Coastal Engineering 1974

The design of coastal works depends on estimating the probabilities of extreme water levels, as well as of waves Previous studies of surge-affected levels have extrapolated observed annual maxima or the n highest levels in n years to predict rarer events In addition to using these well-established methods, in this study of tide levels on the Essex coast of Britain a long term record of extreme levels was synthesised by adding surge residuals at the time ofpredictedHW to predictedHW levels, treating them as statistically independent events Many more large surge residuals have been measured than extreme water levels as many surges are associated with small tides Events with return periods up to 1000 years may be estimated without extrapolating beyond the range of observed surge residuals and predicted tides This method is assessed in relation to previous methods and information relevant to the design of coastal works in the south western part of the North Sea was obtained In addition to forecasting the probabilities of high tide levels, the study included wave forecasts and the encounter probabilities of combinations of sea level and wave height for various aspects of coastal developments

The “Bathystrophic Storm Tide Theory” is used to predict open-coast storm surge due to major hurricanes. The model described here is used to calculate storm-surge effects such as flood elevations needed for designing nuclear power plant safety related structures. In order to establish the model's viability the numerical techniques have been verified and the model calibrated using available field data.

Numerical verification was performed for special cases where the governing equations of the model could be analytically solved. Inherent in the governing storm-tide equations are certain undetermined coefficients that describe the effects of wind drag and bottom friction. These coefficients were determined by correlating computer predicted results to hurricane storm surge hydrographs of record.

As a result of this study, we find excellent agreement between computer predicted and analytical results.

In this paper, the effects of a storm surge that happened on the 16th-17th January 1973 in the harbour of Leixões are analysed and described. These effects were of two types:

- As the storm surge coincided with a spring tide and rough seas, severe damages occurred in the outer breakwater, mainly in its head.

- Associated to the storm surge range phenomena happened in the nS 2 dock; these movements, acting on a ship berthed in a nodal zone, caused several breakings in the ropes and damages in harbour structures.

The characteristics of the storm surge and of the waves are analysed. Their effects on the breakwater are described.

By comparing the periods of long waves observed in the tide records with the resonance periods of the inner docks it was possible to conclude that the intensity of the range phenomena observed was due to a half wave lenght resonance.

Having in mind the affinities with the phenomena referred to above, the effects of range action in an oil terminal and new dama ges in the outer breakwater, that occurred in January and February 1974 respectively, are also briefly examined.

As a forerunner of a comprehensive study of wave and energy climate of the Nile Delta coast covering a period of more than 50 years, wave measurements taken in 3 locations along the coast in the year 1972 were statistically analysed. Shortcut methods based on statistical approach were used to analyse the wave records enabling quicker analysis. Spectral analysis of the wave records indicates narrow spectral band similar to Raleigh distribution. The histograms and frequency distribution curves of significant wave heights, and the relationships between various statistical prarameters such as H_max, H_1/10, H_1/3 and H_rms also agree closely with Raleigh distribution curves and parameters enabling the use of Raleigh distribution function in subsequent studies. Finally since the wave characteristics and wave energy climates are most important in the analysis of coastline changes, they are drawn from the data obtained from the analysis.

An instrumentation system to record direct measures of both wind and wave conditions has been installed at the Wash. Data from these instruments are used in conjunction with long term wind records from another station to predict the frequency and duration of extreme conditions.

Wave data obtained in the North Sea for stormy weather conditions are analyzed to determine the extent of wave group formation among large waves; i.e. the number of large waves succeeding each other in one single run. Three periods associated with the passage of high sea states are examined. The average correlation between succeeding wave heights is found to be +0.2H, which indicates that wave heights do have a “memory”. Wave group formations are found to be more pronounced when the sea is growing than decaying. The average lengths of wave runs are calculated.

Two commonly used deep-water wave recorders which depend on acceleration measurement were calibrated on a Hi metre diameter vertical wheel, and also on much smaller laboratory test rigs, over a range of wave periods likely to be encountered at sea. The results showed that the instruments behaved according to expectations. In addition, spectra from two instruments of the same types which were deployed within one mile of each other were compared and shown to be similar.

Although many attempts have been made in the past to measure the direction of propogation of ocean waves, a need for a simple, reliable solution to the problem has remained. The technique described here, intended for near-shore usage, makes use of a simple bottom-mounted flow direction indicator. The influence of rip and longshore currents on wave direction recordings is identified and a means of reducing these steady state current effects by a reduction in gauge sensitivity is presented, along with various possible recording and analysis techniques. Usefulness of the gauge is established as a simple engineering tool with certain limitations and examples are given of wave direction recordings related to meteorological data. A possible usage of the gauge as an approximate sediment transport indicator is also proposed.

The dynamic response of the spar to oscillatory flow has been examined by modeling as well as computer analysis of the non-linear differential equation. Field measurements using the tilting spar have been made. These measurements are compared with theory and with other more direct measurements of the wave field.

The tilting spar has been used to estimate wave direction. These estimates generally agree well with directional estimates made using a pressure sensor array and a two-component current meter.

Determination of the directional distribution of ocean surface waves is of practical importance and analytical schemes for it are developed and discussed here. Based on a generalized representation of wave properties such as surface elevation, subsurface pressure or horizontal components of water particle velocity, acceleration or wave force, two general schemes of analysis are developed. In one scheme the predictive equations for the directional distribution of both the amplitude and phase of waves are derived. Distribution of energy as a function of direction for random waves is obtained in the other scheme. Fourier series parameterization is used to represent directional spectrum. The truncation of the series dictated by data limitations introduce directional spread and negative side lobes for the estimated directional spectrum. A procedure to remove these undesirable side lobes by a non-negative smoothing function is described. The smoothing causes further directional spread. Methods for obtaining better directional resolution are discussed. Data adaptive spectral analysis techniques such as Maximum Likelihood Method and Maximum Entropy Method are suggested.

Non-stationarity in an actual wave field restricts the application of the existing methods of estimating spectra. Despite the enormous amount of research work in the past, an analyst today is still faced with the lack of a unique procedure capable of providing a spectrum estimate which can be considered as the most accurate for the wave data collected under conditions where the stationarity assumption is in doubt. In this paper a generalized method is presented for estimating one dimensional frequency spectrum considering the non-stationarity. The generalized method and the associated design relations provide an effective measure for assessing the statistical quality of spectrum estimates, and a natural criterion as to how to select an optimal sample size. Concepts are illustrated by actual wave data analysis, and the validity of the procedure is demonstrated by simulation. In a simple manner, all concepts and methods developed for the non-stationary frequency spectrum apply to the wave number spectrum with spatial inhomogeneity. For simplicity, the presentation here will be primarily directed to the frequency spectrum.

The paper reports measurements of waves generated by a piston type wave generator. The experiments show that for 0.10 < h/L < 0.65 the waves produced by a sinusoidal piston motion can be described as a second order Stokes wave superimposed by a free second harmonic wave. Results are presented for the height and phase velocity of the free second harmonic wave and compared with theories by Fontanet (1961) and others. Finally, the height of the free second harmonic wave is successfully reduced by a non-sinusoidal time variation of the piston motion, whereas addition of a rotation to the flap motion appears to yield only minor improvements.

An account is given of the various design considerations in the development of a low-cost programmable wave generator for a laboratory channel. The ability of this equipment to reproduce prototype spectra is critically discussed.

The computer programmed implementation of a pseudorandom noise generator based on the use of a binary feedback shift register and an associated digital filter is described. Descriptive details are given for the compensation of the filter for the various dynamic transfer functions in the system. The random signal generator has been programmed both for a dedicated computer (NOVA 1200 with 4K core) which can carry up to 50 different spectra in core at any one time and for the EAI 64 0 with 16K core and disc storage which was used to investigate the spectral and statistical properties of the generated wave. JONSWAP spectra with 0.6 and 1.0 Herz centre frequencies were generated and observed at locations from 5 to 40 meters from the wave maker using a hydraulically operated machine in a partial piston and partial hinged flap mode m 0.9 meter of water. Measurements indicate that JONSWAP spectra can be closely matched in the flume. The 1.0 Herz spectrum is less stable as a function of distance, all spectra indicate a significant decrease of the spectral peak as a function of distance from the wave maker and the ratio of H_max/H_av is in general larger than that observed by Wiegel and Kukk.

A method is proposed for measurement of the incident wave height in a composite wave train. The composite wave train is assumed to consist of a superposition of regular incident and reflected waves with the same wave period. An approximate value of the incident wave height is obtained as the arithmetic mean of the wave heights measured by two gauges separated a quarter of a wave length. The accuracy of the method in relation to the location of the gauges and the wave parameters is investigated using linear and second order wave theory. Results of the calculations are presented in diagrams.

Beach profile formation may be severely affected by secondary waves which, together with the basic wave, always originate from a sinusoidally-moving wave board The ascertainment of this experimental fact is followed by an investigation of the behaviour of the generated waves and their interactions It appears that the many characteristic features, among which the spatial beat phenomenon and the secondary crest formation, are generally in good accordance with the theories of Fontanet [14], and Kravtchenko and Santon [20] It is concluded that an “outer” analysis, e g by plotting the x-t-lines of visible peaks, is only of limited use to describe the “inner” character of the complex phenomenon. The subsequent study of the effect of secondary waves on a horizontal sand bed reveals that not only the wave form, but also the sand transport varies spatially, resulting in the formation of bars and troughs This typical behaviour of the onshore-offshore transport is provisionally investigated in a small pulsating water block. Finally, a method is described which suppresses the secondary waves, by using a low rectangular sill on the otherwise horizontal bottom

In the numerical method of prediction of wind waves in deep water, Hasselmann's nonlinear interaction theory is applied. This method assumes the energy balance of individual component waves. However, the total energy balance must exist in the transformation of irregular waves in shoaling water. In this investigation, experiments were carried out on the transformations in shoaling water of composite waves having two components and random waves having one or two main peaks.

It was found that the elementary component wave height of the composite waves and the elementary peak power of the random waves decrease with decrease in the water depth. This reason can be explained qualitatively by the theory of the elementary component wave height change of finite amplitude waves in shoaling water. The secondary component wave height of the composite waves and the secondary peak power of the random waves increase with decrease in the water depth. This can be explained qualitatively by Hamada's theory of nonlinear interaction in uniform depth.

A new criterion for shallow water wave analysis is evaluated from prototype data off the German coast on the reef and wadden sea areas south of the outer Elbe river. Correlations of mean wave heights $\overline{\text{H}}$ with mean wave periods$\overline{\text{T}},$ and wave height distribution factors${\text{C}}_{1/3}=\frac{{\text{H}}_{1/3}}{\text{H}}$ respectively show that the mean periods and both complete height and period distributions of waves in shallow water can be expressed as functions of mean height and topography. So the mean wave height$\overline{\text{H}}$ proves to be the characteristic parameter for the description of the complete shallow water wave climate. The upper envelop of the values$\overline{\text{H}}=\text{f}$ (meteorology, topography) is defined as the case of fully developed sea, which leads to the function of the highest mean wave heights${\overline{\text{H}}}_{\text{max}}\text{.}$ This parameter is plotted with 5 topographical parameters:

depth of water d, distance s from deep water area, and mean wave steepness δ.

The curves$\frac{{\overline{\text{H}}}_{\text{max}}}{\text{d}}$ versus s for different d show distinct maxima for varying distances s_crit. from the deep water area. This critical travel distance of waves in shallow water is dependent on the depth of water only. It represents the length, on which the waves grow before the beginning decay due to shoaling effects:

This paper deals with the following aspects of periodic water waves breaking on a plane slope breaking criterion, breaker type, phase difference across the surfzone, breaker height-to-depth ratio, run-up and set-up, and reflection. It is shown that these are approximately governed by a single similarity parameter only, embodying both the effects of slope angle and incident wave steepness. Various physical interpretations of this similarity parameter are given, while its role is discussed in general terms from the viewpoint of modelprototype similarity.

Waves will dissipate their energy rapidly after breaking. In this paper, the three factors, (i) formation of a horizontal roller, (ii) bottom friction, and (iii) turbulence with air entertainment, which will contribute to the energy dissipation, are dealt with experimentally and theoretically

The horizontal roller formed by a plunging breaker is approximated as a Rankine-type vortex by experiments, and it is calculated that 15%-30%of wave energy is dissipated due to the formation of horizontal roller alone from a breaking point to a point of the roller disappearance.

A bottom shear stress due to a breaker is measured by the shear meter deviced by the authors and it is clarified that the energy dissipation due to bottom friction is a little

Main part of the energy dissipation is taken to be caused by the turbulence with air entrainment. It is indicated that an incident monocromatic wave is transformed into a higher frequency wave due to the turbulence. Furthermore, a new basic equation for breaking waves with a turbulence term expressed by a Reynolds stress is presented The theoretical curves computed numerically have a consistent agreement with the experimental results

In the surf zone on beaches, there are strong effects which cannot be described by linear equations. This paper describes a number of wave interactions that can take place, using the simplest set of equations that give an adequate qualitative description. The results are of value for comparison with detailed experimental measurements and for gaining understanding of surf zone processes.

During storm surges considerable wave energies are dissipated in surf zones; the energy transfer rates are in the order of one up to two powers of ten higher than outside the surf zone. A breaker parameter β introduced by FÜHRBÖTER (1974) with regard to a quantitative breaker classification, especially of the intermediate types between surging and spilling, was found to be convenient for practical application. The breaker parameter β is in close relation with the horizontal asymmetry parameter α of the breaking wave. With decreasing breaker parameter the asymmetry is increased and reverse.

Within the longshore currents macro-turbulences were discovered. The periodical fluctuation parameter γ was found to increase nearly linearily with decreasing breaker parameter; the narrower the area is, where the main energy is dissipated the smaller becomes the mean periodical fluctuation which seems to be independent of the wave period but reaches up to 7 and more fluctuations within the wave period.

The mean longshore currents velocities reached up to 1.5 m/s above the seabottom; the coefficient of variation was scattering considerably between 400 per cent at low velocities $\left({\overline{\text{v}}}_{\text{L}}=0.1\text{m}/\text{s}\right)$ and 20 per cent at the highest velocities$\left({\overline{\text{v}}}_{\text{L}}=1.5\text{m}/\text{s}\right)$ . The instantaneous longshore current velocities were nearly symmetrically distributed around the mean velocity, the mean amplitudes were nearly constant and reached approx 0.35 m/s whereas the periodical fluctuation decreased from 2.6 s at low mean velocities up to 1.7 s at high velocities.

Two component electromagnetic flowmeters are being used as the basis of an apparatus to measure nearshore velocities on natural beaches. The flowmeters are mounted on free standing tripods, 1 m. base side and 0.3 m. high, to measure the two components of horizontal flow, and have been used in depths of up to 4 m. and up to 150 m. from the shoreline. The apparatus has proved both flexible and reliable on beaches ranging from steep shingle (slope ~ 0.13) to very shallow sand (slope ~ 0.01) and under a wide variety of wave conditions, including full storm waves on a beach of intermediate slope (~ 0.04).

Results show that a single flowmeter can be used on a tidal beach to measure the variation of the flow field along a line perpendicular to the shoreline. In this way edge waves and steady nearshore circulation patterns have been detected. If several flowmeters are placed on a line perpendicular to the shoreline, the progress of individual waves can be followed as they pass over each flowmeter in turn, and hence propagation speeds, changes of wave form and the development of lower frequency wave motion close to the shoreline can be studied.

Using the linear approximation for predicting velocities under periodic water waves, relationships are established between the velocity spectrum and the surface elevation spectrum for three-dimensional waves. The two dimensional forms of these relationships are used for comparison with velocity and elevation spectra measured in a laboratory wave tank. The predicted distortion of the spectrum shape can be observed in the experimental results. Velocity measurements were recorded using a laser velocimeter employing a rotating diffraction grating for shifting the optical frequencies. This allows measurement without sign ambiguity. The random waves were generated using a servo-driven paddle with a filtered white noise input.

In an earlier paper the authors reported the results of both field and hydraulic model investigations into the reaction of beaches to the action of waves of low phase difference. These waves are those whose time of uprush on the beach is equal to or less than 0.7 T, where T is the wave period. The present paper summarises the study of the internal velocity field under similar conditions. By making certain simplifying assumptions based on observations of the profile of the wave during uprush and backwash, the surging wave is open to quantitative description. For very low phase differences the uprush is approximately the reverse of the backwash, but to a different time scale. However, as the phase difference approaches the limit for the surging condition, the uprush starts and may remain in the form of a bore

Extensive wave refraction computations and analyses have been made utilizing eleven depth grids on the inner continental shelf along the east coast of the United States. The most important process determining shelf and shoreline wave energy distribution is the interaction of the ocean surface waves with the numerous shelf relief elements. This ocean wave-continental shelf interaction results in a non-uniform wave energy distribution that varies widely with different wave input conditions such as wave approach direction, wave length, and tide level. Techniques are being developed to manipulate and analyze these extensive wave data (encompassing over 500 wave refraction diagrams and associated computations), in order to increase understanding of the complex wave behavior resulting from the ocean wave-continental shelf interaction.

The combined refraction and diffraction of long gravitywater waves for certain depth variations around large islands is investigated analytically in a circular-symmetric geometry. Creeping waves are shown to exist for bottom profiles less convex than required by the trapping criterion due to Longuet-Higgins and Shen et al. From an asymptotic representation of the solution to the scattering problem the decay exponent and the diffraction coefficient is extracted. These "canonical" quantities may then be used for the construction of diffracted fields around smooth islands of more complex shape in accordance with J.B. Keller's Geometrical Theory of Diffraction.

Preliminary results are presented of a study of the beach erosion caused by wave refraction over offshore dredged holes. A mathematical model is used of an idealised sand beach, typical of those on the English Channel and North Sea coasts of Great Britain. Depth and side slopes of dredged area and original water depth before dredging were varied. Beach erosion increased with increasing hole depth and with decreasing original water depth. The effects of side slope and hole depth will be separated in future work, as will the effects of hole shape. Beach erosion due to holes in water depths greater than half the length of "normal" waves, or a fifth of the length of extreme waves, was negligible.

A water wave theory is presented to describe waves propagating on a bilinear shear current flowing in the direction of the waves. The theory is derived assuming an ideal fluid in which a current exists, having a vertical velocity profile which varies linearly from a mean water level velocity of U_S, an interfacial velocity U_I at depth, d, and a bottom velocity U_B. The theory is developed first for small amplitude waves and then extended to any arbitrary order by a numerical perturbation technique for symmetric waves. For measured waves, an irregular form of the theory is presented to provide a representation of these waves for analysis.

The tsunami process of their generation and propagation to the near-coast offshore region is discussed. Purpose is to give optimum configurations of tsunami waves of large magnitude, which can be used as boundary conditions for the analysis of the dynamic process near the shore or around structures in coastal zone.

They are obtained by numerical computations along the southern coast of the Hokkaido and the Sanriku Coast for various tsunami sources set on the continental shelf facing to the Japan Submarine Trench. Dispersive nature of the tsunamis seems to make the problem very complicated. However statistical results thus obtained can be accepted for the base of design of structures.

The paper deals with the initial ideas and concepts for development of a morphological model for a Delta coast, having particularly the Nile Delta in mind. The paper concentrates on the offshore zone, in which sediment is assumed primarily to be transported in suspension and during periods of sufficient agitation by the combined action of waves and ocean currents. In the Nile Delta great offshore changes take place due to the deprivation of the shelf area of Nile sediments by the closure of the Aswan High Dam, and serious nearshore long-range changes are expected to result from the changes to the offshore morphology. The modelling aids in establishing the mechanisms of the Delta shore, but the primary goal of the model is reliable prediction of future coastal changes. Fundamentally, the modelling is based on verification of the model – by trial and error – against known states of the model domain.

Part A of the paper deals with the general concepts, while especially the entrainment of sediments is treated in Part B of the paper, yielding practical formulas for determining the treshold values for sediment entrainment by unidirectional flow and by wave action.

Littoral currents within the breaker zone and currents other than those induced by waves beyond the breaker zone exist with considerable magnitude along the Nile Delta coast. Analysis of the littoral currents within the breaker zone by four semi-empirical formulae involving energy, momentum and radiation stress principles indicates good correlation between predicted and observed velocities. Galvin-Eagleson approach gives the best fit. Current data are statistically analysed enabling the determination of the magnitude, direction and percentage of occurrence of any particular littoral current for any particular period.

More comprehensive studies of the currents climate within the breaker zone and beyond the breaker zone for the entire Nile Delta coast covering a large number of years are under way,

The steady state profile of the longshore current induced by regular, obliquely incident, breaking waves, over a bottom with arbitrary parallel bottom contours, is predicted. A momentum approach is adopted. The wave parameters must be given at a depth outside the surf zone, where the current velocity is very small. The variation of the bottom roughness along the given bottom profile must be prescribed in advance. Depth refraction is included also in the calculation of wave set-down and set-up. Current refraction and rip-currents are excluded. The model includes two new expressions, one for the calculation of the turbulent lateral mixing, and one for the turbulent bottom friction. The term for the bottom friction is non-linear. Rapid convergent numerical algorithms are described for the solution of the governing equations. The predicted current profiles are compared with laboratory experiments and field measurements. For a plane sloping bottom, the influence of different eddy viscosities and constant values of bottom roughness is examined.

Hindcast deepwater wave statistics and bottom hydrographic data are combined with a water-wave refraction analysis to estimate the littoral transport in a beach zone. The effects of hindcast data station location, of wave ray density in the breaker zone, of changes in the bottom-fitting surface in the depth calculation of the refraction analysis, and of methods of smoothing the contribution of individual rays to the littoral transport computation are explored.

The total annual volume of littoral drift on either side of the mouth of Sergipe estuary, in the Northeast of Brazil, has been determined by applying Caldwell's, Castanho's and Bijker's methods to the wave characteristics that had been recorded at a twenty-metre depth of water, over a whole year, for the design of an offshore oil terminal.

The three computation methods yielded the same order of magnitude which was found to amount to about 800000m³/year. The dominant drift is s outhwes tward, and its predicted amount is 660000m³/year. It was also found that although the three methods lead to total results of the same order of magnitude, they do not agree as to the variation of littoral drift over the year for the s ame waves.

An eight-metre deep shipping channe 1 has been dredgedaccross the bar. The channel was surveyed in December 1971, August and December 1972, and a cubature of the deposits was made after the littoraldrift computations had been carried out. As the latter had been performed on a monthly basis, a comparison became possible between predicted and actual volumes of deposits for the same lengths of time.

The predicted volumes for the whole year were found to be from 34 to 46% greater than the actual results. However, for the time interval August-December 1972 a remarkable agreement was found between predicted and actual results.

The direct and continuous measurement of the littoral drift is an essential problem with investigations on erosion of sandy coasts, as for instance at the island of Sylt. The measuring conditions require equipment of very particular features.

Recent measurements have supplied informations about the conditions of sound propagation in sediment loaded water, leading to the conception of a sand discharge measuring device. It will consist in a combination of a current meter and a sand concentration meter.

A convenient equipment is actually being developed. It is to supply an idea about the magnitude of the instantaneous sand discharge, the approximate remaining sediment transport vector, the phases of maximum and minimum sediment load, and so on. Consequently it will help to obtain a reliable statement about erosion processes, indispensable information for successful coastal engineering work.

As the velocity of the water motion near the bottom under oscillatory waves is increased, there comes a stage when the water exerts a stress on the particles sufficient to cause them to move. This study reviews data on threshold of sediment motion under wave action and compares the results with the established curves for threshold under a unidirectional current.

For grain diameters less than about 0.05 cm (medium sands and finer) the threshold is best related by the equation

Evaluating the drag coefficient with the graph of Jonsson for wave motions, the data on threshold under waves is found to show good agreement with the curves of Shields and Bagnold for the threshold under a unidirectional current.

The possible effect on the stability of a porous sand bed of the flow induced within the bed during the passage of near-breaking or breaking waves is considered. It is found that the horizontal flow rather than the vertical flow within the bed may affect its stability. An approximate analysis, used in geotechnical computations of slope stability, indicates that a momentary bed failure is likely to occur during the passage of the steep front slope of a near-breaking wave. Experimental results for the pressure gradient along the bottom under near-breaking waves are presented. These results indicate that the pressure gradient is indeed of sufficient magnitude to cause the momentary failure suggested by the theoretical analysis. The loss of stability of the bed material due to the flow induced within the bed itself may affect the amount of material set in motion during the passage of a near-breaking or breaking wave, in particular, in model tests employing light weight bed material. The failure mechanism considered here is also used as the basis for a hypothesis for the depth of disturbance of the bed in the surf zone. The flow induced in a porous bed is concluded to be an important mechanism which should be considered when dealing with the wave-sediment interaction in the surf zone.

Sediment transport in random waves at constant water depth is analyzed by dividing the flow field into two regions—the internal region and the boundary layer region. The suspension and transport of sediment in these two regions are treated separately. The total transport is then obtained as the total of these regions through matching boundary.

In the bed layer, the load concentration is assumed to be proportional to the specific weight of the sediment and to the probability that the fluctuating lifting force exceeds the weight of the sediment. The bed load is then transported by the secondary flow (which is unidirectional) in the boundary.

In the internal flow region, the sediment suspension is treated as a diffusion problem with the intensity of diffusion to be proportional to the amplitude of fluid particle motion. The transport velocity is assumed to be the same as the mass transport velocity of the wave.

The predominant mode of transport is found to be suspended load. The total transport in a wind-generated wave field can be expressed as a power law of wind speed. For the case tested, the power should be of the order of 4.

Three almometers-water opacity measuring devices-emplaced perpendicular to the beach,measure instantaneously and continuously the sediment concentration across the surf zone. Most of the variance of the sand movement is centered in frequencies of less than 0.25 Hz and between 1.15 and 1.25 Hz. Modes and frequency of sand transport differ within each of the dynamic zones of the surf. The motion of sediment in the inner and outer surf zones is small and virtually independent of the deep water wave periods. Outside the breaker zone, bed load movement is somewhat coincident with the prevailing swell period. Lighter concentrations move predominantly with a 0.8-0.9 second periodicity. In the breaker zone, sand moves along the bottom with frequencies equal to that of both the swell and sea, but most of the power is in lower frequencies. In the breaker zone sand is rarely thrown into suspension. In the transition zone, sediment motion is largely by suspension with a period a little longer than the swell.

The stability of an alluvial coast depends upon the localsediment budget. Along the shore, changes from erosion to accretion may reflect changing sediment fliixes, sediment residence times and patterns of sediment movement. Processes influencing these parameters, such as mud sedimentation or migration of intertidal channels will, through their influence on beach gradients and sediment transport patterns, affect the processes and rates of coastal dune erosion and the safety of the dune protected hinterland.

A qualitative description of some of the various processes and phenomena linking foreshore and dune stability with sediment circulation and coastal evolution is presented.

This paper mainly describes experiments that have been carried out on two shingle beaches on the south coast of England.

The results for the higher energy environment of Chesil Beach showed that largest tracer material travelled farthest, and best correlations tended to be with the short axis. At Slapton, however, different sediment parameters appeared significant at various times. Where linear parameters were relevant correlations were again best with the short axis, but smaller material travelled farthest. This may reflect different wave regime, a less efficient sediment rejection mechanism, finer grades of sediment or better adjustment of tracer to indigenous background material at Slapton.

There was a marked degree of selectivity at both sites between material recovered along a particular zone of the beach as compared with the overall recovery on the same day, and between the overall recovery for a particular day as compared with the originally injected tracer. Attempts have been made to correlate wave data from f.m.pressure recorders with longshore transport of the coarse grades of sediment in the inter-tidal zone. While at Chesil wave direction, frequency and height were all important there were no obvious relationships at Slapton. The results have relevance in respect of beach stability and in the conclusions drawn from tracer studies using coarse grades of sediment.

Extended sand banks ranging up to some hundred acres with a crest height in the MHW-level are typical structures of the outer tidal flats of the south-eastern North Sea coast (Fig. 1).

Primary forms grow up in the surf zone at the sea-side tidal flat border. They are formed like bars and migrate towards the coast with a surprisingly high velocity, up to 150 m/year.

The movement is caused by strong erosion on the sea-side slope – which is shaped beach-like – and deposition at the steeper land-side (lee-side) slope.

It was found that surf action at the bar is linked with strong unidirectional currents across the crest, Up to 100 cm/s. The currents are most likely generated by wave set-up in front of the bank and by wind-drift water motion.

The migration velocity of the sand banks decreases with increasing distance from the tidal flat border. This effect seems to be most important when generation of new banks continues. It leads to "overtaking" and "interaction" of the single structures, thiswise growing together and building up the large sand banks as described above and gives an explanation of the development of large offshore sand banks and dune islands on tidal flats.

The investigation reported herein covers two aspects of the schematization of coastal processes on sandy beaches in a direction perpendicular to the coastline, viz.: (1) the prediction of equilibrium beach profiles and (2) the corresponding offshore sediment transport due to wave action. A physically-based schematic model of the onshore-offshore profile development was tested on available small-scale and full-scale model tests and physically-based empirical relationships were derived to enable the application of the model to both small-scale and prototype conditions.

Important physical parameters controlling sandy beach transformation were clarified on the basis of the result obtained by a laboratory test. They were not only wave steepness but also beach gradient and a ratio of sand size to wave length. These parameters enabled the previously obtained laboratory beach profiles to be classified into newlyproposed three beach types. These parameters were also found to be effective in grouping the data of shoreline changes both in laboratories and in fields.

In order to obtain design criteria for artificial gravel beaches, a research programme was drawn up to study the behaviour of gravel beaches under wave attack. The present paper gives the main results of the first step in this programme, viz. the determination of the dimensions, form and way of formation of an equilibrium profile under regular, perpendicular wave attack. One of the conclusions is that gravel with a D₉₀ < 6 * 10^-3 m is sensitive to scale effects.

Reflection coefficients and profile changes were measured during four lengthy experiments in two relatively long, narrow wave tanks. Each tank had a periodic wave generator at one end and a 0.2 mm movable sand bed at the other end. Generator period (1.90 sec), water depth (2.33 ft), nominal wave height before reflection (0.36 ft), and initial sand slope (1:10) were constant In the four experiments. Measured reflection coefficients (K_r = H_r/H_i) ranged from 0.05 to 0.30, with the typical time variation of K related to profile changes as follows: K_r increased by a factor of 3 to 4 within the first minutes while a steep foreshore was built on the undeformed profile; K_r fluctuated and dropped to a lower value as the inshore widened; K_r increased as the offshore steepened. Large variations in K_r near the end of the experiments appeared to result from minor profile changes. The apparently similar experiments showed very different rates of profile development, implying control by other variables such as water temperature or tank geometry. "Equilibrium" in these experiments was never reached, even after as many as 375 hours of wave action.

Schematical relations for the size of dunes and for the duration of their development are derived assuming that the large scale formations on the surface of a movable bed are due to the largest eddies of turbulence. The considerations are confined to the simplest case of a two-dimensional flow and to the cohesionless granular material. The relations for tidal dunes are obtained by generalising the relations for unidirectional flow dunes, Special cases and the validity regions of the forms presented are discussed; suggestions for future measurements and model tests are included.

In a lot of regions the bottom of the North Sea is covered with large ripple fields, especially in the estuaries and in the tidal channels. A great number of echo sounding profiles (29.500 n.m.) were evaluated to determine the boundaries of these areas and to describe the dimension of patterns. Special investigations of the hydrographic situation, the distribution of deposits and the migration of ripples under the influence of tidal currents only, were carried out in a testing area in the Lister Tief on 11 cruises since 1971.

In this paper prototype data of echo soundings of tidal dunes are analysed. A good relation between the fresh water discharge and the sand wave migration velocity in the upper part of a tidal river could be determined. The limitation of the dune heights as a function of the mean current velocities over the crests and the bed material characteristics is presented. States of equilibrium are described by dimensionless parameters and the latter compared with model tests.

An experimental study of the variables governing the development of bed forms under wave action has been conducted. A wide range of conditions was covered by the use of a wave flume and an oscillating water tunnel. Scale laws for modelling bed forms are developed using the results of these experiments. It is recommended that the model sediment used should be the same density as in the prototype and its size should be scaled geometrically. If this is not practical, it is shown how the scale laws can be used to minimise the distortion of the bed forms produced in the model.

In the previous paper (Hattori, 1969), a theory for the distribution of suspended sediment concentration due to standing waves was obtained on the basis of the concept of "delay distance" which accounted for the fluid-particle interaction and the inertia effect of sediment particles.

The purpose of this paper is to make clear the physical dependence of delay distance to wave and sediment characteristics.

The evaluation of delay distance from experimental results of distribution profiles of suspended sediment concentration is made by the assumption that the horizontal diffusion coefficient of suspended sediment is nearly equal to the vertical one. An empirical expression of delay distance is obtained as follows;

The following theoretical expression for delay distance is obtained from the equation of motion for a discrete particle suspended in onedimensional unsteady fluid flow.

A radiometric probe and sand traps have been applied to measure a distribution of the suspended sediment in a vertical profile.

The first stage of investigations, comprising the laboratory tests and first experiments in the Baltic Sea, were carried out in 1973.

As results of the above experiments calibration curve for radiometric probe has been obtained and some weak points of the method have been overcome.

Six sand traps of bamboo type were situated in different distance from a shoreline and by turns perpendicular or parallel to the shoreline. It enables the determination of percentage distribution of suspended sand in vertical profile and along a bottom profile during a wave cycle.

The present paper describes the application of a two-dimensional numerical suspended sediment model to problems having analytical solutions, as well as to laboratory and field situations.

The model is based upon an implicit finite-difference solution to a two-dimensional (longitudinal and vertical) diffusion-advection equation for suspended sediment transport. Horizontal eddy diffusion is neglected in comparison with vertical diffusion and vertical water motion is assumed negligible in comparison with the sediment fall velocity.

The various applications indicate that the greatest errors in the model are due to large spatial concentration gradients and that errors can be controlled by a suitable choice of space and time step. In addition, it is considered that the model has great flexibility and seems to have an acceptable level of accuracy, at least in the field situations tested, provided the physical parameters of the model can also be determined accurately.

In this paper first a numerical model is described concerning the velocity distribution in an oscillatory flow, respectively without and with resultant current. From the momentaneous velocity gradients eddy viscosities are derived. Using the approach of VANONI[1] , a numerical model is given for the calculation of sediment concentration and suspended sediment transport. In order to give reliable results, the bed-load concentration should be knowno This will be investigated in the future; at the moment the model only provides qualitative results.

A study of historical information and field measurements in Sargent Beach, Texas, reveal that the shoreline is retreating with historic rates increasing from -10 feet per year in the late 1800's to -31 feet per year (-9.8 m/year) in the early 1970's. The cause of this erosion is the lack of an adequate sand supply to the beach zone. This sand deficiency is due to: a) reduced updrift sand input to the coast by the Brazos River beginning in 1945 and caused by decreased sediment transport capability of the river, b) increased sand storage in the Brazos Delta encouraged by jetties and vegetation, and c) possible offshore losses of sand due to hurricane wave energy focusing on the Brazos Delta in conjunction with river jetting during peak river flows.

Barrier dunes are the natural protective structures against flooding the low-lying land during storm tides. Their strength and resistance are to be estimated in consideration of the total dune-beach-profile. For standardization of dune-beach-profiles 3 types are to be distinguished. For each of these types the necessary and the possible actions for stabilization of the barrier dunes and also of inshore dune areas are described.

Barrier islands and barrier beaches have developed across structurally controlled estuaries and embayments in the southern Gulf of St. Lawrence. The supply of sediments to the littoral zone and the subsequent accumulation of barrier deposits is a result of the reworking, transportation and longshore dispersal of sediments which are moved landward by tidal and wave-induced currents from the adjacent shallow sea floor. The size and stability of the barriers is controlled by the shoreline orientation.

The primary barrier dune on the northern portion of Assateague Island, Maryland is presently being scarped on its seaward face and breached by storm-generated surges. During storms, sediment-ladened water moves across the dune line onto the barrier flats as overwash. The objective of this project is to determine the role overwash plays in barrier island sedimentary dynamics.

An overwash model has been suggested. The nonvegetated overwash fan serves as a reservoir for the eventual distribution of the storm-deposited sand. Eolian processes, after the storm, determine the net contribution of overwash sand to each of the different morphological features, i.e., dunes, marsh, beach, etc.

At many places along the dutch coast especially at the West side of the islands, erosion occurs.

One of the islands where the erosion is severe, is Goeree, situated in the Delta area in the South-West of the Netherlands.

(see fig. 1). This isle is recently connected with other islands by dams, (see fig.2). These dams built within the scope of the Deltaproject plans closing the tidal estuaries and to shorten the length of the coastline thus reducing the wave attack. This paper examines how the influences of the closure of the estuaries affect on the erosion of the neighbouring coast. To this end, the changes in vertical and horizontal tide caused by the closure as well as the wave induced littoral drift and the sandtransport caused by a combination of tidal currents and waves before and after the closure, are computed. On the basis of this computations, a few suitable solutions for the reduction of erosion are discussed.

The depositional characteristics of floes of fine cohesive sediments in a turbulent flow field differ distinctly from those of a cohesionless material such as sand. This difference exists because the floe size and shear strength distributions depend on the sediment type as well as the flow condition itself; consequently, the problem of the depositional behavior of these floes is rather complex, and not easily amenable to analytic treatment.

The present basic experimental study was carried out in a specially designed annular channel. The derived laws of deposition in relation to the time-rates as well as the steady-state concentrations are described and discussed. The reanalyzed results of other limited investigations agree well with the result of the study.

The results of model testing show that the strength and stability of bottom sediments can be substantially reduced by the cyclic loading pulses induced by wave action. The minimum soil strength is approximately equal to the remoulded vane strength and the depth of wave remoulding appears to be mainly a function of the wave characteristics. The phenomenon of wave remoulding should be considered in the design of offshore foundations as reductions in bearing capacity and lateral shearing resistance can develop as a result of the action of storm waves.

Where bottom sediments are sloping such that the static factor of safety against slope failure is less than the soil sensitivity, severe storm conditions may lead to submarine landsliding. Wave induced submarine landsliding has been reproduced in model tests and the results are correlated with current analytical approaches to this problem.

Artificial shipping channels in fine sand tidal estuaries are difficult to maintain. The attempt to stabilize the river beds and thus the fairway in the upper reaches of the Outer Weser by means of systems of river structures has been a success. The further deepening of the fairway necessitated the artificial narrowing of the river bed. The successes of improvement achieved over a prolonged period have up to now been satisfactory. Some explanations concerning the effects of the river structures on the morphology are given in the present report. In the improved river bed a continuous shifting of sediments is taking place, which is mainly due to the incessant action of the tidal currents. It is inevitable in this process that sand is drifted into the deep excavated channel. If one has a good knowledge of the natural shifting processes, it is possible nowadays, by using suitable Hopper suction dredgers, to employ to a certain extent methods of dynamic river engineering by means of the proper artificial shifting of the excavated soil within the cross sections of the river.

The physical characteristics of estuarine sediments provide useful information about sediment sources, the nature of bottom surface stresses and sediment transport mechanisms. Changes in sediment composition and state are also useful indicators for estimating the effects of unnatural stresses on dependent chemical and biological activities. In this study, the changes in several sediment properties have been monitored for an isolated estuarine dredging project.

The effect of estuarine hopper dredge activities has been evaluated for an Army Corps of Engineers project at Coos Bay, Oregon. The project included suction head dredging at a shoal area within the navigation channel and in bay spoiling at a deep section of channel one mile downstream from the dredge site. Core samples were taken five days before dredging and two, thirteen and seventy days after dredging at the dredge and spoil sites. Subsequent laboratory analysis of the core samples revealed that dredging induced redistribution of bottom sediments produced significant changes in several physical characteristics of the dredged material. Repeated resuspension of bottom sediments during the dredging and spoiling operations caused a net loss of fine grained sediments and light organic constituents. Several symptomatic changes were observed which validate this finding, including: an increase in median grain size and decrease in uniformity of dredge spoils due to loss of fine fractions; a decrease in volatile solids in the dredge spoils due to a net loss of organics; a decrease in porosity at the spoils site due to the ability of the coarse grain sediments to resist resuspension; and a decrease in hygroscopic moisture content due to loss of porous organics and silt-clay material from the spoils.

Conditions following dredging were observed for a period of seventy days. Partial recovery of the sediment system was observed after two weeks with no further recovery in two months. The initial recovery came about due to the availability of local sources of resuspended sediment adjacent to the dredge site. This occured under low flow conditions in early fall. Complete recovery of the system was not observed and probably requires the relatively large sources of sediment which accompany heavy winter and spring runoff. Thus, the immediate effects of dredging may persist until the annual cycle of sediment erosion and deposition have occurred.

A number of factors such as wave conditions, tides, river flows, sediment charge, and ocean currents affect the features of an estuary. The understanding of the morphology of an estuary is essential on purely scientific considerations as well as applied to harbours. An attempt is made to study these inter-related and unsteady features and their combined effect on an estuary qualitatively. The estuary selected for the study is the one near Mangalore on the West Coast of India at latitude 12° 51' north and longitude 74° 50' east, where two rivers, viz., river Netravati and river Gurpur meet together and join the sea. An effort is made to analyse the changes in the estuary in terms of prevailing wave conditions, river flows and sediment transport.

A simple method is presented for estimating the relative compatibility of borrow material being considered for beach fill purposes. The method defines the "compatible" fraction of the material as that coarser portion with the same mean diameter (in "phi" measure) as the native material on the beach. A single graph is presented which allows determination of the number of units of borrow material required to obtain one unit of compatible material. Use of this method requires that the size distributions be reasonably represented by the "lognormal" relationship and also requires knowledge of the means of the native and borrow materials and the standard deviation of the borrow material (all in phi measure). This method overcomes shortcomings of the Krumbein-James method published in 1965. Several examples are presented illustrating the application of the method presented in this paper.

The dependence of beach fill stability en the textural properties of borrow material requires development of quantitative methods for use in selection of borrow areas and in prediction of possible maintenance costs associated with periodic renourishment. If a shore segment is viewed as a sediment mass transfer system, where grains of different size have different transport rates, then termination of natural sediment input to the shore segment will cause the beach to retreat and the materials in the active zone will become coarser. The ratio of retreat rates associated with a given borrow material texture to that associated with native material can be used in optimizing economic factors involved in selection among potential borrow zones.

With certain simplifying assumptions the relative retreat rate associated with a given borrow material texture can be predicted from observations of the modifications in textural properties of native material which occur during the eroding condition following termination of the natural supply of sediment. Further simplifying assumptions result in an analytical expression for relative retreat rates which may not require observations of the natural beach in the eroding condition.

The proposed method is in substantial agreement with qualitative guidelines provided in the Shore Protection Manual [2].

Planning has recently been completed for a shore protection project along a 9-mile (14.5 km) reach of shoreline fronting the Towns of Yaupon Beach and Long Beach in Brunswick County, North Carolina. The investigative program related to this planning effort embodied numerous interrelated elements which, on integration, resulted in a rational engineering design having a continuous beach fill as the central feature. Specifically, the investigation included: (a) definition of the environment, viz, wind, waves, storm tide frequencies, beach profile characteristics, shore processes, and ecological habitats along the proposed project area as well as in potential beach fill sources; (b) Designs and cost estimates including establishment of various fill profile configurations, cost optimization of fill positions, evaluation of the frequency of shoreline retreat and the attendant displacement of fill materials, evaluation of the compatability of materials from various fill sources with the natural beach materials, environmental impact studies, and economic studies; and (c) Final plan formulation arriving at the optimum fill plan in terms of engineering functionality, economics, and minimal adverse environmental impacts.

A beach monitoring program between 1962 and 1972 at Atlantic City, New Jersey was designed to observe the response of beaches to waves and tides of specific intensity and duration as a first step in developing a storm warning system for low-lying coastal communities. As a by-product of that study the behavior of beach sand following two beach replenishment projects in 1963, and again in 1970, was determined. Monitoring was done using repetitive beach surveys above mean sea level (MSL) at seven profile lines. Survey results show that following replenishment, losses of the fill material above MSL were between nine and twelve times the losses measured in adjacent non-fill areas. Loss rates were largest at the updrift end of the fill region. About two and one-half times more material appeared to move in a seasonal on-offshore direction than moved permanently alongshore and.above MSL to the southwest. For each meter of beach retreat, 5 to 6 m³/lineal meter of fill were lost.

This paper describes how a once popular pleasure beach became denuded by the abstraction of sand for industry and how, in more recent times, it was restored to its former levels. The history of the area has been studied in some detail, and it can be seen that the lowering of the beach caused progressive damage to the sea wall, eventually leading to flooding of some parts of the frontage.

In the 1960's a parapet was added to certain sections of the sea wall, and local flooding was alleviated, but the lower parts of the wall and apron suffered continuously from wave attack and the situation deteriorated to an extent where complete reconstruction of the sea defences had to be considered. It was shown that a scheme involving beach renourishment by the pumping of sand from offshore provided a more economical solution and the area now enjoys the amenities provided by the restored beach.

Breakwaters in a series can be employed to protect sedimentary coasts. They are used to protect newly reclaimed land along the southeast coast of Singapore; they act as headlands between which sand beaches are formed. The development of these beaches takes place under conditions of low energy waves, a predominant wave direction from the southeast and an east-west littoral drift. The characteristics and development of three beaches over a one-year period are presented. Surveys of the reclaimed land show various beach types between the headland breakwaters. A relationship exists between berm orientation and headland breakwater orientation. Beach stability is tentatively indicated by the formation of a wide berm.

Beach erosion is one of the serious problem in Japan. As a oountermeasure against beach erosion, many preventive works, such as sea walls and groins, have been constructed during the past 20 or more years. However, as the result of field investigations, it has become clear that sea walls and groins are not always effective on beach erosion prevention, and inversely, in some cases, they accelerate the beach erosion.

Based on the above cognition, the author has proposed and tried to apply the detached breakwater system as a measure against beach erosion for the last 8 years. This is for the purpose of developping the sand deposition behined the breakwater. Therefore several experimental works of the detached breakwater system were carried out under the guidance of the present author, and most of these tests were successful.

The design method of this system was composed by the author on the basis of the result of field investigations, which have been conducted for more than 8 years.

The numerous construction works of detached breakwaters have been carried out in accordance with the design method proposed in this paper, and the effectiveness of detached breakwaters has been proved on the several coasts in Japan where severe beach erosion occurs.

The interaction between a normal groyne and waves mostly is by diffraction, i.e. the structure of the groyne, especially the width, is very small in comparison to the wave length. But when a groyne is built with lateral slopes comparable with normal beach slopes, also refraction processes occur and surf zones are created nearly parallel to the center line of the groyne. It can be shown that, for all directions of wave approach, the longshore currents always are directed shoreward. So, when such a groyne is built by sand, due to the erosion of the groyne an artificial sand spit is formed and a beach nourishment at the adjacent areas of the shore can be expected. Furthermore, sand originating from the normal littoral drift can be caught by such a structure as it happens in case of normal groynes.

In a field experiment at the shore of the city of Westerland on the island Sylt/Germany, with 680,000 m³ of sand such an artificial sand groyne was built in 1972. One year later, this sand masses were grown up to nearly 1,050,000 m³. After a sequence of five heavy storm surges in November and December 1973, still 770,000 m³ could be detected before the shore in 1974. The evaluation of the experiment is continued; the aim of it is find out whether repeated beach nourishment is more economic than protective works. For this reason the knowledge of the "half decay time" of a beach nourishment is necessary.

Comprehensive monitoring has been carried out since 1970 to determine the performance and effects of a navigation and inlet stabilization project at Ponce de Leon Inlet, Florida. The improvement plan at the tidal inlet included construction of two jetties, a weir sand by-pass system, and dredging of a navigable channel (Figure 1). An evaluation was made of the general current patterns, the relative refracted wave energy distribution, and the volumetric beach and hydrographic fluctuations associated with the inlet. An analysis of this data was used to interpret the dramatic and unexpected changes which have resulted along the adjacent coastline and within the inlet after the completion of the inlet improvements.

This provides further information and assessment of the three harbour entrance wave traps at Dingwall, Inverness and Pleasant Bay located in Canada. These were constructed to reduce the amount of maintenance dredging required in the entrance channels.

Wave climate data and littoral material analysis are presented.

Observations on the performance of each structure are given and conclusions drawn as to restrictions and constraints on applicability.

Model studies and analysis of oceanographic and littoral drift data were undertaken to advise Howe India (Private) Ltd. on littoral drift, siltation and shore erosion problems to be encountered during and after the construction of Visakhapatnam Outer Harbor Project.

Distorted fixed-bed and movable-bed models with a horizontal scale of 1:300 and a vertical scale of 1:80 were calibrated to reproduce the integrated net effect of an average southwest and northeast monsoon season. Experiments were conducted to assess and predict seasonal changes resulting from the construction of the system of breakwaters under normal and extreme conditions. Recommendations were made concerning breakwater and sand trap location, shore protection, dredging and disposal of dredged material.

A series of laboratory experiments was carried out on an idealized oceaninlet-bay system subjected to reversing flows caused by tidal and surface wave actions. The testing was done in a rectangular basin simulating a "bay" or "lagoon" and separated from an "ocean" basin by a sand barrier across which inlet pilot channels of varying cross sections and lengths were cut prior to starting each run; the ocean side of the barrier formed a 1:30 flat beach throughout the tests. Disturbances in the ocean were created by tide and wave generators. Their effects in the bay and inlet channel were measured by water level and current velocity recording units. Experimental measurements are presented here in normalized form in order to determine the relationships governing the hydraulic behaviour of a tidal inlet. These results are also compared to those obtained from a numerical approximation (the lumped parameter approach), all as functions of a proposed coefficient that includes the ocean-inlet-bay system characteristics. The experimental findings are further compared to available field data. Investigation of the effects of surface waves, controlling jetties, and fresh water inflow into the bay on the dimensionless parameters are also explored.

Data contained in the Tide Tables, Current Tables and navigation charts of National Ocean Survey pertaining to tidal entrances along the coasts of the continental United States are analyzed to obtain flow coefficients defined by a simple hydraulic equation. The evaluation of the published data indicates that the data are sufficiently accurate and representative, despite some unexplained anomalies, to permit determination of the approximate discharge coefficients and, more importantly, to identify categories of flow regimes of inlets. A few conclusions are:

1. The Keulegan approach and similar analyses of inlet hydraulics provide a useful qualitative framework for ordering data but they apply quantitatively only to small inlets and lagoons with simple inlet channel geometry.

2. The lag of slack water in the entrance channel after HW and LW is a powerful tool in the analysis of the hydraulic regime. It is easily measured in the field and should become an identifying characteristic of each entrance.

3. The resistance coefficient F represents the overall impedance and exit losses, reflections from the lagoon shore, fresh water discharge and the configuration of the channel between the inner and outer bars. It may be determined from measurements of lag and maximum velocity at the throat and the range of ocean tide.

This paper is written in continuation of earlier published material (2, 4, 5) dealing with stability of tidal inlets on littoral drift shores. The experience available at that time was responsible for the introduction of two parameters: V_{mean max}, defined as the mean max. velocity in the gorge at spring tide and the Ω/M_tot ratio (tidal prism at spring tide divided by material transport to the entrance from the adjoining shores) as the most pertinent parameters for description of overall stability. A more detailed justification for this choice is given in this paper, based on computation of the relative sediment transport at various tidal phases. Examples of earlier date (4) and twelve new examples from India are given.

Wachapreague Inlet, a downdrift offset inlet in the barrier island complex of the mid-Atlantic U.S. coast was studied during the period 1971-1973. Elements of the study included: (1) the inlet morphometric history (120 years), (2) assessment of surficial and sub-bottom sediments within the inlet complex, (3) response of the channel cross-sectional area to short-term variations in wave activity and tidal volumes, and (4) the distribution of tidal flows within the channel.

It is concluded that: (1) a qualitative correlation exists between short-term channel cross-sectional area change and the ratio of ebb tidal power to wave power. It is inferred that the important element is the direct wave activity on the ebb-tidal delta; (2) duration differences in rising and falling phases of the tide (flood longer than ebb) lead to an ebb dominence in bedload capacity at the inlet with the result that this inlet has a natural flushing ability; (3) there is pronounced sand circulation within the inlet complex via a sediment flow loop which is driven by wave refraction and lateral inflow on the updrift side. The sand volumes thus delivered annually to the inlet channel from the ebb delta appears to far exceed the estimated littoral drift. The local sand circulation should, therefore, be considered in engineering design for inlet control structures.

The contribution deals with the morphologic examinations and calculations for a deep-water harbour which is to be constructed in the tidal flats of the Elbe estuary near the North Sea islands of Scharhorn and Neuwerk. An attempt is made to examine the stability of tidal channels (gullies)and tidal flats which may be disturbed to a greater or lesser extent by the various proposals for the connecting dike between the industrial area near the harbour and the coastline.

The underlying logic for the determination of the equilibrium of the flats and the quantitative solution for the sand-balance is as follows:

It has been shown in several empirical investigations that the increase of the relative volume of the tidal basin (V/V_MLW), referenced to the gully volume for MLW, can be determined as a simple function to the base (ā) logarithm of the geodetic elevation (z^*) between MLW and any higher contour level up to MHW. Furthermore it can be shown that (V_MLW) is also a function of the tidal drainage area (E).

The base(ā) has been related to the size of the tidal drainage area (E), because this area is subject to considerable modification by offshore structures such as dikes and causeways.

Extensive wind profile measurements have been made over beaches, tidal flats, and small dune fields in Barbados, Ecuador, Florida, Texas, and on Alaskan Arctic coasts by the author and his associates during the past several years. The linear relationship between shear and wind velocities was further verified by these measurements, in conjunction with Bagnold's data from experiments in a Libyan desert. From these measurements, a simple method is developed for computing eolian transport of the most common sand particle sizes which occur on coasts and deserts by using only routinely available wind observations from nearby weather stations.

Mishaps with jack-up oil rigs could be caused by scour beneath their legs as they oscillate vertically, either on site or when being shifted to or from site. This action was replicated in the laboratory by moving cylindrical feet to and from a sandy bed at frequencies appropriate to the scale of the model. By retaining equal Reynolds numbers for the sand grains, whose size was commensurate with prototype material, the period of oscillation had to vary with the leg diameter. By adopting a suitable size scale, a range of periods was determined from knowledge of resonant motions of rigs in relatively deep water. Erosion was recorded which appeared sufficient to cause mal-distribution of load in the structure. Even when oscillations occurred in a leg penetrating the bed, no support was available due to liquifaction of the soil. The two pilot studies herein described indicate the need for a comprehensive research program on the subject, due to the large investments in jeopardy.

Model tests with locally generated turbulence near horizontal and vertical cylinders are reported.

Turbulence is measured with newly developed ultra-sonic probes, and spectral density functions and auto-correlation functions are given.

Tests are carried out in uniform currents, in sinusoidal waves, and in combinations of current and waves.

Results are given for a viscous laminar boundary layer corresponding to a very fine sediment, and for a turbulent boundary layer corresponding to a hydraulically rough bottom.

In Norway recent scour research, initiated by the North Sea oil operations, has been guided in three directions:

1) Scour around big gravity structures

2) Distribution of pore pressures in the ground under wave loads.

3) Local scour near unburied pipelines.

Coastal Engineering literature contains many references to coastal structures in the design or construction stage but few references to these same structures concerning their maintenance effectiveness subsequent to completion. This paper describes a successful long-term maintenance history of major coastal public structures in the State of California, U.S.A. It is concluded that proper design combined with prudent maintenance will result in effective coastal structures with long economic lifetimes.

The paper deals with two-dimensional tests on a scale model of a dolos breakwater. It is related with the construction of a large harbour at Sines for tankers with up to 1 million dwt, ore ships with up to 300,000 dwt, general cargo, etc. The main breakwater is designed with 40 t dolos, in order to withstand waves with up to 11 m significant wave height(100 years return period).

Considerations on wave data and on modelling the spectrum (Pierson-Moskowitz) precede the presentation of three sets of tests on LNEC's irregular wave flume. Main results are compared with those from regular wave tests.

The most important conclusions are stressed: influence of placement on dolos damages, irrelevance of maintenance, importance of the singular zone of the dolos support base, disadjustment of Hudson's formula for calculation of dolos weight using H as significant wave height,and importance of individual movements for the risk of breaking of individual blocks.

The stability of dolos armour blocks against wave attack has been investigated in wave model studies.

Simple definitions to describe the block movements are introduced and the following results are discussed:

1. The stability of dolos slopes against regular waves and the influence of the slope.

2. The stability of dolos slopes against irregular waves that are not Rayleigh distributed.

3. Comparison between the stability of dolos, natural stones and cubes.

4. The influence of the surface roughness of the dolos model blocks.

5. The applicability of Hudson's formula.

A proposal is made for new wave pressure formulae, which can be applied for the whole ranges of wave action from nonbreaking to postbreaking waves with smooth transition between them. The design wave height is specified as the maximum wave height possible at the site of breakwater.

The new formulae as well as the existing formulae of Hiroi, Sainflou, and Minikin have been calibrated with the cases of 21 slidings and 13 nonslidings of the upright sections of prototype breakwaters. The calibration establishes that the new formulae are the most accurate ones.

The wave-pressure formulas derived in our laboratory have been verified by the investigations of the slide of the vertical walls of composite-type breakwaters due to severe waves during heavy storms which have attacked numerous harbors in Japan since 1959. Some of the examples are shown in this paper.

Experiments have been carried out by using non-breaking waves and breaking waves to investigate the wave forces on a vertical circular cell located in the shallow water. Based on the experimental data, the drag coefficient and the inertia coefficient of a circular cylinder and the curling factor of breaking waves are estimated, and the computation methods of wave forces are examined. As a result, it is shown that the phase lag of inertia forces behind the accelerations of water particles should be considered for the estimation of the drag coefficient as well as the inertia coefficient. In addition the previous formula of the maximum breaking wave forces acting on a cell or a pile is revised by introducing the effects of the above-mentioned phase lag and another phase difference, both of which are functions of the ratio of the cell diameter to the wave length. It is confirmed that the proposed formula is applicable even to the large cell with the diameter comparable to the wave length.

Field measurements were made of the vertical distribution of impact pressures exerted by breaking waves. Four distinct types are recognized and compared. These are near-breaking wave, plunging breaker, spilling breaker and post-breaking bore. The measurements were obtained by placing a 6 foot aluminum flat plate, backed by a cylinder in the surf zone, so that the fiat faced the approaching breakers. Five sensors were placed at one foot intervals on the flat. The sensors consisted of strain gage mounted aluminum diaphragms.

Results indicated that impact pressure is significantly influenced by breaker type. The bore generated the largest impact pressures, followed in decreasing order by plunging breaker, spilling breaker and near breaking wave. In the vertical array, the largest impact pressures were recorded at or near the top, except for the bore where the reverse occurred. A qualitative explanation is given of various phenomena associated with impact pressures, by considering breaker mechanics.

Experiments were conducted in a vacuum tank in order to investigate the effect which entrained air has on impact loads which are produced when waves break upon a structure. In these experiments a flat plate was dropped onto a still water surface in an environment where the ambient pressure of the surrounding air could be controlled. Rings of varying height were fixed to the surface of the falling plate in order to trap different volumes of air between the falling plate and the water, Experimentally determined values were obtained of the maximum pressure p_max when the plate struck the water surface for various ring heights δ and ambient pressures p_o in the vacuum tank.

Experimental results indicate that the pressure rise or shock pressure Ps = (P_max-P_o) decreased with reductions in the ambient pressure and volume of entrapped air. Even when air was removed such that the absolute pressure in the tank was equal to the vapor pressure of the water, water hammer conditions, where the peak pressures depend upon the celerity of sound waves in the media, were never found to occur.

This paper deals with the estimation of total wave force on a vertical circular cylindrical pile. Firstly, finite amplitude wave theories such as those of Stokes waves and cnoidal waves are recalculated by the Stokes second definition of wave celerity and the applicability of the theories for wave crest height above the still water level, wave celerity and horizontal water particle velocity is briefly discussed. Secondly, the drag and inertia coefficients are estimated respectively from the results of experiments for total wave force by the authors and by other researchers, based on the Morison wave force equation applying the theories and characteristics of the coefficients are considered in relation to the wave characteristics and pile dimension. Lastly, the applicability of the wave force equation proposed is investigated in comparison with experimental and theoretical results for time variation of total wave force and maximum total wave force.

All hydrodynamic forces on submerged objects are shown to be due to the acceleration effects of the fluid flow. However, it is useful to consider separately the influence from the various ambient flow and local flow conditions. At times certain aspects of the flow can be ignored, which simplifies the analysis. Examples are developed for circular cylinders near a plane boundary with a flow direction parallel to the boundary and perpendicular to the cylinder. Potential flow theory predicts that large vertical forces exist away from the boundary when the cylinder is against the boundary and that large negative forces exist toward the boundary when the cylinder is positioned a small distance from the boundary, when the viscous effects are small. When the cylinder is near the boundary, the added mass coefficient is the same regardless of the direction of the flow, providing the flow is perpendicular to the cylinder. In addition, the added mass coefficient is much larger for cylinders near the boundary than when they are in a free stream. Good agreement between theory and laboratory experimentation was obtained for various coefficients with waves on horizontal cylinders near a plane boundary.

This study deals with the interaction of linear, plane water waves with stationary groups of rigid, vertical, circular cylinders under conditions in which the inertial forces on the cylinders dominate over the drag forces. A direct matrix solution as well as multiple scattering as suggested by Twersky (1952) are used to obtain the velocity potential in the vicinity of the cylinders. The groups may consist of a number of cylinders having any geometric arrangement, may have Dirichlet, Neumann, or mixed boundary conditions, and need not have identical diameters. The study represents an extension of the singlecylinder case presented by MacCamy and Fuchs in 1954.

Basic scattering coefficients for 192 different arrangements of two cylinders are obtained with the aid of a Bessel coordinate transformation and a matrix inversion procedure. The resulting potential function is then applied to calculate force components in the direction of wave advance and orthogonal to it. For the cases considered the former departs as much as 65% from the force on a single cylinder and the mass coefficient is found to range from 1.19 to 3.38 – a not insignificant departure from the often used value of 2.0. Furthermore the orthogonal force may be as large as 67% of the single-cylinder force.

A solution of water particle velocities in the boundary layer developed by monochromatic waves on the surface of a circular cylinder is obtained by applying the boundary layer approximations and perturbation method to the Navier-Stokes and continuity equations represented in the cylindrical coordinates. Since, in this process, it is necessary to give the velocity outside the boundary layer, the water particle velocities of diffracted waves around the cylinder are derived from MacCamy-Fuchs' velocity potential. Moreover, the occurrence of laminar flow separation is explained by using this solution.

On the other hand, using a hydrogen bubble tracer some experiments have been performed about the water particle velocities of diffracted waves, velocity profiles in the boundary layer and occurrence of wake vortices. These results are compared with theoretical ones.

Water waves exert a force on a pipeline which is placed within the zone of wave influence. This force is made up of a periodic force which is composed of a drag and an inertial force, and a non-periodic second order force which acts upward.

The coefficients of mass C_M and drag C_D as defined by the “Morison equation” were evaluated for many wave and depth conditions and it was found that the coefficients vary with the wave heights, wave length, depth of the cylinder below still water surface, and within the wave cycle.

This paper deals with a theoretical method of calculation of the fluid motion, when a sinusoidal plane wave incidents to a permeable breakwater of arbitrary shape at constant water depth and shows that the problem for impermeable breakwater is solved as a special case of this method.

The method described here is the extension of the author's method⁽¹⁾ of solution for two-dimensional permeable breakwater by the method of continuation of velocity potentials for two different fluid regions into three-dimensional problems by means of Green functions.

Here, the analytical process of calculation is presented and as representative examples, wave height distributions and wave forces around an isolated elliptic- and rectangular breakwater are calculated and compared with experiments in wave channel.

The principle of this method is also applied to the analysis of submerged and semi-immersed fixed cylinder and the motions of floating body of arbitrary shape.

This paper deals with the wave transmission through a vertical slotted wall. In an experimental study the transmission coefficient has been investigated as a function of the shape of the wall elements (rectangular shape and H-beam shape), of the ratio of solid wall to total wall lenght (wall-element ratio) and of the wave approach direction.

The test results for a wave direction perpendicular to the wall are compared with previous investigations and theoretical derivations. For an oblique wave approach the test results are described by a semi-empirical formula. This formula, combined with a theoretical solution for perpendicular wave approach is used to describe the transmission coefficient for any angle of wave approach.

Theoretical solutions for the transmission beyond and reflection of waves from fixed and floating plates are based upon linear wave theory, as put forth by John (1949), and Stoker (1957), according to which the flow is irrotational, the fluid is incompressible and frictionless, and the waves are of small amplitude. The resulting theoretical relations are rather complicated, and furthermore, it is assumed that the water depth is very small in comparison to the wave length.

Wave transmissions beyond floating horizontal plates are studied in a laboratory wave flume. Regular (harmonic) waves of different heights and periods are generated. The experiments are carried out over a range of wave heights from 0.21 to 8.17 cm (0.007 to 0.268 ft), and wave periods from 0.60 to 4.00 seconds in water depth of 15.2, 30.5, and 45.7 cm (0.5, 1.0 and 1.5 ft). Floating plates of 61, 91 and 122 cm (2, 3 and 4 ft) long were used.

From the analyses of regular waves it was found that: (1) the transmission coefficients, H_T/H_I, obtained from the experiments are usually less than those obtained from the theory. This is due to the energy dissipation by the plate, which is not considered in the theory. (2) John's (1949) theory predicts the transmission coefficients, H_T/H_I, reasonably well for a floating plywood plate, moored to the bottom and under the action of non-breaking incident waves of finite amplitude. (3) a floating plate is less effective in damping the incident waves than a fixed plate of the same length.

This study was conducted to Investigate the effect of incident wave parameters on run-up for both a smooth-faced structure and a structure armored with quarry-stone. The ratio of the depth-to-wave length (the relative depth) was found to be important in defining wave run-up for both cases. The relative run-up (expressed as the ratio of the run-up elevation above still water level to the incident wave height) for waves which break at the toe of the structure was less than the maximum relative run-up for non-breaking waves for the same relative depth. For both structures, the maximum relative run-up for experiments with long waves occurred at a value of the modified Ursell number, (1/2Π)² (HL²/h³), of order unity which indicates that the nonlinear and linear effects are approximately equal in the incident wave.

An efficient computer program for predicting wave runup on beach profiles is presented. The solution is derived through the IBM 370/165 of the Computing Center, University of Florida.

The wave runup data utilized in this study is based on the laboratory-derived curve obtained from the experimental work of Saville, and expressed as linear regression; the historical storm frequency data is furnished by National Oceanic and Atmospheric Administration; and the surveyed beach profile is supplied by the field program of Coastal and Oceanographic Engineering Laboratory, University of Florida.

A broad spectrum of waves are selected to simulate hurricanes approaching the coast. The results thus obtained should provide useful guidelines in establishing the Coastal Construction Setback Line, and to the design criterion of Coastal Structures.

Field and model observations indicate the existence of vifave generated currents in the lee of breakwaters and headlands. It is shown by an idealised laboratory experiment that such currents could be produced by an alongshore gradient of breaker height with wave crests parallel to the beach. The mechanism for the generation of the current is explained together with some of its characteristics including its interaction with the wave set-up which causes it. It is further shown that it is possible to calculate by simple methods the hydraulic conditions causing the current. Currents produced by this mechanism appear to be of practical importance in determining the local plan shape of beaches close to breakwaters and headlands.

This paper tried to formulate the wave overtopping quantity by using a model of overtopping mechanism. Namely, the author investigated the problem by applying the “Calculation method for discharge of overflow weirs” i.e. the method of Fukui et al. (1963)¹⁾ and Shi-igai et al. (1970)²⁾).

For coastal engineering works, as for other structures, the designer must search for the economic optimum point. This point represents the minimum in the sum of direct cost and cost of possible future damage. By setting up functional representations of these costs the optimum can be obtained directly. This approach is illustrated by models developed independently in the Netherlands and in Canada. At this stage the output of the models may be denoted as the ‘perfect knowledge’ optimum, in the sense that parameters of the cost functions are assumed to be known with complete accuracy.

In the ‘real world’ case, however, the estimated values of the parameters will be subject to considerable uncertainty. It is shown that because of this uncertainty the ‘real world’ design optimum will generally be shifted to give a structure larger than that indicated by the ‘perfect knowledge’ assumption. The novel contribution of the present paper consists of analyzing this shift to obtain simple expressions for the apparent overdesign due to uncertainty and for the resulting cost increase. An illustrative example is presented.

The Minoans and Phoenicians appear to have developed a very superior “lay” understanding of waves and currents, which led to the development of remarkable concepts in working with natural forces in their coastal engineering works. For example, the Phoenicians developed a “continuous self-flushing” harbor at Tyre and possibly a “flushable” harbor for the removal of sand and silt at Sidon. It would appear that developments of this type were the outgrowth of the close association with and acute observation of nature that occurs where a coastal people learn to work with currents and sail, in the absence of technology for harnessing large amounts of power. However, harbor design became markedly stereotyped following the development of large engineering corps with the capacity for rapid and massive construction. The earlier innovative, natural concepts in harbor design appear to have become obscured by the end of the Roman era, and have remained relatively unused to this day.

In view of man's present extensive intervention in the coastal zone, mostly based on “brute force” technology, a careful study of the ancients' ability to work with nature provides valuable insight for today's problems.

Modern bulk carriers require deeper and wider harbour entrances. As a result long approach channels have to be dredged outside the breakwaters. These large channels cause considerable changes in the waves due to refraction and diffraction which effect the wave conditions in the harbour entrance.

As part of the Richards Bay harbour entrance studies, two phenomena were found to considerably effect the design of the entrance layout, namely:

(i) wave attenuation for waves travelling near parallel to the channel axis, caused by refraction of wave energy away from the channel, and

(ii) wave concentration on the channel side slopes, also mainly due to refraction, reaching a maximum for a critical approach direction of about 25° relative to the channel axis.

As a result of the wave attenuation, waves travelling within an angle of 20° either side of the channel axis were found to cause no problems whatsoever with regard to wave penetration into the harbour.

Unacceptable wave penetration was, however, experienced for wave directions close to the critical direction. A great number of variations to the entrance layout were tested to minimise this problem. The results showed the superiority of a flat channel slope of 1 in 100 above steeper side slopes and the beneficial effect of a Vee-shaped channel bottom. Also test results with irregular waves with regard to height, period and directions were found to be significantly different from those with uniform waves which considerably exaggerate the wave concentration phenomenon.

In this paper the practical design of coastal mobile bed models is considered. The semi-theoretical approach expressed by the author in earlier publications (9,10,11,12) is extended and used to classify and design coastal models. Fixed bed coastal models are discussed first to form a basis for the argument. Subsequently, mobile bed models are classified according to criteria of dynamic similarity satisfied in their design and scale effects present in their operation. Basic scale laws are next derived for all classifications of coastal models. This is done for both inshore and offshore models, the distinction being brought about by adjusting the velocity scales for unidirectional (and long wave) motion. Time and sediment transport scales are next derived and some well known models are compared. The presence of bedform and model distortion is also treated. The work is compared with that of other authors.

An investigation of errors incurred by scale distortion for fixed-bed harbor wave models has been performed and results of this study applied to the design, construction, and operation of a model of Los Angeles and Long Beach Harbors. Objectives of the model investigation must be clearly prescribed in order that each phenomenon affected by scale distortion can be analyzed. In some cases, if study objectives are too broad, a distorted model may be incompatible with these objectives; however, it will be found that in many circumstances a distorted model will produce valid data with considerable time and cost savings in construction and operation.

In this study, frequency response and transfer function techniques are used together with cross-spectral and fast Fourier transform methods to determine the proper boundary values for computing the flow field of a coastal sea. Tide data containing considerable perturbations from swell and meteorological disturbances are analyzed.

In computing the frequency response estimates, the effect of noise in the input is treated by a cancelling technique and by the choice of a reference station to evaluate the interdependencies among the other stations at the boundary. The usefulness of the network frequency response function is threefold: (1) future conditions can be simulated using observed water levels at any single location, (2) boundary information for models of different grid size can be obtained by interpolation, and (3) missing data at a given location can be estimated optimally using data at neighboring stations and the network response function. The paper discusses an example of such an application, the determination of a boundary of a two-dimensional model of Jamaica Bay, New York City, U.S.A.

The Model Sheltering Experiment deals with the planning arrangement of the proposed harbor and is done by the worst wave condition (with respect to wave direction, wave height, and wave period) which probably occurred on the proposed harbor. The objectives of this experiment are to get the wave pattern of the harbor basin and to understand the various phenomena of the wave refraction, diffraction, and reflection caused by model test due to different harbor arrangement, and to comprehend the sheltering effect of the outer breakwaters. From the analysis of these test results, harbor planning of the most effective arrangement – the most economic length of breakwaters and the most ideal width of harbor entrance could be selected. For the purpose of analyzing results of model tests; comparison of theoretical wave diffraction calculation is proposed.

Water surface oscillations in a man-made marina--Marina del Rey, California--have been studied through prototype experiments and theoretical analysis. The prototype experiments are conducted by using both the floating gauge and pressure type gauge. The field data show that a distinct mode of oscillation with wave periods between 45 minutes and 50 minutes are naturally present almost all the time. Such resonant wave periods also agree well with the theoretical results.

The application of submerged multiport diffusers for the discharge of degradable liquid wastes and of heated cooling water from electric power generation forms an important aspect of coastal zone management. Previous buoyant jet models for submerged diffuser discharge have been developed for the limiting case of discharge in unconfined deep water in the form of rising buoyant jets. These models can be used for sewage diffusers, but are not applicable for diffusers in shallow receiving water with low buoyancy, the type used for thermal discharges (“thermal diffusers”). A multiport diffuser will produce a general three-dimensional flow. Yet the predominantly twodimensional flow which exists in the center portion of the three-dimensional diffuser can be analyzed as a two-dimensional “channel model”. Theoretical solutions for diffuser-induced dilutions are derived for the two-dimensional case and verified experimentally. Furthermore, the theory can be applied to the three-dimensional situation by requiring equivalency of far-field effects, that is the frictional resistance governing the diffuser-induced motion at larger distances from the diffuser line.

When a buoyant plume is discharged into water where wave motions exist, the axis of plume is bent over and horizontally fluctuated. The dilution rate of the plume is affected by this motion. Experiments are carried out to investigate the dilution rate of plumes when they arrive at the free surface. An analogy to the case of buoyant plumes discharged into uniform steady cross streams is applied to analyse the experimental data. Within the experimental range, it is found that the dilution rate is inversely proportional to the square of the ratio of the water depth to the diameter of outlet and is proportional to the ratio of the discbarge velocity to a characteristic horizontal velocity of the ambient fluid. The entrainment coefficient is given as a function of a densimetric Eroude number for small Eroude number and is a constant, 0.28, for bigger Eroude number than 4.3.

Models are developed to describe the gross behavior of air-bubble plumes generated by point and line sources of air-bubbles released in stagnant water bodies of uniform density. The models predict plume width, velocities, and induced flow rates as a function of elevation above the source.

The analysis is confined to the plume mechanics and does not include the horizontal flow created at the surface by the plume. An integral similarity approach, similar to that used for single-phase buoyant plumes, is employed. Governing equations are found by applying conservation of mass, momentum, and buoyancy. The compressibility of the air and the differential velocity between the rising air bubbles and water are introduced in the buoyancy flux equation. Generalized solutions to the normalized governing equations are presented for both point and line sources of air-bubbles.

The results of the analyses are compared with existing large-scale experimental data. The comparisons indicate that the models predict the gross behavior of plumes well and yield estimates of the entrainment coefficients and lateral spreading ratios.

A computer model for simulating oil spreading and transport has been developed. The model can be utilized as a useful tool in providing advance information and thus may guide decisions for an effective response in control and clean-up once an accidental spill occurs. The spreading motion is simulated according to the physical properties of oil and its characteristics at the air-oil-water interfaces. The transport movement is handled by superimposing the spreading with a drift motion caused by winds and tidal currents. By considering an oil slick as a summation of many elementary patches and applying the principle of superposition, the model is capable of predicting the oil size, shape, and movement as a function of time after a spill originates. Field experiments using either cardboard markers or soybean oil to simulate a spill were conducted at the Long Beach Harbor. Computer predictions showed good agreement with the field traces.

This study examines the drifting, spreading and aging of small slicks of crude oil in the middle St. Lawrence Estuary. This region was chosen because it is well documented with field measurements, hydraulic scale models, and mathematical models; and also because it is becoming a strategic area for the development of supertanker ports for 300,000 and possibly 500,000 ton tankers.

Two controled releases of Venezuelan crude (370 and 800 litres) were made in November 1972, as ice began to form in the St. Lawrence Estuary. The experiments were supported by the Canada Centre for Remote Sensing which carried out extensive airborne monitoring.

The results indicate that it is impossible either to recover or to disperse small spills of oil in this region of strong tidal currents. Models also predict slick motion poorly. The alternative is to construct slick-drift roses that will indicate areas of expected beaching and assist in deployment of oil-spill clean-up technology.

The area of oil spread was measured in the laboratory and the predictable model was established in determining the spreading area of oil on coastal waters. The relationship between the oil slick and the Reynolds, Froude, and Weber numbers was examined and the influence of wind, currents, and waves on the spread area was investigated. The effects on the changes in water depth and the alteration of the net spreading coefficient on oil spreading capacity were also examined. Comparison between the existing field measurements and the laboratory work was made.

Measurements of the exchange characteristics at tidal inlets are presented and interpreted in the framework of an idealized conceptual model. The conceptual model considers the primary cause of exchange to be the result of the differences in flow patterns away from and toward an inlet. The efflux from an inlet is considered to occur as a separated flow whereas a sink-type attached pattern is assumed for flow toward the inlet. The combined results of these two patterns is an effective lateral mixing. Field measurements were conducted from an anchored boat and a dye injection and monitoring approach were utilized. The measured results, expressed as “Basin Mixing Coefficients” are presented for three inlets and are interpreted in terms of the geometric and flow characteristics of the inlet and adjacent waters.

This paper examines the tide-induced net discharge in lagoon-inlet systems. In particular, attention is given to the role inlets play in inducing a steady current.

The flow in the lagoon is described by the one-dimensional long wave equations, the flow in the inlets is described by a semi-empirical equation. Both numerical and analytical techniques are employed to solve for the net discharge.

The results of the study indicate that 1) the net discharge can be significant provided the tidal amplitude to depth ratio is not small 2) the net discharge can be considerably increased by the proper selection of the inlet dimensions.

A general numerical model capable of reproducing long internal waves in stratified fluids has been constructed with the aim of investigating the salt wedge penetration in the Delta of the Po river, where the installation of a 2640 MW thermo-electric plant is foreseen.

The working hypothesis of the model, in accordance with the actual phenomenology of the river, is the one-dimensional homogeneous motion of two fluid layers of different density.

The main original aspects of the numerical computation are:

1) – The use of two different space steps (1 km for the fresh water layer; 200 m for salt water) simultaneously allowing a good description of internal waves (the velocity of which is much smaller than that of the external ones) and making it possible to work with economic (100 sec) time steps.

2) – The straightforward description of the wedge head, obtained by making it always freely correspond to one of the grid points.

The model, which has been tested on actual events, reproduces reality with a very good approximation; it also gives evidence of the small relevance of the interfacial stress coefficient in unsteady tidal generated motion of the salt wedge.

The paper describes the environmental problem of the Seto Inland Sea of Japan. A number of model studies of tidal flow and effluent diffusion of this sea are presented. In particular the similarity law that has been developed to model turbulent diffusion is delineated.

The effect of the tidal residual flow on the horizontal diffusion in a shallow tidal bay is investigated through a hydraulic model experiment, for which Mikawa Bay in central Japan was used as a prototype.

A hydraulic model of about 20 x 30 m including Mikawa Bay and neighooring sea area, with a horizontal and vertical scale of 1/2000 and 1/160 respectively, was used, and a semi-diurnal tide was provided for it. Experiments nave shown that tide and tidal current are well reproduced in the model. The tidal locus does not close, that means the existence of the residual flow. The distribution of the concentration of the dye, which is discharged from the bay bottom, corresponds to the pattern of the residual flow.

The diffusion coefficient in the bay obtained through one dimensional analysis is the order of 10⁵ cm²/sec and that through two dimensional analysis is less by one order and the dispersion coefficient becomes 10⁵ cm²/sec. It is concluded that the dispersion due to the residual flow plays more important role on the distribution of the material in the shallow bay, as Mikawa Bay, than the diffusion due to the tidal current itself.

The calculation of turbulent flow using Navier's equations assumes the introduction of a turbulent viscosity coefficient the value of which is normally constant, conforming with Boussinesq's hypothesis.

It was shown that setting aside this hypothesis, a velocity profile quite different to that resulting from the classic theory is obtained in the case of flow induced by wind. This result appears to be confirmed by the tests carried out in the Mediterranean. The advantage of this method is that it gives the vertical turbulent diffusion which is of particular interest to pollution studies.

A set of “averaged” partial differential equations for the circulation in a two layered coastal water is established by assuming each layer to be vertically homogeneous and by performing a vertical integration over the layer thicknesses. Since the phenomena to be investigated typically consist of long waves such as a tidal wave, the hydrostatic pressure assumption is also introduced. The finite element method is employed to transform the partial differential equations to a discrete system of ordinary differential equations which are solved using an implicit time stepping method similar to the trapezoidal rule, but with the variables (elevation and flows) staggered in time. A linear stability analysis shows the initial value problem to be unconditionally stable. In practice, instability due to boundary conditions and non-linearity sets in.

Comparisons between computed and analytical solutions for simple cases give good agreement. The tidal excitation of Massachusetts Bay, represented as a rectangular basin with opening on one side is presented as an illustrative example.

A hydrothermal monitoring program has been designed and deployed to gather data on the temperature distribution in the tidal James River near the outfall of the Surry Nuclear Power Plant at Surry, Virginia, U.S.A.

Monitoring to date has included two years of background data (1971 and 1972) taken prior to plant operation, and one year (1973) of data with the plant in operation.

The results of the first year post operational monitoring effort has been compared with the pre-operation background data and with the thermal effects that were predicted from studies by Carpenter and Pritchard on the James River Hydraulic Model at Vicksburg, Mississippi.

Rains from Tropical Storm Agnes resulted in unprecedented flooding of the Chesapeake Bay drainage basin in June of 1972. A monitoring program was established to follow the effects of the flood in the Chesapeake estuarine system and contiguous continental shelf waters.

Financial and logistic assistance was solicited and obtained from several federal and state agencies. The monitoring program, called “Operation Agnes” offered scientists a unique opportunity to watch the progress of the flood.

Results of investigations into the effects of the flood show that salinity structure exhibited a four stage reaction, tides in the lower reaches of the estuaries were essentially uneffected and currents returned to normal after a short period of continuous ebbing. Total recovery of the salinity distribution was affected within one hundred days of flood crest at the fall line.

A one-dimensional numerical model was used to estimate the location and volumes of water flooding over the banks of the Thames Estuary under several combinations of bank levels and possible storm surges. An assessment of the probable damage resulting from each of these floods enabled a comparison to be made between the various possible schemes for bank improvement and, indeed, showed that there was a serious need for such improvement even though a start on the construction of the Thames Barrier was imminent. In an estuary such as the Thames the overflow may provide a significant turn in the continuity equation and the effect must therefore be programmed as an integral part of the model; one obvious effect of the overspill is to limit the maximum levels to about 0.2 m above the banks in the upper Thames, almost irrespective of the size of the surge.

After the closure of the Haringvliet estuary, part of the Netherlands Delta Project, morphological changes have occurred. Until now it was impossible to give a completely satisfactory forecast of such changes, however, with the aid of the Leendertse tidal computations a good picture of the tidal flow in the estuary can be obtained.

In the paper a short description is given of both the tidal flow and the morphology of the Haringvliet estuary related with some problems of the practising engineers.

The project of a barrage across an estuary in Northern Germany was accompanied by a programme to monitor the hydrologic and morphologic situation. This became necessary in order to avoid dangers resulting from the sensitivity of the shallow wadden area to human interference.

Various methods to record the morphology were tested. The aerial photographic waterline survey proved superior as it supplies a complete and economic record and allows accurate analysis of the topography.

The principle consists in taking aerial photographs at short time intervals between low water and high water, each photo showing a different waterline. The scale chosen was 1:18000, corresponding to a flight altitude of 2700 metres. Rectification of the distorted photos requires reference markers to be distributed over the survey area which measures about 140 km². By using simultaneous tide gauge records, contour lines can be constructed from the photographed waterlines.

This morphologic record is supplemented by submarine survey of the estuary. It is expected that details of sediment transport and of tidal prism changes may be revealed. Predicted and actual effects of the barrage will be compared, which might lead to a better understanding of such coasts.

From the point of view of the Bahamian environment, the most favorable locations for a supertanker port are 1) the western margin of the Great Bahama Bank, 2) the western shores of Grand Bahama Island and 3) the western margin of Little Bahama Bank. A port in any of these areas would a) usually be located down-wind and down-current of the majority of Bahamian islands and shallows, b) be located adjacent to boundary currents, expecially the Florida Current, that would tend to carry large accidental oil spills away from coastal areas and into the North Atlantic, c) be located where wave energies would be relatively low, and d) be positioned close to sea-lanes, obviating supertanker penetration of the central Bahamas.

A site 30 miles east of Freeport, Grand Bahama Island, was chosen for construction of a sea-island supertanker bunker. Six controlled spills (270 U.S. gals, each) of crude and two spills of naptha were made at the seaisland site during the windiest month (February). Slick spreading rates are presented. Cumene and all lower-boiling aromatics disappeared within the first 90 minutes after a crude-oil spill; a majority of toxic fractions (BP < 220°C) disappeared within 3 to 8 hours. Slick-drift roses for extreme-wind-persistence and strongest-coastal-current conditions indicate the environmental suitability of the site for capture and cleanup of small spills (< 1000 gals.).

The first oil pipeline from the North Sea area reached Scotland in 1973. The landfall, at Cruden Bay, Aberdeenshire, is a sediment-filled, bay-head beach with coastal dunes. Environmental and landscaping problems arose with the trenching of the beach and dune areas. Various methods, including flexible fence construction, spraying with a bitumen compound and spreading of soil over vulnerable areas, protected the site successfully. Full revegetation took place later and the beach and dune area are now restored to their original condition. Environmental management techniques were designed to preserve the high amenity and ecological status of the site and minimise the risk of side-effects, both during and after engineering work.

The results of an extensive field study undertaken in the Mersey Estuary and its approach channels are briefly described. These measurements were undertaken to obtain a quantitative understanding of the movement and circulation of water and sediment in the area. There is considerable dredging activity required in the area and the spoil from such operations is, at the present time, deposited at an offshore site in Liverpool Bay.

A simple model is presented which attempts to quantify the movement of sediment into and within the Mersey system. The field measurements showed that considerable quantities of sediment return to the docks, estuary and approach channels from the spoil ground. The model includes this fact and attempts to quantify the amounts returning to various areas. The model equations were applied to each year of the period 1955-65 to determine the various factors and to test its validity: this required the use of the annual hydrographic surveys and dredging records as well as the results of the field measurements. Finally, the model was used to compare the probable results of a number of possible schemes including re-siting of the spoil ground, pumping all dredged material ashore and free-dumping of dock dredgings in the estuary itself.