Coastal Engineering 1986

The frequency spectra of wind-driven waves observed during JONSWAP are re-analyzed to establish whether the Toba formulation for the high-frequency tail (^~f^-4) fits the data better than the Phillips formulation (^~f^-5) used originally in the JONSWAP project. The results indicate that the f^-4-tail provides a better fit to the observed spectra. The proportionality factor in Toba's spectrum, which is theoretically expected to be a universal constant, is found to be uncorrelated with the growth stage of the waves.

This paper presents comparisons between physical and numerical model reproductions on the basis of comprehensive wave disturbance studies of a major Spanish port.

Mathematical modelling has reached in many cases a degree of reliability comparable to that of a physical model, but it is essential that both types of modelling systems are validated against measurements.

The paper discusses the long-term statistical properties of ocean and coastal wave climates derived from the analysis of instrumental wave data. The aim of the work reported has been to determine the theoretical distributions, from those commonly used in analysis of wave data, which best describe the joint probability of significant wave height, Hs and mean zero-upcrossing period, Tz. A method of modelling the wave climate in this manner has been developed utilizing parametric means of specification. The data base used in the study covers records from 18 sites around the British Isles.

A two dimensional numerical longwave model using an appropriate open sea boundary condition has been developed. The use of the open-sea boundary condition makes it possible to simulate longwave propagation using a smaller region without covering the entire ocean. The numerical model is used to predict the arrival time of tsunamis resulting from the 1964 Alaskan earthquake at various stations with reasonable success.

A two-dimensional numerical model of the Yellow Sea has been used to compute cotidal and coamplitude charts and harmonic constants of tidal currents for the four major tidal constituents M₂, S₂, K_l, O_l tides in the region with the mesh resolution of 1/5 degree latitude by 1/4 degree longitude finite difference grid system. An additional model incorporating dynamical grid nesting procedure which employs a one-third grid refinement scheme was also used to reproduce the M₂ tidal regime in more detailed resolution for the part of west coast of Korea where extensive coastal development including potential tidal power and land reclamation scheme is concerned. Comparisons between observations and model result have been carried out based on coastal gauges and moored current meter data. Reasonable agreement was found between observations and model results, thus supporting the computed distribution of tides in the region. It was also shown that the dynamically linkaged model particularly well within 5% in amplitude and 5 degrees in phase of observed M₂ tide in the refined mesh region of the west coast of Korea.

A simple model is presented for steady current profiles in the presence of waves. The current reduction and apparent roughness increase caused by the waves are shown to depend mainly on one dimensionless parameter ũ*/ū* i. e. the ratio between the friction velocity amplitude due to the waves and the time averaged friction velocity. The model recognises the need to apply different eddy viscosities to different flow components. Also, the thickness of the wave influenced layer near the bed is comceptually separated from the vertical scale of the wave boundary layer.

The paper deals with measurements of horizontal orbital velocities near the surface of mechanically generated waves in a wave flume.

Due to the characteristics of most velocity probes, it is difficult or impossible to measure with a fixed probe in the area above the lowest trough. As the probe is not submerged continuously, failures or uncertainties in the measurements may occur.

To overcome these limitations, a movable frame for the velocity probe was designed, which can be moved vertically up and down with the surface elevation by a disc rotor servo motor, controlled by a wave gauge. By that continuously velocities up to 3 cm below the surface could be measured.

Theoretical velocities have been calculated for comparison with different simulation methods for irregular waves, based on linear wave theory.

Based on a previous study by the authors of regular breaking waves in the surf zone, a model for random wave transformation across the nearshore region is developed. The results of a laboratory investigation of the effect of a steady opposing current on the wave decay process are presented and a proposed governing equation verified. Surf beat effects on wave transformation are then included in the model by representing the long wave as a temporally and spatially-varying current and mean water level. The concept of an equivalent water depth, which contains the effect of the current, is introduced and then included in a stochastic form in the random wave model. Surf beat is found to noticeably increase the decay of the root mean square wave height, especially in the inner surf where the beat is strongest. Comparison of the models to two field data sets show very good agreement for Hotta and Mizuguchi (1980), but rather poor for Thornton and Guza (1983). Possible explanations for the unexpected behavior of the second data set, pertaining to filtering, are discussed. Finally, a possible explanation for the dependence of random wave decay on deepwater steepness, noted by Battjes and Stive (1985), is presented.

A new numerical technique for solution to transient linear long wave induced oscillations is introduced. It is based on the boundary element method, which is well recognized by its numerical efficiency and convenience. Several harbor models are investigated. Advantages of the proposed method as compared to the existing techniques are discussed.

Potential inconsistencies in the predictions of long term wave heights can be experienced as a result of different methods of analysis possible when using directional wave data. This paper attempts to illustrate some of them. It involves analysis of two sets of directional wave data – one from a coastal location in the Irish Sea and another from an offshore location in the North Sea. An attempt is made to eliminate the discrepancies between the long term return-value wave height predictions based upon the conditional height distributions associated with different direction sectors and those derived from the omni-directional data set.

Nonlinearities (wave-wave interactions) play a vital role in many aspects of nearshore dynamics, such as wave shoaling and breaking, wave forces, wave-current interactions, radiation stress effects, and sediment transport. The importance of nonlinearities in the nearshore region cannot be overemphasized. At present, however, there is no wave theory that adequately accounts for these interactions, and field observations are sparse. Herein, the bispectrum is used to investigate the temporal and spatial variation of wave-wave interactions in cross-shore velocity for shoaling surface gravity waves in several nearshore environments. The implications for sediment movement of the sign of the observed wavewave interactions for both the real part of the velocity bispectrum (which is related to the skewness of the horizontal asymmetry) and the imaginary part of the velocity bispectrum (which is related to the skewness of the temporal derivative) are discussed. A parameterization is given for the amplitude and phase evolution of the self-self sum interactions within the wind-wave peak for both planar and barred nearshore topography. The results of this paper underline the potential importance of infragravity wave energy in determining nearshore morphology.

Accurate numerical computations of wave trains with small modulations that grow are described. The range of wave steepness and modulation lengths that give breaking waves are determined. The number of wave crests is reduced for a time at greatest modulation but frequency downshifting is not observed. Near-breaking wave-group structure is always similar, with energy concentrated into one or two wavelengths.

The paper gives details of a two-dimensional depth averaged nested numerical model and its application to a range of idealised rectangular harbours, having a constant plan cross-sectional area and varying length to breadth ratios. The main aims of the study have been to investigate the problems associated with nested numerical modelling and to apply this modelling approach to assess the influence of the shape of a harbour on its natural tidal flushing efficiency and mixing characteristics.

A different approach to the solution of water wave problems is considered. Instead of using an approximate wave theory combined with highly accurate global spatial approximation methods, as for example in many applications of linear wave theory, a method is developed which uses local polynomial approximation combined with the full nonlinear equations. The method is applied to the problem of inferring wave properties from the record of a pressure transducer, and is found to be capable of high accuracy for waves which are not too short, even for large amplitude waves. The general approach of polynomial approximation is well suited to problems of a rather more general nature, especially where the geometry is at all complicated. It may prove useful in other areas, such as the nonlinear interaction of long waves, shoaling of waves, and in three dimensional problems, such as nonlinear wave refraction and diffraction.

Uncertainty about kinematics in the crests of high waves has prevented random wave simulation from being accepted as a reliable method for computing wave forces for platform design. A theoretically defensible method of calculation for wave crest kinematics has been developed recently. The method produces a potential function which fits the kinematic boundary condition specified by second order wave theory and is thus named the Kinematic Boundary Condition Fitting (KBCF) method. KBCF agreed well with measurements of mechanically generated irregular waves made by a laser Doppler current meter in a wave tank. In order to obtain further data during high, short crested storm waves, instruments for the Fulmar Wave Crest Kinematics (FULWACK) experiment were installed in the North Sea early in November 1981. During a storm later in that month, good velocity measurements at heights up to 25 feet above mean water level were obtained in over 30 waves. For comparison with this data, KBCF was extended to three dimensions. Statistics of the velocities thus simulated agreed well with statistics of the measurements. KBCF has thus been verified as a accurate method for simulating the kinematics of natural storm waves.

Of the more than 90 tide gage records in the Mediterranean, 10 representative gages were analyzed for indications of sea level rise (SLR). No definitive trend of regional sea level rise has been discerned for this area. The lack of SLR may be partially attributed to local effects on sea level such as seasonal water temperature and wind differences, and to local tectonics. The extent of these seasonal changes is in the order of tens of cms/year, and varies greatly from year to year, probably masking the trends of long-term SLR of mm/yr.

According to Brink-Kjaer et al.'s discussion(1984), the expression of the wave direction change velocity is modified in our numerical model for the directional wave spectra change due to current-depth refraction (Sakai et al., 1983). The wave reflection and breaking conditions due to current are discussed from a view point of numerical analysis. Effects of the refraction term in the modified wave action equation on the directional spectra change are examined. The relative importance of current and water depth change in the directional spectra change is also examined.

Prior to the investigation of rough turbulent boundary layer in a short-crested wave, the oscillatory laminar boundary layer at the bed is considered. Supported by numerical results of water-particle motions close to the bottom, the general patterns of kinematics in the laminar boundary layer within this wave system are reported in order to promote the understanding of the complex phenomenon. To propose a suitable method for turbulent boundary layer within such a wave system, a two-layer model using time-independent viscosity coefficient is first studied. Potential application of this model to short-crested waves is considered. From numerical results it is found that the time-invariant viscosity model is useful but can not produce velocity profile with flow reversal. It is suggested that a time-varying viscosity model may be more appropriate.

On the basis of a parametric model of wind stress (drag) coefficient over water surfaces and related experiments, objective procedures to obtain this coefficient under variable wind and wave conditions are outlined and recommended for oceanographic applications and air-sea interaction studies. Methods for both fully and non-fully developed sea conditions are given.

In order to understand the characteristics of tidal elevation changes along the western coastaline of Taiwan, the authors collected the tidal records at the same duration from eleven stations and made an elaborate analysis in this paper.

First step, the main tidal constituents were picked out from spectrum analysis, and the amplitudes and phase angles of these tidal constituents would be obtained by harmonic analysis. Then thevariations of amplitude and phase lag of the main constituents and the variations of mean high water level and mean low water level along the coastline would be presented in the figures respectively. Finally, based on the results of harmonic analysis, the energy density of tide for every station could be calculated separately, and the location of the maximum energy density would be determined by cubic spline method.

The parabolic equation method has been extensively used for combined refraction and diffraction problems of water waves. However, a parabolic equation is valid only when the direction of wave propagation nearly coincides with that of a coordinate; therefore, the validity ranges of the parabolic equations developed so far are restricted.

In order to achieve a wide range of validity, a parabolic equation is derived in this paper by employing a curvilinear coordinate system which has a pattern similar to that of wave rays and fronts. A computer program which is applicable to an arbitrary arrangement of coastal structures is then developed.

Results of numerical calculations are compared with available analytical solutions and laboratory data. It is proved that the present parabolic equation has a high accuracy for a wide range of incident wave direction and structure arrangement.

This paper deals with the breaker height on non-uniformly sloping beaches. A large number of experiments were carried out to obtain a breaking criterion on bar and step-type beaches. Based on the experimental data, a relationship among the breaker height, water depth, and wave period is investigated for various bottom configurations. As a result, the breaker height on non-uniformly sloping beaches is found to be well predicted by substituting an equivalent bottom slope in Goda’s breaker index which has been obtained for uniformly sloping beaches. The equivalent bottom slope is defined as the mean slope in the distance of 5h_B offshoreward from a breaking point, where h_B denotes the water depth at the breaking point. The method for calculating the breaker height on natural beaches is also presented.

Due to the special bathymetry in Taiwan Strait, the waves off the western coast of Taiwan are considered to be composed of two-source wave system. One propagates from the central part of the Strait named main wave, and the other is generated by the local wind known as local wave which occurs along the shore. After the combination and the transformation procedure from these two-nonlinear-source wave system, the wave height distribution in Taiwan Strait should be modified. A comparison of the wave height distributions based on the present proposed method with the field data indicates that the present method yields a better result than other theorems. Furthermore, the result of application of two non-linear wave theorem to wave prediction are also presented.

In 1976 the Belgian Government decided to enlarge the harbour of Zeebrugge and to execute an artificial beach renourishment on the beaches at Knokke-Heist. A comprehensive survey program along the 24 km coastline was conceived using remote sensing techniques. This enabled correct momentary recordings of the beach areas, the production of differential charts and calculations of dune and beach volumes. However, the observations of the nearshore and offshore areas from ordinary survey vessels take too long so that no accurate momentary recordings of the seabottom topography can be achieved. On these grounds, in 1983, the Belgian Authorities have instructed the Eurosense Belfotop Company to develop an effective measuring method based on the use of a hovercraft.

This hovercraft platform, named "BEASAC" and designed for hydrographic surveys, is now used for monitoring the coastal morphology and the dredging activities in the access channels to the major Belgian seaports. On the basis of the "Beasac"-soundings of the nearshore area and the aerial remote sensing data of the beach, charts and differential charts of the combined beach and nearshore area are produced.

The results of this technique are very promising and will be incorporated in the further survey programs ordered by the Belgian Authorities as a substitute for the classic bathymetric vessel soundings.

This paper investigates the utility of winds obtainable from a numerical weather prediction model for driving a spectral ocean-wave model in an operational mode. Wind inputs for two operational spectral wave models were analyzed with respect to observed winds at three locations in the Canadian east coast offshore. Also, significant wave heights obtainable from the two spectral models were evaluated against measured wave data at these locations. Based on this analysis, the importance of appropriate wind specification for operational wave analysis and forecasting is demonstrated.

The lateral mixing coefficient, in which the wave energy dissipation by wave breaking is taken account and the assumption of Richardson's 4/3 power law is involved, is derived for the surf zone and the diffusion of tracers injected in the wave-current interaction region is discussed experimentally to investigate the proposed lateral mixing coefficient. Furthermore measurements of velocity field on the three dimensional sloping beach of plane wave flume have been made by a bidirectional electromagnetic current meter. The results were used to investigate the characteristics of the structure of on-offshore and alongshore mean currents and the techniques for the determination of wave angle in the surf zone.

A weakly nonlinear solution is presented for the two-dimensional wave kinematics forced by a generic wavemaker of variable-draft. The solution is valid for both piston and hinged wavemakers of variabledraft that may be double articulated. The second-order propagating waves generated by a planar wave board are composed of two components; viz., a Stokes second-order wave and a second-harmonic wave forced by the wavemaker which travels at a different speed. A previously neglected time-independent solution that is required to satisfy a kinematic boundary condition on the wavemaker as well as a mixed boundary condition on the free surface is included for the first time. A component of the time-independent solution is found to accurately estimate the mean return current (correct to second-order) in a closed wave flume. This mean return current is usually estimated from kinematic considerations by a conservation of mass principle

This paper deals with a new method to decompose incident and reflected waves from the measured data of irregular standing waves. The theory by Goda et al. is extended to cope with the reflection from such a coastal structure that has a sloping surface and brings about different reflection coefficient for each incident waves. Irregular standing waves are decomposed into incident and reflected irregular waves by the shortterm wave spectrum analysis method. And the reflection coefficient of the approximated zero-up-cross waves are defined as the ratio between envelopes of these irregular wave profiles. The calculated reflection coefficients can be discussed in terms of the incident zero-up-cross wave parameters such as a wave steepness, Ursell parameter, etc. An effective wave gauge system to measure irregular standing waves which have a wide band spectrum is also discussed and a method to compose the system is proposed.

Large-angle parabolic equation methods for the propagation of surface water waves are discussed. The methods described here are limited to forms which are solvable by the Crank-Nicolson method, but are successful in opening the allowed range of propagation directions to ^~50° with respect to normal incidence.

This paper is intended to propose a simple, yet highly reliable approximate method which uses a modified transfer function in order to evaluate the water particle velocity of finite amplitude waves at shallow water depth in regular and irregular wave environments. Using Dean's stream function theory, the linear function is modified so as to include the nonlinear effect of finite amplitude wave. The approximate method proposed here employs the modified transfer function. Laboratory experiments have been carried out to examine the validity of the proposed method. The approximate method is shown to estimate well the experimental values, as accurately as Dean's stream function method, although its calculation procedure is much simpler than that of Dean's method.

In this paper, to the third approximation, we used the Fourier-stieltjes integral rather than Fourier coefficient to develop a weakly nonlinear theory. From the theory, the nonlinear spectral components for water particle velocity and wave pressure can be calculated diretly from the directional spectrum of water surface displacement. Computed results based on the nonlinear theory were compared with that of experiment made by Anastasiou (1982). Furthermore, in accordance with the different characteristics of wave properties, such as wave steepness, water depth and so on, the nonlinear effects on wave kinematic and pressure properties were extensively investigated by using some standard power spectra.

Large scale ocean currents, such as the Gulf Stream, Kuroshlo, Peru Current, Agulhaus Current, etc., strongly modify the surrounding wave characteristics. As the Gulf Stream moves along the Continental Shelf of the southeast coast of the United States, the local ocean environment is divided into three wave climatic regimes. They are the offshore, the Gulf Stream, and the nearshore regimes. The nearshore zone is bounded by the land to the west and the Gulf Stream to the east. The distance between land and the Gulf Stream varies from 10 to 60 miles. Most of the waves in this regime are generated offshore and cross the Gulf Stream. The correlation of local wind and waves in the nearshore regime is poor except in the presence of a persistent onshore storm.

A semi-empirical approach has been developed to compute the nearshore wave climate. The hindcast/forecast directional waves from the Spectral Ocean Wave Model (SOWM) of the Navy Fleet Numerical Oceanography Center have been used as the source of the initial offshore wave conditions. After crossing the Gulf Stream, which is assumed to be a uniform current with a velocity of 2 m/s, the waves are either refracted to the nearshore regime or reflected to the offshore regime following ray theory. The onshore waves in the nearshore zone are confined to the sector from 30 to 150 degrees. The computed results are then compared with measured data with good agreement.

In summary, the Gulf Stream acts as a barrier to damp long waves and to regroup short waves. The refraction of long waves can be predicted by using ray theory. Further field experiments are needed to quantify the variation of the Gulf Stream and to investigate the interaction with approaching long waves and local wind generated short waves.

For the practical application in coastal engineering, the universal model of water wave, momentum conservation and energy conservation equation with considering of energy loss due to bottom friction and wave breaking is adopted in this paper to evaluate the wave transformation on general slope, which including wave shoaling, breaking and attenuation after breaking as well as wave set-up and set-down during the waves advancing toward the coast.

In comparison with the results of theoretical approaches as well as experimental data accomplished by the traditional method, very good coincidence is obtained besides the mean sea level variation.

Data from a low energy swell-dominated surf zone are examined for indications that observed low frequency motions are simply group-forced bounded long waves. Time series of wave amplitude are compared to filtered long wave records through cross-spectral and cross-correlation analysis. These methods are found to have limited usefulness until long waves are separated into seaward and shoreward components. Then a clear picture of a rapidly shoaling bounded long wave emerges, with a minimum of nearly one fourth of the long wave amplitude being explainable by this type of motion close to shore. Through the zone in which waves were breaking, and incident wave amplitude variability decreased by 50%, the contribution from the bounded long wave continued to increase at a rate much greater than a simple shoaling effect. Also present are clear signs that this amplified bounded long wave is reflected from a position close to the shoreline, and is thus released from wave groups as a free, offshore-progressive wave.

The Wave Climate Synthesis method, which derives long-term wave statistics from long-term wind statistics directly, is tested with four years of wind and wave measurements recorded from eight NOMAD buoys in the Great Lakes during 1981-1984. The results show that it is an excellent method for estimating long-term wave statistics and design wave height. While the method is by no means intended to replace wave hindcasting procedures, it is shown to be a useful additional tool for the coastal engineer.

A numerical solution to periodic nonlinear irrotational surface gravity waves on a horizontal sea floor is developed using an iterative Boundary Integral Equation Method (BIEM). This solution technique is subsequently applied to determine the characteristics of limit waves for which the wave crest theoretically ceases to be rounded and become angled with an included angle of 120 degrees.

The construction of marine works necessitates a good knowledge of the extreme events which can affect it, such as the storm waves or the water levels. A statistical method of estimation of these extreme events has been developped at L.N.H. The principle of this method, based on the theory of renewal processes, is presented hereafter, as well as the results that it can provide. Some applications of the method are described in the paper ; in particular the application to a site where the available data are insufficient, and where the method enables to precise the results by using complementary numerous data on a neighbouring site, is presented.

This paper discusses wave grouping of wind waves from the physical viewpoint of wave modulational instability. Amplitude modulation periods obtained from the smoothed instantaneous wave energy history (SIWEH) of the observed data are compared with the predicted values by the modulational instability theory using the Zakharov equation for a finite constant water depth derived by Stiassnie and Shemer (1984). The modulation period normalized by the typical wave period corresponds to the length of total run. It is shown that the amplitude modulation periods of the observed data agree satisfactorily with the predicted values. Thus we conclude that the modulational instability is a hydrodynamical cause of grouping of high waves.

The growth of water waves by turbulent wind is studied on the basis of typical results of recent studies. It is shown that the energy input from wind to a spectral component is not much affected by the existence of the other spectral components, and the dimensionless growth rate β/f is uniquely determined by u_*/c if the friction velocity u_* measured over the water surface is used for the analysis. It is also shown that steep monochromatic waves without wind action show very complicated spectrum, but, under the wind action, they tend to be a continuous spectrum which has a spectral peak near the frequency of the lower side band and satisfy the 3/2 power law.

Data are presented for ship waves generated and measured in deep water. Results show the variation of maximum vessel waves with both vessel speed and distance from the vessel sailing line. Three automobile ferries of different configurations were tested. Field test procedures, limitations, and problems are described.

This study is concerned with the operation of spectral wind wave models. Many spectral wind wave models use a growth mechanism which operates on the point spectrum with directionality being introduced after the fact by the use of a spreading function. It is recognized here that this approach leads to errors whenever the wind and wave fields are not aligned. This is demonstrated by comparing the performance of two first generation models under various conditions. One makes use of a point spectral growth mechanism and follows the operation of the Spectral Ocean Wave Model (SOWM). The other uses a directional growth mechanism but is otherwise the same as the first. A large difference between the models is noted for swell corrupted seas.

The concept of local approximations via locally defined frequencies is introduced as a tool for dealing with irregular, non linear waves. Practical testing has been performed on the problem of estimating surface elevations from measured bottom pressures. In these tests the new method even in its simplest form proves more accurate than the linear spectral method. With respect to computational effort the new method requires orders of magnitude less than spectral methods, or wave by wave analysis of similar accuracy.

This paper presents the results of a study to statistically estimate the most severe sea state (significant wave height) expected in 50 and 100 years from analysis of data consisting of the largest significant wave height observed each day by applying the Type III asymptotic extreme value distribution. In applying the Type III asymptotic distribution, the distribution parameters are estimated by three different methods: the maximum likelihood method, the skewness method, and a nonlinear regression method. Since none of these methods estimates values of the parameters which satisfactorily yield a distribution representing well the daily maximum data, a modified Type III asymptotic distribution is newly developed in the present study. The modified distribution yields an excellent fit over the entire range of the cumulative distribution, and the probability density function agrees well with the histogram constructed from the data.

In order to clarify the characteristics of the velocity field in the surf zone, three sets of detailed and precise two dimensional laboratory experiments were performed. Spatial distributions and time histories of velocity were measured by using a hot film velocimeter with a split type probe or a two components laser doppler velocimeter for regular wave conditions. Typical plunging breakers were formed during the experiments. Based on the experimental results, a model was investigated in order to estimate the two dimensional distribution of the on-offshore steady current below the trough level.

Underwater shoals and spurs focus water waves that propagate over them. The normal theoretical approach to finding a more accurate solution of the linear equations is to interpret the envelope of crossing rays as a cusp of caustics (see Figure 1) and to use Pearcey’s function (Pearcey 1946). In practical cases the ray pattern is rarely sufficiently well defined to enable the cusp parameters to be deduced. An alternative approach is presented in which a length of wave crest heading towards the focussing region is approximated by an arc of a circle or parabola (Figure 2). Corresponding approximate solutions for linear and weakly nonlinear waves are described.

A model for wave height decay of a spilling breaker is proposed. The energy dissipation of a breaking wave is approximated by that of a propagating bore. In order to explain the gentle decay of spilling breaker at the initial stage, a development of a foam region, which indicates the amount of foam on the wave profile and determines the rate of energy dissipation, is considered. In addition to this formulation, the energy and momentum balance equations are described by a linear wave theory in shallow water and are simultaneously solved. Comparisons with experimental results show that the model gives a good prediction in both inner and outer regions, and that two coefficients in the present model are related to the deep water wave steepness and the slope of beaches.

Transformation of irregular waves affected by opposing currents on a sloping sea bed was discussed, experimentally and theoretically. It was found that representative values of wave height, such as a significant wave height, are larger before breaking and the wave height decaying occurs more promptly in a surf zone as opposing currents become dominant, and that characteristics of a irregular wave transformation are determined by the dimensionless unit width discharge q* and the deep water wave steepness. This means that the effects of opposing currents on irregular wave transformation are qualitatively identical to that on the regular waves.

A transformation model of irregular waves affected by opposing currents was presented. In the model, formulations for a regular wave transformation, in which the effects of opposing currents were taken into account, were applied to individual waves defined by zero-down-cross-method from irregular wave profiles.

Comparisons between experimental results and the prediction by the model showed that the present model gives a good explanation for wave height distributions and the experimental finding that the surf zone is moved offshore by opposing currents.

By a flow visualization of a plunging breaker on 1/20 slope beach in a wave tank, an existence of 2nd and 3rd horizontal vortices (Miller, 1976) and slanting vortex (Nadaoka et al. , 1986) is confirmed. A MAC method is applied to simulate a violent motion after an impinging of a jet from a crest of a plunging breaker on the trough surface. The calculated maximum water particle velocity in the jet is found to reach three times the linear long wave celerity. Values of circulation of the first four horizontal vortices are calculated and their changes in time are discussed.

AXCP data obtained during Hurricane Josephine in 1984 are analyzed in this paper. In addition, wind-driven currents at several XCP’s during Josephine are simulated using a one-dimensional ocean current model.

The complex envelope function is presented as the natural analysis technique for wave records where the identification of wave groups is a dominant interest. Algorithms have been developed and confirmed for separation of the complex envelope function, estimation of the dominant frequency and unwrapping of the phase function. Cross-correlograms and coherence spectra reveal a link between the envelope amplitude and phase traces that appears to be an intrinsic property of wave groups. Nevertheless, the majority of the information in typical wave records can be described as random, accounting for the relative success of the Gaussian random wave model.

We discuss statistics of wave groups containing the maximal wave height over wave records of 20 minutes. These wave groups are called extreme wave groups (EWGs). The concept of the EWG combines the two previously separately considered design factors of extreme waves and wave groups into a more severe storm seas wave action. The wave data used in this investigation consists of near 540 records of wave staff measurements in the Gulf of Mexico. Specifically, we shall present (a) the dependence of EWG properties on the bandwidth of wave spectra, (b) the mean envelope shape of EWGs, exhibiting distinct differences from the envelope shape of regular basis.

Different Methods have been developd to calculate the deformation of spectrum as waves advance to the shallow water. Wave ray method is a traditional way to compute the change of wave ray after refraction. It is restricted to the regular wave. After slicing the linear spectrum, a lot of components of spectrum can be gained, and each component can be considered as a monochromatic wave. And then after the deformed components are worked out at the same point in sea, a deformed spectrum in shallow water is gained by summing up them. Therefore the wave ray method could be extended to the irregular wave in ocean. In real bathymetry, the difficulty in applying such method is to solve the wave ray which must pass through the assigned point. In this paper, calculation approach as well as computer program are contrived to adopted in real bathymetry. The results of computation reveal some significant characteristics of directional spectra in shallow water. Furthermore, the statistical features of waves at the point of interest are to be evaluated.

The formulation for shallow water wave shoaling and refraction-diffraction given by Liu et al (1985) is extended to include reflected waves. The model is given in the form of coupled K-P equations for forward and backward propagation. Shoaling on a plane beach is studied using the forward-propagating model alone. Non-resonant reflection of a solitary wave from a slope and resonant reflection of periodic waves by sinusoidal bars are then studied.

Results are presented of experiments in a wave basin on the increase of the mean bottom frictional stress in a flow when a wave field is superimposed on a current. The bottom friction was derived from the mean water level measured at various places. Measurements of wave orbital and mean current velocities were done both with a micro-propeller and with a new type immersible Laser Doppler Anemometer.

The data indicate an increase of the mean bottom shear stress due to the presence of the waves, but less than predicted by Bijker (1967). A suggestion is made to improve the accuracy of this theory. The bottom stresses as predicted by Fredsøe (1984) are somewhat larger than the experimental results.

With the increasing development of coastal areas, it is necessary to have a sound method for predicting hurricane-induced flooding in these areas, especially for studies such as the coastal construction set-back line, flood insurance rate-making and county land use planning. The objective of this study is to develop the capability of describing the friction factor in coastal areas for improved representation in numerical models of storm surges.

Five types of areas are considered: A, ocean bottom with bed forms and some vegetation; B, mangrove fringes and areas; C, forested areas and cypress swamps; D, grassy areas and saltwater marshes; and E, developed residential and commercial areas. The friction factors, which incorporate both the bottom friction coefficient and drag coefficient due to the submerged parts of obstructions were verified by conducting laboratory experiments for mangrove and developed areas, using the typical distribution found in each of these coastal areas. The formulas of the friction factor for the ocean bottom, forested areas and grassy areas are determined by adopting results from previous investigations and discussed with the results of the current study.

A method is described for improving the accuracy of the wave predictions which are required for the operational guidance of the shipping traffic in approach channels to harbours and to support offshore activities. The method, as being described here, is based on the assimilation of wave physics and real-time hydrometeorological observations into a statistical time series model called ARMAX.

A numerical model of wave-Induced nearshore currents taking into account the finite amplitude effect is developed, with a cnoidal wave theory used for the estimation of wave characteristics. The model is applied to the computation of wave transformation and nearshore currentson uniformly sloping beaches and on two-dimensional model topographies. The comparison with the results obtained by a linear model shows that wave nonlinearity has a strong influence on wave transformation in shoaling water and in the surf zone and on the strength of nearshore circulation, but that it does not have much effect on the longshore current profile. Moreover, the validity of the present model is supported by the quantitative agreement with the experiment for wave height variations, and the qualitative correspondence with the experiment for mean water level variation and longshore currents and the observation for nearshore currents.

An approach, that treats natural sea states with remarkable groupiness as random sequences of envelope solitons, is suggested here to explain their dynamical and statistical properties from the viewpoint that wave packets contained in the states have their own characteristics and should be regarded as elementary modes. Some examinations are made on its applicability to the temporally observed waves. And the approach is shown to be effective also for waves with a non-zero nonlinearity and finite spectral band-width. Further, a formulation based on envelope solitons is made on the wave drifting force and is shown to be useful for analyzing the time series of drifting forces.

Using the laser-induced fluorescent method, the detailed transition process from bore to run-up mode is clarified experimentally. The transition process is found to be different from the previous predictions, and might provide an explanation for the discrepancies of the run-up height between the theory and laboratory measurements. Turbulence generated in a bore appears to be highly three-dimensional and sporadic. Turbulence generated close to the shore is advected with the bore-front motion and violent turbulent actions result during the transition from bore to run-up mode.

The sediment transport due to waves and currents depends on the distribution of sediment concentration and on the distribution of the velocity over the water depth. Our knowledge of both phenomena for practical applications is still rather poor. Some results of wave flume tests concerning the distribution of sediment concentrations due to wave action will be discussed. It turns out that the sediment size of the bottom material has a rather unexpected effect hereupon. With respect to the velocity distribution only some qualitative remarks can be made at the moment.

According to wave theories the depth limited wave height over a horizontal seabed has a wave height to water depth ratio (H/d) of about 0.8. Flume experiments with monochromatic waves over a horizontal seabed have failed to produce H/d ratios greater than 0.55. However designers still tend to use H/d 0.8 for their design waves. Experiments have been carried out using random wave trains in the flume over a horizontal seabed. These experiments have shown that the limiting H/d ratio of 0.55 applies equally well to random waves.

Changes in current properties due to wave superimposing are investigated experimentally. Variations of the mean water level gradient and the current velocity profile after wave superimposing are examined. Experimental results are discussed in relation to the energy conservation equation including the bottom friction term. It is found that changes in current properties can be well explained by increase in the time averaged bottom shear stress.

Two mathematical models for the simulation of the dynamics of sheetflow are presented, an analytical and a numerical one.

In the analytical model the theory of Bagnold (1954) is implemented: a constant ratio between shear stress and normal stresses is assumed. In the numerical model the motion of each layer of grains is considered separately; each layer exists of a rigid rectangular structure of spherical grains. Grain- grain interaction between the successive layers occurs in two ways: on one hand viscous interaction forces, comparable with squeezing forces in lubrication problems and on the other hand direct contact with elastic response when the distance between the grains becomes less than .01 of the grain diameter. When the relative motion of adjacent layers results into compression or dilatation, a resistant force analogous to the Darcy law is assumed.The numerical model has been combined with the turbulentboundary layer model of Bakker and v. Kesteren (1984).

Results of computations are compared with measurements of Bagnold (1954) and Horikawa et al (1982).

The analytical model predicted the concentration in the sheet flow layer and the intrusion depth rather well, where the numerical model gave reasonable results with respect to the velocity pattern above the sheetflow layer.

It is concluded, that up to now the more sophisticated assumptions of the numerical model do not lead as yet to higher accuracy with respect to the intrusion depth of the sheet flow, probably because the separation between sheet flow and the turbulent boundary layer above has been assumed too smooth.

Breaking waves undergo a transition from oscillatory, irrotational motion, to highly rotational (turbulent) motion with some particle translation. On plane or monotonically decreasing beach profiles, this physically takes place in such a way that the mean water level remains essentially constant within the transition region. Further shoreward a rapid set-up takes place within the inner, bore-like region. The new surf zone model of Svendsen (1984) begins at this transition point and the new wave there contains a trapped volume of water within the surface roller moving with the wave speed. This paper describes a simple model over the transition zone designed to match the Svendsen (1984) model at the end of the transition region. It uses a simple, linear growth model for the surface roller area development and semi-empirical model for the variation of the wave shape factor. Breaking wave type can vary from spilling through plunging as given by a surf similarity parameter.

The model calculates the wave height decrease and width of the transition region for all breaker types on plane or monotonically depth decreasing beaches.

A numerical model is developed which calculates the longshore current profile for an arbitrary bottom profile. The basis of the model is the use of radiation stress theory in a longshore momentum balance equation which includes a driving stress, a bottom stress, and a lateral mixing stress. Each of the stresses is derived from previously developed formulations, rederiving them to take into account separate cross shore variations in the wave height and the water depth, as well as the wave approach angle. This is done to dispense with the constant wave breaking index assumption used to model wave decay in the surf zone, which is rejected as unrealistic for natural beaches A numerical model is used to calculate distributions of the wave height and water depth across the surf zone for arbitrary, yet realistic, bottom profiles. A numerical model of the theoretically derived longshore momentum balance equation is developed and solved using the distributions obtained from the wave decay model. The profiles calculated are compared to previous theoretical models and to laboratory and field measurements.

Four types of sediment concentration under waves are discussed: (a) instantaneous, local, (b) time-averaged, local, (c) instantaneous, bed-averaged and (d) time and bed averaged. The first three mentioned are either hard to interpret or difficult to obtain experimentally. The time and bed averaged concentration is discussed in particular, both its interpretation and its measurement. Two features are discussed: the vertical concentration distribution and the bottom concentration.

The paper describes the application of two dimensional vertically integrated models (WAQUA system), the results being used for the calculation of sandlosses during sandfill closure operations.

Investigations with test models, physical scale models as well as numerical models, are presented to prove that the WAQUA system is not only suitable for large scale applications, but also for the simulation of detailed flow patterns.

Movements of borrow sand replenished at two coasts of different configurations are investigated by analyzing the topographic data which were surveyed periodically after the beach fill placements. One is a long straight beach and borrow sand was placed behind a submerged breakwater. Another is a pocket beach which has an arc-shoreline with a groyne at one end and a headland at another.

It is found that the amount of borrow sand moved in the longshore direction surpasses the amount of borrow sand transported in the cross-shore direction regardless of the shape of the coast. A clear correlation is also found between displacements of shoreline and changes of sectional areas. These results imply that the deformation of the artificially nourished beach and the dissipation rate of borrow sand can be predicted by the so-called one-line theory.

A theoretical model for the equilibrium dimensions of offshore sand waves is presented. The model is an adaptation of the dune model by Fredsøe (1982) to the marine environment, making use of the physical analogies between offshore sand waves and river dunes. The predicted sand wave heights and lengths conform well with the observations of sand wave formation reported in the literature. One of the results from the model is that for a given wave climate sand waves will only be formed under a certain range of mean current velocities. This range becomes narrower for increasing wave height or decreasing water depth and grain size.

Wave-induced currents and sediment concentrations in suspension across the surf zone were investigated at prototype scale in the BIG WAVE FLUME in Hannover for combined beach and dune profiles as well during the development phase until quasi-equilibrium stage as after beach equilibrium conditions had been reached. The selected initial profiles were partly investigated in repeated tests with regular and irregular waves. Based upon the obtained experimental data a comparison is presented between the measured and calculated landward displacement of sediment volume through a selected point on the beach into seaward areas. The discrepancies in between the results for measured profile change and for calculated sediment transport volume derived from vertical current and suspension distributions are discussed.

A large tidal flat area of about 40 tidal basins with catchment areas of between 10 and 790 km² exists along the coast of the German Bight. Not all of these tidal basins are morphologically stable.

The main parameter necessary for determining the state of equilibrium is the volumetric capacity of the concave portions of the tidal basin. In order to examine the equilibrium state it is necessary to compare the volumetric capacity of the tidal basin determined from hydrographic charts (measured volume) with a theoretical volume given by newly developed stability criteria representing averaged conditions (volume balances). Significant deviations between the theoretical and the measured volumes indicate a state of non-equilibrium.

Using stability criteria it is possible to desribe the state of equilibrium of a tidal basin in a stepwise manner either from the bottom of the tidal basin to the datum plane MHW in order to obtain a cross-sectional stability profile, or from the shore to the seaward boundary of the basin in order to obtain a longitudinal stability profile.

The applicability of the new method for analyzing the equilibrium of a tidal basin will be demonstrated by the example of the Suderau tidal basin in the north of Germany.

Recently, a depth and current refraction model has been developed for the computation of directionally spread, random wave propagation in coastal regions (Booij et al., 1985). For the verification of the performance of this model laboratory measurements in a directional, shallow water wave basin were conducted. Specific attention was given to the verification of the new features of the numerical model, viz. the effects of directional spreading and ambient current field on the wave propagation and transformation process, and the change of characteristic spectral wave frequency due to wave dissipation processes.

A series of field experiments was made to evaluate the use of a laboratory derived relationship between the force in the wave uprush and the erosion of beach dunes. Measurements of the swash velocity and height at the dune face were used to compute a specific force parameter. This force term was correlated with the specific erosion of the dune. A linear relationship similar to that found in the laboratory was determined with a R squared value of .87.

Analyses of sand samples collected along and across the Atlantic Ocean shore of Virginia Beach, Virginia, suggest that sand placed on the shore should have a minimum median diameter of 0. 20 mm to efficiently benefit the beach. Size analyses and shoreline change data show that the existing long-term beach replenishment by mechanical bypassing across Rudee Inlet and by truck-hauled sand from land sources is effective and necessary to maintain the shore along the commercial segment of Virginia Beach. The data also indicate that the northern segment of Virginia Beach shore, occupying more than half the distance between Rudee Inlet and Fort Story, is gaining sand. About two million cubic meters of sand to be dredged from the Atlantic Ocean Channel offshore of Virginia Beach will be suitable for placement on the beach.

Prior to construction at Fire Island Inlet, Fire Island was moving westward at more than 200 feet per year, the north shore of the inlet was eroding severely, and navigation in the inlet was difficult. The Federal Jetty, completed in 1941, and the sand dike, built in 1959, have halted the westward migration, eliminated the severe erosion, and partially improved navigation, with minimal maintenance or repair to the structures. There has been a large net accretion of sand east of the jetty and west of the dike, an unknown part of which is at the expense of shores to the west of the inlet. At the State Park on the south side of the inlet interior, erosion accelerated, probably because of the dike.

The middle and ocean segments of the 4750-foot Federal Jetty are now (1987) in good condition, although the design implies a stability coefficient for the quarrystone jetty head at time of construction that would now be considered risky. Stability has been promoted by a stone blanket under and east of the jetty, a thick stone apron seaward of the jetty, a low (8 feet MLW) crest, and armor stone that has been partially keyed in place. Damage due to scour, common at other single-jetty inlets, is absent here because longshore transport, which easily overtops the low crest, keeps the inlet channel away from the jetty. Although the two seaward segments of the jetty remain in good condition, the inshore segment of the jetty is in poor condition, despite its apparently sheltered location. The cumulative effects of waves, possibly channeled to the site along recurved spits during storms, have damaged 1200 feet, and tidal scour has destroyed about 230 feet. The damaged segment has a design cross section which is onefifth and one-twelfth the cross sections of the jetty trunk and head.

The dike was constructed with sand dredged from the inlet, and its seaward shore was later armored by dumped riprap. The dike moved the tidal channel away from the north shore, shifted the ocean entrance of the inlet eastward (against the direction of longshore transport), and shortened the distance to the ocean.

The results presented in this paper are from a series of experiments in a wave flume modelling the onshore-offshore water motions over a bar bottom profile.

In a true 3-dimensional natural situation the flow of water over the bar varies along the coast. In the experiments the flow of water over the bar is simulated by a controlled discharge through the flume.

A two-dimensional empirical eigenfunction model is proposed for the analysis and the prediction of beach profile change due to longshore and cross-shore sediment transports. Beach profile data from Redhill coast, Taiwan, measured every two months at 150 meters interval along the detached breakwaters are analyzed and the relative importance from two directions is investigated. Furthermore, by employing the method of Markov process and linear regression, a prediction model is formulated which takes into account the effect of breaking waves, bottom sediment and radiation stress of waves. This 2-D model is shown to be effective in the analysis and the prediction of beach changes near the coastal structures.

A time scale in the similarity of beach change between model and prototype in transitional beach processes from an initial even slope to an equilibrium is developed using a series of small- and large-scale experiments in which the experimental conditions were set up with the scale-model relationship by the authors (1984). The time scale is obtained empirically as a function of experimental scale. Applied the proposed time scale and the scale-model relationship to model experiments, similarity of morphological beach change such as shoreline change and relative breaker point was well reproduced within the allowable range of experimental error. A semi-theoretical time scale is obtained from the continuity equation, the sediment transport rate, and the scale-model relationship of equilibrium beach profile in two-dimensional beach change. The relation between experimental and semi-theoretical time scale is discussed.

This paper is aimed to investigate theoretically and experimentally the variations of the probability distribution and mean values of the run length and total run length of just breaking and broken waves in an irregular wave train on gentle slopes. The theoretical model developed here is shown to be valid for evaluating the lengths of runs of just and broken waves from deep water up to the shoreline.

In the present paper the vertical distribution of turbulent kinetic energy k under broken waves is calculated by application of a one-equation turbulence model. The contributions to the energy level originate partly from the production in the wave boundary layer, partly from the production in the roller. Further on, the findings for k are used to calculate the vertical distribution of suspended sediment in broken waves.

The fluorescent sand tracers are injected in a point in the surf zone. Core samples are taken from the sixteen points on the circumference with the time intervals of fifteen minutes for about five hours. At the same time, the horizontal two components of fluid velocities are measured at the injection point by using an electromagnetic currentmeter. The field observations have been carried out three times on two beaches facing to the Pacific Ocean. The relations between the local sand movements and the fluid dynamics are examined on the basis of the data obtained.

We performed experiments in the laboratory under controlled conditions in order to determine the applicability of a sub-sand filter system to the beach erosion control work. The filter system is used to control a flow condition at the sediment-fluid boundary. In the foreshore, it increases the inflowing velocity into the beach and thus results in increasing the threshold of beach sediment movement. The sub-sand filter system accelerates accretion of much beach sediment in the foreshore through the development of a berm under normal wave conditions. When wave conditions change from normal to stormy, it is also applicable to stabilize the beach profile, and thus decrease loss of beach sediment from the foreshore to the offshore.

A two dimensional model study, carried out for a structure in a flume using irregular waves, presents the problem of determining the relationship between the total incident wave energy attacking the structure and its response to that attack (displacements, forces, etc.) in various sea states, The total incident wave energy can be evaluated indirectly only, because the wave energy measured in the flume contains an extent of residual wave energy in addition to that generated by the wave machine. This residual energy consists of the re-reflected wave energy from the paddle of the wave machine, assuming the existence of quasi-stationary wave conditions in the flume. A method originally presented by Gravesen et al. (1974), was applied in this study to evaluate the total incident wave energy. In view of the results obtained by this method, a physically more sound refinement is proposed for the evaluation of the total incident wave energy (and characteristic wave height). Results of model tests were analyzed by the CAMERI refinement and compared with the Gravesen method and with a cross-spectral least squares method, separating incident and reflected wave spectra from wave spectra measured in the flume, Good agreement was found between the results obtained employing the CAMERI refinement and the cross-spectral least squares method, Advantages and drawbacks of these methods are indicated.

Offshore dredging has been taking place in the coast of the Genkai Sea, Japan, since the early 1970’s, which totaled more than 20 million cubic meters. In order to evaluate the impact of offshore dredging on shorelines as well as the adjacent sea bed, comprehensive coastal engineering studies were carried out over the last four years. The results obtained are not sufficient to establish a direct cause-andeffect relationship between offshore dredging and beach erosion; however, the correlation is sufficient to serve as a warning of a potentially serious problem. Moreover, the dredged holes above 30 meter depth are found to trap the sand from the neighboring bed, and considerable movement of sediment by wave action was observed above 35 meter depth. Thus, offshore mining that would minimize interruption of beach littoral system should be operated below 35 meter depth in the study area.

Small scale movable bed wave tank experiments were carried out according to undistorted Froude model laws with the sediment fall time, H/wT, as the governing parameter for scaling the model sediment. Four questions addressed in this study included: (a) the ability to reproduce larger scale model results for both erosional and accretive conditions, (b) the effects of more realistic concave upward initial beach profiles instead of the more usual planar initial slopes, (c) the criterion for onshore-offshore sediment transport, and (d) the capability of the model to simulate post-storm recovery.

Based on a comparison with large scale results of Saville (1957), it was found that the model provided good agreement for erosive conditions. For accretive conditions, the results were less conclusive although the general patterns of profile change were similar. The final beach profiles resulting from concave upward initial profiles were found to be substantially different from those for an initially planar profile. It appears that the initially planar profile unrealistically affects the breaker type and results in a more pronounced longshore bar and offshore slopes that are steeper than found in nature. Tests conducted to evaluate the criterion separating onshore-offshore transport suggested a higher value of the fall time parameter, H/wT, than was originally proposed by Dean (1973); this is interpreted to be due to scale effects in most of the model data used in the original development. Tests to simulate post-storm recovery were affected by the presence of “reflection bars” associated with a partial standing wave system. The reflection bars appear to strongly affect the sediment transport limiting the post-storm profile recovery. The most effective recovery was induced by continually changing wave conditions to maintain the wave breakpoint slightly landward of the bar crest.

Equations for wave kinematics and wave dynamics based on small amplitude wave theory have been used in the prediction of wave deformations and wave-indused currents. However, the applicability of the linear wave theory is questionable in a river mouth where forced wave breaking and strong wave-current interaction take place.

A numerical model based on the non-linear dispersive wave theory has been developed, the results by this model was compared with the values of the experiments and the linear theory. Wave transformations including shoaling, wave-current interaction and wave breaking by the model showed a good agreement with the experimental result. In the prediction of wave-induced currents, the excess momentum flux (Pxx) computed by the model has more reasonable value than the radiation stress ( Sxx) calculated by the small amplitude wave theory.

In order to investigate the mechanism by which turbidity currents cause sedimentation in closed-end channels such as pier slips or residential canals, a laboratory investigation using fine-grained sediments was carried out. Two similar flume systems were used, each consisting of a main channel carrying sediment-laden flow and an orthogonally placed closed-end channel with a gate at the entrance. Characteristics of the turbidity current and sediment deposition in the closed-end channel were investigated following gate opening. Behavioral similarities between turbidity current and non-settling gravity currents were observed. Several properties, e.g. suspension concentration, showed exponential-type decay with distance. The ratio of sediment settling velocity to the densimetric velocity was found to be a useful parameter for comparing different test results. A relationship for estimating the sediment influx through the entrance is presented.

The land reclamation of Lunwei subdistrict A in the development of Changhua Industrial Estate Project was commenced in May 1980. Fill sand was dredged by suction dredgers from borrow area and placed in the south and central parts of this subdistrict. Bamboo fence was used as sand retaining structure. In November, a new tidal channel occurred between two fill sand islands and across the head of seawall, it caused the increase of materials and the difficulty of construction of the seawall.

Closure of the tidal channel was completed by constructed a sand embankment dike with low cost materials such as; bamboo piles, bamboo mattress and sand bags.

A simple model to predict the longshore current velocity at the breaker line on a beach with oblique wave incidence, is presented. The model balances driving and resistance terms (gradients of radiation and turbulent Reynolds stresses and bottom friction) to get a general expression for the velocity. This equation shows explicitely the influence of Iribarren’s parameter on longshore current generation. It has been tested with field and laboratory data, obtaining a reasonable fit to measured values. The resulting (predictive) model is expected to be valid for any type of breakers though the calibration has been mainly done for spilling and plunging types, due to the scarcity of results for other breakers.

The purpose of this paper is to predict the physical and mechanical properties of deposits near the surface of the seabed by in-situ measurements of the wave-induced pore pressure.

First, the wave-induced pressure both at the surface of the seabed and inside the seabed are examined by frequency analysis, to clarify the propagation characteristics of pressure in the seabed.

Secondly, a theoretical equation which gives the relationship between pore pressure fluctuation and wave pressure fluctuation is proposed.

Thirdly, the porosity of the seabed is predicted by the propagating characteristics of the pore pressure within the seabed based on the results of both the model tests by wave tank and the field measurements of the wave-induced pore pressure.

Finally, by fitting the theoretical equation to the spectral ratio of the in-situ measured pore pressure fluctuation to wave pressure fluctuation, the bulk modulus of the seabed and the degree of saturation are predicted.

In the present study, effects of irregular waves on two-dimensional beach transformation and related phenomena were investigated through a series of laboratory experiments. Attempts were made to determine a representative wave of irregular wave trains which controlled individual phenomenon related to the two-dimensional beach profile change. It was found that the representative wave is different for each phenomenon. For the macroscopic beach profile change, it is the mean wave which represents whole incident waves. On the other hand, some of microscopic phenomena, such as initiation of sand movement and sand ripple formation, are controlled by larger waves in the wave train selectively, of which representative wave is the significant wave.

This paper describes a diamond mining operation on the west coast of Africa in Namibia (South West Africa, see Figures 1a and 1b), where a sea-wall of normal beach sand has been built out to a distance of more than 300 m seawards of the original coastline. The wall which runs alongshore is maintained in the high energy environment, which is characterized by northbound longshore transport rates, by means of artificial suppletion at a rate of up to and more than 300 000 m³/ month. Before embarking on the project the company had to be assured of the sand on the sand-wall; to allow completion of the project free of severe damage by wave action. This implied being able to predict the erosion rate of the sea-wall by the waves. The data set used consisted of wave measurements by Waverider and wave observations obtained from voluntary observing ships; aerial photographs at monthly intervals of the waterline in the study area; and soundings of the beach, sea-wall and nearshore topography by using a helicopter as a platform. Various methods of prediction and projection were used to quantify sediment movement

The automated measuring system Oortkaten (AMO) was established in order to determine the balance of suspended sediment and associated parameters. Morphological and velocity weighted averaged samples are taken using the newly developed MOSTRA-Method. This results in a cross-sectional average value.

Changes of wave climate due to breaking on a tidal inlet bar are investigated by analysis of field measurements prosecuted offshore and onshore of the bar. Quantitative results for wave height reduction, period and length transformation and energy dissipation are presented as well as a study considering the dominating breaking criterion.

This paper presents an overall numerical model for predicting beach profile changes due to waves. The local rate of net on/offshore sediment transport is empirically formulated as a function of the Ursell number and Hallermeier parameter. A sub-model of two-dimensional wave transformation includes the wave shoaling, breaking and damping in a surf zone. It is combined with another sub-model of beach profile change for the analyses of wave-profile interaction. The validity of the model is examined through hindcasting of profile changes observed in ordinary and prototype-scale flumes.

A study was recently undertaken to investigate sediment transport on a section of coastline where recreational beaches have experienced periodic erosion. Alongshore, onshore/offshore and aeolian sediment transport processes were investigated and quantitative transports predicted with the aid of calibration using surveys and aerial photographs. This paper describes the study and the recommendations proposed for beach quality improvements.

Mechanism of sand movement due to asymmetric oscillatory flows was investigated through experiments. Measurements of bed forms, suspended sand concentration and net sand transport rate were carried out by using an oscillatory flow tunnel. The process of entrainment and suspension of sand above asymmetric ripples was quantitatively described. The geometry of ripples and the net sand transport rate in regular and irregular flows were expressed in terms of hydraulic parameters characterizing the oscillatory flow. Two-dimensionality of ripples was found to be an important factor in the estimation of the net sand transport rate.

This paper presents a modeling approach aimed at soving a complete hierarchy of turbulent bottom boundary layers which are often encountered in practical coastal and oceanographic engineering problems. The practical problem is extremely complex due to the presence and interaction of competing processes. A comprehensive model is thus needed to first provide fundamental understanding of a variety of turbulent bottom boundary layers before any simple model for the complex problem can be meaningfully constructed. This paper presents a comprehensive second-order closure model of turbulent transport and in addition, discusses some applications of the model to wave boundary layer, wave-current boundary layer, sediment-laden boundary layer and two-dimensional boundary layer. Example is provided to show how such a comprehensive model may be used to guide the development of a simple model.

In the surf zone, the agitation of the bed materials by breaking waves is strong and the suspended sand concentration in the vicinity of the wave plunging point is extremely high. Sand movement in this region was observed and sand concentration was measured in a wave flume. The sand movement in the region was divided into the following two categories: 1) sand suspension due to the large vortex which is created by wave plunging, and 2) sand deposition under turbulent flow. The condition for exciting this suspension process was considered and the result was well explained by the two parameters which are the deep water wave steepness and the bottom slope. Then a numerical model of the sediment suspension process was formulated and the process was well simulated by the model.

Iwo-jima is a small isolated volcanic island located in the Pacific Ocean. Due to the continuous upheaval of the island, foreshore area of this island has been increasing since 1911.

Investigation is made to clarify the variation of the foreshore area of this island by analyzing the various field data obtained during the past three years.

Analyses reveal that the foreshore area is currently increasing at an approximate rate of 180,000 square meters per year due to the unusual upheaval of the island exceeding 45 centimeters per year although seasonal variation of the foreshore area reaches 300,000 square meters.

Reduction processes of the cross-sectional area at a river mouth were investigated on the basis of numerical simulations and field measurements, in order to predict the possibility of closing of the mouth of the Samegawa River, Fukushima, Japan. As a result, it was found that the decrease in tidal prism, induced by a reduction of the cross-sectional area, had an important effect on the closing of the river mouth. By considering this effect and estimating the sediment transport rate properly, a practical prediction model was successfully established for simulating the reduction processes of the cross-sectional area at the river mouth.

A model for cross-shore sediment transport due to random waves is described which adopts a vertically integrated transport description for sheetflow situations. The formulation of the transport as a function of the instantaneous velocity field is based on the approach of Bailard (1981). This approach assumes in essence that the instantaneous transport is proportional to some power of the instantaneous near-bottom velocity. Implementation of this transport description in a time-dependent model requires a formulation of the time-mean and some low order moments of the near-bottom velocity field. An initial formulation based on a monochromatic, second order Stokes wave representation is presented. The model is checked on the basis of both field and laboratory data. Some consequences for further study are indicated.

Field experiment of sand bypassing was conducted on the Shimoni — ikawa Coast in Toyama Bay. The materials of 5900 m³ dredged on the updrift coast of the harbor were thrown into behind the detached breakwater. After the nourishment detailed surveys of the bottom topography around the breakwaters, wave observations and tracer tests using colored concrete blocks were carried out in order to investigate the movement of the nourished sand. Temporal and spatial changes of the shoreline positions and the sectional area of the beach in the shoreward zone of the detached breakwater are examined. It is found through the field experiment that the materials nourished behind the detached breakwater were carried slowly in the longshore direction by the westward littoral drift, dominating on the coast, without the outflow of sand through the openings of the breakwaters. It is concluded that the detached breakwater is useful to control the on — offshore sand movement and to retain the sand behind the detached breakwater.

A two-dimensional model for waves and steady currents in the surf zone is developed. It is based on a depth integrated and time averaged version of the equations for the conservation of mass, momentum, and wave energy. A numerical solution is described based on a fourth order Runge-Kutta method. The solution yields the variation of wave height, set-up, and current in the surf zone, taking into account the mass flux in the waves.

In its general form any wave theory can be used for the wave properties. Specific results are given using the description for surf zone waves suggested by Svendsen (1984a), and in this form the model is used for the wave motion with a current on a beach with a longshore bar. Results for wave height and set-up are compared with measurements by Hansen & Svendsen (1986).

The rate of wind-driven sand movement in a dune field is an important parameter needed to establish management strategies for sand dune fields. Until recently not much attention has been given in engineering circles to the possible effect of wind-blown sand transport. However, there is a wealth of literature on the subject which goes back as far as 1936. A study of literature reveals that there are at least 16 formulae for the prediction of the aeolian transport rates which are readily available. This paper describes a technique which utilizes these 16 formulae in the most effective manner for predicting the best estimate of the potential wind-blown transport rate. Restrictions on the applicability of the method are discussed and fields for further research are recommended.

Monitoring of beach profiles was carried out during one-year period at two sites located 3 km apart along a Pacific beach, Japan. These two sites are composed of beach sand with different grain size: 0.76 mm and 0.26 mm. It was found that the shoreline did not move even in storm wave events at the site with 0.7 6-mm sand, where the “seesaw mode” profile change took place in the subaerial portion of the beach. It was also found that the shoreline was not always retreated by storm waves at the 0.26-mm sand site, where the “parallel mode” profile change dominated, at the time of presence of bars working as a submerged breakwater to protect the beach from erosion.

This paper reports numerical computations of fully rough turbulent boundary layers produced by first and second order Stokes waves. The computations are based on a mixing length turbulence closure and on a slightly more sophisticated turbulent kinetic energy closure. The first order results compare well with existing laboratory results. Reversal of the second order steady streaming under relatively long waves, which has been predicted analytically, is also predicted in the numerical results, The steady second order velocity field is found to become fully established only after a development time on the order of a few hundred wave periods. Both the first and second order results indicate that advection and diffusion of turbulent kinetic energy play a minor role in determining the Reynolds averaged velocity field.

A knowledge of sediment transport rates due to wave action is essential for an understanding of various coastal engineering problems. Many problems have to be resolved before successful measurement can be made for sediment transport rates due to waves.

Since gradients of sediment transport cause changes of beach morphology, the sediment transport rate outside breaker can be determined from measured beach changes. Measurements of ripple growth and migration yield their mathematical descriptions in the same manner as those of surface waves. Expressions of sediment transport rates are then derived.

It is found from the study that the sediment transport rates are strongly controlled by the rates of growth and migration of ripples.

Due to the sheltering effect of the Wai-San-Ding Sand Barrier, the hydraulic condition of the putia harbor site is quite favorable. Since the relatively well-protected location of the Putai harbor area with regard to both waves and wind, no special navigational problems have to be envisaged.

The wave energy of the Putai harbor site is computed from the measured waves by considering the refraction effect down to breaking line. As the lack of wave records, the wind speed is used by applying the regression equations among the wave height, period and wind speeds, and then compute the wave height and period for obtaining the breaking wave energy. Therefore the total breaking wave energy (Pl ) of the whole year along the Putai harbor coast is summated.

The littoral transport rate (Il ) is calculated from the mesh method by comparing the echo-sounding maps of two continuous different years. Therefore, the relationship of Pl and Il is correlated in the Putai harbor site.

The paper presents a mathematical model for describing wave climate and wave-induced nearshore circulations. The model accounts for current-depth refraction, diffraction, wave-induced currents, set-up and set-down, mixing processes and bottom friction effects on both waves and currents. The present model was tested against published experimental data on wave conditions within a model harbour and shown to give very good results for both wave and current fields. The importance of including processes such as advection, flooding and current-interaction in coastal models was demonstrated by comparing the numerical results without each process to the results from the complete scheme.

The interaction between the constituent models for waves, currents, sediment transport and bottom level changes in a class of compound 2DH mathematical models of transient sea bed evolutions in the coastal zone is investigated mathematically, using the theory of characteristics and a harmonic analysis technique. This leads to contrary indications as to the importance of including diffraction in the wave model and to the unambiguous conclusion that the bottom slope effect on the sediment transport is indespensable for the mathematical system to be inherently stable. This conclusion is shown to imply that depth-integrated current model are insufficient to describe the flow in this type of morphological computations for the nearshore zone or complex coastal areas.

More than 150 tests have been analyzed in order to describe the dynamically stable profiles of rock slopes and gravel beaches under wave attack. Relationships between profile parameters and boundary conditions have been established. These relationships have been used to develop a computer program. This program is able to predict the profiles of slopes with an arbitrary shape under varying wave conditions, such as those found in storm surges and during the tidal period.

Wave transmission across a submerged breakwater at Santa Monica, California, is examined through a three-dimensional model test. The results agree with empirical criteria previously proposed by Tanaka (1976).

A rational approach to the design of rubble mound breakwaters that incorporates both the hydraulic stability and the structural integrity of individual concrete armor units is presented. A key element of this improved design procedure is the development of instrumentation to measure loads occurring on armor units in a physical model of a breakwater. Numerical methods have been employed to determine stresses throughout the armor unit once the loads are known and interaction design curves were developed from measured data. These interaction curves provide a useful assessment of the structural integrity of the armor units. The curves clearly demonstrate the overall factor of safety associated with the armor unit and the expected mode of failure. Based on the results of this type of analysis, the cost effectiveness and safety associated with different design alternatives may be explored and a breakwater that is both hydraulically and structurally efficient may be designed.

The physics of scour around structures and especially underneath pipelines is discussed. It is demonstrated that a combination of current and waves with an equal bottom shear stress as a uniform current gives lower scour rates than a single current with the same bottom shear stress.

The principle of the performance of scale series is discussed and it is shown that this method has still some weak points.

This paper summarises many of the recent advances in the testing of rock quality for coastal structures. Advanced work on armour profile and armour unit shape descriptors is identified. A set of assessment methods for monitoring armoured slopes in the field are described, with examples drawn from recent monitoring exercises. The paper concludes by describing future directions of research in this field.

The paper presents results from experiments with Dolosse having the same mass and volume but with different waist thickness to height ratios. The armour was exposed to irregular waves simulating one storm with increasing wave heights and the effect of waist to height ratio on the hydraulic stability was studied. A low packing density of approximately 0.65 was used corresponding to a two-layer armour with high porosity.

From the results it is concluded that the hydraulic stability of Dolos armour is not very sensitive to variations in the waist to height ratio. Only for damage levels exceeding displacement of approximately 5% of the armour blocks in the most exposed area there seems to be a significant decrease in hydraulic stability with increasing waist to height ratio. Thus the waist ratio only influences the residual hydraulic stability.

Based on a short discussion of stressed in armour units it is concluded that design criteria solely based on movements of armour units as observed in hydraulic models are not adequate for the assessment of structural integrity of the units.

The paper also presents the results of each stability test as well as the scatter and the distributions. The large scatter found underlines the need for adoption of more restrictive safety factors than generally used in rubble mound breakwater design. It also supports the idea of a probabilistic approach in the design process.

Wave pressure is the most important external force for the design of breakwater. During recent years, there has been considerable development in the technology of vertical face breakwater; however, there is no reliable method to compute wave forces induced by irregular waves. The purpose of this study is to obtain statistical characteristics of irregular wave pressure distribution from the data of model tests.

The results of this study shown that vertical face breakwater under the action of irregular waves, some waves are reflected, so that the next wave breaks a critical distance resulting in a rapidly rising shock pressure on the breakwater. On the average, the wave pressure increase with incoming wave height, but the maximum wave force does not necessarily occur for the largest wave height. It can be occurred for serval larger wave group in an appropiate phase composition. The irregular wave pressure distribution on the breakwater is quite uniform; the ratio of tested and calculated wave pressures decreases with the reduction of relative crest height of breakwater.

Coda formula can predict the total horizontal force of the upper part of breakwater quite well except exetreme shock pressure occurred by non-breaking waves. Wave forces calculated by Miche-Rundgren and Nagai wave force formula are about 10% cummulated exceeding percentage of wave force obtained from model test.

Every coastal engineer realizes that the weight of armour blocks decided by Hudson's formula is safe enough for short steep waves, however, suffering damage from long period swells, even though the incidental wave height is the same. Several corrections have been made and submitted to ICCE as well as in other occasion. The authors try to explain analytically the influence of wave length on the design weight of armour blocks and justify by much of experiments in order to offer new formula and graphs for practical application.

The refraction of water waves around the heads of breakwaters can lead to large wave heights along the sheltered side of the structure. These waves are shown to be edge waves, trapped on the breakwater, based on the comparison of laboratory data and linear edge wave theory.

Laboratory model test results for the ultimate pullout resistance of vertical square anchors embedded in saturated or near saturated clay have been presented. The undrained shear strength of the clay and the embedment ratio of the anchors have been varied. Based on the model test results, an empirical parametric relationship for estimation of the ultimate pullout resistance of shallow and deep square anchors has been presented.

An attempt is made to conduct a rational assessment of the potential adverse effects of coastal armoring on adjacent shorelines and to propose methodology for mitigation, where appropriate. Specific attention is directed toward claims that armoring causes: profile steepening, increased longshore sediment transport, intensified local scour, transport of sand to substantial offshore distances, etc. The assessment presented here is based on a combination of sound principles and the availability or lack, of laboratory and field data to either support or refute the claims. Although it is found that data relating to coastal armoring effects are sparse, conclusions can be drawn. There seems to be no factual data to support the contentions that armoring causes profile steepening, increased longshore transport, transport of sand to a substantial distance offshore, or significantly delayed profile recovery following a severe erosion event. Armoring does have the potential to cause intensified local scour both in front of and at the ends of an armored segment. Reasons for these effects, based on knowledge of response of a natural profile, are presented. Additionally, armoring which projects into the active surf zone can act as a partial barrier to the net longshore sediment transport, thereby causing downdrift erosion.

Methodology is presented for quantifying the appropriate mitigation for a particular armoring situation. The proposed mitigation is the annual placement of sand in the vicinity of the armoring to offset its potential adverse effects. The two potential adverse effects addressed in the methodology include the reduction of sediment supplied to the system as a result of the armoring and the blockage of longshore sediment transport by a protruding armoring installation.

In 1978 an out-of-control ship hit and severely damaged a bascule bridge across the Duwamish West Waterway in Seattle seriously affecting both ship and highway traffic. The high level West Seattle Bridge was subsequently constructed to handle all through-highway traffic. A swing bridge was also designed to handle local traffic over the ship channel. The function of the pier protection system described in this paper is to protect the pivot piers and swing spans of this new bridge from damage by absorbing the part of the transverse energy component imparted by a colliding ship, which is not absorbed by deformation of the ship's hull.

A probabilistic approach to the lateral stability of a pipeline on the sea-bed is considered. The uncertainties involved in the deterministic approach, due to the stochastic nature of variables, inaccuracy of models and statistical error are discussed. Variables representing these uncertainties are identified and their statistical properties investigated. Procedures for computing the probability of stability failure are developed using both analytical and Monte Carlo simulation techniques. Example calculations are presented indicating typical applications. It is concluded that the probabilistic procedure, as presented here, can serve as a valuable tool in the stability analysis of ocean pipelines.

The present study deals with analysis of results from a new experiment in which local wave forces on a vertical pile penetrating the free surface were measured, both in transient breaking waves and in 2- and 3-dimensional irregular seas, regular waves, and waves and uniform currents superposed. The performance of the entire experimental programme showed that extreme wave load intensities are associated with transient 2- or 3-dimensional breaking waves, of relatively short wave periods, and not with the highest waves in the simulated sea states. The total integrated in-line force and the total overturning moment caused by breaking waves exceeded the values measured in monochromatic regular waves by a factor of 3. Inception of wave breaking was caused by phase superposition, and occurred also for very low values of wave steepness s = 0.05.

This paper discusses the application of two-dimensional tidal models to the hydraulic research for the storm surge barrier in the Eastern Scheldt in the Netherlands.

At the site of the barrier local energy losses dominate the flow. Three methods are discussed for dealing with these energy losses in a numerical model based on the long wave equations.

The construction of the storm surge barrier provided extensive field data for various phases of the construction of the barrier and these field data are used as a test case for the computation at methods developed. One method is preferred since it gives good agreement between computations and field data. The two-dimensional flow patterns, the discharge and the head-difference agree well.

The results of scale model tests were also available for comparison. This comparison demonstrated that depth-averaged velocities, computed by a two-dimensional numerical model, are as accurate as values obtained from a large physical scale model. Even compicated flow patterns with local energy losses and sharp velocity gradients compared well.

A numerical model has been developed to predict the wave motion on a rough impermeable slope and the hydraulic stability and sliding motion of armor units under the action of a specified normally incident wave train. The developed numerical model has been compared with riprap test results to calibrate and verify the model.

On the Fuji Coast 15 detached breakwaters and 17 wave dissipating breakwaters have been constructed to prevent beach erosion. By virtue of the construction of the breakwaters the retreat rate of the shoreline position has decreased. However a large number of concrete blocks have been scattered due to waves. This study investigates the actual circumstances on the scattering of the concrete armour units of the detached breakwaters through the field observations on the Fuji Coast located in Suruga Bay facing the Pacific Ocean. The change rate of the plane area of the breakwater is examined from the aerial photographs, and the relationships among the parameter, the depth at the offshore foot of the breakwater and the number of the removed concrete armour units are investigated.

Field investigations were performed in order to establish the reflecting characteristics of a steel sheet-piling type seawall and two vertical wave-dissipating type seawalls through directional wave measurements of wave reflection systems. A pre-designed line array of several capacitance-type wave gauges was used to measure the wave field just in front of the seawall, and the MMLM (Modified Maximum Likelifood Method) was applied for the calculation of the directional wave spectrum and the reflection coefficient. The estimated directional spectra demonstrated that the MMLM has high resolution power and can sufficiently separate the incident and the reflected wave energies. As a result, it was found that the reflection coefficient of the vertical steel sheet-piling seawall is about 0.9 and is independent of the incident wave conditions, whereas those of the vertical wave-dissipating type seawalls show considerable change in correlation to the incident wave period or the mean water level.

A finite element model for combined refraction-diffraction problems of linear water waves has been extended to include the effect of various dissipative mechanisms on wave excitation response in harbours of arbitrary shape and variable depth. Especially, the effects of bottom friction, partial absorption along the harbour contours, and transmission through permeable breakwaters have been considered. Although, within the mild slope approximation, the model is valid for arbitrary wave lengths, in this paper its effectiveness for harbour design applications is demonstrated for long wave induced resonance phenomena. For this purpose a realistic harbour geometry has been selected. A hydraulic scale-model of this harbour enabled experimental verification of the computational results.

A new type of floating breakwater composed of net-tubes and buoy-balls is presented in this paper. A series of model studies have been carried out for several arrangements of this structure. As wave damping effect is concerned, a case that the structure being set vertically is shown to be better than the one being set horizontally, while more than two rows of the structures are set vertically and separately, a case which being connected with ropes between adjoining rows is proved to be better than the case without connecting ropes.

Wave uplift forces on two dimensional platforms or docks in a variable depth medium has been studied theoretically and numerically. The incident waves are non-linear waves with maximum amplitude greater than the clearance between the still water surface and the underside of the platforms or docks.

The flow is assumed to be inviscid, irrotational without ambient current. Thus, the theoretical model solves the Laplace equation along with full nonlinear free surface conditions. In order to conveniently handle the moving free surface in an irregular bottom topography with the presence of platform or dock an isoparametric mapping technique was used to transfer the fluid domain and its boundaries into a regular geometry. A Galerkin finite element model is developed to model the transformed fluid region. The resulting discrete equations are solved iteratively by using adaptive Line SOR (Successive-Over-Relaxation) technique. Artificial viscosity is included in both the dynamic and kinematic free surface equations to damp out the free surface oscillations in the front region of the platform or dock. The Runge-Kutta method is employed to integrate the time variation in the nonlinear free surface equations.

Results obtained by the numerical method were compared to the available experimental data obtained by others in order to demonstrate the workability of the proposed algorithm.

The aim of this research is to investigate qualitatively the influence of short-crested waves on the scouring around the breakwater through mainly laboratory studies. At first, we succeed to observe clearly in laboratory some sedimentary bed forms such as troughs, holes, triangle bars and longitudinal bars under short-crested wave actions. Then we elucidate the association of their formation mechanism with theory of short-crested waves, and indicate its effect on scouring at the toe of breakwaters. In addition, it is shown that the breaking wave height of short-crested waves is certainly higher than that of two-dimensional standing waves. Finally we demonstrate some facts of failure of breakwater caused by short-crested wave breaking based on some field results.

The "Dolos" is now used widely for harbor and shore protection works in various ports of Taiwan (R.O.C.) and some damage has been noted. The purpose of this research is to understand the major factors which influence dolos breakage. The factors studied include plain or reinforced concrete, rebar arrangement, chamfered or enlarged fillet corner and the fracture behavior by pendulum and drop test.

Site observations and laboratory dynamic tests are included in this paper. The site observation investigated the behavior of the broken dolos at each habor. In the laboratory dynamic tests 42 specimens of 1.5 tons dolos were used for drop tests; frontal and transverse pendulum tests (Fig.l).

The results show that the fracture behavior in the laboratory tests agree with those of site observation, i.e. cracking due to frontal impact is more severe than that of transverse impact. The arrangement of rebar also influences the strength of the dolos. Therefore, it is suggested that the dynamic tests are necessary for dolos tesing.

At the 19th ICE Conference in Houston in 1984 an alternative concept for the design of rubble mound breakwaters was introduced. This concept has the objective of providing a leastcost structure by optimizing the use of locally available materials and utilizing simple construction procedures. Contractors’ bids demonstrated that significant cost savings could be achieved, when compared to the cost of traditional designs.

Considerable prototype experience has now been obtained with this concept of breakwaters. Breakwaters have been built using the concept in Canada, the United States, and Iceland since 1984 and have been subjected to storms and ice action.

Prototype observations have supported the performance predicted during the design process. In this paper surveys of a breakwater taken after construction and after storm action are presented. In addition to wave action, this breakwater has also been subjected to extensive ice action. The response of the breakwater has been monitored and observed and is discussed.

An analytical model for wave-soil-caisson interaction is verified by comparison with a finite element model and large scale experimental results. The analytical and finite element model estimates of the stresses and surface displacements of an elastic layer of finite thickness are in good agreement. The physical model experiments were conducted at the O.H. Hinsdale Wave Research Facility at Oregon State University. A 10-ft high, 8-ft long caisson was constructed on a bedding layer overlying 1 to 3 ft of soil. The caisson was exposed to waves with heights of 0.68 to 4.4 ft with periods of 1.77 to 8.80 sec. Experimental and analytical comparisons for porewater pressure were in agreement but the displacements were quite scattered.

This paper discusses the characteristics of hydraulic and water exchange due to the wave action against vertical slit-type breakwaters. The theoretical solution of the reflection and the transmission coefficients for the breakwater models is compared with the experimental results. Furthermore, the water exchange discharge and the water concentration change through the gap of the permeable breakwater are examined experimentally. Finally the most effective geometry of the cross section is suggested for the breakwaters used here.

Recently, as well as hydraulic stability, structural strength of armor blocks has emerged as a major problem in breakwaters. This problem is studied by research organizations in many countries. In Nippon Tetrapod Co., Ltd., a series of hydraulic model tests was conducted to measure the surface strain on Tetrapods under wave action.

In this paper, the results of the hydraulic model test are described. Prior to the hydraulic test, a similitude relation on impact stress and strain between the prototype and model was derived and a drop test was performed to investigate the scale effect on impact strain on Tetrapods. The hydraulic test was conducted to measure the surface strain on 50kg model Tetrapods using strain gages. In addition, impact strain on 50t Tetrapods under wave action was estimated applying the similitude relation.

The strain on Tetrapods under wave action was clarified through this study.

Susceptibility to breakage is of major importance to the long-term stability of armour layer units, particularly for dolos and similar less massive element types. An attempt is made in this paper to discuss various factors on the basis of extensive testing of rubblemound breakwaters recently conducted at the Franzius Institute for Hydraulics and Coastal Engineering at the University of Hannover. Standardized procedures, which are independent of the type of element, are introduced for conducting model tests as well as for systematically evaluating and quantifying the results. Results are presented from tests using both concrete and aluminum dolos with different unit weights, in addition to concrete cubes and tetrapods.

This paper will discuss experience and approaches to the use of segmented breakwaters for beach erosion control in the United States. Several prototype cases are examined and generalizations drawn concerning the resultant beach response. This experience is further evaluated in order to develop a preliminary approach for developing design criteria.

The design process for the calculation of wave forces and movements for a flexible (plastic) ocean outfall is described. The design procedure is illustrated using a case study of the design of two High Density Polyethylene (HDPE) pipelines of 0,9 m and 1,0 m 0D (4 290 m and 5 45Q m long) constructed at Richards Bay, South Africa, to dispose of dense and buoyant effluent respectively.

The pipeline anchor weights are based on the 1 in 1 year wave forces on the pipeline, implying that the pipeline is allowed to move during its design life. Special star anchor weights are used which keep the pipe clear of the bed while maintaining the stability of the pipeline.

Friction tests were undertaken with a section of pipeline and two star weights, above water on concrete and sand and below water on sand, to determine realistic friction coefficients for the pipeline design. The results of these tests are summarised in this paper. It was found that the mean friction coefficient for submerged star weights on sand was 0,75.

The movements of sections of the 0,9 m OD pipeline were calculated using a finite difference computer programme developed by Prof I Larsen and the results are summarised in the paper. It was found that movements of 1 to 2 m could occur under design wave conditions (50 to 100 year waves) and these were considered acceptable provided that the pipeline was not obstructed by rock outcrops.

A new design method of rubble mound structures with stability and wave control consideration is proposed, by which the reduction of wave reflection and run-up and increase in rubble stability are assured under the given wave conditions. Wave control and stability increasing functions due to change of the slope shape of rubble mound structures are discussed on the basis of the experimental results for regular and irregular waves.

The new design formula developed here considered the allowable percentage of damage and the wave grouping effects on rubble stability using a new assumption of the mean run-sum as an index of the irregular wave force. The run-sum is defined as the energy sum of a run satisfying a critical wave condition and the mean run-sum is the mean of run-sum for a irregular wave train.

For the probabilistic design of dikes it is necessary to know the failure probability of the dike as function of the load of the dike (wave attack).

This paper reports on the statistical analysis of the failure behaviour of the dikes around the Eastern Scheldt after the storm surge on February 1, 1953.

Basic investigations on wave reflection have been performed with different partially-reflecting structures, wave spectra and wave approach angles. In addition to laboratory experiments using both a wave flume and a wave basin, a theoretical solution based on diffraction theory was determined to describe the wave field in the reflection area of various structures. The investigations were restricted to non-breaking wave conditions. The reflection behaviour of structures is expressed by a complex reflection coefficient, containing two parameters, which have to be determined by model tests.

An instrumentation scheme for the measurement of the structural response of dolos units in a physical model due to static and quasistatic forces is presented. This was achieved by the development of a specialized armour unit "load cell". The load cell was tested under a variety of loading conditions ranging from static point loads to the complex forces arising from simulated prototype wave action. In the final stage of testing, a model breakwater was constructed and analyzed. The results of these tests demonstrated the accuracy of the developed instrumentation and the feasibility of its use for measurements conducted in physical models. Knowledge of the structural response of armour units in the breakwater environment may be incorporated into an improved overall design procedure for armour units that considers both the hydraulic stability and the structural integrity of the individual units.

This study aims at clarifying the difference between irregular and periodic wave run-ups on a slope or a sea wall. Since hydraulic phenomena on a slope are the induced result of an interaction between a running up wave and a back-wash. The run-up height, therefore, has to be investigated in terms of a back-wash properties in addition to run-up wave properties. The experiments which are so designed that waves can run up on a slope without meeting back-wash, were conducted to evaluate the back-wash effects. The relative run-up heights R_r/H_O of periodic waves in these experiments reached up to about two times as high as those of periodic waves which have the same steepnesses.

The run-up heights of irregular waves on a slope were also investigated experimentally. There are no clear relations between R_r/H_O and H_O/L_O as those for periodic waves ordinary observed, and they distributed widely. The upper-most value of R_r/H_O in the distribution for any H_O/L_O was almost equal to the value in the above experiment. The uppermost (critical) relative run-up heights R_r/H_O for the given H_O/L_O and slope may exist. The differences between the critical and ordinary run-up height of periodic waves on the sea wall were also experimentally investigated. The difference is prominent when a sea wall is set on-shore from the shore-line. It reaches up to about 4 times when a sea wall is set a little on-shore from the shore line.

Some statistical discussion on the probability of the situation in which the critical run-up may be brought about is given at the last part.

In the studies on stability of the armor units and reflection from those, there are some indications on scale effects which are included in the results of small scale experiments. In this study, the fact has been confirmed with large wave flume test, and estimated the critical Reynolds Number where was no scale effect. And by this result on the stability of armor units, we can evaluated the results in small and middle scale test, and can correct the minimum weight of armor units. So we can design the breakwaters and seawalls rationaly and economically.

However, it has not been confirmed the critical Reynolds Number where the influence of scale effect on reflection became negligible.

The degree of reflection from rubble-mound breakwaters, even those comprising large pre-cast concrete armour units is greater than is usually thought. This is because the bulk of the face consists of smaller stones where water exchange in voids is minimal. Theory and experiment have shown that for 100% reflection of oblique waves the orbital motions are very complex, varying across the crest length of the short-crested system from rectilinear oscillation to circular or vortex motion. Also the influence of these high velocity orbital motions on a sedimentary bed have been shown to have a high scouring capacity. This has been exhibited in hydraulic models and in the field.

On the basis of eleven poster presentations on beach protection schemes and/or devices, at the recent 20th International Conference on Coastal Engineering, the various levels involved in the design and evaluation of beach protection schemes are discussed in this paper. These are: (1) the assessment of the problem and processes operative in the area; (2) the establishment of an overall master plan for development; (3) the design stage; (4) the construction phase, and (5) the post-construction phase. It is concluded that it would be useful if some form of international co-operation could be instigated to allow the collation of techniques used at the various levels in one handy location, for dissemination by all contributors.

A calculation method of the impulsive breaking wave forces on piles is proposed in this paper. It is derived on the basis of experimental results with some theoretical considerations. Wave forces on a cylinder caused by both regular and irregular trains of waves are measured in a large wave flume. The experimental results are compared with the values predicted by both Wagner and Karman. In the proposed method, it is assumed that the impulsive force acts on the upper half of the pile between the still water level and the wave crest, and that the force distribution along the pile is triangular shape. The peak value in the distribution is expressed by the function of both the breaking force parameter and the inclination angle of the cylinder. The breaking force parameter is the ratio of the bottom slope to wave steepness. The time history of the impact force is given as a triangular pulse with a vertical rise. The duration time is determined as half of the value predicted by Karman's theory.

Several previous investigators have conducted experiments leading to expressions for predicting the transformation of waves passing through closely-spaced pile breakwaters. The present study extends those earlier experiments using monochromatic waves to the case of a spectrum of random waves.

Records of incident waves and of waves after transmission through a model pile breakwater were compared to determine a coefficient of transmission. Results are presented for several cases of pile spacing and pile diameter. Good agreement is found between observed transmission coefficients and those predicted using the expression proposed by Hayashi et al. (1966).

An analytical model is developed to predict the soil responses induced by waves and caisson motion. The caisson is founded on a rubble bedding layer overlying a soil of finite depth. The responses are modeled by the Biot consolidation equations. Two approximations are employed to reduce mathematical difficulties: 1) a boundary layer approximation to decouple pore pressure and soil motion in the Biot equations and 2) a contact solution approximation for a thin elastic layer to address mixed-type boundary-value problems.

The coast of Ibaraki Prefecture, facing the Pacific Ocean, has an alongshore stretch of 181 km. On this coast many structures associated with harbors have been constructed since early 1960s. Since then 25 years have passed, and some notable beach changes due to the influence of the construction of the coastal structures have been observed. This study aims to examine the actual situation of the beach change around large-scale structures and the damages of the coastal structures selecting the coast of Ibaraki Prefecture as the study area. For the purpose aerial photographs were taken along the coast, and the topographic surveys and measurements of median diameter of beach-face materials were made. Data of the soundings having been conducted once a year since 1975 around Oharai Port and Hazaki Fishery Harbor were collected in order to study the beach changes around the large-scale coastal structures. For the analysis of these data the comparison of the shoreline changes were performed by using four sets of aerial photographs since 1947 to the present. Moreover, temporal and spatial changes of the beach topography were investigated by the sounding data.

The hydrodynamic coefficients are computed based on the measured total force on the single slotted wall in the wave field, or on the measured head loss in the uniform flow channel. The reflection, transmission and force coefficients on the single slotted wall are computed based on the mean values of the hydrodynamic coefficients. The correlations between these calculated values and measured values are found to be good. A design procedure of the single slotted wall is given the paper.

When a submerged, flexible bag is filled with air about 60∼70 % of its full volume ( it is called " sea-balloon " ), it has a stable shape with vertical axis of symmetry, on which several vertical wrinkles appear with folds of membrane. If two or more such sea-balloons are arranged to the direction of wave travel and connected pneumatically, balloons are deformed periodically and the air flows reciprocally in connecting pipe, following to the fluid pressure fluctuation due to incident waves. Such a system of sea-balloon intercepts incident waves effectively ( it is called " sea-balloon breakwater ").

The wave interception by the breakwater is analyzed numerically by three-dimensional boundary integral method, assuming that the fluid motions both in- and out-side of the balloon are potential and that the tension in balloon membrane is proportional to the apparent elongation of membrane with virtual elastic constant.

After analysis and experiments, it is made clear that in relatively long waves the incident wave is canceled by the radiation wave which is generated by volumetric change of sea-balloons, being affected by air-flow resistance in connecting pipe. In short waves, sea-balloons seem to behave like as rigid piles and the incident wave is absorbed by airflow resistance in pipe and by the turbulence of fluid motion around balloons. Moreover, the effect of gaps between sea-balloons along wave crest on wave interception for relatively long waves is expressed by a simple empirical formula, by which the transmission coefficients at various types of sea-balloon breakwater is easily estimated by two-dimensional computation.

For the improvement of wave interception effect and from the point of practical use, the effects of other sea-balloon breakwater system are investigated by two-dimensional computation and experiments.

This paper summarizes the results of a research program conducted to examine the structural behaviour of nine full scale ten ton Dolos armour units subjected to a well defined loading regime. Three unreinforced and six reinforced units were tested. The effects of three different types of reinforcement (rebars, hollow steel tubes, and prestressing bars) on the behaviour of the units was determined. Different design approaches for armour units are discussed and one possible new approach is presented.

The composite type breakwater used in Taichung Harbor contributes economical cross section and better consideration of drifting sand control. Also, with the plan of making caissons on the sand beach and installing caissons by using an unprecedented "Island" method, it shorten the construction period of breakwater significantly.

Study is performed on a vertical flap type energy converter, "Pendulor System". The power absorbed with the system in random waves is estimated using a transfer function of absorbed power (absorption coefficient) in regular waves and wave spectrum. A boundary element technique is applied to compute the hydrodynamic problem associated with the system which is placed in regular waves. The applicability of the method has been examined by a series of field test at a test plant caisson. The agreement between estimation and experiment was found to be good except near the resonance frequency of the system.

The dolos armour unit has been used all over the world and, although most projects have been successful, there have also been some major failures. When moved around, armour units in general and the rather slender dolosse in particular are prone to structural damage and when dolosse break through the shank, one is left with very unstable pieces of rubble. It is shown in this paper that a safe and economic dolos structure can be obtained if the correct design process is followed. The "optimum" design is based on a reasonable degree of dolos movement which must be established in detailed and representative model tests.

To ensure that the dolosse can withstand these movements, prototype dolos behaviour must be monitored, and such monitoring must be supplemented by representative structural tests, analytical studies and special prototype measurements.

To increase the structural strength of dolosse, the waist to height ratio can be increased and some (simple) form of reinforcing can be included.

A system composed of two buoyant flaps hinged at the sea floor and coupled with weighted mooring lines is modeled analytically and experimentally. The system behavior is described theoretically utilizing an eigenseries representation of linear wave theory in the vicinity of the breakwater. The structure dynamics are modeled in terms of structure weight, inertia, buoyancy, damping, mooring line tension and the wave pressure field.

The mechanically coupled system provides shelter by reflecting incident waves and by attenuating wave energy through structural and viscous damping. The structure can be tuned to minimize wave transmission within a particular frequency range by changing the flap spacing and adjusting the mass and equilibrium position of the mooring line weights.

The theory is validated with experimental results for models fabricated from inflatable, parallel-tube membranes. Buoyancy and inertia are changed by filling tubes with air and/or water. Single and double flaps are examined with and without mooring lines. Incident, reflected, and transmitted waves are measured as well as flap motion. Theoretical results are corroborated by the experiments and the importance of including damping in the model is demonstrated.

Reliable estimates of coastal flooding from tides and storm surges are required for making sound engineering decisions regarding the design, operation and maintenance of many coastal projects. A recent investigation of flood frequency along the coast and within the bays of southern Long Island, New York, produced new and optimal approaches to obtain meaningful statistical estimates of flood levels. This paper summarizes various elements of the study and concentrates on the problem of stage-frequency computations in the inland bay areas. Methods for optimizing the number of necessary storm/tide simulations and estimating the accuracy of results are presented.

The paper refers to mathematical modeling of the 2-D hydrodynamic circulation in the Saronic Gulf, in Greece. The finite element method is followed to evaluate the flow behaviour. Two grids are employed, a coarse one for initial model adaptation and a finer one for a more detailed study of circulation patterns. Actual tide data are obtained at the boundary of the domain and a typical compound tide is introduced; however residual tidal currents are found to be negligible. Wind-generated flow fields under several prevailing wind directions are determined and their comparison to qualitative field evidence is satisfactory. Further-more, a possible surface tilt along the open boundary associated with large scale circulation in the Aegean Sea, is studied and shown to produce significant motion in the Gulf. Based on circulation patterns obtained, preliminary estimates of dispersion from a proposed sea outfall for Athens sewage can be made. Further work proceeds towards quantitative verification of the model in connection with the proper description of forcing mechanisms and their superposition.

The numerical simulations on thermal diffusion always concentrated upon the raised temperature and temperature distributions after the heated water discharged from outlet into surrounding water, and the surrounding water temperature was assumed to be a constant. Actually, the water temperature on surface layer in shallow water area varies several centigrade degrees depended upon the weather conditions during a whole day. In order to obtain the absolute water temperature prepared for the ecological changes assessment and even provided for the operation basis of the cooling water system that air-sea heat exchange has to be considered in the numerical simulation of thermal discharges.

For the practical application of this numerical simulation, the first nuclear power plant in Taiwan was taken as an example and simulated in this paper. And the results were presented in figures.

Water pollution in the near shore area has become a serious problem in coastal engineering. In such a situation, not only wave dissipation but also the functioning of water pollution control is expected from the coastal structure. Since breaking waves are accompanied by many bubbles and intense water turbulence, they promote the contact between organic matter and bacteria and between water and air. Therefore the water quality related to organic matter seems to change under the effect of breaking waves. In this study the variation of the dissolved oxygen and the organic matter near the surf zone were considered. First, a self purification model in the surf zone was developed. Second, the efficiency of breaking waves on reaeration and organic matter decomposition was estimated by an experiment in the laboratory flume and numerical simulation.

Taiwan is now served by five international ports, two of which were newly opened since 1970. They have been under continuous expansion in recent years to meet the needs of the island's burgeoning foreign trade. Due to recent trend of vessel developed to huge load-capacity, the existing port of Taiwan district is inconvenient to the ULCC or VLCC. For decreasing the shipping cost and accomodating the cargo handing of over 100,000 DWT, the deep water port is urgent to be developed in order to promote the competent capability of port cargo handling.

This research is divided into two parts, at first, the prediction of cargo handling and the cargo sources which are adapted to the huge vessel shipping need to be studied for the development of deep water port. the next, then the oceanographical data for the design and the planning of deep water wharf and breakwater need to be surveyed around this Island for possible site of deep water port.

This study deals with the related problems of deep water breakwater construction and discusses how to apply the present design and construction method to the deep water wharf and breakwater. Further analyses are conducted for this research in the coming three fiscal years.

A Shore Protection Master Plan (SPMP) for the Nile Delta Shoreline, extending from 30 kms west of the city of Alexandria (Arab Republic of Egypt) to 30 kms east of Port Said, is developed and reported. The SPMP was developed in three stages: (1) collection and analysis of relevant data to identify existing and future coastal problems and limits of needed shore protection, (2) development of shore protection alternatives with costs and economic evaluations, and (3) detailed design and technical specifications for the selected shore protection schemes along the SPMP zone. This paper summarizes Tetra Tech, Inc./Honeywell work and achievements on this project while under contract with the Egyptian Shore Protection Authority (SPA). The SPMP considered the Egyptian Government and the SPA national needs to the year 2000.

Interaction of periodic waves with a moored inclined floating breakwater has been studied theoretically and numerically. The floating breakwater is inclined at a well defined angle with the sea bottom; its seaward end in protruding above the water surface. In static equilibrium, without incoming waves, the body weight, the buoyance force, and the restoring forces from the mooring lines which are modeled using linear springs keep the breakwater at a fixed angle. The theoretical formulation is based on a suitable variational principle. For the numerical solution a combination of finite element approximation as well as eigen function expansion technique is used.

The result is obtained in terms of wave transmission and reflection coefficient as well as the sway, heave and roll motion of the breakwater. The sensitivity of the solution on the parameters such as the bottom gap size, angle of inclination, and the mooring line stiffness are investigated over a range of incident wave transmission coefficient for dimensionless wave number hk > 0.60 ( k is wave number, h is the water depth). The results suggest that a certain degree of sheltering effect can be realized by employing this type of sloping breakwater.

Since 1984 Hsin-Ta LNG Terminal has been under construction for the purpose of importing liquefied natural gas because of increasing demand and possible depletion of natural gas in Taiwan. Several alternatives were taken into account during the feasibility study. The Terminal is built with only a southern breakwater due to its good natural coastal conditions. Each construction item has been coordinated closely in order to advance the schedule. The first phase of land reclamation was finished by 1986. Three tanks have been under construction since soil improvement was finished. The entire project will be completed in 1989.

Studies were made on a surface buoyant jet from a coastal power plant. The cooling water discharges into shallow waters of irregular bottom topography forming a partially enclosed embayment that connects to the open ocean. Near field mixing was found to be influenced by bottom bathymetry, lateral confinement and a large obstruction. Surface centerline temperature decay, bottom separation and the heat and mass distribution within the embayment were analyzed.

Tsunami hazard is investigated using the indirect approach with simple seismological and hydrodynamic models. It is assumed that earthquakes of random magnitude may originate anywhere with equal like-lihood from a single straight fault and the site is located on the perpendicular plane bisecting the fault. The ground displacement is instantaneous and consists of a block uplift type of movement which may be circular or elongated in the plan view. The hydrodynamic model is based on linear long wave theory wherein the ocean is of constant depth and infinite in the horizontal extent, and the earth is flat. Tsunami hazard is computed for various values of the parameters and a sensitivity study is carried out to examine the effect of certain parameters on hazard.

This paper presents the development of a three dimensional model of the Gulf of Alaska. The model extends between the Vancouver Island and the Aleutian Islands covering approximatedly 1.5 million square kilometers over the northern Pacific Ocean. Formulated on an ellipsoidal horizontal grid and variable vertical grid, the model is schematized over a 81 × 53 × 10 grid structure. The solution scheme is implicit over the vertical and is programmed using one-dimensional dynamic array for the efficient use of machine storage. The turbulence closure scheme for the non-homogeneous vertical shear is formulated so that the potential and kinetic energetics are monitored and transferred in a closed form.

The hydrodynamic model is coupled to a two-dimensional stochastic weather model and an oil-spill trajectory/weathering model. The former also simulates stochastically the cyclogenetic/cyclolytic processes within the modeled area.

The paper also compares the computed results with the available field data. Good agreements are found in tidal amplitude and phases as well as currents.

An evaluation of local tsunami threat was studied first refering to the historical documents and the catalogs. Secondly, an example of a numerical model of a finite difference method was discussed in relation to problems for reproducing the past local tsunamis and predicting a forthcoming tsunami. Lastly, a stochastic model was utilized in order to evaluate an exceedance probability of tsunami occurrence in an interested time period at an interesting local area where the concerened information or prediction was in need. The evaluation of a local tsunami threat is useful to get a more effective measure for the tsunami warning system and for protection works.

Singapore is an island republic with about 10% of her land area reclaimed from foreshore during the last century. In this paper, past reclamation works are reviewed and possible future reclamation works are predicted.

In general, hydraulic model tests and numerical simulations can be used for securing enough informations in order to assess the environmental impact by thermal discharge after the power plant operation. However, the numerical simulations should be verified by the consequence of hydraulic model tests or the field data. Then, the numerical model can be used as a prediction model to foresee the nature of thermal diffusion when the additional generators will be operated.

The third nuclear power plant in Taiwan was constructed in 1984. In order to protect the abundant corals which are distributed on the rocky bottom around this power plant, complete studies on thermal diffusion have been performed, accordingly, a verification with field measurements as also made in this paper.

Calibration and verification of a 1:75 scale undistorted hydraulic model is described. The model was used to simulate the waste heat distribution in shallow and semi-confined receiving waters. The study was carried out in the laboratory by analyzing the effect of several parameters in comparisons of model and field data. Because of the shallow receiving waters, it was found that the near-field bathymetry, bottom roughness and waves were the critical parameters in achieving a reasonable simulation.

In some configurations of cooling water systems for thermal-electric power plants, which use sea water as a source, a certain amount of recirculation occurs. A theory is developed to predict this recirculation.

In the past, only the ship motion due to wave is studied. This study is focused on the ship motion induced by a steady oscillating wind. The oscillating wind is assumed to be sinusoidal of a constant frequency. The wind direction θ, number of mooring lines and the wind frequency are the parameters in simulating an Evergreen's Ever Garden class container ship. The results show that the worst angle between the quay and the prevailing wind direction is 45°. Surge and roll are the most significant motions induced by the oscillating wind. By changing the number of mooring lines, the natural frequency can be kept away from the dominant wind frequency, except roll.

To optimize structure design it is useful to conduct detailed physical model tests. Tests of various basic physical phenomena (e.g. resonance problems), reproducing a sea state of prototype duration and then from the behavior of entire structure, the optimal design to the wharf structure will be obtained.

Preliminary analyses are made by basing upon experience for structure submitted to the similar action of wave or climates, combined with knowledge of available construction materials, i.e. selection of the rubber fender and the mooring system. Therefore, ship impaction force model simulation could lead to an ideal design.

A lot of experimental research work is conducted in order to facilitate determination of its test value when different factors are involved. Some design recommedations are commonly based on experimental results rather than that from mathematical iterations.