number of profile lines is the error introduced if even one line has to be discarded from the dataset because of field survey errors.

Watertable overheight in beaches due to waves is investigated through laboratory experiments and field tests. Infiltration from wave runup onto the exposed beach creates a significant lifting of the coastal watertable. The infiltration velocity distribution is obtained from both the laboratory and field conditions. The inland overheight for the steady state (regular waves and no tide) is found to be 0.62tan$\text{β}\sqrt{{\text{H}}_{\text{o}}{\text{L}}_{\text{o}}}$ and that for the unsteady state (irregular waves) is estimated as 0.55tan$\text{β}\sqrt{{\text{H'}}_{\text{oRMS}}{\text{L}}_{\text{o}}}.$

In this paper a mathematical model for the computation of the cross shore sediment transport for random waves is presented. The model consists of the hydrodynamic, the suspended sediment transport and bed load modules. The suspended sediment concentration is computed with the use of the wave-averaged convection diffusion equation. The vertical structure of both the wave-induced current and suspended sediment concentration are modelled with the use of quasi-3d techniques. Mechanisms for the offshore transport (undertow) and the onshore transport (Lagrangian transport, transport due to wave asymmetry) are included. The model is tested against an experiment with random waves at prototype scale.

In order to simulate flow over ripples more accurately than existing approaches, a modified MAC scheme (called SOLA) proposed by Hirt et al.(1975) was adopted in the present study. Primitive equations composed of velocities and pressure were directly solved instead of the usual vorticity and velocity potential function. The governing equations were the Reynolds momentum equations in the x and z directions and the water continuity equation. The driving force was assumed to be the acceleration of the wave orbital movement just above the wave boundary layer. A mixing length hypothesis was adopted to describe the time-and-space varying turbulent eddy viscosity and the shear stress. An explicit difference method was used to solve the equations on a regular grid. The model showed good result when applied to Sato's(1987) laboratory data. The model was applied to a series of ripple tests, using similar hydraulic conditions to Sato, to study the effect of bed ripple steepness and asymmetry. Only a small effect was found on vortex movement and flow characteristics, although a clear offshore vortex movement was found.

A horizontally two-dimensional, numerical model is developed for predicting the time-dependent free surface elevation and fluid velocities in the swash and surf zones under obliquely incident waves. The assumptions of shallow water waves with small incident angles are made to simplify the continuity and momentum equations and reduce computational efforts considerably. The developed numerical model allows gradual alongshore variations of the bathymetry and the incident regular or irregular waves at its seaward boundary. The numerical model is compared with available regular wave data of alongshore uniformity as an initial assessment of the model. The wave height, setup and runup are predicted well. The numerical model with the bottom friction factor calibrated previously for swash oscillations predicts the magnitude of longshore current but can not reproduce the longshore current profile probably because it does not model the transition zone and lateral mixing.

Studies have been undertaken along the Oregon coast to better understand the processes involved in sea cliff erosion in order to develop improved predictions of the susceptibilities of properties to wave attack. A model has been developed that includes evaluations of extreme water elevations measured by tide gauges, calculations of wave run-up levels due to major storms, and a documentation of beach morphology variations that affect the wave run-up and determine the elevation of the junction between the beach and toe of the sea cliff. The occurrence of erosion depends on the combined water levels compared with the beach/cliff junction. All of these factors vary with time and also spatially along the coast. A program has been initiated to measure wave run-up on Oregon beaches ranging from reflective to dissipative in order to test the model predictions.

Special sensor was developed in the Southern Branch of of the P. P. Shirshov Institute of Oceanology, Russian Academy of Sciences Oceanology Institute, able to register variations of sediment layer thickness in any point of interest on reservoir, sea, channel or river bottom under any hydrodynamic conditions.

Uninterrupted information on geometry, rate and direction of migration of bedforms (ripples, ridges, dunes, bars) in the chosen point of underwater slope can be obtained in the following manner. Three or more sensors are placed by a diver on bottom in a horizontal plane in apieces of equilateral triangle on metal girder. The construction is put deeper into ground to 20-25 cm. Distance between sensors and their spatial orientation are set beforehand. Height and "period" of sand bedforms are found from time variations of sediment layer thickness above any of the sensors. Rate and directions of their migration are calculated by time of bedform crest transit above sensors. Sand wave length is calculated from its "period" and migration rate. A series of laboratory and field experiments has been performed for the purpose of clearing up a sensor working capacity, calibrating and work methods.

In the Netherlands the Technical Advisory Committee on Waterdefences (TAW) is developing a new safety philosophy, in which safety levels will be expressed in terms of risk of flooding. At present safety levels are expressed in terms of probability of exceedance of a certain water level. Risk is here defined as the product of probability of failure and expected damage. In order to be able to assess the expected damage, the flooding discharges in case of a dike failure have to be determined. These flooding discharges largely depend on the process of breach growth. The TAW has started a study on the breach growth mechanism, which is carried out by means of a step by step approach. Firstly laboratory experiments have been carried out to investigate the essential features of the total process. Mathematical models have been developed that describe the different phases of the breach growth process as observed in the laboratory. Recently a large field experiment has taken place in order to validate the mathematical models. So far, all research on breach growth has been focussed on sand-dikes and dunes, which implicitly means that the models are upper bound approaches. In next phases of the research programme breach growth in dikes containing less erosive materials such as clay will be investigated.

Measured values of shoreline wave setup and shoreline wave heights are summarized from the SUPERTANK Laboratory Data Collection Project. Water surface elevation time-series in the swash zone were measured by capacitance wave gages that were partially buried in the sand beach. As a result, wave measurements were obtained on the actively eroding/accreting beach-face where little data has traditionally been available. Results presented in this paper include examples of wave transformation across the entire beach profile. Mean water level and wave height conditions at the still water shoreline are then summarized for 19 sets of random wave conditions tested during the first two weeks of the SUPERTANK Project.

The morphological behaviour of a shoreface nourishment site is studied. The originally observed patterns in bar development before the nourishment are disturbed by the extra volume of sediment in the cross-shore profile. Attention is focused on the morphological development of the nearshore bars and troughs after the nourishment.

After almost a year, the bar at the landward site of the nourishment showed a reversal in bar behaviour in comparison with the natural conditions as described by Ruessink and Kroon (in press). The bar was slightly moving landward and was growing in height, whereas a similar bar at this position within a non-nourished environment would move seaward and reduce in height. The bar at the seaward side of the nourishment is quickly adjusting itself to the situation before the nourishment.

The bar behaviour after the nourishment is accompanied by a redistribution of the sediments over the profiles. The net amount of sediment losses in the nearshore area is negligible. This also means that the nourished volume of sediments is still available in the central part of the nourishment area. Longshore movements of the nourished volume are in the order of 400 m to the east over a period of about a year, and are not observed in the cross-shore profiles with a longshore spacing of 1000 m.

A numerical model for the time-averaged nearshore current in the surf zone is developed to simulate the longshore current distribution on a bar-trough beach that has a peak velocity shoreward of the bar crest. Momentum fluxes due to mass transport under broken waves, which are ignored in other models, are included in the present model. The validity of the model is verified with field data.

A mesoscale model is presented to calculate the average net cross-shore transport rate and beach profile evolution under random waves. Cross-shore transport formulas for random waves are derived by superimposing the transport from individual waves, which belong to an ensemble that represents the random wave field. The transport relationships for individual waves are based on experiments with monochromatic waves in large wave tanks. The model is validated using beach profile data from the SUPERTANK Laboratory Data Collection Project and three different types of profile evolution events are studied, namely equilibrium erosion with bar formation, berm flooding, and the impact of breaking waves on an offshore mound. Berm flooding includes the erosion of a well-developed summer berm and the erosion of an artificially constructed foredune, and the offshore mound tests encompass narrow- and broad-crested mounds.

This paper presents theoretical circulation patterns in both cross-shore and longshore directions on the plane beach slope. In the model an amended form of radiation stress which is consistent with the wave energy flux in the wave-current coexisting field is presented. Comparison of theoretical surf zone properties with laboratory experiments showed good agreements. Finally, a quasi-three dimensional model suitable for the entire nearshore zone is presented by linking the depth-integrated properties with vertical profiles.

Many in situ measurements of hydrodynamic parameters and sediment transport in the surf zone have been carried out on the beaches of the western coast of Normandy. The vertical and cross-shore distributions of the sediment transport induced by breaking waves have been identified in a set of various hydrodynamic conditions. Several longshore sediment transport formulas have been devised. The comparison between measured and computed transport rates enables choice of the best formulation according to the hydrodynamic context. This formulation emphasizes the indirect effect of tidal fluctuations on the wave characteristics and the sediment transport processes.

A three-dimensional model based on the Navier-Stokes equations is developed. The finite volume method and a time-splitting technique are used to solve the equations. Longshore and crossshore currents induced by waves are reproduced by the model and the results are compared with existing experimental data.

A numerical model has been used to study the influence of offshore sand banks on the wave climate along a stretch of the Belgian coast. Results of the model have been interpreted to provide predictions of wave height under several scenarios, assuming that the banks do not respond quickly to changes in the local hydrodynamic environment. Results show that the sand banks afford substantial protection to the coast and that this effect may be reduced as a result of rising mean sea level and dredging.

Laboratory experiments were carried out for regular and irregular wave runup over non-uniform beach profiles, including both bi-linear and concave "equilibrium" beach profiles. Measured runup is shown to be substantially less than that predicted by the Hunt Formula if the exposed beach-face slope is used to define the typical beach slope. More accurate runup estimates are obtained using Saville's hypothetical slope concept; and, Saville's method is integrated with the Hunt Formula to provide simple analytical estimates of wave runup over complex beach topography.

This paper describes a deterministic modelling system under development at the Institute of Fluid Mechanics in Hannover to simulate three dimensional wave induced currents and the morphological evolution in the nearshore region. It is basically a coupling of a 2d Boussinesq wave model which predicts the wave motion along the horizontal direction with a 3d hydrodynamic, sediment transport and morphodynamic models that simulate the time averaged wave induced currents and the associated changes in the bathymetry due to sediment transport. It is intended to improve the understanding of morphological processes, investigate the impact of sea level rises due to climate change, study extreme events and assess in the selection of cost effective measures for coastal protection. Results of a demonstration of the simulation of the wave induced currents along a nearshore region in the Baltic Sea are shown.

Experiments have been conducted to investigate the transformations of the wave characteristics induced by a uniformly decreasing sea bed. These transformations were recorded on both the frequency and the time domain representations of random wave trains. The coastal zone upwind of severe breaking was studied. Among the findings it is noted the tendency of the spectrum width parameter to decrease at a slowing rate as the waves propagate on shoaling waters. Also, the correlation coefficient between wave heights and periods seems to inversely follow the variations of a measure of the wave heights. A mathematical model has been developed based on existing results for shoaling, wave breaking and decay. This model applicable to a wide area of the surf zone predicts adequately the evolution of the joint probability between wave heights and periods provided by the experimental results.

The description of nearshore structural and sedimentary dynamics is highly dependant on a quantification of the nearshore wave regime, which is subject to bathymetry induced transformation effects. Assuming straight and parallel bottom contours, computed wave heights and water levels using variable wave shoaling, incipient breaking, wave decay and transition zone formulations are compared with measurements.

The paper summarizes the analysis of the coastal processes which have been responsible for the evolution of the Toronto Islands sand spit feature. Both natural and artificial influences have created a situation of a rapidly evolving landform. The purpose of the study was to evaluate the feasibility of rebuilding a school near the shoreline of this rapidly evolving feature. Several different techniques were employed to evaluate the changes including: shoreline recession rate estimates, lake bed surface change comparisons, sediment budget calculations and alongshore and cross-shore sediment transport calculations. These techniques were combined to develop a descriptive model of the changes in order to forecast future changes to the landform over the next 100 years.

An example of an artificial beach constructed for recreational purposes is presented. The beach stability and its impact on the marine environment is discussed. Also, the beach maintenance and management during almost 20 years is reported.

The motion of suspended sediment particles is discussed with the aim of determining which aspects are important and which ones can be neglected when the goal is to model coastal sediment transport. It is shown that the key lies in the structure of the flow, i e, vortices versus wave orbital motion, rather than in details of the drag law. With a proper description of the flow structure the most important phenomena can be modelled under simple assumption that the sediment velocity is everywhere the sum of the local, instantaneous fluid velocity and the still water settling velocity of the sediment: u_s = u + w_o. Guide lines are also given for dealing with sediment in numerical models. This paper considers only non-cohesive particles in thin suspensions where the interaction of sediment particles can be safely neglected.

The morphology of the East Frisian Islands and Coast has experienced enormous changes in the course of the last centuries. The resedimentation of medieval sturm bays has played a dominant role within these morphodynamical processes which could no longer only be credited to the impacts of littoral drift. Reconstructions of former coastal morphology have been used to quantify the long-term development of significant parameters for the tidal basins of the East Frisian Wadden Sea. Additionally also the tidal volumes for situations since 1650 could be determined. On this basis the long-term stability of common empirical relationships was checked.

Beach and dune scarps are prominent erosional features and probably interfere with post-storm beach profile recovery because of wave reflection on the scarp face during high tide and reduced swash height. As examples, beach and dune scarps, created by typhoon waves on the Pacific Coast and on the East China Sea Coast in Kagoshima Prefecture, were investigated. The highest scarp elevation on these coasts were found to be approximately to 7 m on the Pacific Coast and 10 m on the East China Sea Coast. Following the field observation, a numerical study was conducted to study the generation of scarps.

The purpose of this study is to improve general understanding of beach profile dynamics as affected by the interaction between the beach profile and the water table level within the beach by presenting the results of laboratory and numerical studies. Two series of laboratory experiments were conducted in "large" and "small" wave tank facilities. Special attention was given to elevated water table levels to investigate whether or not erosion of the beach face is enhanced. The results of the large wave tank experiments demonstrated a surprising influence of beach water table on profile dynamics including changes in the bar region. Although the experiments in the small wave tank used correctly scaled sand, it was found that the effects documented in the large scale tests could not be duplicated. Furthermore those results were supported by numerical simulation of the internal flow inside the beach. One possibility for the difference is that the sand in the large scale tests was more poorly-sorted than that in the small scale experiments.

Laboratory experiments are performed in a wave basin to investigate the characteristics of three dimensional distribution of the nearshore current. Direction and amplitude of the nearshore current significantly change along the vertical axis and have spiral distribution. A quasi 3-D model which gives the 3-D distribution of nearshore current is proposed. Momentum flux due to the large vortexes formed on the front face of breaking waves is included in the model to evaluate the depth averaged current. The model is examined with the experimental results.

A procedure to estimate vertical diffusion coefficient and reference concentration of time averaged suspended sediment concentration caused by waves and current are discussed based on experimental results obtained in a laboratory.

It is found that the non-dimensional diffusion coefficient normalized by the product of shear velocity u^* and the equivalent roughness k_s is more closely related to the Shields' number when the shear velocity is evaluated by using the equivalent roughness where the effect of ripple geometry is taken into account. The reference concentration is not a unique function of the sediment Shields' number. Incident wave period has also influence on the reference concentration.

A model predicting dune erosion under storm conditions has been developed using data from SUPERTANK laboratory experiments. In this model, the swash approach is applied with the basic assumption that the volume eroded from the dune is a function of the swash force acting on the dune. The swash force is characterized with swash parameters, specifically the swash height, the swash velocity and the swash period. For given storm conditions, the model predicts wave height variation across-shore, swash height variation on the beach face, swash velocity, swash period, swash forces and finally volume eroded at the dune. Predictions of swash parameters and dune erosion are compared with measurements from SUPERTANK laboratory experiments.

The numerical modelling of time-averaged three-dimensional currents due to breaking waves is presented. The basic equations and the closures are described. The driving terms in the momentum equations are the radiation stresses derived from "organised" velocity of waves and the roller contribution. The model is validated on measurements collected in a flume. The application to the case of a rectilinear beach with oblique incidence wave displays a helicoidal circulation. In the situation of a detached breakwater with a normal wave, depth-integrated currents show two large symmetrical cells in the lee of the structure whereas streamlines near the bottom converge spirally toward the centres of the eddies.

Some basic sediment movement characteristics such as critical velocities of motion, bed load layer thickness, as well as local and overall sediment transport have been measured in field at Lubiatowo, Poland.

The survey was carried out in a multi-bar (4-5 bars) Polish coastal zone with the medium grain diameter D₅₀ from 0.2 to 0.25 mm. Irydium glass grains tracer, close in size to the natural sand, has been used. The investigations embodied 8 hydrodynamical situations in various climates of waves and currents.

For oblique wave incidence it has been found that local intensity of long-shore sediment transport can reach 40-100 kg/(m h) under storm conditions, strongly dependent on local bed topography. The overall sediment transport rate across the entire surf zone can exceed 7.10^-3 m³/s under storm conditions. For weak wave motion the bed surface layer of sediment transport has a thickness of several grain diameters, while it may be even 4-6 cm thick during storms. Vertical distributions of sediment concentration beneath of bed surface are identified. Transport rates are related to the product of squared breaker height and longshore velocity. Annual time series of sediment transport are presented.

Two series of experiments were carried out in the Large Oscillating Water Tunnel of Delft Hydraulics, which was recently extended with a recirculation flow system. Combined wave-current boundary layer flows were studied with a mobile sand bed in the sheet flow regime. Detailed intra-wave concentration and velocity measurements were carried out and revealed a three-layer system, i.e. a pick-up layer, a sheet flow layer and a suspension layer. In the suspension layer time-lag effects of the sediment concentration led to sediment fluxes in upstream direction. The suspended sediment was more confined to the near-bed region than according to diffusion theories, most likely due to turbulence damping. The horizontal time-dependent and net sediment fluxes were concentrated in the sheet flow and pick-up layer. Measured net sediment transport rates could be described as a linear relation with the third-order velocity moment <U³⁾> near the bed.

The wave incidence and the wave-induced circulation in the surf zone (SZ) is studied from both experimental and numerical point of view. The DELTA'93 experiments were carried out in the Trabucador bar of the Ebro Delta, in the Spanish mediterranean coast. The emphasis of DELTA'93 was on the SZ vertical flow structure, measuring simultaneously undertow and longshore current in a barred profile. The numerical simulation with NEARCIR Q3D model assumes longshore uniformity and stationarity. The wave decay, 2DH currents and 1DV undertow and longshore currents are modelled. The agreement is quite reasonable as can be seen in the included figures.

A numerical wave model based on the Boussinesq equation was extended to the computation of two-dimensional wave-current field including diffraction, refraction and wave breaking. The energy dissipation due to wave breaking was modeled by a momentum mixing term using eddy viscosity. Beach deformation was estimated based on the wave-current field simulated in the nearshore region. Energetics-based equations were used to estimate the total sediment transport in the cross-shore and longshore directions. The model applicability was confirmed with laboratory experiments.

The performance of a coastal drain system was investigated experimentally. When the drain pipe was buried in the seaward area of a shoreline, the system was most effective. When the discharge is large, the drain system could accumulate a large amount of sediments on a beach face even under erosive wave conditions without drainage. The flow toward shore induced by drainage seemed to play an important role.

Wave breaking and wave induced currents are studied in two horizontal dimensions. The wave-current motion is modelled using a set of Boussinesq type equations including the effects of wave breaking and runup. This is done without the traditional splitting of the phenomenon into a wave problem and a current problem. Wave breaking is included using the surface roller concept and runup is simulated by use of a modified slot-technique. In the environment of a plane sloping beach two different situations are studied. One is the case of a rip channel and the other concerns a detached breakwater parallel to the shoreline. In both situations wave driven currents are generated and circulation cells appear. This and many other nearshore physical phenomena are described qualitatively correct in the simulations.

The ability to predict the time-averged longshore sediment transport rate accurately is essential for many coastal engineering applications. Because the longshore transport formula in the Shore Protection Manual (SPM; US Army, Corps of Engineers, 1984) is possibly the most widely used, it is important to know its accuracy. The aim of this paper is therefore to investigate the accuracy and applicability of this formula (the SPM formula). In addition, a number of variations to this formula are presented; these are also tested against a comprehensive data set. Finally, the SPM formula is re-calibrated and guidance is given regarding the use of this formula for coarse bed material.

A practical method for estimating the undertow velocity and its direction is developed and verified on the basis of field measurement data. It is found that a simple vector addition of nearshore current and undertow gives a good approximation.

The actual bottom topography change during a year is simulated by the 3-D beach evolution model taking into account the cross-shore sediment transport due to waves and undertow as well as the transport due to nearshore currents. The results of both measurements and calculations show that the sediment transport due to nearshore current is predominant and the contribution of cross-shore sediment transports is cancelled for a long-term beach evolution.

In this work, the main variables involved in one-line shoreline evolution models have been identified and typical values for them have been found for different zones of the Catalan Coast. These values have been employed in a shoreline evolution model. The model has been calibrated in several points of the Catalan Coast, adjusting the free parameters in a longshore sediment transport formula. Taking into account the quality of the results, the model seems to be an efficient tool for medium term coastal engineering purposes.

A comprehensive test series at full-scale was performed on a grass dike to obtain quantitative information on the wave loading, erosion rate, residual strength and overtopping under design storm conditions. The purpose was to establish design and assessment criteria for this type of dike, which exists in many places in The Netherlands. The particular dike tested exhibited, in general, a considerable resistance to erosion. However, such a non-homogeneous surface is subject to weak spots which can erode very quickly. The most critical region, where the wave loading is the highest, has been identified. The residual strength of the underlying layer of clay is defined as the time it takes for erosion to progress through the entire layer and expose the sand core of the dike. For the dike tested, the residual strength of the 0.8 m thick clay layer is estimated to be 10 hours under design conditions. Measurements of the average overtopping rate and the volumes per overtopping wave were compared to existing formulae, developed from the results of small-scale tests. The comparison was favourable, indicating that scale effects are not substantial for these quantities.

An algorithm is developed that is capable of calculating the formation of a tombolo in the lee of an offshore breakwater in a shoreline numerical model by inversely applying the method proposed in 1985 by Hanson and Kraus for constraining the shoreline not to retreat landward of a seawall. The algorithm is linked to a shoreline numerical model which uses curvilinear coordinates that follow the shoreline. The project of six segmented breakwaters at Chippokes State Park, Virginia is reported. The developed model is applied to the simulation of the shoreline change during the first nine months after construction of the Chippokes breakwaters.

A physical sediment model was used to design two beach improvement schemes in False Bay near Cape Town. Different layouts of T, L and detached breakwaters were tested to determine their effect on the beach and how they improved bathing conditions. Although caution was exercised to eliminate scale effects, it was found to be necessary to minimize their influences. A method was devised to do so which proved successful. It was found that equilibrium shoreline positions were reached after 4 years (prototype time). Sand feeding after construction will be necessary to minimize the deleterious effects of the breakwaters on the adjacent beaches.

Due to the construction of an airport runway, severe beech erosion has taken place on the Kuta beach, a coral-sand beach in Bali. Introducing the most effective wave for beach change in terms of wave transformation on a coral reef, the long-term shoreline change is predicted with changing the positions for the boundary conditions to be used as headlands for stabilizing the beach in the large scale coastal behavior. We could find a possibility of stabilizing the beach against beach erosion by constructing three headlands at the positions found. In this beach, a very small amount of sediment source can only be produced from the activity of sea animals. On the basis of the long-term shoreline change and the theory of the formation of static stable beaches, therefore, a methodology for coral-sand beach stabilization was proposed, and parts of this were constructed. Further improvement for the headlands is needed, but as of 1989, a static stable coral-sand beach has been well-formed between the headlands.

When a sand bed is liquefied due to a high pore pressure gradient, it significantly reduces the height of waves passing over it. This study investigates the fundamental characteristics of a liquefied sand bed including the wave damping effect.

Wave height, wave set-up, undertow, and turbulent velocity on a plane beach and a barred beach were compared in the case of regular waves. The study showed that the presence of an offshore bar altered the turbulent flow in the surf zone by altering the characteristics of the broken waves. It was found that the magnitude of undertow and turbulence intensity were smaller in the inner surf zone on the barred beach. These results suggest that it may be possible to reduce the erosive wave action on beaches by construction of underwater berms in the nearshore zone. Further studies are needed to determine the effects of water depth, berm width and crest elevation on surf-zone turbulence under different wave conditions in order to provide explicit design guidance.

Topographic changes around Mihono-Matsubara Sand Spit were studied based on bottom sounding data and aerial photographs. On the Shizuoka and Shimizu coasts located upcoast of the sand spit, erosion waves are generated due to interruption of longshore sand transport by the construction of coastal structures. The propagating velocity of these erosion waves was found to range from 0.5 to 0.8km/yr. This agrees considerably well with the theoretically estimated value of 0.47km/yr. Comparison of beach profiles showed that the dominant beach changes take place at depths shallower than -7m, and this provides the closure depth for profile changes on this coast. The longshore sand transport rate was evaluated to be 1.3 x 10⁵m³/yr at specific locations on the Shizuoka and Shimizu coasts, and it was found that this transported sand discharges into submarine canyons, forming a steep slope of around 1/2, thus resulting in the net loss of sand from this coast.

A depth-integrated, short wave-averaged nearshore circulation model is presented, which includes the effects of the 3-D current structure over depth. The model includes the description of time-varying currents such as infra-gravity waves. Two numerical schemes are developed, which will be used for intercomparison in the absence of analytical solutions. An absorbing-generating boundary condition is developed based on the Method of Characteristics in order to allow propagating waves to leave the computational domain with a minimum of reflection while specifying incoming waves at the same boundaries. The model is tested for the time-varying start-up of a longshore current on a cylindrical coast, and the temporal development of both the cross-shore profiles of the longshore current and characteristic samples of the vertical structure of the velocity profiles are given.

A mathematical model for breach growth in sand-dikes and dunes is presented. The model is based on the five-step breach erosion process as observed in several laboratory and field experiments. A simplified Galappatti (1983) pick up mechanism for sand from the bed is combined with Bagnold's (1963) modified (Visser, 1988) energetics-based sand transport conception to describe the breach erosion. The comparison of the model predictions with the data of the Zwin 89 field experiment shows good agreement.

A modified modeling law based on the comprehensive work by Wang, etal. (1990) has been derived with the assumptions that the suspended sediment transport is the dominant mode under storm wave condition inside the surf zone and the wave breaking index is preserved. This, in essence, adds to the constraint that wave height is properly modelled in accordance to the preservation of breaking index instead of simple vertical geometrical scale. Four different scaling laws including the one proposed presently were examined in the laboratory using 2-D wave tank and 3-D basin models. The model results were compared to prototype data from German large wave tank experiment. The model performances under different scaling laws were evaluated separately in the dune region and bar region of the entire model beach profile. Several statistics, including the errors of sand bar location, bar volume, bar profile, dune erosion volume, and dune profile, between model and prototype, were calculated and the result showed that the newly proposed scaling law presented the best overall model performance among the ones compared.

First a discussion is made on the relation between the time-average of a Boussinesq-type equation and the mean flow equation. Then nonlinear wave transformation on a sloping bed is computed by a set of Boussinesq equations including a breaker-induced energy dissipation term. Comparisons are made between the computations and laboratory measurements for cross-shore distributions of the wave height and mean water elevation, and for time-histories of the near-bottom velocity near and after breaking. Undertow current velocity in the nearshore zone is calculated by a semi-empirical formula and is also compared with measurement data. A beach profile change model is set up by combining the Boussinesq-type equations, a sediment transport rate formula for the sheet-flow proposed by Dibajnia and Watanabe, which incorporates the asymmetric orbital velocity due to wave nonlinearity as well as the undertow current, and a sediment mass conservation equation proposed by Watanabe et al., which includes the effect of local bottom slope. The validity of the model is examined through the comparisons of the computed transport rate distributions and beach profiles with the laboratory data obtained in large wave flume experiments.

Surfzone measurements of longshore sediment-transport with optical backscatter sensors and current meters are compared to transport estimates from offshore wave data. Several methods from the Shore Protection Manual for computing longshore sediment transport from waves are compared and correlated. Some formulas work well some of the time. Circumstances of which equations perform well/poorly under which conditions are specified, and reasons for poor performances are speculated upon. Advice is given for placement of wave gages and methods of analysis, which would increase the probability of obtaining good estimates of longshore sediment transport from directional wave data.

Simple formulas to predict time-averaged suspended sediment concentration are formulated using steady diffusion equation. Empirical formulas are developed to compute reference concentration (boundary condition) and diffusion coefficient. For suspended sediment concentration in the field, the same formulas with regular wave condition can be applied by using root mean square wave height and average wave period. Total 139 data sets are used for calibration of empirical formulas and 175 data sets are used for verification.

Measurements of surface elevations and horizontal orbital velocities in regular waves and two component wave groups were performed to prove the experimental validity of periodic wave theories for regular waves, and empirical engineering methods for calculations in irregular waves. Besides the traditional wave theories a LAGRANGEian approach was introduced. With this LAGRANGEian method for waves of finite height, based on the geometry of orbital paths given by STOKES wave theories, it is possible to extend the region of validity of STOKES theories over a wider range of wave parameter. The use of a superposition method with LAGRANGEian approach and the application to two component wave groups, results in the appearance of non linear interaction components in surface elevations and horizontal orbital velocities, which are in fair agreement as well with a 2nd order approach for irregular wave surface elevation as with the measurements of surface elevation and horizontal orbital velocities.

This paper presents part of the test results conducted in the Large Wave Flume (LWF) for 2D beach profile response under random wave input as well the numerical modelling effort to simulate the laboratory data. The tests were conducted with various input wave spectra, initial profiles and for both erosional and accretional cases. The numerical model is a 2DV(two dimensional vertical) beach profile model. It couples a sediment transport model with a random wave model. The sediment model is a modified version of the SBEACH model developed by Larson and Kraus (1989) for regular waves. The input wave condition is a time-series of irregular waves simulated from a given wave height probability density function, here selected as the Rayleigh distribution. The final profile is then computed from the cumulative changes due to each randomly occurring individual wave.

Using a two-dimensional wave flume and a two-videocamera system, mechanism and process of multiple bar formation were investigated in the light of breaker-induced vortices. A fixed-bed experiment revealed that (1) the vortex formed at the wave break point can be classified into three: oblique, A-type horizontal, and B-type horizontal vortices; (2) the vortex formed in the surf zone is always oblique; and (3) the location of a vortex reaching bottom can be described by wave properties and the bottom slope, and its water depth can be expressed by breaker height alone. A movable-bed experiment indicated that bars are initiated by the vortices reaching bottom in the surf zone; the number of bars formed coincides with the number of such vortices. Suspension of the bottom sediment due to vortex action and the mean-drift-velocity pattern can play an important role in multiple bar formation; mechanism for break-point bar formation is "convergence", while that for inner bar formation is "congestion". Two major modes for the development of multiple bars were found: simultaneous and successive: these depend on the interaction of vortex action and topography in the surf zone. Multiple-bar features such as trough spacing and crest depth could be explained from vortex features found through the fixed-bed experiment.

This paper presents a coastal morphology modelling system based on an explicit forward time integration scheme for the morphological evolution involving the following stages: a) Initialisation, b) Sediment transport computation using a deterministic sediment transport model, c) Wave computation using an arbitrary wave model, d) Hydrodynamic computation assuming a mobile bed evolving at ∂z/∂t, with optional use of a module to determine the apparent roughness in combined wave-current motion and e) Bed level update scheme using an improved second order Lax Wendroff scheme. A series of numerical tests is performed with the aim of evaluating the effect of space-varying hydraulic roughness in combined waves and current, choice of wave modelling approach and of directionality of the waves on the morphological evolution. A detached breakwater is used as test case.

An experimental shoreface nourishment was implemented at Terschelling, the Netherlands in 1993. The effectiveness of this nourishment will be evaluated in the framework of an EU sponsored project NOURTEC.

The design of the Terschelling nourishment including the objectives and alternatives, are described in detail. Preliminary monitoring results lead to a cautious optimism with regard to the performance of the nourishment.

This paper first presents a literature review of permeability laws. A link between hydraulics and geotechnics formulations is pointed out. Second, reduced permeability expressions are discussed from experimental data available in literature. An extented exponential expression of reduced permeabilty is proposed.

A series of wave flume experiments for wave-current-mud system has been performed. The results reveal that the rate of wave attenuation increases in the opposing currents and decreases in the following currents. The results are the same with the waves on the fixed bed. Another important result is that the mud mass transport velocity increases in the opposing currents and decreases in the following currents. The visco-elastic-plastic model which was proposed by Shibayama and An (1993) for wave-mud interaction has further been extended to the wave-current-mud system by taking a wave deformation effect into considerations. The extended model succeeds in predicting the laboratory results. The model shows that due to pressure gradient in wave propagating direction, the largest mud mass transport velocity occurs in the strongest opposing current and the smallest one in the strongest following current.

In the paper the influence of some physical and numerical effects on computations of residual transport in shallow tidal basins is analysed. Investigations deal with: i) the Coriolis acceleration, ii) the specification of the tidal forcing, iii) the diffusion coefficient, iv) a time weight in a standard implicit numerical scheme. The analysis has been carried out by means of intratidal mathematical models with reference to three schematic basins, with the tide being the only forcing of the system. These are typical conditions in which critical environmental events like anoxia occur. Usual assumptions in mathematical modeling of 2D flows in shallow basins regarding the above effects are tested both in the short and long term. The different importance of that effects depending on both the time scale of processes and the basin morphology is shown. Results are presented in terms of turbulence-time-averaged circulation patterns, Lagrangian residual circulation patterns, distributions of relative differences induced in the latter by including or not the investigated effects, and convection-dispersion of a passive solute.

The erosional impacts of improved inlets upon adjacent shorelines may be best estimated by first computing the volume of material removed from the littoral system and then examining the adjacent shorelines to identify the length along which this volumetric impact has been manifest. This contrasts with the traditional approach whereby erosion is identified along a finite reach of shoreline and attempts are then made to link the erosion to a plausible cause. The length and volume of inlet-related erosion at two inlets considered herein are significantly greater than that traditionally ascribed to the inlets. Both feature near-field and far-field downdrift erosion signatures separated by stable shoreline.

An overview of the model complex, including a combined Lagrangian and Eulerian approach to simulation of sediment transport, developed to study spreading of dredging spoils in connection with off-shore earth works necessary for construction of the Denmark-Sweden Link is provided; - together with in-depth descriptions of two particular work topics: (a) Model representation of flow friction to allow application of an inherently depth-integrated model system to a partially stratified environment, and (b) overall design of the model complex to make it fit as a versatile tool at several stages of this large project.

The effects of offshore dredging at Chang-Hwa reclamation area, Taiwan, are investigated by using movable bed model tests. A practical scale relation for the design of movable bed model is presented. It takes the advantage to give more flexibility for the selection of model sediment. The scale relations of wave conditions in the model test are obtained based on the similitude of two parameters: wave steepness and mobility number. Time scale of sea bottom changes is determined by longshore sediment transport rate. Experimental results show that the proposed scale relations are able to reproduce beach changes in nature. Topographical changes before and after dredging are predicted in model tests. Special attention was made to study the location of erosion and accretion of sea bed configuration owing to offshore dredging.

An approach for predicting the harbour oscillations induced by undirectional irregular waves in a harbour of arbitrary shape and variable water depth is presented. Effects of partial reflection along harbour and breakwater boundaries were considered by involving an energy dissipation coefficient in boundary conditions. Numerical results on wave heights within a rectangular harbour were presented and a realistic harbour geometry was selected for trial computations. The results of the computations were verified through hydraulic model experiments.

Mechanism of sedimentation in Bangkok Bar Channel in Thailand is investigated by using the periodically measured water depth around channel, dregded volume and the relation between discharged sediment concentration and discharged velocity measured at the river mouth of Chao Praya. Simple numerical simulations for predicting sedimentation volume in the channel are also carried out. The results show that both discharged sediment from the river and sedimentation around Bangkok Bar caused by waves and current play an important role in the sedimentation in the channel.

A field observation program was carried out to measure natural and maninduced fluctuations in suspended sediment and turbidity in connections with a beach nourishment project. The project was carried out at Longboat Key, on the west coast of Florida. The analysis of the manual turbidity, sedimentation, and wave data revealed several significant facts concerning the differences between the hard bottom sites and control sites and the interactive dynamics between these three phenomena. The sedimentation measurements indicate that the sand sedimentation rates are highly variable, particularly with time. In contrast, the fines sedimentation rates are relatively less variable with respect to both location and time. It is evident from the examination of the sedimentation data that the sand sedimentation rates at the hard bottom sites were approximately 2.5 times higher than those of the control sites. The statistical analysis indicated that there is less than a 10% probability that this difference is due to chance. In contrast, there were no significant differences in fines sedimentation rates between the hard bottom and control sites. The manual turbidity measurements indicate high variability in space and time. Based on approximately 15 measurement dates, following nourishment the hard bottom sites experienced approximately 50% less turbidity than the control sites. The variations in sand sedimentation rates are believed to be directly related to the hydrodynamic forces resulting primarily from waves. The wave height was approximately 33 % greater at the hard bottom sites.

When a ship hits a soil or gravel slope it will create a large transient pore pressure in the soil which will force the ship bow upwards. At the same time the pore water will cause ruptures in the soil which influences the lifting forces on the ship bow. Methods of analysis are presented for the pore water build up, the soils rupture and the resulting reactions on the ship bow for frictional soils. Soil slopes with low permeability (sand in connection with a scour protection) generates large reactions on an impacting ship with the result that the ship will ride up on the surface of the slope and be brought to a stop by friction. Soil slopes with high permeabilities as pebbles or quarry run generate smaller reactions, and the ship will plow itself into the slope. It will then be stopped by a combination of friction and passive soils pressure. The analytical results are compared with test results made in a hydraulic laboratory and by full scale testing in nature of a ship sailed into a beach. Good agreement was found between the theoretical findings and the test results.

To investigate the angle effects on the initial mixing processes of the buoyant jet under wave action, the flow visualization and concentration measurements based on laser-induced fluorescence are employed in this study. The dilution improvement of the effluent in the co-wave and opposing-wave is mainly caused by the velocity gradient increasing due to the opposite wave flow and the wave tractive mechanisms resulted from the onshore and offshore wave motion. When orthogonally discharged into wave motions, the effluent is increasingly diluted by the formation of wake vortex and trajectory deflection curved by the wave flow. From the quantitative measurement of tracer concentration, the dimensionless dilution rate shows a function linearly increasing with the dimensionless wave parameter whose coefficient in the orthogonal discharge is above 33% higher than the other two cases. For practical design, it suggests that the orientation of the nozzle should be orthogonal to the propagation of principal wave motion.

In order to study the deposition and erosion behaviors of the cohesive sediment in the navigation channel through the bar of the Yangtze Estuary, a series of experiments have been made with a standard settling tube and Ubbelodhe viscometer. The tests show that the flocculation and rheological behaviors of the cohesive sediment differ from the clay mineral contained in the fine sediments. Different clay mineral aggregates or floes have their apparent volume due to the thin layer of water surrounding the aggregates or water entrained in the floes. The Bingham relative viscosity and yield stress are obtained: μ_r = (1-KC_v)^-2.5, τ_y = 0.13Kexp (7kc_v). The suspended load transport rate and depositional behavior of the cohesive sediment have been studied with rotating annular channel. It is shown that there is a certain silt carrying capacity for a certain flow condition. The equilibrium silt concentration can be expressed: C_eq = A(τ_b – τ₁) and the concentration-time relation is C=C_eq + (C_o – C_eq) exp (- α ω t/2H). Using the above formulas and tidal velocity analysis the yearly average dredging amount in the the navigation channel can be calculated.

This paper concerns the wave-induced mixing of a discharged contaminant, and presents the results of a two-part laboratory investigation in which both a two-dimensional and a three-dimensional jet were discharged beneath a series of progressive gravity waves. In each case the measured data is compared to an identical discharge in a quiescent ambient. This comparison suggests that the oscillatory wave motion generates a region of intense fluid mixing which cannot be predicted by the existing integral solutions. Comparisons with a Lagrangian model, first proposed by Chin (1988), highlights the importance of the "apparent" mixing associated with the wave-induced deflection of the jet-axis. This provides a convincing explanation for both the non-Gaussian distributions observed by Sharp (1986), and the multi-stage structure of the centre-line decay (Chyan et al., 1991). Furthermore, quantitative comparisons with the Lagrangian model suggest that in addition to the wave-induced deflection, the oscillatory motion produces a significant increase in the rate at which ambient fluid is entrained into the emerging jet.

This study aimed to develop a numerical method of calculating bivalve movement by waves, and to consider the validity of this model with comparison between the calculated distribution of bivalves and real sampled data.

The distribution of bivalves calculated by this numerical method coincided well with the real sampled data. This numerical method can predict the difference of distribution according to shell length, specific gravity of bivalve, shape of bivalves and so on. Thus, this method will be able to explain the mechanism of zonation of bivalves.

An analytical formulation is presented for the analysis of the breakout of a half-buried submarine pipe due to wave action. The formulation accounts for the contact between the pipe and the soil due to the horizontal hydrodynamic force. An asymmetric gap geometry is described that incorporates a second order expansion in the gap opening due to the pipe rise. Results with this formulation demonstrate the existence of an initial gap of the order 1 mm in the breakout experiments. With this initial gap, the gap flux dominated the influx of water into the gap from the beginning of the breakout process.

This paper presents the analytical solution to the wave-induced excess pore-pressure oscillations in permeable seabed sediments, derived for the case of limited thickness of the seabed layer. In order to show the utility of the analytical solution, a wide parameter study has been performed with a special emphasis to the relative compressibility of the two-phase (soil skeleton – porefluid) medium. The results of example computations are discussed with respect to the accuracy of the 'finite-thickness' analytical solution for the pore-pressure.

Based on the observations, response characteristics of sand barrier and flood terrace for the Abukuma River mouth are analyzed in wide time scale range spanned from several hours to half century. We propose some measures representing magnitude of the deformation and the external forces to find quantitative relationship between them. The analyses deal with breaching in the flood process, development of the sand barrier, alternation of the barrier side, and the formation and decay of flood terrace, together with their time scales. There will be also shown interaction between the barrier and the terrace.

In the framework of an extension plan for a large cargo handling berth, it is necessary for one alternative to build an artificial approach. The bottom of this dredged channel will lie approx. 6 m under the natural seabed level. The run of the axis is unfavourable since it is perpendicular to strong tidal currents which reach 2 m/s in the 705 cycles per year. In a model test, re-sedimentation for a volume of approx. 210,000 m3 was observed indirectly in the standard procedure with repeated measurements by echo sounding as well as with a direct method using a sand-surface-meter combined with wind, tide, current and wave measurements.

This paper describes risk assessment techniques developed in a research project carried out for the UK National Rivers Authority (NRA) (Meadowcroft and Reeve, 1993). The main aim is to develop probabilistic design and analysis methods to assess the risks of failure for new and existing sea and tidal defence schemes. The flood risk takes account of the failure probability and the consequences of failure. There is a contrast between conservative design criteria that attempt to minimise failure rates, and risk-based design criteria that offer a more cost-effective solution despite a possible increase in failure frequency. The procedures are intended to be used in the design of new schemes, for assessment of existing defences and prioritisation of maintenance and refurbishment.

Experiments on oxygenation due to breaking waves on a uniformly sloping beach and on an S – type breakwater were performed. The water was chemically deoxygenated and dissolved oxygen (D.O.) concentration was followed over time in characteristic locations. Experimental data showed that the transfer velocity increased with increasing wave height for waves of the same frequency. Experiments with waves of the same wave height but increasing wave frequency showed also an increase in transfer velocity. The breakwater data give lower transfer velocities as compared to the sloping beach data for the same wave characteristics.

The one – dimensional transport equation was used for the determination of the transfer coefficients. Analysis of the data indicated that the transfer coefficients varied almost linearly with the vertical wave velocity at the water surface. A rather good linear correlation was obtained for the breaking wave data on the sloping beach, with much higher slope as compared to the case of non-breaking waves.

In urban coastal areas in Japan, large-scale reclamation projects have recently increased, which have caused drastic changes in topographical features of the coast-line. In Osaka Bay, the sea area of 5,200 ha have been reclaimed in the past 40 years and many development projects are under construction. As a natural consequence, the sea water has been polluted due to poor exchange of water with outer oceans and the load of nutritious substances discharged from rivers; hence, algal blooms occur independent of season and anoxia appears near the sea especially in summer. A 3-D baroclinic flow model is proposed to predict the tidally-interacting estuarine circulation and residual baroclinic currents in Osaka Bay and to evaluate the effects of hypothetical large-scale reclamation on the estuarine system.

Low-lying countries such as the Netherlands are very vulnerable to climatic changes, which are likely to cause an increase in sea-level rise. The most obvious threat is permanent inundation of unprotected low areas. However, such a 'final' situation will be preceded by a period of increasing episodic flooding and coastal erosion. Sea-level rise causes safety against flooding and erosion to reduce which should be accounted for in long-term coastal zone management plans. The question is to what extent such increases are tolerable and what can we do about it. This problem concerns the levels of safety which are desired, also in coastal areas which are already protected from flooding: is there a surplus of safety so that no intervention is required, or does the coastal defence system need to be adapted? The relevance of this question lies not perse in the threat of sea-level rise: the same question may be raised in the case of developing coastal areas, where economic values at stake increase: such developments cause a relative weakening of the flood defence system: the desired safety standards increase so that the existing defence system may not meet any longer the changed demand for flood protection and is to be adapted.

The above problem description was the background of a number of studies in the Netherlands to assess the impacts of a possible climatic change and to evaluate potential counter measures. A model has been developed for quick analysis of combinations of scenarios for climate change and potential counter measures. This paper describes the limitations of Cost Benefit Analysis as a tool for the appraisal of flood alleviation in view of the inaccuracies in investment costs and material flood damages.

In the last decades two methods of coastal protection have become increasingly popular for the protection of sandy shores: beach nourishments and offshore breakwaters. In The Netherlands the first of both is well known and applied regularly. The second method has not been applied yet. With the increasing cost for beach nourishment and the apparent succes of offshore breakwater systems abroad, a study has been executed to the technical and economic feasibility of offshore breakwater systems in The Netherlands compared to the present strategy of beach nourishments. This paper highlights the results of this feasibility study.

DELFT HYDRAULICS' morphological model system is applied to the case of Keta Lagoon, Ghana; the results are compared with a physical model test carried out by DELFT HYDRAULICS in 1982.

The paper describes the methodology established in Spain to assess shore protection investments. The method consists of two phases: a pre-assessment based on physical and economic indicators and an assessment in which the financial, economic and social appraisals are estimated using cost-benefit analysis techniques.

The paper also contains the preparatory works to create a data-base necessary to establish a demand-modelling.

Climate changes could lead to remarkable changes of boundary conditions with respect to the interactions between hydrodynamics and morphology. This would impact especially coastal areas with movable beds like the Wadden Sea of the Southern North Sea. Therefore applicable tools for a prediction of morphodynamical development due to changing conditions are demanded. The German-Dutch research project "Morphological development of the Wadden Sea region with special emphasis of the impact of an increasing relative sea level rise – WADE" deals with the described problem by developing suitable conceptual morphodynamic models. An essential part of these models is parametrization. Empirical investigations were carried out for different tidal basins of the German Wadden Sea leading to parameters which describe and quantify the interactions between hydrological impacts and morphological responses. The gained results had been applied to a case study based on an empirical model.

The present study focuses on numerical simulation of wave height decay and muddy bottom deformation under wave action. Experiments have been performed to determine the vertical distribution of the water content ratio of mud. Using the experimental results, a simulation model has been set up to estimate change in the water content ratio in the mud bed. Also, a simple one-dimensional numerical model has been developed to predict the muddy bottom deformation under waves as well as the wave height decay. Wave flume experiments have been carried out and the changes in the bottom topography and wave height have been compared with the calculations.

A field and modeling study on the resuspension and vertical mixing of sediments in Tampa Bay, a large shallow estuary, and Lake Okeechobee, a large shallow lake in Florida, U.S.A. has been studied. The study was aimed to obtain a quantitative understanding of the fundamental processes controlling resuspension and vertical mixing of sediments in the water column and to develop models for simulating resuspension and mixing of sediments in shallow waters. For the field study, field data (including wind, wave, currents, suspended sediments and water quality parameters) were collected from Tampa Bay and Lake Okeechobee during several episodic events. These data were then used for the development of a one-dimensional water column model of hydrodynamics, sediment dynamics and water quality dynamics. Results of the study indicate that during episodic events, bottom stresses induced by the wind waves are very effective in causing significant resuspension of sediments and nutrients from the bottom of shallow estuaries and lakes. Vertical turbulent mixing due to wind-driven and tidal currents, however, are more effective in distributing suspended sediments through the water column.

A numerical model is proposed for beach deformation under wave and current in river mouth area. The model includes three major driving forces for sediment transport which are wave, wave-induced current and river discharge. Interaction of wave and current is also included. Laboratory experiments are performed to be compared with numerical results. Wave field, current field and beach deformation are compared between laboratory and numerical results and good agreements are obtained.

A numerical simulation method, which combines the Marker And Cell method and the Discrete Element Method, for analyzing the settling behavior and deposition configuration of the particles dumped into waters is described. Some calculated results are compared with the experimental ones, and what the settling behavior of the particles and the deposition configuration on the water bottom depend on is discussed.

Discussion is carried out on stability of submerged outlet structures of thermal power plants sited on sandy ocean beaches. The authors conceived the new scouring protection "SPAC" constructed by riprapping of the seabed just in front of the outlet. In this study, the authors investigated the plane design of the SPAC by means of 1/25 scale physical model. First of all, properties of seabed scour due to submerged discharge and monochromatic or multi-directional waves were examined. Secondly, the spreading process of the SPAC was investigated, and the necessary width of the SPAC was evaluated based on width of discharged current, and on the drift of discharged current effected by longshore current due to oblique incidence of waves. Finally, the physical model was verified by comparison with field data.

The extraction of diamondiferous ore deposits along the coastal strip of southern Namibia has called for novel mining techniques. Quantitative analysis of coastal processes incorporating the prediction of short and long term shoreline response has proved particularly useful in optimizing such techniques. Further attention has been given to assessing the impact of mining operations on the nearshore ecosystem through comprehensive monitoring and modelling analyses.

Flow slides can play an important role in the stability of coastal foreshores and structures, in harbour design, in dredging activities and placing of hydraulic fill structures. In the south western part of the Netherlands the phenomenon is of major concern for the protection against flooding by means of dikes. More than 1100 slides have been registered since the year 1800. In the paper the practical experience and the knowledge obtained from experiments and fundamental research is briefly summarized. An engineering approach to coastal flow slides that combines the Dutch experience with flow slides with results of fundamental research of the past 10 years, is described.

In a laboratory flume the formation and erosion of stratified sand-mud beds in uniform flow was studied. The experiments showed that depending on the initial conditions of suspended sediment concentration and mixture composition, consecutive inputs of a mud/sand suspension will lead to the formation of a layered sediment bed. Peaks in the measured density profiles show the different layers and indicate a possible segregation of the sand due to differential settling. During the erosion of the stratified bed, the sediments are eroded layer by layer. This results in a sequence of suspended load (fines) and bed load (sand) transport phases.

This paper presents the experimental results of the pore water pressures within the soil under the action of standing waves. Both the spatial and time variation of pore pressures are generally well agreement between the theory and the experiment. The experiments also show some nonlinear phenomenon of the pore pressures within the soil.

Due to the construction of Naoetsu harbor, severe beach erosion has taken place on the Joetsu-Ogata coast facing the Japan Sea. To establish a principal methodology for beach stabilization, large scale coastal behavior first is investigated by constructing a long-term shoreline change model in which the representative monsoon wave is introduced. Comparison of hindcast and actual long-term shoreline change shows that the proposed model can predict long-term shoreline change. Shoreline change after the construction of Naoetsu harbor also was predicted under the condition that natural sandy beaches had been retained. Results show that shoreline retreat is severe near the harbor and extends to the central part of the coast. To determine the most suitable location for headlands to be used for stabilizing the coast, long-term shoreline changes were calculated under the condition that a headland is given at several locations. We conclude that in principle when the boundary condition for shoreline change by headland is given near the Shinbori River, a sandy beach tends to have stable large scale coastal behavior during long-term shoreline change. We propose a principal methodology for beach stabilization, part of which is being used in current construction.

Phuket is a well-known island resort on the west coast of the peninsula of Thailand and it is rich in tin deposits. Tourist and tin mining are conflicting especially in Bang Tao Bay. Before offshore tin mining in the bay, the bathymetry is quite simple/natural and the bay is almost in equilibrium with offshore sand movement by storm waves and onshore sand movement by swell. After tin mining in 1987, people in Villages 4 and 5 sent a petition to district and city officers from May to June 1988 to the effect that offshore tin mining in the bay had caused beach erosion and road damage, and that the dredger owner should be responsible for the cost of repairs. The sounding map makes in this study reveals that deep holes are created by dredgers, those nearshore are found to interrupt the cyclic changes and sand movement on the beach that results in a permanent loss of sand into the dredged holes and causes shoreline erosion; the maximum erosion in the middle of the bay is 40 meters in the 3 years from 1987 to 1990. A field test during May to June 1991 confirms that the high rate of shoreline erosion is consistent with that found in large wave tank experiments. Offshore tin or sand mining should not be made in shallow water where sand is mobile. If offshore mining were allowed nearshore, conditions should be imposed so that the bathymetry in the vicinity of the offshore mining should not change significantly.

Characteristics of settling velocity of fine particles and movements and the mechanism of maintenance of the fluid mud layer under oscillatory flow are investigated to control the transport flux of suspended solids in estuaries and the coastal zone. Settling velocity of fine particles under oscillatory flow is reduced as a function of only the local concentration. Motion of fluid mud depends on shear stress acting on the interface between the overlying water layer and the fluid mud layer and the horizontal pressure gradient. Especially, the horizontal pressure gradient causes a phase lag between the overlying water layer and the fluid mud movements. Velocity profiles calculated by a linearized model agree well with the measured velocity profiles in spite of assuming the kinematic viscosity in the fluid mud layer to be homogeneous. The apparent viscosity in the fluid mud layer is approximately 200 times as large as that of pure water.

Impacts of the construction of large-scale port and harbor at open sandy beach on inhabitation of the Japanese surf clam (Spisula sachalinensis) have been studied. It has been found that the populations of the Japanese surf clam has been increasing with the extension of the breakwater since the start of the construction of Ishikari Bay New Port in 1972. A series of numerical simulation was carried out to estimate the changes over time in the currents distribution around Ishikari Bay New Port associated with the construction of the breakwater for each construction phase. The change in dominant areas of the Japanese surf clam in the harbor over the years is explained by patterns of nearshore currents around the port. The construction of Ishikari Bay New Port resulted in the formation of a new fishing ground of the Japanese surf clam and an increase in the populations of the clams.

This study utilizes a multi-dimensional hydrodynamics model originally developed by Sheng (1989) and later modified by Sheng et.al (1992) to first quantify the flow field in Little Sarasota Bay in Florida, USA with a closed (present condition) and an opened (proposed condition) Midnight Pass, and then to produce a closure curve of the Midnight Pass. This study demonstrates that robust multi-dimensional hydrodynamics models can be used to provide more quantitative analysis of tidal inlet stability.

The field data analyses and both two dimensional hydraulic and numerical experiments were performed to understand the physical features of the 'A-oshio' appearance in Tokyo Bay. Lots of field observations show that the 'A-oshio' phenomenon may be intimately related with the upwelling of the anoxic water in the bottom layer under the wind blowing towards off-shore for more than a couple of days. Therefore, the two-dimensional hydraulic and numerical experiments are performed for clarifying the wind-induced upwelling and mixing processes in a two-layered stratified flow system with a downstream open boundary, which is exposed to wind stresses at the water surface. In these experiments, the upwelling phenomena are found to occur only in the range of Ri_*×(2h₁/L) ≤ 12.0. The numerical experiments are quantitatively confirmed to show a good agreement with the results of field observation and hydraulic experiments.

Trends established for ten Polish tide gauge stations show the annual mean sea level (AMSL) growth rate from 0.8 to 2.9 mm per year in recent 35 years, and a linear trend computed for the years 1901-1990 yields some 1.2-1.6±0.2 mm/yr. Annual SL maxima (ASLM) trends are about one-half of the ASLM trends. Positive 6-hr SL increments Δh from storm events show a growing trend associated with 'storminess'.

In the 'retreat' option for Polish coast, the impact zones between contour lines 0-0.3 m, 0.3-1 m, and 1-2.5 m cover respectively 845, 883 and 476 km², thus 2204 km² in total, in addition to 30 km² of beaches and dunes likely to disappear for ASLR2. Described by Zeidler (1992) are various 'full protection' techniques adopted.

The Baltic atmospheric circulation is found to change as to direction but not as to wind speed. Subsequent (Fig. 9) insignificant changes in the net sediment transport, in the order of 15% per century are noted. Hence the coast evolution due to climatic changes in wind circulation patterns seems less important than the anticipated sea level rise induced changes.

Due to the construction of fishery harbors up coast, severe beach erosion has taken place on the Amanohashidate Coast of Japan, a typical sand spit, resulting in such a reduction of the sand spit that countermeasures have had to be taken. The sand bypass method recently has been used to stabilize the sandy beaches on this spit. Annual change in the configuration of a sandy beach formed between groins first is considered in relation to erosion countermeasures and the sand volume by passed. We found that the sandy beaches along the Amanohashidate Coast are being formed with little fluctuation at what approaches the stable condition. On the basis of the theoretical background of the formation of stable sandy beaches (Tsuchiya et al.,1993; Tsuchiya, 1994), a satisfactory comparison of the actual and theoretical shoreline configurations was made.

Next, alongshore change in the longshore sediment transport rate was investigated in relation to the sand volume nourished and bypassed. We found that when the sandy beaches formed between groins have nearly reached the stable condition, the relation between the longshore sediment transport rate and wave energy power results in an estimated necessary sand volume to be bypassed of 5,000m³/yr. We conclude that in the case of the Amanohashidate Coast, the use of sand bypassing could well form a series of dynamically stable sandy beaches between groins, the sand volume required for bypassing being only 5,000m³/yr.

Folly Beach is an island, nearly 10 km long, south of the entrance to Charleston Harbor. A large beach nourishment plan was planned and conducted to counter the large erosion rates the Island has suffered for several decades. Because of the limitation on operations dictated by the turtle nesting season in the local area, it was required that all construction be completed in one season and extending from November 1 until May 15, 1993. During the construction of the Project, which included 1,908,000 m³ of material, two very significant winter storms caused some loss of material to the offshore and some damage to the pipeline system. The majority of the material moved by the storm has either migrated back onto the beach or stabilized in a lower part of the subaqueous profile. The success of the first phase of construction of this 50 year project is in many ways attributed to the excellent working relationship between the City of Folly Beach, the Charleston District of the Corps of Engineers and the contractor. The long term success of the project will depend upon the frequency and severity of the storms which attack the project.

This paper describes several results on beach nourishment and harbour management interaction, within the authors' area of responsibility. These positive results show the socio-economic benefits which can be achieved through effectively combining harbour and coastal requirements.

During the past five years an extensive program of field measurements has been carried out to evaluate the effects of wave impacts on the Eastern Scheldt Barrier in the Netherlands, under operational conditions. High impact pressures were measured. The evaluation of the measurements shows that these high pressures affect only a small area simultaneously.

Today the Weser Estuary (Unterweser) is one of the most regulated rivers in Europe. It connects the harbour of Bremen with the Southern North Sea (German Bight) and is used by ocean-going ships. The first substantial deepening was done during the last decade of the 19th century. As the vessels became larger, the river has been deepened and widened for several times. The sequence of engineering works changed drastically the hydrological, morphological and ecological conditions within the Unterweser. The tidal water levels and the salinity had been measured since the beginning as part of an extended interdisziplinary monitoring program providing sound data over one century. These data are a valuable base to investigate the impact of the regulation works on the natural ecosystems of the coastal environment and on demands of the society, such as flood protection, irrigation, drainage. New questions arise from the vision, that impacts might be amplified by global climate changes.