Coastal Engineering 1976

The North Sea (Fig. 1) is known as a random sea with depths in the southern part between 40 m and 100 m so that in contrary to the Atlantic and Pacific coastlines deep sea wave conditions do not exist. After four years of comprehensive wave measurements in the offshore area of the Island of Sylt near the Danish border a general analysis of the wave climate in that region was possible. In this paper results and suggestions will be presented under the aspect of replacing qualitative judgements by quantitative statements which are derived from the knowledge of the adjacent wave climate. Because the wave action varies from year to year a general time unit is not advisable for the evaluation of shore processes; therefore the time scale should be substituted by the integral of incoming wave energy occurring after a certain time. The investigated method of expressing the total energy of one season or one year in the electrical unit Kilowatthour (kWh) per meter (m) width of shoreline could prove in future as a feasible way of classifying the irregular seasonal and yearly wave intensities.

It is further shown that wave measurements over a period of several years can be sufficient for the investigation of correlations between the wind velocities occurring from all directions and the resulting wave heights. In case of satisfying correlation factors it will then be possible to carry out feedback operations for periods from which only records of wind velocities and directions are available and even to hindcast the wave heights for certain not yet measured wind velocities.

Two episodes of Great Lakes waves for which both wind and wave data are simultaneously available are used to examine the applicability of the empirical fetch-limited spectral wave formulas developed by JONSWAP, Mitsuyasu, Liu, and Sverdrup-Munk-Bretschneider. Comparing the results hindcast from the formulas with those recorded shows that, for hindcasting significant wave heights, Liu's formula gives better results for less than fully developed Waves, while formulas by JONSWAP, Mitsuyasu, and Sverdrup-Munk-Bretsehnelder give better results for fully developed waves. In hindcasting average wave periods and peakenergy frequencies, all the formulas result in a deviation of up to 2 s and 0.5 rad s⁻¹, respectively. These results can he used as a reference in evaluating and interpreting wave predictions made by these formulas as applied to the Greak Lakes.

The problem of statistics of numbers of consecutive high waves has not yet been treated in detail. Some numerical results (Goda, 1970) and evaluations of prototype data in water depths of 100 m (Rye, 1975) and 40 m (Wilson and Baird, 1973) respectively were published. Data from measurements in nearshore coastal waters, with unbroken, breaking and broken waves, obtained in the Elbe estuary, are treated in this paper.

Measurements needed to calibrate both significant wave and wave spectrum methods. These concern extreme waves hence related more to design than operations.

Climatological wave data that may be shoaled and refracted from a deep-water wave station can be compiled in two forms from spectral ocean wave analyses produced by the Fleet Numerical Weather Central at Monterey, California: (1) significant wave statistics, which are similar to statistical tables currently in use, and (2) spectral element statistics, which give the frequency of occurrence of energy densities contained in a matrix of 15 frequency bands and 12 direction bands. Experimental formats of both types of statistical compilations are presented, their properties are examined, and the coastal engineering applications of these statistics are discussed.

The Fetch Area Method ( FAM ) derived from Elementary Wave Model is used to analyze the winter monsoon wave of Taichung Harbour. The empirical wind-wave energy transfer coefficient $\overline{E}$ determined by FAM for this area is 7.25 x 10⁻⁴. A relationship between g ${\text{T}}_{1/3}/2\pi \overline{\text{U}}$ and g ${\text{t}}_{\text{d}}^{\text{'}}\sqrt{\text{U}}$ is also found, where $\overline{\text{U}}$ is the average wind speed and ${\text{t}}_{\text{d}}^{\text{'}}$ the duration. A comparision of the wave hindcasting of FAM has shown that the latter is better than the former, and the former is valid only as the wind velocity increases, once the wind decreases the SMB Method is no more valid.

The wave period estimates obtained from different procedures are not consistant unlike statistical distribution analysis of wave heights. Thus not one difinition of wave period is satisfactory for engineering analysis of coastal processes.

There are at least 10 different measures of wave periods including the zero up-crossing period, the average wave period, significant height period and peak of the energy density spectrum period.

For the analysis of periods, 20 min. records were obtained from offshore pressure recorders. Summer and winter records were analysed separately.

In the analysis, zero up-crossing period and average period were taken as reference periods. There were significant differences between the wave periods and they were found to depend also on the spectral width parameter.

Finally comparison was made between the energy flux obtained under the spectral diagrams and energy flux obtained using various wave periods and heights.

Study shows that if the total energy flux is desired, then the most appropriate values to be used are the root mean square wave height and period corresponding to that wave height. Use of significant wave height, along with zero up-crossing period gives higher values.

In an attempt to develop a systematic series of wave spectra covering a variety of spectral shapes observed in the ocean, this paper presents a newly developed series of wave spectra which involves six parameters. In the development of the six-parameter wave spectra, the spectra are decomposed into two parts. Each part is expressed by a mathematical formula with three parameters, and the total spectrum is expressed by the combination of two sets of three-parameter spectra. Results of analysis have shown that the six-parameter wave spectra thus derived appear to represent almost all stages of development of a sea during a storm. Then, from the statistical analysis of 800 spectra observed at the North Atlantic Ocean, the values of the six-parameters are expressed in terms of significant wave height so that a family of spectra for a desired sea severity can be generated.

From 1971-74 seven cruises were made to measure the directional spectrum of ocean waves by using a cloverleaf buoy. Typical sets of wave data measured both in open seas and in a bay under relatively simple conditions have been analyzed to clarify the fundamental properties of the directional spectrum of ocean waves in deep water.

Most of coastal engineering problems have been studied with monocromatic waves. However, sea waves which arrive at the coast are random. It is very difficult to estimate exactly the influence of these random waves to coastal structures. Then the model tests in a laboratory wave tank using random wave simulation techniques seem to be most desirable way to estimate the influence of randomness of sea waves. For this purpose, the accomplishment of random wave simulation system, which make possible generating random waves having statistically same properties as those of sea waves, has long been desired. The authors achieved to establish such a new wave simulation system. In this paper, the characteristics of this system are demonstrated experimentally through several cases of random wave simulations.

Influence of long wave on the wave height distribution of wind waves was studied through the laboratory experiment. Experiments were conducted in a wind-wave tank where the wind waves were generated by a wind blower and the long waves were developed by an oscillating pendulum type wave generator.

The wave height distribution of the wind waves over long wave is slightly different from the Rayleigh distribution in the small steepness of long wave. The ratios between the average of highest l/n-th waves vary with the steepness of long waves. The magnitude and the location of the spectral peak of wind waves are altered. The amount of the attenuation of wind wave energy is larger than the results of Mitsuyasu (1966).

An experimental investigation was made to study wave-current interaction. Wave amplitude attenuation was measured along a laboratory wave channel to compare wave dissipation with and without flow. Mean, wave, and turbulent velocities were also measured to determine the modifications of the flow imposed by the gravity waves propogating with the current. The process of energy transfer in the wavecurrent system was studied. Energy was found to be extracted from the waves, diffused downward and dissipated by an increase in bottom shear stress.

Measurement of waves, and vertical and horizontal water particle velocities were made of spilling, plunging and surging breakers at sandy beaches in the vicinity of Monterey, California. The measured breaking waves, derived characteristically from swell-type waves, can be described as highly nonlinear. Spectra and cross spectra were calculated between waves and velocities. Secondary waves were noted visually and by the strong harmonics in the spectra. The strength of the harmonics is related to the beach steepness, wave height and period. The phase difference between waves and horizontal velocities indicates the unstable crest of the wave leads the velocities on the average by 5-20 degrees. Phase measurements between wave gauges in a line perpendicular to the shore show breaking waves to be frequency nondispersive indicating phase-coupling of the various wave components. The coherence squared values between the sea surface elevation and the horizontal water particle velocity were high in all runs, ranging above 0.8 at the peak of the spectra. The high coherence suggests that most of the motion in the body of breaking waves is wave-induced and not turbulent.

An experimental description is presented for the transformation of periodic waves which approach breaking on a gently sloping beach. The data include the variation of wave height, phase velocity, wave surface profiles, and the maximum value of the wave height to water depth ratio (H/h)_max around the breaking point.

The results are compared with the theories of sinusoidal and cnoidal wave shoaling, and the latter is shown in most cases to agree remarkably well when the laminar energy loss along the walls and bottom of the wave tank is included.

An empirical relation is established between wave length to water depth ratio L/h at the breaking point and the deep water wave steepness H_o/L_o. Also the maximum wave height to water depth ratio at breaking shows considerably less scattering than found previously, when plotted versus S = h_x L/h, h_x being bottom slope.

Wave shoaling is calculated, based on finite amplitude wave theories on a uniform depth which were extended by the authors using the Stokes second definition for wave celerity. Change of wave characteristics with decrease in water depth is discussed from numerical computation, and difference in shoaling characteristics is considered in comparison with results obtained from usual wave theories by the first definition. Theoretical results are compared with preliminary experimental ones on the wave transformation in shoaling water conducted by the experimental facilities satisfying the physical conditions corresponding to the definition for wave celerity as well as possible, and the validity of each theory for practical purposes is investigated.

The primary objective of this study was to ascertain the influence of wave height and breaking on wave refraction over a three-dimensional shoal. The subject wave transformations were studied in an hydraulic model. Wave shoaling, decay in the breaker zone, and phase velocities were analyzed in a base test series over a bottom slope of 1:30. A second test series was conducted over a three-dimensional shoal. Wave patterns were photographed and wave heights and celerities were measured. The measurements were compared with wave refraction patterns and coefficients computed by analytical methods. Wave shoaling observed over the constant 1:30 slope was 25 percent greater than predicted by Airy theory at the breaking point for wave steepness H_o/L_o=.030 and 50 percent greater than predicted for H_o/L_o = .002. Shoaling measurements were compared with other empirical data sets, confirming the inadequacy of commonly used practice using linear wave theory near the breaker zone. The celerity measurements indicated that the non-breaking celerity was given by C = (1+.25 H/d)C_a, where C_a is the Airy celerity. The discussion and results give a basic understanding of wave refraction near the breaker zone, supplementing analytical papers on refraction procedures using finite amplitude wave theories.

Wave height variability along the crest of breaking waves is shown to be a significant factor in the assessment of surf zone dynamics. Variations in excess of 50 percent of the maximum wave height can occur along a single crest without significant variations in bathymetry. The horizontal scale of this longshore variability in crest height corresponds to the wave length of incident breaking waves. Four possible mechanisms for this variability are postulated and then evaluated individually on the basis of field observations. A major result of these evaluations is that two-dimensional shallow-water wave equations appear to be inappropriate for expressing natural surf zone wave transformations and water motions even under the condition of waves encroaching on a plane sloping bottom. Consequently, three-dimensional equations of surf should be used for describing most natural surf zone dynamics.

The investigations under consideration are based on synchronous measurements of waterlevel deflections n(t) at some positions in a beach profile with a slope of approximately 1:40.

Surf conditions are studied during a severe storm surge as well as during periods of attenuating wave action.

By the use of a FOURIER ANALYZER 40 energy spectra are calculated which are also presented in integrated form (co-cumulative spectra). Because of different site arrangements it is possible to analyze the deformation of the spectra due to tide dependent changes of the water depth as well as due to coastward decreasing water depth.

It happens that there are some phenomena associated with certain frequency bands.

With the water depth decreasing the energy densities in surf spectra are distributed over a wider frequency band.

In the present case unbroken waves are characterized by energy spectra in which at least 90 % of the energy is represented by FOURIER components in the frequency range 0 ≤ f ≤ 0.5 Hz. Increasing distribution of the energy densities over a wider frequency band represents at first breaking and finally broken waves. Sometimes the amount of energy coastward of the surf zone is higher than seaward ofthe breakers. This phenomenon can be explained by refraction effects caused by local nearshore bathymetry. All of there investigations were sponsored by the DEUTSCHE FORSCHUNGSGEMEINSCHAFT (German Research Foundation).

A laboratory and theoretical study of the transition from strongly reflected surging to dissipative plunging breakers on a relatively steep plane beach (1:8) has revealed the following: (1) The run-up and offshore variation of sea surface elevation of surging waves are well predicted by linear theory. (2) The fluctuating part of the run-up (related to the amplitude of the reflected incident wave) reaches a maximum value; a further increase in incident progressive wave energy results in increased dissipation. (3) Subharmonic edge waves (the growing instabilities of surging waves) are driven primarily by the swash motion, which does not increase with increasing incident breaking wave height. However, the turbulence accompanying incident wave breaking, and the effective eddy viscosity, rapidly increases with increasing breaker height. As a result, subharmonic resonances do not occur with spilling or steep plunging waves; very strong viscous effects suppress the nonlinear instabilities. (4) edge waves generated by a surging incident wave can be suppressed by superimposing an additional breaking wave of different frequency on the incident wave field. Thus, any excited edge waves are likely to have length scales at least the order of a surf zone width.

By wave breaking, an incident monocromatic wave is transformed to a wave composed of its harmonic frequency waves inside a surf zone.

Based on a dimensional consideration, the “-1 power law ”, the “-2 power law”, the “-2/3 power law” and the “-1/2 power law” on the wave height spectrum, H(f), are derived as sorts of equilibrium spectra.

These spectra except “-l/2 power law” are shown to agree with experimental data.

A bottom friction is an effective factor which will prove the deformation of progressive waves in shallow water, and many investigators have obtained the friction coefficients from field observations. However, they have not considered the effect of turbulent loss due to sand ripple at a sea bottom.

The authors, first of all, study on the friction coefficient for artificial fixed ripple by using the boundary layer theory of rough turbulence, and a new formula on the friction coefficient is proposed. The proposed friction coefficients are compared with Zhukovets’ experimental results which were performed on a movable bed, and it is found that the theoretical friction coefficients for artificial fixed ripple have to be modified in order to apply for the natural beach. Lastly, the wave deformation due to the bottom friction on the movable bed is calculated by the modified friction coefficient and the effect of bottom friction on the wave deformation is discussed.

The authors developed a new field observation system called STEREOBACS by which simultaneous measurements of a spacial distribution on waves and currents in the nearshore environment can be obtained. This system was applyed on Ajigaura Beach, Japan, and several analyzed results are presented. Also field observations of infragravity low mode edge waves to support the Infragravity Domain Hypothesis on nearshore currents concerning a gently sloping beach [Sasaki(1974,1975), Sasaki and Horikawa (1975)] are introduced.

A two-component electromagnetic flowmeter has been used on a natural beach of slope 0.01 to measure mean longshore currents and the horizontal fluctuating velocities in the frequency range 0-1 Hz. The measurements extend up to 120 m offshore and span about one third of a wide surf-zone. The cross product of the fluctuating horizontal velocities, assumed to contain the combined effects of radiation and Reynold's stresses, is plotted as a function of distance from the shoreline. The on/offshore gradient of the cross-product is then equated with a bottom friction term either in the form used by Bowen (1969a) or in a form similar to that used by Longuet-Higgins (1970). The apparent values of bottom friction coefficient obtained in this way are at least a factor of two smaller than expected for Reynolds numbers and bottom roughness appropriate to the beach. Attempts to separate the radiation stress and the Reynold's stress contributions to the total stress term using cospectra fail to show distinguishable Reynold's stress contributions. Although this may be construed as being consistent with Battjes’ (1975) beach slope dependent form for horizontal eddy viscosity rather than Longuet-Higgins’ (1970) form, it is argued that, in fact, the significant horizontal turbulence was not measured at all but was confined to a surface layer above the flowmeter. This leads to the hypothesis that lateral friction, as a surface boundary layer, and the bottom friction act on a less turbulent central layer, and that the small measured friction coefficient in the present experiment is the result of the combined effects of these layers.

During constant sea state conditions, longshore current velocities were monitored continuously for fifteen minute periods separated by fifteen minute periods separated by fifteen minute intervals. Three ducted impellor flowmeters were placed at equally spaced vertical positions through the water column. Sequential measurements were made with similar vertical current meter arrays at different locations across the surf zone. Simultaneous measurements of wave height, period and celerity were made at stations placed at equal intervals from the outer surf zone to the beach. The fifteen minute continuous records were subjected to spectral analysis. This analysis showed that the major power associated with fluctuations in the longshore current velocity field occurs in two major frequency bands. A significant spectral peak was coincident with the breaker period of the incident wave field, 4.2 seconds and, another dominant signature occurred at 78.8 seconds. Attenuation with depth of both the steady and fluctuating components of the longshore current flow field was relatively small. The maximum observed velocities for each station and each vertical current meter position varied from 90 to 150 percent above the observed mean longshore current velocity. However, at each station, variation of the means with depth was not appreciable and thus supports the results from time and space averaged theories of vertical uniformity in longshore currents, away from the boundary layer. Results from the field investigation of Wood and Meadows (1975) indicated that the steady state components are dominated by the fluctuating portions of the flow field. Therefore, time averaging of conservation equations in longshore current theory is a physically inappropriate procedure. In order to evaluate the magnitude of the unsteady components, a close examination of surf zone dynamics was made. The most obvious contribution to unsteadiness in longshore currents arises from the longshore component of the maximum horizontal particle velocity. However, the magnitude of observed current fluctuations is too large to be completely accounted for by this component. Spectral peaks at longer periods appear to be related to modes of edge wave phenomena. The long period spectral signature of 78.8 seconds is in direct agreement with the calculated period for a zero mode edge wave in shallow water. This agreement supports the contention that oscillatory components, other than the longshore component of the wave particle velocity, are contributing to unsteadiness in longshore currents and are manifested throughout a wide range of frequencies.

Alongshore gradients of breaker height have been shown to significantly influence the velocities and circulation patterns of nearshore current systems. Experimental data from an idealized laboratory experiment shows that the form of the nonuniform wave generated current system resulting from diffraction behind an offshore breakwater is essentially determined by the beach-breakwater geometry while its magnitude depends upon the wave height. Furthermore the current may produce significant increases in the magnitude of the wave set-up within the three dimensional system. For the case investigated, where the alongshore gradient of breaker height is comparatively large, the maximum mean alongshore current velocity is not greatly affected by bottom resistance and may be computed for plunging breakers from a relation of the following form;

derived from a simple momentum analysis including “radiation stress” terms. The influence of bottom resistance can be included if necessary.

A computational model is presented for the steady state prediction of currents, waves, and sea surface elevations in a coastal region outside the surf zone. Irrotational flow of surface gravity waves on large-scale steady currents over a gently sloping sea bed is considered. A second order Stokian approach is used, and all dynamic quantities are integrated over depth and averaged over time, in that order. The flow equations and the boundary conditions are presented. A method is developed for the solution of the non-linear steady model by introducing a sequence of two-level calculations, viz. a ‘wave level’ and a ‘current level’. The variables are split on the two levels. The wave field is found, using that the flux of wave action is constant between adjacent wave rays. The current field and the mean sea surface elevation are determined using a Galerkin finite element method. The current field is approximated by triangular elements with linear interpolation functions, and the mean sea surface elevation is approximated by a triangular element with quadratic (parabolic) interpolation functions. A quasi-twodimensional test solution is tabulated.

This paper reports the results of a series of laboratory experiments with periodic waves breaking on uniformly sloping impermeable beaches with the object of distinguishing set-up from dynamic shoreline motions due to partial reflection, the combination of which is normally referred to as ‘run-up’. The principal findings are:

A set of experiments concerning wave run-up in the presence of an offshore bar is described. Results pertaining to the direct relationship between incident waves and run-up heights are presented. It is clear that in the majority of cases the offshore bar does reduce run-up heights. The experiments showed that under certain conditions very large run-up and rundown heights are produced. This is ascribed to a resonance effect between either the basin, formed between the bar and the beach, or the beach face and the incident waves.

The height of dikes and other coastal structures can only be calculated after determination of the wave run-up. Several formulas for the calculation of wave run-up are developed after model tests as a rule. But the influences of scale effects and natural wind conditions are practically unknown. To clear these questions further investigations and especially field measurements should be carried out.

By measuring the markerline of floating trash on the slope of the seadikes the maximum wave run-up could be found out after four storm surges in 1967 and 1973- In two graphs it will be shown that on the tidal flats the run-up depends on the waterdepth. The run-up was higher than it could be expected after model tests of 1954.

With a newly developed special echo sounder the run-up could be measured in January 1976. The waves and the run-up could be registrated synchronously during two severe storm surges. As shown in Fig. 9 it was found a logarithmic distribution of the wave height, wave period and the higher part of the wave run-up. The found wave run-up is considerably higher than estimated before. The measured 98 % run-up is found about twice the computed value. That is an interesting and important result of the first synchronous recording of wave run-up on sea dikes.

An experimental study is presented of some characteristic parameters of the flow in the up-rush and down-rush of periodic waves breaking on a plane, smooth slope. The water layer thickness has been measured as a function of time at four locations above still water level. Discharges and particle velocities have been calculated. The results have been made nondimensional on the basis of Hunt's formula for the run-up height. They appear to be either independent of the wave steepness H/L_o and slope gradient tan ⍺ or to be a function of a single similarity parameter $\text{ξ=}\text{tan}\text{α}/\sqrt{\text{H}/{\text{L}}_{\text{o}}}$ only. An hypothesis is stated concerning a relation between the mean rate of overtopping of a dike by waves, and the run-up which would occur under the same circumstances on an uninterrupted slope. On the basis of this hypothesis the overtopping volume per wave can be normalized so as to make it independent of slope angle and wave steepness. A comparison of the result with measurements from other sources indicates a rough agreement.

As under oblique wave approach water waves are reflected by a vertical wall, a wave branching effect (stem) develops normal to the reflecting wall. The waves progressing along the wall will steep up. The wave heights increase up to more than twice the incident wave height.

The study has pointed out that this effect, which is usually called MACH-REFLECTION, is not to be taken as an analogy to gasdynamics, but should be interpreted as a diffraction problem.

A one-dimensional finite difference model is developed to simulate the action of long non-linear shallow water waves at a solid barrier. A damping parameter is introduced to account for the centrifugal effects in the incident wave. A stability criterion for Δt/Δx is suggested. The numerical predictions of reflection and run-up compare satisfactorily with experimental results.

A technique to resolve the incident and reflected waves from the records of composite waves is presented. It is applicable to both regular and irregular trains of waves. Two simultaneous wave records are taken at adjacent locations, and all the amplitudes of Fourier components are analyzed by the FFT technique. The amplitudes of incident and reflected wave components are estimated from the Fourier components, and the incident and reflected wave spectra are constructed by smoothing the estimated periodograms. The wave resolution is effective in the range outside the condition of the gauge spacing being even integer of half wavelength. The ratio of incident and reflected wave energies in the effective resolution range is employed in estimating the overall reflection coefficient. The incident and reflected wave heights are estimated from the composite wave heights by energy consideration.

Wave trapping by refraction can give rise to resonance of a kind unfamiliar in oceanography. Trapping over realistic seabed topographies is incomplete, but conversely, possesses a mechanism for direct, harmonic excitation from the open sea that is unknown in classical resonance. These phenomena have been studied for the simplest example of an axisymmetric island of typical shape with small seabed slope. Asymptotic analysis has led to simple formulae for resonant frequencies, energy leakage rates and resonant response coefficients. Resonances of extraordinarily large but narrow response have been found.

This paper presents a discussion of four methods available for the computation of small amplitude periodic waves in coastal zones of arbitrary topography. With no reflections (or reflection from a single structure) the methods that proceed in space (Refraction and Propagation) or time (Timestep) seem the natural ones from a physical point of view. With repeated reflections, recourse must he taken to the solution of an Elliptic “boundary value problem. – It is suggested that a P-method based on (energy) flux lines and energy fronts be developed for cases where the R-methods give crossing orthogonals.

The Atlantic coast of the United States is affected by extratropical storm surges several times each winter. The most devastating storm of this type on record is that of March 1962. This storm caused damage estimated at over $200 million. The National Weather Service has developed an automated technique for forecasting such storm surges. Statistical forecast equations have been derived for 11 locations from Portland, Me., to Charleston, S.C. Input data to these equations are values of sea-level pressure as forecast by an atmospheric prediction model of the National Meteorological Center. A sample forecast equation is shown.

The method was put into operation in 1971. Forecasts are transmitted via teletypewriter and extend to 48 hours at 6-hour intervals. A sample teletype message is shown. Forecasts of the devastating storm surge of Feb. 19, 1972, are discussed. These forecasts agreed reasonably well with observations of the storm surge. Experience with the method indicates it to be useful and therefore it will be expanded to include additional forecast locations.

A two-dimensional numerical simulation model of storm surges based on the vertically integrated hydrodynamic equations of continuity and m.onmentum is adopted. The model embodies the inundation over the lowlying land surface with moving water-land interfaces. Kind stress coefficient is considered not only function of wind speed but also dependent on the temperature differential between air and water. Bottom stress is treated by an evaluation of convolution integrals over the surface slope pressure depression and wind shear. The contribution of momentum by river inflows is taken into account. Particular attention is directed to the treatment of nonlinear terms in the governing equations to insure the improvement of numerical stability and accuracy. The model is applied to the New Jersey Coastal area and reproduces the historical storm surges quite well both at Atlanta City and Sandy Hcok.

A significant portion of the damage by hurricanes is the storm surges. The National Weather Service has developed a dynamical-numerical model to forecast hurricane storm surges. The model is used operationally for prediction, warning, and planning purposes.

The model requires fixed oceanographic and real time meteorological input data. The oceanographic data were prepared for the Gulf and East coasts of the U.S. and are stored as an essential part of the program. Meteorological data for any tropical storm are supplied by the forecasters or planners using the model.

The model was applied to hurricane Camille 1969. Comparison between the observed and computed surges for Camille was satisfactory for prediction purposes.

The Alaska tsunami of March 28, 1964, caused by a tectonic uplift, propagated across the Pacific Ocean and was even recorded at the shores of New Zealand and the Antarctica. The large distance propagation of this tsunami is investigated by a numerical model based on the shallow water equations. The model includes bottom friction, eddy viscosity and Coriolis acceleration and yields the water elevation and the vertically integrated current velocity. The generation mechanism is given by a simplified initial condition, that is derived frompthe observed average uplift of 1.8 m for an area of 110000 km² on the Continental Shelf. The computed tsunami propagation is presented by means of the first wave travel time and height on Pacific Ocean maps and by giving sea surface time series for selected stations. These computed results are compared with observations, especially considering the limitations of the model due to the coarse grid net having been used.

This paper concerns the run-up and inundation characteristics of tsunami surges. The forces and moments produced by the waves are not discussed, however, the proposed technique does provide the necessary information for their determination. The method relies on the knowledge of the wave elevation at the coast (as determined from historical data or other means) and an estimation of the bed roughness. The considerations and calculations involved in determining these parameters are discussed in detail. Twenty-four observed run-ups on the island of Hawaii in the case of the 1946 Aleutian tsunami, and 18 run-ups on the island of Maui for the Chilean 1960 tsunami are used to illustrate the technique. Methods are also presented to predict the shoreline heights and extent of inundation of tsunami surges where historical data is not available.

Although numerical computations of the generation and propagation of tsunamis are successfully achieved in recent years, modeling of their wave sources is still a big problem. Three kinds of, wave source model, that is statistical, oceanographic and fault model, are studied in this paper.

It is found that the first model gives reasonable wave heights as shown in the previous paper, the second one presents roughly one half of those for the first model and the last one produces too small wave heights.

Based on the analysis of computed results, nature of undulations off from the shore boundary, directivity of wave propagation and the spindleshaped leading part are discussed.

Comparing magnitude of various wave parameters for the leading wave along the minor axis of the wave source, it is shown that the long wave approximation modified by the slope effect illustractes the tsunamis in deep region of the sea and the slope effect is most dominant in shallow region.

Measurements were made of the water waves generated by the horizontal motion of submerged plungers. The results obtained in a three-dimensional hydraulic model experiment, using a plunger 0.5 ft. wide and 0.25 ft. high, were compared with both the experimental results and theory for the twodimensional case. It was found that at a given location the ratio of the elevation above the still water level (SWL) of the first wave (the largest wave of the group for the range of variables tested) to the displacement of the plunger (H₃/λ) was found to be dependent upon the Froude Number N_Favg (based upon the average plunger speed and the water depth) and upon the ratio of the height of the plunger to the water depth (D/d). For a constant value of θ, H₃/λ increased with increasing N_Favg and D/d. A few additional tests were made using a plunger 2.0 ft. wide and 0.25 ft. high. The results show that H₃/λ depends also upon the ratio of water depth to the width of the plunger (d/W).

The wave motion resulting from cavities in the ocean surface was investigated using both the long wave, shallow water model and the incompressible Navier-Stokes equations. The fluid flow resulting from the calculated collapse of the cavities is significantly different for the two models. The experimentally observed flow resulting from explosively formed cavities is in better agreement with the flow calculated using the incompressible Navier-Stokes model. The resulting wave motions decay rapidly to deep water waves. Large cavities located under the surface of the ocean will be more likely to result in Tsunami waves than cavities on the surface. This is contrary to what has been suggested by the upper critical depth phenomenon.

The 1973 Shore Protection Manual (SPM) predicts longshore transport rates that are 83% higher than its 1966 predecessor, for the same wave conditions. This upward revision is the result of concurrent increases due to (1) deletion of all laboratory data used to establish the 1966 prediction, (2) addition of Komar's (1969) field observations, and (3) limiting energy flux values computed from previously unused data obtained at Santa Barbara (Johnson, 1952). A derivation based on conservation of energy shows that P_l is the longshore component of the energy flux confined between two wave orthogonals spaced a unit distance apart in the longshore direction, and that a term previously identified as the onshore component of energy flux is identical with the total energy flux in the direction of wave travel between these orthogonals. Use of submerged weight transport rates has no engineering benefit at the present time because: (1) all available data are in terms of volume rates, (2) conversion to submerged weight requires estimates of the void ratio and sand grain density which have been assumed constant in practice, and (3) the engineering problem needs volume rates which would require reconversion back to volume rates if an immersed weight prediction were established.

Mudbanks have been observed to have an extraordinary calming effect on the sea surface. In certain cases this effect is due primarily to the transfer of energy through the sea/mud interface and its frictional dissipation within the bottom sediments. This paper describes an experiment that measured wave characteristics and the resulting sea floor oscillations in an area where the bottom is composed of fine-grained sediments. The energy lost by the waves at the position of the experimental setup is calculated and compared with a direct measurement of the net energy lost by the waves in going from the point of the experiment to a station 3.35 km inshore. Results show that bottom motions in the range of wave-induced bottom pressures from near zero to 2.39 x 10³ Pascal have the appearance of forced waves on an elastic half space. The apparent effect of internal viscosity is seen in a phase shift between the crest of the pressure wave and the trough of the mud wave. Measurements show this angle to be 22° (±11°) for the peak spectral component (T = 7.75 seconds). The energy lost to the bottom by the waves at the field site was found to be at least an order of magnitude greater than that resulting from the processes of percolation or that caused by normal frictional effects. This newly observed mechanism for the dissipation of wave energy is particularly important for waves in intermediate-depth water and could be a prime factor in determining design wave heights in muddy coastal areas.

A mathematical model for sediment transport under waves has been developed from concepts that have been used successfully for unidirectional flow. This model has been combined interactively with numerical models of wave refraction, wave diffraction, longshore currents and circulation currents in order to predict local topographical changes in the vicinity of a cooling water intake basin for a nuclear power station. The sediment model is calibrated using field data of sediment concentration profiles. Verification and adjustments may be made by analysing deep water wave statistics corresponding to periodic beach and hydrographic surveys.

The model can be used to investigate the effects of any wave climate and consequently different layouts of coastal structures can be examined very rapidly. For the particular problem considered it was necessary to optimise the configuration of the breakwaters forming a cooling water intake basin in order to minimise the sediment concentration at the intake, estimate maintenance dredging quantities and investigate extreme events.

Analysis of longshore transport at a littoral barrier is presented. Channel Islands Harbor, California was selected as the study site because its offshore breakwater and jetties form a unique complete littoral barrier. Through repetitive surveys an accurate determination of longshore material transport in one direction was made. Measured transport rates ranged from 160,000 to 1,284,000 cubic meters per year. Utilizing visual observations of surf parameters, estimates of longshore wave thrust were computed. The range of wave thrust was 145 to 1,988 Newtons per meter. Comparison of the relation of wave thrust and longshore sediment transport is made. This study indicates that in an environment of high transport, nearly twice as much transport is predicted tinder corresponding wave thrust as that of the data summarized in the Coastal Engineering Research Center's Shore Protection Manual.

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 investigations into beach formation and equilibrium profile characteristics, including the longshore transport rate of beach material under regular wave attack with varying angles of wave approach.

The use of the dimensionless fall velocity for determining equilibrium foreshore slopes, -modeling of natural beaches in the laboratory, and for determining shoreline erosion rates is examined. Encouraging results are found for relating foreshore slope uniquely to the dimensionless fall velocity and possible model law is proposed.

Beach profiles have been measured at Torrey Pines Beach, California for four years and correlated with tides and accurate spectral estimates of the incident wave field. Characteristic equilibrium beach profiles persist for time spans of up to at least two weeks in response to periods of uniform incident waves. These changes in the beach profiles are primarily due to onoffshore sediment transport which can be related to variations in wave characteristics and tidal phase. The most rapid readjustment of the beach profile occurs during high wave energy conditions coincident with spring tides. Alternatively, the highest berm building is associated with moderate to low waves that coincide with spring tides.

The statistical method of empirical eigenfunctions has been applied to four years of beach profile data. The eigenfunctions associated with the three largest eigenvalues are shown to be stable for data sets of one, two, three, and four years length, and they correctly describe beach changes caused by storm activity. The usefulness of the eigenfunction representation is confirmed as a concise means of representing beach profile variability.

Crenulate shaped bays are ubiquitous and constitute the largest proportion of coastline length. The characteristics of stable bays (i.e., no littoral drift) are known, so that realistic encroachment limits can be defined. Allowances for long term changes in direction of persistent swell and annual attack from multidirectional storm waves may have to be made. The exposure of a rock outcrop during an erosive sequence will create a new fixed point on the coast and hence a new bayed system. An existing non-stable bay can be prevented from indenting to its equilibrium shape by the construction of one or more fixed points around its periphery. Research should be conducted to minimise the cost of headlands which might start off as offshore breakwaters, even mobile units.

This paper refers to bathing beaches. It presents a method for beach design which provides both coastal protection and protection for the bathing public. Reasons are pointed out as to why the open sea foreshores are, in many cases, not suitable for recreation.

The method uses an enclosing submerged breakwater coupled with short groins to provide a bathing beach with a safe swimming area and a controlled sand plaza. Economical in execution and maintenance, the method can be used for sandy or rocky coasts.

In order to check the results of Bakker's theory [1], [2] concerning the influence of groynes on a sandy beach, a comparison is made with experimental results obtained in model tests performed in the Delft Hydraulics Laboratory [3], and in the Laboratorio Nacional de Engenharia Civil, Portugal [4]. The theory gives the bathymetric development in terms of a set of two schematized contour lines, representing the onshore and offshore parts of the model where longshore sand transport occurs. As input in the theory the characteristics of the undisturbed sand transport should be known, i.e. without groynes. This is achieved by computing the longshore sand transport acoording to Bijker's method [5] and the transverse sand transport according to Swart's method [6], starting from the hydraulic conditions as measured in the model without groynes. In order to make a comparison with the theoretical lines, the bathymetric development as measured in the model with groynes is also schematized to a set of two contour lines. In some cases the result is quite good, whereas in other conditions the theory does not even show the right trend; see [7] for details. Possible causes are discussed, and shortcomings of the model as well as of the theory are mentioned.

A series of wave basin experiments were undertaken to better understand the selection of groin spacings and lengths. Rather than obtaining edge waves with the same period as the normal incident waves, subharmonic edge waves were produced with a period twice that of the incoming waves and a wave length equal to the groin spacing. Rip currents were therefore not formed by the interactions of the synchronous edge waves and normal waves as proposed by Bowen and Inman (1969). Rips were present in the wave basin but their origin is uncertain and they were never strong enough to cause beach erosion.

The generation of strong subharmonic edge waves conforms with the work of Guza and Davis (1974) and Guza and Inman (1975). The subharmonic edge waves interacted with the incoming waves to give an alternating sequence of surging and collapsing breakers along the beach. Their effects on the swash were sufficient to erode the beach in some places and cause deposition in other places. Thus major rearrangements of the sand were produced between the groins, but significant erosion did not occur as had been anticipated when the study began.

By progressively decreasing the length of the submerged portions of the groins, it was found that the strength (amplitude) of the edge waves decreases. A critical submerged groin length was determined whereby the normally incident wave field could not generate resonant subharmonic edge waves of mode zero with a wavelength equal to the groin spacing. The ratio of this critical length to the spacing of the groins was found in the experiments to be approximately 0.15 to 0.20, and did not vary with the steepness of the normal incident waves.

This paper outlines the results obtained from monitoring the Beach Nourishment Project at Jupiter Island, Florida. Jupiter Island is a 16 mile long barrier island on the east coast of Florida. Five miles of the beach were nourished in two stages in 1973 and 1974. A total of 3.4 million cubic yards of sand were dredged from an offshore borrow area and placed on the beach. The monitoring program included: seasonal hydrographic surveys of beach and offshore profile to 3000 feet offshore; climatological monitoring of wind, waves, tides and currents over a oneyear period; tracer and dye studies; and sand sampling and coring at selected beach and offshore locations. The results indicate that beach restoration has a groin effect in the sense of producing favorable changes in littoral drift due to shore alignment changes. A net accretion updrift of the restored area occurs. The results demonstrate the importance of the offshore profile in accounting for the total sedimentary balance. Shoreline recession coupled by a build up in the offshore profile may reflect accretion rather than erosion. Finally, the results show that the littoral drift formula using the wave climate as input provides inadequate prediction estimates for erosion or deposition following construction of a beach restoration project.

The 1973 beach nourishment at Cape Hatteras placed approximately 465,000 m³ on the subaerial beach. Eighteen months later, about 51 percent of this material remained on the beach. During this period there were relatively few major storms, and this mild wave climate is largely responsible for this high retention. At the end of this monitoring period the beach was stable and fully capable of providing shoreline protection and recreation.

A correlation is presented relating storm erosion with the complete storm wave climate, including a post-storm period. A new parameter is defined which includes a measure of wave steepness and longshore current velocity.

A three dimensional facility for testing dynamic equilibrium and artificial nourishment of beaches was developed. Specific conclusions are drawn with respect to trap location and re-reflection of waves. It was found that dynamic equilibrium is achieved faster in three dimensional tests than in previous two dimensional work and that the profiles are eroding profiles rather than potential (limit) profiles. It was seen that profiles develop around the offshore bar which is shaped early in the experiments. Also the depth of the summer step was found predictable from critical shear stress considerations. Finally, onshore nourishment of eroding beaches was found to be successful.

Proposals to “improve” a pocket beach at Kaimu, Hawaii have been under active consideration for a decade. The beach, which is famous for its jet black color has been receding for at least a century. The plans proposed have called for its enlargement, and most of them for its protection by an offshore breakwater. Advantages of a larger beach area, and of the improvement of swimming conditions if the breakwater were constructed, are undeniable. Loss of surfing sites would, however, have resulted from the adoption of any of the plans involving breakwater. Other disadvantages associated with some of the plans proposed would have included alteration of beach color, other visual impacts, and threats to archaeological sites from the quarrying of breakwater stone. Sand-loss estimates and breakwater construction criteria dependent on them were based on probably erroneous interpretations of historical evidence. Possible alternative sites for the provision of the swimming opportunity were not investigated.

Serious question was raised whether the project would result in overall improvement. However, recent coastal subsidence has rendered all of the plans obsolete and the question is probably moot.

Scour at the foot of vertical homogeneous crib style walls which were used as models for detached breakwaters, and the rise of mean water level in the shoreside region of the breakwaters were experimentally investigated, and the experimental results were compared to some field data.

Foundation design for offshore structures in areas where wave-induced bottom pressures cause submarine mud slides requires a knowledge of the potential depth of slide and of the magnitude and distribution of soil movements below the slide. Several methods have been developed to evaluate the stability of the seafloor due to wave-induced bottom pressures. These methods are reviewed and an improved procedure is presented. This procedure makes use of finite element analysis and combines in a rational manner oceanographic information on wave statistics with stress-strain behavior of soils under cyclic load conditions in order to evaluate the effects of a given storm history on the behavior of submarine sediments.

The size, number and application of offshore pipelines are steadily increasing. At the same time, the incidence of reported pipeline failures is also increasing. There appear to be several reasons for these failures, and they can be placed in two basic categories:

Under the first category the depth of burial may be insufficient, the type of burial material may be inferior to the material alongside the trench, or the compaction of cover material may be inadequate. Under the second category the pipe may actually float up to the surface from the ocean bottom as material around the buried pipe liquifies.

An extensive literature search revealed that many studies were conducted by Meyers (1936), Waters (1939), Johnson (1940), W.E.S. (1940), Rector (1954), Wiegel, et al (1954), Saville (1957), Iwagaki and Noda (1962), Nayak (1972), Noda (1972), and Earattupuzha (1974). In general, two types of “equilibrium profiles” were developed in the laboratory flumes, the “ordinary” and the “storm” (sometimes referred to as summer and winter profiles). Despite numerous previous investigations, knowledge of the “scale effects” involved in equilibrium beach profiles is inadequate. Many authors have analyzed model data without stating the relation between model and prototype dimensions. In addition, many have claimed certain phenomena observed in the model to be independent of initial slope.

An extensive laboratory study was conducted to evaluate the development of underwater bars and scour patterns with the pipeline buried at various depths below the ocean bottom. Pictures of the beach profile were taken at specific time intervals through the glass wall of the wave tank.

Attempts were made to correlate equilibrium profile geometric quantities, such as depth of offshore bar, scour depth and berm height with the wave characteristics. Qualitative agreement between laboratory and natural beach profiles were demonstrated by trial and error fitting of one to the other.

Reversing currents in inlets on the Great Lakes are generated primarily by long wave seiching modes of the lakes rather than by the tide. In order to investigate the nature of long wave excitation and the generating mechanism for significant inlet velocities, to establish techniques for predicting inlet-harbor system response, and to develop base data for future planning and design studies, field measurements were conducted in 1974-75 at several harbors on the Great Lakes. Data collected includes continuous harbor water level measurements at all sites, inlet velocity measurements at the primary site (Pentwater, Michigan), and channel hydrographic surveys at the sites where more recent data were needed. Historic water level and velocity data for some of the harbor sites was also available.

Amplification of harbor oscillations and generation of the highest inlet velocities are caused by the Helmholtz resonance mode which has a period of 1 to 3 hours for the inlet-harbor systems studied. A recently developed simple lumped-parameter numerical model is shown to be quite effective in predicting inlet-harbor response over the range of excitation periods encountered. Selected data from Pentwater are presented to demonstrate the hydraulic response of the inlet harbor system and the applicability of the lumped-parameter numerical model.

Tidal inlets on the Pacific coast of Japan were studied with respect to three characteristic variables of the throat section:(1) Throat area,A;(2) Throat width,B; and (3) Direction of throat section, θ_ts. For each of these three variables, multiple regression analysis was performed stepwise by introducing external variables such as tidal prism, mean flow rate of tidal flow, wind energy, wave energy and so on into a linear regression model. Exposure condition of throat section to open sea was also introduced into the analysis.

First step analysis derived quite reliable result on the direction of throat section; θ_ts(degree) = −60.0 + 0.88 θ_pwv(degree), r=0.964 where θ_pwv is the direction of wave energy which penetrates into a backed bay through tidal inlet and r the correlation coefficient between θ_ts and θ_pwv However, results on both throat area and throat width were not satisfactory enough even after the performance of more than eighth step analysis on them.

Similar analysis was further performed on both throat area and throat width of the classified data due to the magnitude of geometrical parameters r_as and r_hxb respectively, where r_as is the ratio of throat area to mean surface area of backed bay and r_hxb the ratio of the maximum depth at the throat section to throat width. As a result, the former regressions on both throat area and throat width were improved remarkably. Multiple correlation of the regressions were all greater than 0.930.

A numerical simulation model for the computation of tidal and fresh water flow exchange through a coastal inlet developed by Amein) was modified and calibrated with field data (current, water surface elevation and bottom topography) for Lockwoods Folly Inlet, North Carolina. The calibrated model was then used to predict the changes in the flow regimes brought about by natural and manmade changes such as storms and dredging, respectively, and to predict the changes in flow regimes caused by the Lockwoods Folly River.

A generalized hypothesis of the patterns of sediment through and bypassing the inlet were formulated from an evaluation of the flow data and from an analysis of the orientation and structure of the bedforms observed in the inlet and on the offshore bar. The bedforms were analysed in the field and from an uncontrolled mosaic made from multispectral aerial photographs. Confirmation and refinement of the transport rates and movement patterns during ebb tide were made by introducing 454 kilograms (1000 lbs.) of fluorescent tracer sand in two colors into the inlet channels. The sediment movement through the inlet was established and correlated with the numerical simulation model. Confirmation and refinement of the transport rates and movement patterns during flood tide were made by introducing 680 kilograms (1,500 lbs.) of fluorescent tracer sand in three colors into the surf zone on the updrift beach and on the offshore bar. The sediment movement indicated the existence of bar bypassing (which was the dominant bypassing mechanism) and tidal flow bypassing. The bypassing mechanism of the inlet was found to agree with other atlantic coast inlets.

When used in conjuction with an analysis of bedform and tracer sand data the numerical simulation model was found to be a valid method for monitoring the high energy inlet environment.

The flow characteristics and the stability of a tidal inlet are governed, among other factors, by the channel bed friction. In order to determine the bed shear stress regime and the frictional characteristics, near-bed velocity profiles.were obtained at the throat sections of two inlets, John's Pass and Blind Pass, on the Gulf Coast of Florida. A specially designed steel cage with five current meters in a vertical array was used to obtain the profiles in the bottom one meter of the flow.

The profiles were found to be logarithmic but it is noted that, especially near the times of slack water, the effect of inertia becomes significant. However, during the major part of the flood or ebb flow period, frictional effects are dominant. In the fully rough regime of flow, the bed-shear stress – velocity relationship is found to follow the square law, with a constant, characteristic friction factor and Manning's n for each inlet. This friction factor is used in hydraulic formulas, based on uniform, steady open channel flow relationships, to obtain the tidal prism – throat cross-sectional area ratio, which is then compared with that obtained from flow discharge measurements. Agreements and discrepancies in the comparison are discussed. The relationship between the bed shear stress at incipient motion and the grain size at the bed is reviewed, and it is noted that the observed relationship at the two inlets does not agree with the well-known correlation of Shields for uniform sandy beds.

The mouth of the Shoalhaven River on the southeast coast of Australia is subject to direct attack by high energy waves and offers a general model of wave-dominated river-mouth deposition. During river floods seawater is completely flushed from the lower reaches of the channel and significant quantities of sandy bed load and suspended silts are debouched into the Tasman Sea. However, breaking waves cause intense mixing between the effluent and ambient waters while wave-induced mass transport and setup oppose and partially impound outflow. Unusually rapid deceleration and lateral effluent expansion result. Sediments accumulate in the form of a broad creseentic river-mouth bar with its crest situated about 2 channel widths seaward of the outlet and as broad shallow subaqueous levees capped by swash bars. Post-depositional shoreward return of sands by shoaling waves produces a constricted outlet. During low river stage wave setup enhances flood tidal currents and partially inhibits ebb tide outflow. This leads to a gradual shoreward migration of the river-mouth bar, a narrowing of the constricted outlet and to upstream migration of river-mouth sands into the lower reaches of the channel.

A case study is given of river training works at the mouth of the Clarence River. The study spans a period of ninety years. Extensive hydrographic data from the later part of this period is presented and examined in detail.

Prior to 1903 internal training walls had been constructed to stabilise the internal channel and stabilise the bar location at the mouth of the Clarence River. In 1956 construction started on entrance jetties with the aim of deepening the bar. The work was carried out over a period of 16 years. The slow rate of construction has allowed changes in bar depth to be compared with depths estimated by an empirical formula which relates bar depth to tidal flow and channel width. Results have shown that the empirical formula gives a reasonable estimate of bar depths and that bar depth is independent of jetty length.

Results have shown that the behaviour of the bar is strongly affected by floods. Some details of bar volume and movement are presented.

Estimating the rate of sediment deposition and annual maintenance dredging at offshore dredged channels have been two of the most challenging tasks confronting coastal engineers in the past 10 to 15 years. Because of the complexity of the mechanism of sediment-flow interaction and the lack of available practical methods for estimating the sediment transport rate under waves and current action, it is felt that a simple and rational method is needed for describing sediment behavior at offshore dredged channels and estimating accretion rates. It is hoped that this paper contributes to the answer of this problem.

The paper describes the mechanism of sediment deposition and presents a simple method for estimating the rate of annual maintenance dredging. The effect of using a submerged breakwater for relieving the sedimentation problem within the dredged channel is also presented.

Many authors have dealt with the migration of sand in front of the German coast of the North Sea. Especially the movement of sand-banks and deep channels in the Weser-estuary was subjectmatter of several investigations with different results.

Thorough investigations of selected cross-sections point out, that the movement goes on in some regions. The important shipping channel however has obtained a certain stability during the last 30 - 40 years, because the migration of sand occurs otherwise than in former days.

This phenomenon coincides with the extensive and decisive river improvement measures in the inner part of the Weser-estuary.

Current measurements in the investigation area demonstrate, that concentrated tidal currents in the deep channels guarantee a sufficient clearance for shipping purpose.

It seems to be sure, that for the present no essential shifting of the main channel calls for important measures in the field of shipping, dredging and building of sea-marks.

Bayocean Spit, separating Tillamook Bay from the Pacific Ocean on the north'Oregon coast, underwent severe erosion following construction of a north jetty at the bay entrance in 1914-17. This erosion ultimately led to the complete breaching of the spit in 1952. Simultaneous to the spit erosion south of the entrance, the shoreline north of the north jetty advanced seaward by some 600 m (2000 ft). This pattern of erosion and deposition following jetty construction has generally been interpreted as the jetty blocking a large north to south net littoral drift in the area, estimated by a previous study at 620,000 m³/yr (800,000 yd³/yr). Our reexamination of the shoreline changes and patterns of erosion and deposition following jetty construction disagrees with this interpretation, and instead we conclude that all of the changes resulted from local rearrangements of the beach due to the disrupted equilibrium following jetty construction, but at the same time maintaining an overall condition of zero net littoral drift. This interpretation is supported by other evidence that indicates a near-zero net drift on this portion of the Oregon coast. Thus severe coastal erosion can result from jetty construction even in areas of zero net littoral drift.

Available evidence indicates southward littoral transport through the Merrimack Embayment. In apparent contradiction, the beach on the southern (Plum Island) side of the inlet has built seaward of the updrift beach. This phenomenon is related to a balance between storm and fair weather conditions. Wave observations under a variety of surf conditions show that during storms, sand is transported southward along the face of the nearshore bar fronting Plum Island. During calm periods sand is moved northward along the beach until it is trapped by the southern jetty and removed from the then active tidal current transfer system. Using discharge data and wave measurements from the Merrimack Inlet area, Bruun's bypassing coefficient (r = Q_ls/Q_max. where Q_ls is the longshore transport rate in M³/yr and Q_max is the maximum inlt discharge in M³/sec) was computed for storm and fair weather conditions. During storms, the bar bypassing observed in the field was clearly indicated. During calmer periods tidal current transfer was predicted. This relationship is considered only an approximation as it does not consider many important physical parameters (grain size, nearshore slope, wave type, etc.).

This paper presents some general properties on topographic change on the shore and sea bed in the vicinity of ports and harbours constructed on the sandy beach, mainly with the case study of Kashima Port. Following three characteristics of the topographic change due to prolongation of breakwaters are discussed; that is,

A sand circulation pattern has been determined for Price Inlet, South Carolina, using wave refraction diagrams, littoral process measurements, bedform orientations and inlet hydraulic data. The dominant process acting on the ebb-tidal delta is wave swash which impedes the ebb-tidal currents and augments the flood-tidal currents. This produces a net landward transport of sand on the ebb-tidal delta as evidenced by the landward migrating swash bars. Bedform orientations and velocity measurements taken on the swash bars also support this conclusion.

Countering the general landward transport direction is the ebb dominance of the main channel. This dominance can be explained by higher inlet efficiency at low water than at high water. Consequently, bay tide phase lag is larger at high than at low water resulting in a longer flood duration. This causes higher mean ebb-tidal currents and a consequent larger potential net ebb transport of sand. This inlet characteristic explains why little sand is transported inside the inlet, why the throat remains scoured and why sand entering the main channel is carried seaward.

A comprehensive investigation of coastal processes active within and in the vicinity of Beach Haven and Little Egg Inlets was completed as part of the Coastal Processes Investigation for the proposed Atlantic Generating Station. The suspected complex nature of this dual natural inlet system was documented and a process-response model is presented to relate the more significant physical forcing functions to observed morphologic and hydraulic changes. A rising sea level, a net littoral drift from the north and the sediment scouring power of the flow in the two main channels serving the tidal basins are the principal factors related to the geographic and hydraulic stability of the system. The results of the study can be used to evaluate the potential impact, if any, of the proposed Atlantic Generating Station on the adjacent coastal environment.

Inlets act as large sand sinks for sand derived from adjacent beaches. An attempt to quantify the amount of sand in an outer bar is made with the major governing parameter of inlet hydraulics, tidal prism. In areas of high wave activity there appears to be a well defined limiting relationship to the amount of sand stored in the offshore bar as a function of tidal prism. In areas where inlets are exposed to lower wave activity, more scatter is noted in this correlation.

Relationships for estimating the equilibrium storage volume of sand in the outer bar/shoal of newly cut inlets on highly exposed, moderately exposed, and mildly exposed coasts (where degree of exposure relates to wave action offshore) are proposed for use in estimating quantities of sand which will eventually be lost to adjacent beaches.

A conclusion of the study is that more sand is stored in the outer bar of a low energy coast than in the outer bar of a high energy coast. An upper limit to outer bar storage in low energy zones may be a function of additional parameters other than tidal prism such as longshore energy flux at the inlet site and inlet history.

The seven sandy islands of the Eastfrisian group would appear to be initially formed and now continually supplied with sand from the Westfrisian group and the mainland to the west. The inlets between' these islands are in dynamic equilibrium with the strong tidal currents of the near 2,5 m range in the area. Hydrographic information dating back to 1650 permits the development of a hypothetical model which explains the historic changes and might predict future trends. The installation of coastal defence structures on the eroding western extremities of some islands in the mid 19^th century has greatly influenced the bars by which sand is transported from island to island in an easterly direction.

The northern 5 miles of shoreline at Assateague Island, Maryland are presently being eroded. During storms, swash surges are able to overtop the most landward (storm) berm as overwash with deposition occurring on the barren flats. Where primary barrier dunes still exist, sediment-charged surges are funneled through breaches in the dune field for deposition of the entrained material on the washover fan.

Sediment budget computations show that there has been a small net loss of material at each washover area, in spite of 7 discrete overwash events during a 26 month time interval. The predominant northwest winds effectively eroded the overwash material, transporting the majority of the sand back to the beach. This analysis indicates that there exists a balance between overwash and eolian processes with wind transport being slightly dominant.

Detailed field investigations of barrier beach morphology and processes at adjacent sites in the Magdalen Islands, Gulf of St. Lawrence, show that the two beaches are in distinctly different morphodynamic environments. The differences are expressed in terms of wave energy levels, sediment dispersal patterns, and nearshore, littoral, and dune geomorphology. The exposed west-facing coast has a steeper offshore gradient, is a zone of sediment bypassing, and has a complex sequence of three nearshore bars. Wave energy levels are lower on the sheltered east coast, and this is a zone of sediment redistribution and deposition with a single, linear nearshore bar. The different morphological characteristics of the two barriers are attributed to the spatial variation in energy levels and to the differences in offshore gradients on the two coasts. Computed wave energy values, derived from data monitored during two study periods (August and November, 1974), indicate that the mean wave energy levels were greater on the west coast as compared to the east coast by factors of 2.25 in summer and 2.95 in winter. This is due primarily to the dominance of winds out of the westerly quadrant throughout the year.

The shoreline of southern Alaska is a narrow coastal plain dominated by large glaciers, periodic earthquake activity, and strong extratropical cyclones. Studies on the coastal geomorphology and sediments carried out in 1969-71 and in the summer of 1975 were directed at defining geological hazards with respect to developing shore facilities for OCS oil exploration activities. Most of the shoreline was found to undergo rapid changes and experience a variety of serious environmental hazards. The safest potential port areas are located inside Icy Bay and Yakutat Bay. The coastal areas in the vicinity of the Malaspina Glacier and the Copper River delta are examples of the two principal shoreline types (glacial outwash plain and deltaic).

Tracing the movement of dredged sediments in north San Francisco Bay was accomplished jointly by the San Francisco District of the U.S. Army Corps of Engineers, Explosive Excavation Research Laboratory (now the Explosive Effects Division of the Weapon Effects Laboratory, U.S. Army Waterways Experiment Station), and the Stanford Research Institute. The study involved developing a technique which would permit the longterm tracing of fine sediments dredged from Mare Island Strait after disposal at the Carquinez Strait disposal site; application of the tracer; disposal of the tagged sediment for the February-March 1974 dredging of Mare Island Strait; sampling bottom sediments throughout the study area for a 10-month period; and, quantitative analysis of the collected samples.

The objective of this study is the application of hydrodynamic and material transport mathematical models for Mobile Bay in predicting sediment transport and deposition profiles within the bay system. Of particular importance are the seasonal variations of sediment distribution which are critically influenced by current patterns within the estuary. Both point and non-point sources of sediment will be included in the analysis.

Results will be presented in two ways. The first or long term variations in sediment distribution will be assessed by correlation with tidal cycle average velocities at various locations within the bay. Calculated distribution patterns will be compared with observed bathemetic data over the past century. The net effect of the construction of the Mobile ship channel on deposition patterns within the bay will also be evaluated. Secondly, short term variations in sediment transport and deposition resulting from man-made and natural disturbances will be analysed using a sediment transport model. This model will include deposition, bulk fluid transport and resuspenslon characteristics and will be capable of predicting localized, short term sediment patterns from maintenance dredging operations within the bay. Model trend results will be compared with field data collected during recent dredging activities and high altitude photographic data obtained for the bay area.

Ripples are generated and modified by wind-generated waves and their profiles are controlled by the nature of the near-bottom wave motion and by the size of the bed material. Wave-formed ripples develop under a definable set of conditions called the ripple regime. The ripple regime is bounded by those conditions that initiate grain motion, low-wave intensity, and by those that cause the disappearance of ripples, onset of sheet flow. Sheet flow occurs when intense wave motion causes several grain layers to be in motion. Three distinct ripple types occur in nearshbre areas of fine sand – relict ripples, vortex ripples, and transition ripples. Vortex and transition ripples lie within the active ripple regime, whereas relict ripples do not.

Ripples in fine sand were studied in the field at La Jolla, California, where profiles were obtained using a newly developed high-resolution sonar capable of vertical resolution of the order of one millimeter. Simultaneous profile and wave-pressure measurements permit correlation of the ripple profiles with individual waves and with the wave spectrum. The sonar, with its rapid scan capability (~ one meter per second), gives instantaneous measurement of the actively changing bed features in nearshore waters. The combination of bottom scans and wavepressure measurements extends previous wave-ripple studies to include all of the nearshore ripple regime.

The relation between the wave and ripple data from this study is best shown by plotting ripple steepness η/λ against the wave form of the Shields relative stress criterion θ. Vortex ripples (η /λ ⋍ 0.15) occur for θ values less than 40 but greater than the minimum value which is determined by the onset of grain motion.

The transition from vortex ripples to sheet flow commences at a θ value around 40 and ends at θ_C ⋍ 240, where θ_C is the critical value for the onset of sheet flow. With transition ripples, the decrease in steepness is caused by a decrease in ripple height, since the ripple wavelength remains essentially constant. Beds that become planar as a result of intense wave conditions (θ > 240) re-ripple in a few wave cycles once the intensity decreases. For this reason, bottom scans taken before equilibrium is reestablished show ripples that have a low steepness.

During some experiments where no sheet flow occurred between scans, migration of transition ripples was measured and found to range between zero and four centimeters per minute, increasing with increasing values of the theoretical bottom wave-drift current. Whenever migration was observed, it was in the direction of wave propagation, i.e., onshore.

Ripple symmetry is the ratio of the horizontal crest-to-trough distance β (in the direction of wave travel) to the ripple wavelength λ. A β/λ value of 0.50 indicates a symmetric ripple. Measured values of β/λ ranged from 0.36 to 0.61 with 74% of the values in the range 0.45 – 0.55, and 55% in the range 0.47 – 0.53.

The turbulent bursting process is outlined and attention is drawn to the fact that the “coherence distance” of the regenerating macroturbulent eddies is of a magnitude that is much the same as the length of dunes. Consequently it is postulated that the length of dunes is merely the “imprint” of the coherence distance on the deformable surface of a movable bed and the origin of dunes is explained accordingly. It is shown that the frequently observed similarity between tidal and unidirectional dunes is due to the similarity of the tidal transport and the transport corresponding to an intermittent unidirectional flow. The explanations presented herein are expected to be valid for dunes caused by both unidirectional flows and tidal currents.

Along the northern bank of the so-called “Maasgeul” scour has occurred, causing a trough. It is concluded from field measurements that the trough development is induced by density currents along the slope of the bank. The stratified flow system is dealt with mathematically. The calculated results are compared with the field measurements and agree fairly well. Trough development can be avoided by flattening the slope or by a bottomprotection.

It is proposed to show in this paper that there is a solution to the problem of non-uniform flow and this solution not only explains in detail many land forms which occur naturally, but thereby, yields a definition of ‘form’ loss.

If a channel, in which the transverse distribution of specific energy is uniform, converges and/or diverges,and the bed changes so that the flow will be critical at all cross-sections at the same time, the channel appears to be close to being hydraulically smooth.

Many natural forms, particularly estuaries, are readily explicable in this way. The most obvious one is the bar at the mouth of a river. It follows, if the river enters the sea with reasonable uniform grade, which most rivers do, the bed must rise as the flow loses the restricting influence of the banks (i.e. the width increases) if constant specific energy is to be maintained.

It is possible to calculate with considerable accuracy the dimensions of useful structures based on this concept. A large number of full size but nevertheless experimental structures have been built making use of the resultant benefits which develop:- low turbulence, accurate differential water levels and a clearly defined flow pattern, allowing very considerable savings to be made by eliminating expensive protective works.

The paper describes investigations carried out in order to design for the wave action, both wave force and scour, on large off-shore berthing structures sited approximately 1.3 miles (2.1 km) off-shore near Hay Point, North Queensland, in 56 feet (17 m) of water at low tide, the tidal range being 20 feet (6 m). The region is a cyclone area and the structures must be capable of withstanding attack from maximum predicted waves with period of 8.25 seconds and amplitude of 24 feet (7.3 m).

The main units in the berthing structures are concrete caissons sunk on to the ocean bed and the largest of these have plan dimensions of approximately 150 feet (46.7 m) by 135 feet (41.4 m) with four columns approximately 40 feet (12.2 m) square projecting through the water surface. No theoretical method available at the time of the investigation was capable of accurate calculation of wave forces on these structures. A scale model was tested to obtain wave forces and the paper compares results from the model with those of numerical methods and discusses the application of the results to the design functions. Scour effects were also modelled and the results used as the basis for design of scour protection.

Damage of coastal structures by tsunamis results by the direct and indirect action of hydrostatic and dynamic pressures, foundation failures, overtopping and flooding. Reliable assessment of the potential tsunami hazard at a coastal site and adequate engineering design of critical structures require analysis and understanding of all aspects of a tsunami system leading to its terminal behavior. Description of the space-time history of tsunami waves generated by impulsive disturbances require consideration of events and processes in the following regimes: (a) generation; (b) propagation and dispersion; and (c) termination. Processes and events in each regime during the development of a tsunami are under their own unique hydrodynamic constraints but are dependent on what has preceeded. In predicting tsunami wave characteristics at some distance from the generating source, the error structure may be pyramidal. Essential to any method of tsunami prediction at a distant or a nearby coast will be the full consideration and study of tsunami generative mechanisms. If the tsunami generation mechanics cannot be deduced with a reasonable degree of accuracy, it is not likely that the tsunami terminal aspects will be reliably predicted. Prediction of tsunami height at a distant or at a nearby coast requires knowledge of the magnitude and type of ground displacements in the tsunami generating area and of the characteristics of the surface waves resulting from such action. Although all mechanisms involved during tsunami generation are not fully understood, it is possible to obtain a suitable tsunami initiating function through the use of experimental data, historical data, and established empirical relationships, for each type of generating mechanism. Reliable computation of the tsunami propagation effects over and across the ocean can be obtained with proper modeling to provide an adequate description of the tsunami energy flow through the use of physical and numerical studies. Similarly, the terminal aspects and nearshore modification of the tsunami wave system can be approximated to provide the engineering criteria necessary for the assessment of the potential tsunami hazard at a coastal site.

The forces and overturning moments exerted by waves on large vertical square-section caissions have been measured in the laboratory. Each model caisson extended from the bottom of a wave flume through the water surface and was oriented either with one side perpendicular to the direction of wave propagation or turned through an angle of forty-five degrees to this position. For a given orientation, each model was tested for a range of wave heights (up to the point of breaking) for various wave periods and water depths. A digital computer was used for the acquisition, processing, plotting and storage of the experimental data.

In addition to the experimental work, an approximate theoretical method is presented which allows the wave loadings on a square caisson to be estimated by means of a simple desk calculation. The experimental data shows that this simple method of calculation is reasonably accurate over a wide range of wave conditions and caisson sizes.

The field observations on wave pressures on large circular cylindrical structures are performed at the cooling water intake structure for Hamaoka nuclear power plant, which is located at the coast of Pacific Ocean. In this report, the results of the field observation on wave pressures are compared with the results of the calculation by small amplitude wave theory considering wave diffraction around the cylinder.

This paper presents the results of an extensive experimental investigation of the in-line and transverse forces acting on sand-roughened circular cylinders placed in oscillatory flow at Reynolds numbers up to 1,500,000, Keulegan-Carpenter numbers up to 100, and relative roughnesses from 1/800 to 1/50. The drag and inertia coefficients have been determined through the use of the Fourier analysis and the least squares method. The transverse force (lift) has been analysed in terms of its maximum and root-mean-square values. In addition, the frequency of vortex shedding and the Strouhal number have been determined.

The results have shown that all of the coefficients cited above are functions of the Reynolds number, Keulegan-Carpenter number, and the relative roughness height. The results have also shown that the effect of roughness is quite profound and that the drag coefficients obtained from tests in steady flow are not applicable to harmonic flows even when the loading is predominantly drag.

In order to determine the added mass, drag and lift coefficients of a smooth cylinder at various distances from a plane boundary, the forced cylinder oscillation tests at high Reynolds number 10⁵ to 10⁶ and the wave force tests at moderate Reynolds number 10⁴ to 10⁵ have been carried out at the Wave Research Facility at Oregon State University.

It is found that the drag, lift and added mass coefficients are all strongly Reynolds number dependent. The effect of the near by plane boundary is to increase all of the force coefficients two to four times as compared to the free stream flow values. This is a most important factor to be aware of for design purposes.

Flow separation of a laminar boundary layer on the surface of a circular cylinder developed by monochromatic waves has been investigated both theoretically and experimentally, and next, characteristics of vortex formation and shedding have been discussed with Keulegan-Carpenter's number and Reynolds number, and finally, local depressions of the wave pressure around the cylinder induced by wake vortices have been examined in the experiment.

The distribution of shock pressures on a vertical face breakwater is so random from one shock to the next that the determination of the internal forces in a thin-balled reinforced-concrete structure is difficult even when a large number of pressure cells is used in a model test. Therefore a technique has been developed that allows the direct determination of the internal stresses by means of strain gauges.

The new technique has been applied to a breakwater consisting of a series of cylindrical caissons. The results show that a strain gauge model is more advantageous than a pressure cell model because of its simpler data analysis and better determination of the quantities required for design.

A two-year ocean experiment involving wave-induced forces on a test pipe mounted on the sea floor [Grace and Nicinski (1976)] involved the measurement of various quantities other than the pipe forces per se. A pair of these involved surface wave characteristics and wave-induced water motion at the level of the pipe centerline but off to one end of the pipe. These wave-kinematics data have been combined, and the results of this work make up this paper in which the emphasis is on the deterministic approach to data interpretation. Presented are comparisons of the velocity and acceleration data with the predictions of Airy and stream function theories plus discussion of the dispersion of the field data. The primary intent of the paper is to suggest to designers of bottom-laid structures, such as pipes, how values of the peak velocity and maximum acceleration of the water motion associated with a non-breaking design wave of specified characteristics can be chosen.

Limitations of the Morison equation for computing wave forces on small submerged structures have encouraged the use of dimensionless relationships containing only height, period and water depth. However in dividing the force by the theoretical drag force or inertia force a relationship can be found with the Keulegan parameter (U_im T/D) over a wide range of conditions and different types of wave. The U_im value can be determined from empirical and theoretical data for all depths and wave steepnesses. The relating coefficients for various dimensions and shapes of submerged object are predictable from potential theory or modified slightly because of viscous and such other forces induced by bottom and free surface boundaries.

For computing wave forces on a submerged object which is large compared to the wave length, the Morison equation is replaced by the Diffraction theory. Criteria for selecting the latter theory are presented.

The rms horizontal forces which result from the action of a linear, deep and intermediate water, laboratory scale waves were measured on submerged spheres removed several diameters from the free surface. The study focuses on unseparated flows encountered at small values of (d₀/D), where d₀ is the orbital diameter and D is the sphere diameter. Under these conditions, a steady streaming around the vertical equator of the sphere was observed, giving rise to a circulation in the sense of rotation of the orbital motion. This phenomena was found to diminish the resultant of the wave pressure on the sphere predicted by potential theory. In approaching the onset of separation, the drag coefficients were found to compare in size with those reported for similar motions in steady unidirectional flow.

This paper describes the effect of wave period on the stability of rubble mound breakwaters. Introductorily wave run-up and run-down on smooth slopes and on rubble mounds were measured, and breaker types were observed and recorded for different incoming wave and slope characteristics. The surf similarity parameter, $\text{ξ}=\frac{\text{tg}\alpha }{\sqrt{\text{H}/{\text{L}}_o}}=\sqrt{\frac{g}{2\text{π}}}.\frac{\text{tg}\alpha }{\sqrt{\text{H}}}.\text{T}$ was found practical for description of breaker type, run-up and run-down on both smooth and permeable slopes. Pressure measurements along the smooth slopes and in the core of a rubble mound were undertaken with two different core materials. It was shown that the most dangerous condition for the stability of rubble mounds occurs at the so-called “resonance condition”. Resonance refers to the situation that occurs when run-down is in a low position and collapsing- plunging wave breaking takes place simultaneously and repeatedly at or close to that location. This corresponds to a range of ξ values in between 2 and 3. Photographic instrumentation was introduced and tested to quantify the initial damage on a rubble mound.

This paper is a 1/3 abstact of a thesis for the Dr. Eng. degree by Ali Riza Günbak.

In the Chief of Engineers annual report of 1877, it was concluded that “The only way...in which a safe entrance could be obtained into this harbor would be by the construction of two parallel jetties, of very heavy stone, about 500 yards apart, from the north and south spits at the entrance.”

In 1882, a special Board of Engineers concluded that the “occupation of the south breaker spit by a structure...carried to low water and running from the south head (spit) in a north-westerly direction...” be built. Construction of the south jetty began in 1889 and of the north jetty, subsequently authorized, in 1891.

Due to the severe wave action, a number of rubble-mound construction techniques including stone, concrete cubes, tetrahedrons, and finally dolos armor units have been used. A description will be given of the construction and associated results. Experience with the reinforced and unreinforced concrete dolosse units will also be discussed.

Large scale model studies reveal that Reynolds scaling can affect the apparent stability and wave modifying properties of layered breakwater structures. Results of a study for a breakwater configuration designed to protect offshore power and port facilities in water depths to 60 feet are presented and discussed. The armor layer of this structure is formed from quarried rock of irregular rectangular parallelepiped shape, individually placed perpendicular to 1:2 seaward slope and crest. The resulting armor layer is relatively smooth, densely packed and very stable. Model studies of similar configurations were studied at 1:10, 1:20 and 1:100 scale ratios. Stability, runup, rundown and reflection were measured for a variety of water depths, wave heights and periods. Analysis of the large scale test results establish that the placed stone armor is approximately as stable as dolos armor units. Runup, rundown and reflection respond similar to rough, impermeable slopes. Comparison of large and small scale results demonstrate that relative increases in drag forces at lower Reynolds numbers decrease stability and runup in small scale models.

This paper describes the design and construction of the protective structure for a new Reef Runway at the Honolulu International Airport with special emphasis on the use of dolosse concrete armor units.

Damages on seadykes and revetments are mainly caused by wave impacts due to breaking waves. These impact forces act on small areas for a very short time and cause crater-like formations, when the forces are transmitted instantaneously to the side-walls of cracks in the cover of dykes or through joints into and below revetments. In this paper the results of investigations on impact forces are presented. A comparison of field data and laboratory data proves considerable differences, which must be explained mainly by the different air entrapment for prototype and small-scale conditions in the breaking waves. Both the data from field and small-scale model emphasize, that the slope of the dyke or revetment is responsible at first for frequency and magnitude of the impact forces.

Furthermore the effect of impact forces is demonstrated by the results of investigations on the stability of stone revetments with joints.

Interesting facts that a uniformly permeable seawall of vertical faces with appropriate reservoir has remarkable characteristics of absorbing wave energy even for long period waves in the same degree of usual sloped-face seawall and that these characteristics appear most clearly for permeable seawall of trapezoidal cross-section with backward-sloped reservoir wall are found theoretically and experimentally. Moreover, it is shown that a perforated wall with reservoir has similar characteristics to those for uniformly permeable wall with reservoir.

“Warock” is a type of concrete blocks which was invented in order to realize the wave absorbing seawall in practical works. Several examples of ever constructed wave absorbing seawalls, quaywalls and breakwaters by means of “Warock” in Japan are introduced.

Effects of permeable core layer installed in trapezoidal and rectangular breakwaters have been studied experimentally and analytically. As the materials for armour and core use of the lattice composed of circular cylinders was made in addition to rocks. Perforated plates were also applied as a kind of very thin core.

Expermental results show that the reflected wave heights from breakwater could be reduced considerably by locating the core layer shoreward within it while core thickness controls the transmitted wave heights in the protected water area. Harmonic analysis about the water surface in lattice armour reveals that the second harmonic waves take a pattern of standing wave distribution having a node at the seaward face of breakwater. Thin perforated plates work successfully for reducing the transmitted wave heights when they are installed at the rear face of breakwater.

An analytical approach to predict the transmission and the reflection coefficients is applied for the present experimental data and shown to be useful.

This report summarizes the results of the research on a gravity type quay wall comprising several layers of concrete blocks with a special shape called “Igloo” as shown in Photograph–1.

A box-type wave absorber, which is composed of a perforated vertical front-wall and a perforated, horizontal bottom-wall, has been proved by a number of experiments to show lower coefficients of reflection and more distinguished reduction of wave pressures than the perforated vertical- wall breakwater.

A breakwater of composite-type, which is 1500 m long and to be built at a water depth of 10 to 11 m below the Datum Line in the Port of Osaka, is being designed to set this new type of wave absorber in the concrete caissons of the vertical-walls which is named “a slit-type breakwater”. The typical cross-section of the breakwater and the advantages of the slit-type breakwater are presented herein.

One of the most powerful tools to analyze the boundary-value problems in water wave motion is the Green's function. However, to derive the Green's function which satisfies the imposed boundary conditions is sometimes difficult or impossible, especially in variable water depth. In this paper, a simple method of numerical analyses for two-dimensional boundary-value problems of small amplitude waves is proposed, and the wave transformation by fixed horizontal cylinders as an example of fixed boundaries, the wave transformation by and the motion of a cylinder floating on water surface as example of oscillating boundaries and the wave transformation by permeable seawall and breakwater as example of permeable boundaries are calculated and compared with experimental results.

This paper deals with the analytical and experimental studies on a new device to prevent the accidents of ship collisions with maritime structures. The practical protection device was designed on the basis of this study and it has been in use for the prevention of ship collisions of a class of 1,000 G/T with a boring tower for the geological survey of the sea beds of a narrow straits in which quite a many ships navigate.

The added masses of large tankers berthing to dolphins are studied both theoretically and experimentally. The movements of large vessels in shallow water in the directions normal to their planes of symmetry cause counter-flows of appreciable velocities under the hulls. The inertia of these counter-flows is shown to have an important effect on the added masses of the vessels. A theoretical formula is derived to determine the mass factor of an ocean vessel in shallow water as a function of the ratio Draught/Water- depth, the Froude number of the vessel and the coefficient of head loss of the counter-flow under the hull.

Experiment is made to determine the mass factor. Comparison:, between the theory and the experiment shows a good agreement.

Forces in mooring lines and fenders of a moored vessel exposed to waves have a mixed harmonic and a subharmonic character. The subharmonic oscillations, with periods well beyond the range of wave periods, may cause forces that are as large as, or even larger than the forces associated with the harmonic oscillations.

The origins of the subharmonic oscillations are discussed and it is shown that in model testing, the correct reproduction of both the mooring arrangement and the irregular wave motion is essential.

The subharmonic motions, and consequently the total forces, can be partially reduced by specially adapted mooring arrangements as tests on various mooring systems have shown.

As the public interest in low-cost, self-installed solutions to shoreline erosion continues to grow, the involvement of private enterprise in developing solutions intensifies. Now that low-cost devices are identified as a salable commodity as goods or services, the number of inventors, creative engineers, agronomists, and foresightedplanners producing potential designs are rapidly growing. Over two hundred devices, both proven and untested devices, have been cataloged as a part of the National Shoreline Erosion Demonstration Program. This program calls for the Corps of Engineers to plan, establish, and conduct for a period of five years a shoreline erosion control development and demonstration program including physical and vegetative devices.

This paper deals with the effects and the method of laying of some recent emplaced artificial seaweed fields in the Netherlands. The weed is placed on the bottom in coastal waters to promote accretion or at least to prevent erosion along beaches and in gullies. The results of the three field trials, and some of the conditions, that govern the succesful application of the seaweed, which will be discussed.

This paper discusses procedures for designing ocean outfalls and offers the coastal engineer a practical design guide outlining the necessary steps required to plan, design, and construct an outfall. The design steps reviewed in this paper include site location considerations, environmental studies, outfall and diffuser hydraulics, pipe materials selection, pipe support systems design, and construction techniques.

The behavior of negatively buoyant slot jets discharged from near the bottom of stagnant and flowing receiving-water environments of uniform density was studied in laboratory experiments. In particular, the locations of the maximum height of rise and maximum horizontal displacement were determined as well as the centerline dilutions at those points. Experiments in stagnant environments were conducted for discharges at angles of 30°, 45°, 60°, and 90° from the horizontal and with discharge densimetric Froude numbers of 10, 20, 30, 40 and 50. For flowing environments, discharges at angles of 45° and 90° for the same range of densimetric Froude numbers were directed into uniform currents with discharge to ambient velocity ratios of 15 and 25. The reattachment eddy formed between the jet and bottom boundary was found to have significant effects on the slot jet trajectories and dilutions. Dilutions at the maximum height of rise and maximum horizontal displacement were less than those predicted for slot jets far removed from the influence of the bottom boundary. The strictly two-dimensional discharges studied provide lower bounds on the dilutions to be expected for the cases of slots of finite length or merged multiport diffuser discharges in which the reattachment eddy is not as well developed.

Based on a literature review of theoretical and experimental work on air-bubble systems, guidelines for the ideal design of submerged distributors discharging air into water are presented.

A comprehensive study of gas-liquid dispersions was carried out to find out the effect of physical properties, distributor arrangement, and the air flow rate, on the flow pattern within the jet. This review revealed that the distributor arrangement largely influences the characteristics of the dispersion within the zone of flow establishment. Also, upon analyzing the experimental results of air-water systems, it was found that the zone of flow establishment extends to greater distances of the water depth than that in the case of one-phase turbulent plumes. Furthermore, the experimental results showed that the efficiency of air bubble plumes can be increased by the proper design of the distributor.

Recommendations for the distributor design are given, which include, diameter of orifices and their spacings, pressure drop across orifices, number of manifolds, and the maximum air flow rate.

Thermal plumes from submerged discharges of cooling water from two power plants on Lake Michigan were studied. The system for the acquisition of water temperatures and ambient conditions permitted the threedimensional structure of the plumes to be determined. The Zion Nuclear Power Station has two submerged discharges structures separated by only 94 m. Under conditions of flow from both structures, interaction between the two plumes resulted in larger thermal fields than would be predicted by the superposition of single non-interacting plumes. Maximum temperatures in the near-field region of the plume compared favorably with mathematical model predictions. A comparison of physical-model predictions for the plume at the D. C. Cook Nuclear Plant with prototype measurements indicated good agreement in the near-field region, but differences in the far-field occurred as similitude was not preserved there.

Data on physical parameters in the James River around the condenser cooling water discharge of the Surry Nuclear Power Plant, taken prior to and during plant operation, were analyzed to determine the physical effects of the thermal discharge on the area and to compare the prototype distribution of excess temperature to predictions based on hydraulic model experiments.

The results of this investigation indicated that the increase in water temperatures due to the thermal discharge did not represent a significant alteration of the physical environment outside the mixing zone. The thermal discharge experienced turbulent mixing and entrainment near the outfall and temperatures decreased rapidly in this region.

Field data on temperature distributions around the discharge, when compared to predictions based on hydraulic model experiments, indicate that the model predictions were conservative.

A numerical model is developed for the quantitative description of the dispersion process in a two-layer system which represents an approximation for a natural coastal water body during the summer season when a distinct thermocline usually exists. The formulation is based on the convection-diffusion equation, vertically integrated between the layer boundaries. Layer velocities and thicknesses are assumed to be obtained from a separate hydrodynamic model. The quantification of the physical processes of entrainment and mixing through the density interface as well as the horizontal dispersion mechanisms is discussed.

The finite element method is chosen for numerical implementation because of its flexibility in grid layout and easier handling of spatial and temporal variability. Triangular elements with linear interpolation functions are used for the spatial discretization, while a simple implicit iterative scheme based on the trapezoidal rule is employed for time integration. The method is shown to be unconditionally stable, for an arbitrary grid and both one- and two-layer problems, when there is no iteration and the parameters are constant. General convergence criteria required by the iteration procedure are developed and expressed in terms of the basic parameters of the problem and are subsequently confirmed by numerical experiments. Verification of the model is performed by comparison with analytical solutions derived for counterflow conditions. Finally the model is applied to a particle dispersion experiment carried out recently in the Massachusetts Bay and comparisons with field data are presented.

Viscous perturbed velocity field induced by interfacial waves is solved to the first order in terms of wave amplitude for sharply stratified flows described in a curvilinear coordinate system assuming that the external velocity is uniform and constant along the interface. A new type of formula for the interfacial friction coefficient is proposed based on the theoretical result on viscous dissipation in the boundary layer along the interface. The interfacial friction coefficient is supposed to be inversely proportional to the square root of the product of the Reynolds number of a moving layer and the densimetric Froude number to the fifth. The new formula agrees with observed data better than the best empirical law does especially in the range of large Reynolds number.It is found out, however, that the proportional constant may be affected by stability of the two-layered flow system concerned.

This paper describes various features of tidal effects on the behavior of a salt wedge and on the mechanism of mixing between the salt water and the fresh water in the vicinity of a river mouth. The studies have been performed through experiments, field observations and throretical considerations. The condition upon which the fresh water begins to show an intermittent flow-pattern owing to an increase of the tidal action, and the criterion of a transition of the mixing type from negligible into intense, were obtained, with two dimensionless parameters λ and θ. The former parameter λ is given by λ = A_o/U_oT_o, in which T_o is the tidal period, A_o is the tidal amplitude of the sea level, and U_o is the temporal mean velocity of the fresh water at the river mouth. The latter parameter θ is the so-called Keulegan number. Besides, it came evident that a tidal motion of the salt wedge couldn't be understood without a consideration of the internal wave inside the mouth, which were induced by the tide, in addition to a direct effect of the tide.

A theoretical analysis, laboratory experiments, and the routine availability of infrared remote sensors for boat, airplane or satellite use are combined to provide a simple method for evaluating the total heat flux through the air-water interface under nighttime field conditions in which the water surface is rough; all indications are that the technique can be extended to other conditions as well. To evaluate this flux all that is required is the local windspeed, the water surface temperature, a subsurface temperature, and the character of the sea surface. Conversely, the theory can also be applied to predict temperature differences across the interface if the heat transfer can be otherwise established.

This paper describes a hindcast of post-rainstorm coliform bacteria distributions in Jamaica Bay made by use of a water-quality simulation model of that bay and models of the surrounding drainage basins on the basis of tide, wind, and rainfall data. That hindcast is then compared with coliform estimates obtained by field sampling.

Although the investigators did not have access to the results of the field sampling until the hindcast was completed, the estimates obtained by simulation agree well with the estimates from field data. It is concluded that the models used here are capable of making predictions for engineering assessments.

After the completion of 5 years of field measurements, complemented by extensive numerical modelling in 1974, the hydraulics of Cockburn Sound, Western Australia, are now understood in enough detail to allow the rate of exchange of water between the Sound and the ocean to be determined. Flow patterns in Cockburn Sound tend to be complicated by the superimposition of many driving influences, the most important being wind, but by using the output of a numerical model most of these patterns are predictable.

Current magnitudes within Cockburn Sound have not reduced so that the rate of dispersion of effluents released by the industrial complex on the eastern side of the Sound has not changed. However, flow rates through the southern entrance to Cockburn Sound have been reduced to between 30 to 45% of the rates which occurred prior to the causeway construction. This means that the mean discharge rate is now 570 m³/sec through the causeway bridges compared to a rate of about 1500 m³/sec before the causeway construction.

A combination of Lagrangian measurements and fixed current meter moorings were used during the summer of 1974 and the winter of 1974-75 to determine the circulation patterns of Saginaw Bay. Because the bay is shallow, the water responds rapidly to wind changes. Distinct circulation patterns were determined for southwest and northeast winds. These directions parallel the major axis of the bay and were the prevailing wind directions during the study. A typical exchange rate between the inner and outer bay during moderate winds aligned with the bay axis is 3700 m³ s^-1 If sustained, this flushing rate would completely exchange the water of the inner bay in about 26.5 days. However, winds perpendicular to the axis of the bay cause little water to be exchanged and the residence time of water in the bay is much longer. Comparison of measured currents with the results of an indpendently-developed numerical model for the bay indicates there is good agreement between the observations and the simulation of the circulation in the shallow inner bay. Agreement is poor in the deeper outer bay, where specification of proper boundary conditions at the open mouth of the bay is important for meaningful model simulations. Ice cover during winter shields the water surface from wind stress. Currents are sluggish and driven almost entirely from interactions with the lake-scale circulation of Lake Huron.

A method was developed for predicting the distribution of sewage constituents which would result from a proposed sewage outfall in estuaries or coastal seas. The method is based on the mathematical relationship between the solutions of the mass-balance equations with and without a decay term and on the assumption that both the dispersion and decaying processes are linear, acting independently. The application of the method requires dye dispersion experiments and a numerical model employing the results of the experiments. This approach makes it possible to predict the concentration field of sewage constituents with differing decay rates by using tracer release experiment employing a conservative tracer.

The method has been applied to assess the environmental impact of a proposed sewage outfall in Hampton Roads, Virginia. Two dye dispersion experiments were performed, one a continuous release over a flood tide cycle and the other over an ebb tide cycle. Horizontal distributions of dye were measured at subsequent slack waters before flood and ebb. The results were used to predict the concentration fields of total nitrogen, total phosphorus, coliform bacteria, biochemical oxygen demand, dissolved oxygen deficit and chlorine residuals, which would result from the proposed sewage outfall.

A.mathematical method and a computer algorithm is developed for the case of one-dimensional vertical mixing for an estuary with rather small advection. In the case under consideration varies the diffusion coefficients both with time and depth, and the case is therefore closer to actual estuaries than earlier computing methods that applies constant coefficients. Model experiments with a small grid oscilliationg with high frequecies in two fluids with different densities were performed to test the algorithm. Reynolds number for turbulence was near 1.6·10⁴.

The results showed that the ratio between the stabilizing Brunt-Väisälä frequency and the agitating cyclic frequency was a governing parameter for the system, and dimensionless. diffusion coefficients could be expressed as a function of this parameter.

Analytical results are presented which describe the mechanisms of longitudinal dispersive mass transport in rectangular channels of finite and infinite widths for both unidirectional (river) and oscillatory (tidal) flow regimes. Emphasis is placed upon the discussion of results and the characteristics of longitudinal dispersive mass transport revealed by the analytical treatment. Expressions presented for the dispersion coefficient were obtained from solutions to four sets of boundary value problems for the velocity and concentration variation components u” and c“. Examination of these expressions reveals that in oscillatory flow the dispersive mass transport is described by a type of resonant interaction between the period of oscillation and the time scales of vertical and lateral mixing. The analysis also shows that for oscillatory flow regimes the effect of lateral shear becomes negligible for very wide channels and the three dimensional solution collapses to the two dimensional case in which vertical shear and mixing effects dominate. It is shown analytically that this is not the case in unidirectional flows. For this case the lateral shear and mixing effects dominate the corresponding vertical effects and dispersive mass transport increases without bound with increasing channel widths.

Installation and operation of an automated model data acquisition and control system have made it possible to make a quantum advance in the accuracy and time required for verification of tidal inlet (or estuary) hydraulic models. The flexible sampling rate (usually about 200 samples per model tidal cycle for each gage) and digital recording of these data make them ideal for harmonic analysis and comparison with prototype data defining the coefficients and phase for each tidal constituent at various key locations within the tidal lagoon and at an open-ocean station removed from the immediate influence of the tidal inlet. The concept used is to force the model with the M₂ tidal constituent with the amplitude being correct at the ocean tide gage. A harmonic analysis is performed at all other gage locations corresponding to the prototype measurements, and the amplitude and phase (relative to the ocean tide gage) are calculated and compared with the prototype data. Investigation of the relative phases between various gages quickly shows those areas where either more or less model roughness is required. It is reasonable to expect to be able to have all phases for the M₂ constituent verified within 1 degree. Tidal elevations can almost always be expected to be verified to within a maximum deviation of ±0.1 ft in both tidal height and mean tide level. Upon verification of the M₂ constituent, which practically insures that the proper channel roughness is obtained, a progressive tide can be constructed; and it should be attempted to perform a verification for a 14.765-day (synoptic period for M₂ and S2 components) progressive tide at east coast locations using the prototype measurements of tidal velocities for the final verification data. Should additional roughness be necessary, it will almost always be on the mud flats or marsh areas. Computations are made to illustrate the energy transfer from the M₂ constituent to higher order harmonics as the wave propagates from the ocean to the back of the estuary, and it is shown that this energy transfer is, at worst, the same order of magnitude in both the model and prototype.

The concept ventured in this paper has been applied to verification of the Murrells Inlet, South Carolina, hydraulic model. Model scales were 1:60 vertical and 1:200 horizontal (a distortion ratio of 3-1/3:1).

Major conclusions are that verification based on the M₂ constituent is feasible and was quite successful in the Murrells Inlet, South Carolina, model, and it is postulated that a method similar to that contained in this paper should be used for the verification of numerical models.

This paper deals with finite element formulations for the numerical computation of two-dimensional incompressible longperiod shallow water waves. The described mathematical model is used to reproduce the dynamic situation occuring at the tidal propagation in estuaries. Areas which fall dry and wet again within a tidal cycle - so called inter-tidal flats are taken into account.

Hybrid models for the investigation of tidal waves in rivers and estuaries are a combination of mathematical and hydraulic models, which are coupled under real-time conditions. The coupling procedure cannot be performed without some time delay which mainly depends on the time needed for the computation of the mathematical model and for the control operations on the instrumentation. An analysis of their influence on the accuracy of a hybrid model is given and experimental results from a feasibility study are presented.

Laboratory data showing the influence of planform geometry on the tidal flushing characteristics of small harbors of simple surface shape. The tide ranges, water depths, and planform areas are typical of those encountered in small-boat marinas in Puget Sound, Washington. Each harbor investigated had a single, asymmetric entrance.

Flushing and circulation patterns within such harbors depend strongly upon the characteristics of the angular momentum established within the basin and upon the effective penetration distance into the basin of the stream of ambient water entering the harbor on the flood tide.

Experimental results confirm that best gross tidal flushing occurs when rectangular harbors have an aspect ratio L/B near unity, and that rounding interior corners of the basin has little effect on the gross tidal flushing but does improve local exchange. Aspect ratios L/B less than 3 lead to the creation of more than one circulation cell (gyre) within the basin.

As an island state with about 900 miles of coastline, Sri Lanka is endowed with a large natural resource: its 720 miles of sandy beaches. The coastal zone is under stress by a burgeoning population, living in the coastal belt,and a variety of other demands with conflicting interests. Due to natural causes and interference of men, erosion is a serious problem in the densely populated southwest part of the island.

This paper describes the principal characteristics of the coastal environment and discusses the nature of some of the basic problems. In the recommendations, emphasis is placed on the setting up of an organizational structure to study the problems, both in the field and in the laboratory, with respect to the management aspects in the coastal zone.

A numerical method is presented to treat the wave-induced oscillations of a harbor with a variable depth and width. A two-dimensional finite difference approach is used inside the harbor matched at the entrance to a solution for the open-sea based on the Helmholtz Equation which includes incident, reflected, and radiated wave energy. Examples of the response and the modal shapes of the water surface are presented for harbors with simple and complex shapes.