Coastal Engineering 1972

This paper gives a brief review of the history of coastal defence as it has developed since the year 1,000. It makes an attempt to outline what may be termed "the philosophy" and its relation to development.

The "State of the Art" is described by figures of characteristic designs including new developments. The paper establishes some general rules for future coastal protection and gives an outlook for the future.

Research during the past ten years into coastal problems around the coasts of South Africa has resulted in the development of measuring instruments and techniques which, although specifically designed for conditions around these coasts, could possibly be used equally well in other areas.

This paper deals specifically with measuring instruments and techniques used for collecting data on offshore and nearshore currents, wave conditions and beach profiles extending through the surf zone. Also included are examples of the data collected and some discussion on the accuracy of these data.

A system, designed to give maximum flexibility and portability, has been developed to collect wave, current and other physical data within the dynamic environment from the surf zone to the edge of the shelf. The system consists of a radio-linked shore station, housed in a mobile van and as many as six shelf stations mounted in bottom referencing spars.

A shelf station can be deployed from a small boat with minimum diver time. The ease of deployment of the shelf stations coupled with the mobile self-contained shore station, allows the use of a modern data acquisition system, and rapid deployment of sensors, for the field study of remote coastal areas.

Each of the shelf stations is designed to accomodate as many as fifteen sensors. All simultaneous sensor outputs are digitized and transmitted by radio to the mobile shore station, where the received signals are processed and selected for recording on strip charts or digital magnetic tapes for computer analyses. Very high sampling rates and a real time system are used to insure precise time correlation between all data channels including those from separate shelf stations.

A single shelf station would transmit data from an array of wave sensors, thus providing continuous wave climate including the two dimensional wave spectra. Some different combinations of shelf station ensembles are shown.

The significant wave height and peak period as derived from the spectral analysis of 171 measured wave records taken in the ocean off Western Head, Nova Scotia are compared to the more classical parameters derived from individual wave heights and by the Tucker method. The highest surface elevation and the maximum wave height occurring in the records are compared to values predicted by Cartwright and Longuet-Higgins (1956), Goda (1970), and Longuet-Higgins (1952).

An experimental deep water wave recording station has been operated in Lake Ontario, Canada, from 1969 to 1971. The station included a triangular array with four wave sensors and a stable platform. The aim of the study was to obtain a better understanding of the usually rather vaguely defined wavelength parameter of a wind-generated sea and to record the direction of wave propagation directly in the wave generation field.

The station has also been used to test newly developed wave sensors, or to check and calibrate some of the existing wave recording systems, including staff gauges, pressure cells and accelerometers.

The paper describes briefly the mooring system of the floating stable platform and the triangular array. A comparison is made between various wave recorders, mainly by using spectral analysis, and some results of the wavelength and wave direction study are discussed.

A project to derive a wave climatology for that portion of the Atlantic Ocean between 30° and 60° N. and west of 30° W, recently begun by the Atmospheric Environment Service of Environment Canada, is described. The data base is produced from isolines of significant wave height and from plotted ship data. Details of the preparation of the basic analysis as well as the design of the remainder of the project are presented. Intermediate results will provide guidance to potential users of the wave climatology until sufficient data have been accumulated to lend statistical reliability to the analysis.

Information on extreme wave conditions is needed in the design of offshore structures. This paper present the results of calculations of the parameters in the 50-year storm; the work has been based on extreme wind data and on instrumental wave measurements. The results are complementary, and are combined in two maps, one of extreme wave height and the other of the corresponding wave period.

The 1959 paper "Hurricane Design Wave Practices" (ref. 1) has been widely used in the past for obtaining design wave criteria. Additional wave data and revisions in wave forecasting procedures, including computing techniques, ideas and experience, make it possible to bring these techniques up to date.

This paper should be considered also as an extension of the paper "A Non-Dimensional Hurricane Wave Model" (ref. 2) as well as revisions to the 1959 paper (ref. 1).

Graphs, formulae and procedures are presented making it possible to calculate the entire deep water wave fields from model hurricane wind fields.

The revisions have been applied to the U.S. East and Gulf coasts past historical hurricanes and also to the U.S. Weather Service standard project and probable maximum hurricanes for deep water conditions. The results of these calculations are presented in figures and tables and can serve as inputs for particular locations to calculate design storm surge and design wave criteria over the continental shelf to the coast line, making use of the material in the references listed at the end of this paper.

The wave-group period, T_g, is obtained by a eimple manual procedure from the periodic wave groups and sequences that appear in strip-chart records. A dozen or more values are commonly derived from a 20-minute record. When plotted as a time-series, T_g values form patterns that represent individual wave trains, each generated by a synoptic weather event. Swell trains and wind-wave trains can be distinguished by their characteristic period distributions.

In view of resource exploration, hydro-electric power development and other activities, there is a clear need for a better understanding of the hydrodynamics of Hudson Bay. One particular area that has received little attention in the past is storm surges. It is likely that a storm surge prediction will be very useful in the future and towards this goal a two-dimensional homogenous model has been constructed. A hindcast of the storm of October 15, 1969 is presented here. The calculated surge for Churchill, Manitoba compares favourably with observed residues. The overall response of the basin and the types of oscillations that are produced are also described here. In addition, the differences in behavior between James Bay and Hudson Bay proper are demonstrated. Finally the results also indicate the steady circulation which the storm has produced.

The random nature of ocean wave records introduces statistical variability into the wave spectrum estimates based on these records. This may cause inaccuracy in subsequent calculations such as the prediction of the primary wave direction or the estimation of structural response. Confidence intervals on such estimates are needed to evaluate whether adequate estimate accuracy has been obtained.

The chi-squared confidence interval commonly used for wave spectra is based on the assumption of a Gaussian sea surface. Its applicability for hurrican size waves has been open for question. Therefore, after a brief outline of the relevant statistical relations basic to the chi-squared procedure, wave data from Hurrican Carla is empirically analyzed and compared with the theoretical conclusions. A simulation procedure is used to proceed from the data to probability interval statements. A comparison of these with the correponding chi-squared statements shows the chi-squared relations to be fairly reasonable approximations for spectral estimates averaged over bands of at least eight values. The empirical simulation procedure can be extended to subsequent calculations based on the spectral estimates while the chi-square method encounters difficulty for such problems.

Priestley's method [1, 2, 3]^** of non-stationary spectral analysis is extended to the case of digitally sampled records. A computation procedure previously proposed in an earlier work [4] is further investigated. This procedure compensates for the inherent difficulties in the theory and computes time-dependent spectra from a sample in an iterative manner. Validities of the theory and the iterative procedure are tested with a simulated non-stationary process. Results establish a general agreement with theory, especially when spectra vary smoothly with time and frequency. Consequently, the procedure is applied to estimate non-stationary spectra for two wave records. A comparison is made between the non-stationary estimates and the stationary results derived from the same set of wave records.

In order to devise more rational approach to predicat the wave features in intermediate water area, energy spectra in deep water area are to be changed to histograms, and every stripe of the histogram is to represent an elementary small amplitude wave. The deformation of such elementary waves over intermediate water area can be calculated theoretically by energy flux equation. Spectra in intermediate area can be worked out by summing up the wave energies deformed by shoaling, bottom friction and refraction.

Calculation are carried out by computer. The peak of spectra will never change when it propagates from deep water to intermediate water area if the bottom contours are parallel to the shore line. Tangible process for using this approach to practical engineering problems is pending investigation.

The data for the spectra of wind-generated waves measured in a laboratory tank and in a bay are analyzed using the similarity theory of Kitaigorodski, and the one-dimensional spectra of fetch-limited wind waves are determined from the data. The combined field and laboratory data cover such a wide range of dimensionless fetch ${\widehat{\text{F}}\text{(= gF/u}}_{*}^2\text{)}$ as ${\widehat{\text{F}} \text{: 10}}^{\text{2}}\sim {10}^6$ . The fetch relations for the growthes of spectral peak frequency ω_m and of total energy E of the spectrum are derived from the proposed spectra, which are consistent with those derived directly from the measured spectra.

Prototype data from 24 wave stations on and around the tidal flats south of the Elbe estuary enable us to elaborate special shallow water wave characteristics, concerning the variations and correlations of heights, periods, lengths and velocities. This paper deals with some interesting aspects from the engineer's point of view. It turns out that the steepness factor $\frac{\overline{\text{H}}}{\overline{\text{L}}}$ or $\frac{\overline{\text{H}}}{\text{g}·{\overline{\text{T}}}^{\text{2}}}$ of breaking waves is much smaller than of nong-breaking waves and that steepness is no suitable parameter to describe a natural wave spectrum in shallow waters.

A solution of finite amplitude long waves on constant sloping beaches is obtained by solving the equations of the shallow water theory of the lowest order. Non-linearity of this theory is taken into account, using the perturbation method. Bessel functions involved in the solution are approximated with trigonometric functions. The applicable range of this theory is determined from the two limit conditions caused by the hydrostatic pressure assumption and the trigonometric function approximation of Bessel functions.

The shoaling of this finite amplitude long waves on constant sloping beaches is discussed. Especially, the effects of the beach slope on the wave height change and the asymmetric wave profile near the breaking point are examined, which can not be explained by the concept of constancy of wave energy flux based on the theory of progressive waves in uniform depth. These theoretical results are presented graphically, and compared with curves of wave shoaling based on finite amplitude wave theories.

An equation is derived which governs the propagation of a cnoidal wave train over a gently sloping bottom. The equation is solved numerically, the solution being tabulated in terms of f_H (Eq. 47) as a function of E₁ = (E_tr/ρg)^1/3/gT² and h₁ = h/gT². Results are compared with sinusoidal wave theory. Two numerical examples are included.

This study investigates the transformation of nonbreaking waves that pass over a submerged longshore bar. An envelope for the occurrence of transformation of nonbreaking waves is established and compared with existing information. Power spectral analyses are made of both the incident and transformed waves to determine quantitatively the change in wave characteristics. The conclusion is made that the transformation process is a nonlinear phenomenon occurring over the bar, but, in the deeper water in the lee of the bar, a combination of linear wave forms results.

Using a critical value for ϒ_b = H_b/h_b as a wave breaking criterion, where H_b and h_b are respectively the wave breaker height and depth, applying Airy wave theory, and assuming conservation of the wave energy flux, one obtains $${\text{H}}_{\text{b}}={\text{kg}}^{\text{1/5}}{({\text{TH}}_{\infty }{}^2)}^{2/5}$$relating H_b to the wave period T and to the deep-water wave height H_∞. Three sets of laboratory data and one set of field data yield k = 0.39 for the dimensionless coefficient.

The relationship, based on Airy wave theory and empirically fitted to the data, is much more successful in predicting wave breaker heights than is the commonly used equation of Munk, based on solitary wave theory. In addition, the relationship is applicable over the entire practical range of wave steepness values.

A re-evaluation of previously published breaking wave data is used to develop a relationship for the maximum breaker height in terms of the depth in which the wave breaks, breaker steepness and the local beach slope. This relationship is used with the breaker travel distance equation of Galvin (3)* to estimate the maximum breaker height to which a coastal structure might be subjected. In addition, the range of depths in which a wave of given height will break is found by examination of the upper bound of observed values of d_b/H_b. An example problem is presented to illustrate the use of the general maximum breaker height design curves.

Breaking criteria in the vicinity of the crest, such as limit crest angle and limit form, and larger dimensions such as limit height (H/L) and breaker height (H_b/d_b), are found experimentally to be significantly affected by change in surface tension. A number of wave types were examined, including periodic waves, solitary waves, and standing waves, over both constant depth and uniform slopes. Variations in natural waters in some cases were found to be of equivalent magnitude to those induced for the experiments. The conclusion is drawn that surface tension should be taken into account in development of a satisfactory theory of breakers. It is also an important factor in experimental studies, particularly engineering model studies involving breaking waves.

An experimental investigation utilizing nonbreaking waves and one bottom topography with parallel circular contours symmetric about the center of the basin was performed to assess the limits of applicability of linear wave refraction theory in a convergence zone. Analytical computations of reflections from underwater topographic variations and of viscous dissipation of energy at the bottom agreed with experimental measurements. It was vividly illustrated that a significant amount of energy was involved in diffraction along the wave crest, thus the necessity of developing a theory to include the stepwise computation of diffraction processes simultaneously with the computation of wave refraction is now evident. Nonlinear transfer of energy from lower to higher frequency components was investigated by performing a harmonic analysis over one wave period. As expected, nonlinear effects increased with both wave period and wave height (for a given wave period). Only 20 percent of the energy remained in the fundamental component for the longest period largest amplitude wave tested. Higher frequency components ranged from being completely coupled to the fundamental frequency to almost completely uncoupled. It was clearly demonstrated that in some circumstances the consideration of nonlinear effects becomes extremely important.

This paper treats the derivation of a two-dimensional differential equation, which describes the phenomenon of combined refraction — diffraction for simple harmonic waves, and a method of solving this equation. The equation is derived with the aid of a small parameter development, and the method of solution is based on the finite element technique, together with a source distribution method.

A method is presented to obtain numerically wave patterns in the region of arbitrary shape. The principle is to solve the linearized wave equations under given boundary conditions from a certain initial state.

In this paper, two principal applications of our method of numerical analysis are presented in the fundamental fashion.

The first application of our method is related to wave diffraction. The distribution of wave height along a semi-infinite breakwater and a detached breakwater is calculated and compared with that obtained from the conventional analytic solutions to confirm the validity of our numerical method. Three examples of application are presented to the wave height distribution along breakwaters of arbitrary shape and of arbitrary reflecting power and to wave force upon a large isolated vertical structure.

A basic mechanism is proposed to explain the growth of finite amplitude water waves due to the effect of normal stresses. The proposed mechanism can probably be applied to the whole range of wave's growth, starting from a small amplitude wave up to the case of a limiting and breaking wave condition. The transfer of energy from air flow to the water wave is explained by the existance of a circulation flow pattern above the water surface, which is responsable for a phase-lag of the normal stress distribution in relation to the wave's profile. Such a circulation flow pattern extends throughout the whole wave length and it is quite different from the classical concept of flow separation, as postulated by Jeffrey's. The difference becomes as a result of considering a different boundary condition at the interface. Experiments performed on wavy models with moving boundary conditions, for small amlitude waves and finite amplitude waves showed that the normal stress distribution is similar in both cases, and displays a noticible phase-lag with respect to the wave's profile. It was observed that for both cases a circulating flow pattern was present above the water surface, which indicated some relation between the flow vorticity above the wave and the normal stress distribution.

To prove the role of circulation in the energy transfer mechanism, a model was built with water and mercury as working fluids. In this model the interface was initially non disturbed, when both fluids move in opposite directions. However, when a forced circulation was applied by means of a variable speed rotor located above the interface, a wave would form. The wave would be inicially of small amplitude, but with an increase of circulation would become of finite amplitude, then reach the angular crest condition and finally would reproduce the breaking condition at the crest.

The obtained experimental results proved the importance of the circulation flow pattern present above the wave surface, and suggest that a mathematical model could be formulated based on vorticity analysis, which would be able to provide an explanation for the energy transfer mechanism due to normal stresses at all stages of wave's growth.

Measurements of drift were made in a wind and wave facility at different elevations below the mean water level. The drift profiles were obtained for reference wind speeds, U_r = 3.1, 5.7 and 9.6 m/sec. The measurement technique involved tracing the movement of small paper discs which were soaked in water to become neutrally buoyant at the elevation of release. A logarithmic drift profile is proposed. The water shear velocity, U_*w, predicts a surface stress, ${\tau }_{\text{s}}=\text{ρw}{\text{U}}_{\text{*}}{}_{\text{w}}^2$ , in agreement with that obtained from the wind shear velocity, ${\tau }_{\text{s}}=\text{ρa}{\text{U}}_{\text{*}}{}_{\text{a}}^2$, where ρ_a and ρ_w refer to air and water densities, respectively.

The influence of wind on phase speeds of waves was investigated by solving the first order perturbation problem of the coupled shear flows in air and water. The air velocity profile was described by a logarithmic distribution and the drift profile was described by the proposed drift profile. Adequate agreement is found between the calculated and measured phase speed using Doppler radar in the wave number range 1.9 − 10 cm⁻¹. In the wave number range 0.05 − 0.5 cm⁻¹, measurements of phase speeds were obtained by using two wave gages. The waves were mechanically generated without wind and the wave gages were spaced to obtain coherent signals. The wind was then allowed to blow over the waves and the distance between wave gages was increased to maintain coherence. The wave length and frequency were obtained from the distance between the gages and from the generator frequency, respectively. The measured phase speeds were found to increase with wind speed consistent with theoretical computations.

Measurements of horizontal and vertical water particle velocities induced by regular waves, wind waves generated by a wind wave tank and ocean waves in shallow water were made using a Doppler-type sonic current meter. For regular waves, the validity of wave theories such as Stokes and cnoidal waves is investigated by comparison between theoretical curves and the experimental results. For wind waves and ocean waves, power spectra of water particle velocities and cross-correlations between surface displacement and water particle velocity are considered, especially in the latter case, directional spectra calculated from both the records are compared each other.

Shear stress measurements on both smooth and sand roughened beds were carried out in an oscillating water tunnel using a flexurally supported shear plate. The range of simulated wave boundary layers covered practically any situation possible in the field or laboratory.

In the laminar range good agreement is obtained with the theoretical shear stress calculated from first order wave theory. However, in the turbulent flow regimes the experimental data indicates that theory results in an overestimate of the shear force by 20-50%. Limits of laminar, smooth turbulent and rough turbulent flow regimes are determined and it appears that the rough turbulent flow regime may itself be subdivided into two sections, each having different turbulence characteristics.

Energy dissipation and wave height attenuation were analysed theoretically for surface waves propagating against uniform flow. Energy dissipation was estimated from evaluation of work by internal and boundary shear stresses. Experiments were conducted in a test flume of 20m long, 0.8m wide and 0.5m high. Results showed that tested values of rate of wave height attenuation were comparable with theoretical values.

This paper presents an approximate theory for the reduction of the velocity of a current due to the presence of sinusoidal waves.

For a given slope, S, in water of constant depth, d, the current velocity profile is

as a function of the height, z, above the bed. Eq. 1 is valid only above the thin wave boundary layer near the bed, the roughness of which is k = 30 z_o. U_f is the current friction velocity defined by

where τ_cw is the current shear stress in the presence of waves.

The two systems based on the principle of photogrammetric surveying have been developed in order to accomplish the field observations of nearshore current system induced by waves, and were applied to the field investigations on the Shonan Coast, Kanagawa Prefecture, Japan (Horikawa, Sasaki et al, 1970). The first is called as the Balloon Camera System and the other is the Synchronized Helicopter System. The main efforts were concentrated to the simultaneous observations of waves and current fields in and out the surf zone. Even there still exist some difficulties to be overcome in applying the present systems, the validity and usefulness of these systems were demonstrated by the obtained data. In this paper are presented the details of the developed systems and a part of the analyzed results by using the data obtained in field.

The generation and stabilization of rip — current circulation patterns is considered herein. An analytic model is developed to simulate the wave hydrodynamic processes in the nearshore zone, strongly influenced by the local bottom topography. The wave induced nearshore circulation pattern is computed and the results compared to prototype field data.

An experimental study was conducted in a three-dimensional wave basin to investigate the manner in which surface gravity waves propagating toward a tidal inlet are altered. Dimensional analysis of the pertinent variables indicates that a functional relationship exists between as many as five dimensionless terms, and the functional relationship is displayed in graphical non-dimensional form to apply to all scales. Results indicate the ebb current increases the steepness in the ocean region to such an extent that the wave begins to lose energy by the crest spilling down the front of the wave, and the wave characteristics in the inlet proper may never reach the breaking limit unless factors other than a current alone are involved.

A technique for simulating an infinitely long beach in the laboratory is introduced, with the objective of eliminating end effects usually present with short straight beach sections. The technique involves the spiral wavemaker generating waves in the center of a circular basin.

The wavemaker, consisting of a vertical right-circular cylinder oscillating in a small circle about its axis, is described in detail. Theoretical developments, using small-amplitude wave assumptions, show that the surface wave crests generated by the wavemaker may be described, at a particular time, as an Archimedian-type of spiral, with the wavemaker at its origin. Also, the crests impinge on the circular beach everywhere at the same angle of incidence.

Experiments with a prototype spiral wavemaker verify the theory, with close results for shallow water waves. Littoral drift applications of the wavemaker are given.

In a flume equipped with an irregular wave maker the motion of the paddle and the resulting waves may be thought of respectively as input and output of a system which, if linear, is for some purposes described by the so-called gain function.

A theoretical and experimental study of this function is carried out making use of paddle movements that produce transient surface motion.

The collection of most data on littoral phenomena usually is based on the requirement of personnel and equipment actually being on-site for specific periods of time.

An approach to minimize this requirement involves the use of a photographic technique, using time-interval cinematography. Two such systems have been used at sites in California; Point Mugu and Newport Beach. This method incorporates commercially available 16 mm motion picture cameras with automatic lenses, remotely programmed to shoot selected lengths of film at predetermined periods during a day, everyday. At Point Mugu the camera, housed in a weatherproof enclosure mounted atop an existing 100-foot tower, records shoreline conditions, wave characteristics and existing weather twice a day for a period of 20 seconds per exposure.

The cameras are normally serviced on a weekly basis but are capable of longer unattended operation. To date this method has provided data which on preliminary anaylsis has revealed it to be of significant value for the purposes intended.

Sequential photographs from aircraft and satellites provide a source of data for studying dynamic features of coastal waters. Procedures for detecting features in sequential photos follow two approaches; (1) application of sequential signatures, (2) simple comparative analysis. For quantitative analyses images of two or more frames must have proper registration and comparable tones, i.e. tones free of photographic variance from film processing, varying exposure and solar illumination. After a normalization correction for variance is determined through use of density control points, density of successive frames is measured with a microdensitometer, the correction is appplied and tonal differences determined. Such differences relate to the time character of a feature and to causal processes. Application of correction values and numerical differencing is best accomplished in a digital or computerized densitometer. However, corrections and differencing can also be accomplished graphically from line traces or plots of an objective densitometer. Application of the procedures is demonstrated by analyses of tonal patterns of suspended sediment concentration in an estuary.

A method is presented for investigating the stability of coastal inlets against closure due to transport and deposition of sand in the inlet cross-section. The method utilizes earlier contributions by: (1) Keulegan representing the hydraulics of inlets, (2) O'Brien which describes an equilibrium relationship between the cross-sectional area of an inlet and the bay tidal prism, and (3) Escoffier which relates to the stability of an inlet under changes in conditions which tend to close or enlarge an inlet. A "stability index" is defined which incorporates the buffer storage area available in the inlet cross-section, prior to the onset of closure and also includes the capability of the inlet to transport excess sand from its cross-section. In order to apply the method, geometric and hydraulic data representing the inlet are necessary; the minimum data required include a survey of the inlet throat cross-section and the lag between high (or low) water in the ocean and the following slack water in the inlet. In addition, it is necessary to conduct measurements or make assumptions concerning the minor and gradual hydraulic loss coefficients. Based on assumed depositional patterns in the inlet, the method is applied to five real inlets and the stability indices are presented.

An environmental study was conducted at Brown Cedar Cut, a natural unstable barrier beach inlet connecting East Matagorda Bay, Texas, with the Gulf of Mexico. The objectives of this study were to determine the physical and hydraulic properties of the inlet, and to investigate the inlet's historical stability, as well as its short-term response to a number of physical processes. Results of the study indicate that hurricanes and continuing erosion of adjacent beaches enhance the long-term stability of the inlet. During winter months, the rapid passage of strong frontal systems and associated winds, as well as substantial amounts of rainfall, are primarily responsible for the day-to-day viability of the channel boundaries. In the absence of such forces, the predominance of littoral drift over the limited flushing ability of astronomical tidal currents leads to degradation of the inlet channel and westward migration of the entire inlet system.

The Mission Bay Inlet was designed as a "Non-Scouring" entrance channel by the Los Angeles District, Corps of Engineers, in 1946. Construction of the inlet was completed in 1959 and the entire project was completed in 1963. A channel with over twice the crosssectional area required by the "O'Brien" equation was developed to reduce the average cross-sectional tidal currents to less than two feet per second. The design depth of −20 feet MLLW eliminated bottom movement induced by wave action- except during the most severe storms. The jetties are sealed to the +4 foot elevation and extend to the −25 foot depth almost entirely eliminating the intrusion of littoral drift. The channel has shoaled at a rate of less than 20,000 cubic yards per year since final dredging in 1959, indicating the soundness of this concept. This case history was prepared under contract to the Coastal Engineering Research Center, U. S. Army, Corps of Engineers, and project data and aerial photographs were obtained from the Los Angeles District, U. S. Army, Corps of Engineers, and the City of San Diego.

Tidal flow and suspended-sediment discharge were measured in or near the inlet to Bolinas Lagoon through seven ebbtides and six floodtides. The highest flows and suspended-sediment discharges occurred during the major daily ebbtide. Most transported sediment was sand and most sediment deposited in the lagoon was sand. Computations from a relation of suspended-sediment discharge and tidal range indicated that the annual suspended-sediment discharge of ebbtides exceeded that of floodtides by 9,000 tons. The highest concentration of suspended sediment occurred near the east shore of the inlet, which is at the end of a sand spit.

The measured volume of water moved by a tide ranged from 180 to 2,740 acre-feet and the maximum flow measured was 7,900 cubic feet per second. The highest average velocity for a measurement was 4.9 feet per second. The maximum average velocity in the inlet occurred within an hour after midtide during a floodtide and usually at about one-third tide during an ebbtide. The relation of average tidal velocity (ū_t) to tidal range (R), was ū_t = 1.21R.508; the average flow for a tide can be estimated by multiplying this calculated average velocity by the average cross section of the inlet.

Extensive coastline changes around the Ponce de Leon Tidal Inlet, Florida, are described, discussed and explained. These changes started developing immediately after the beginning of the construction of two jetties on both sides of the inlet forming part of a plan to stabilize the inlet, improve navigation conditions and bypass sand effectively. The mean annual littoral transport of sand was considered to be from north to south.

Rapid sand accretion south of the south jetty started immediately after the beginning of its construction in 1969, reaching by November, 1971, a volume of approximately 1,400,000 cu. yds. Aerial photographs suggest that the sand was transported there from the south during the summer periods of northerly drift and from the offshore bar by refracted waves from the north. The accumulated sand is well protected by the south jetty during the winter storms from the northeast. Coastline and duneline recession occurred north of the inlet due, at least partially, to the described sand retention.

It is concluded that for inlets where the littoral drift reverses its direction, the net annual rate of littoral transport is not a unique design criterion. Instead the total sand volumes transported annually in either direction should be considered.

A method is presented for estimating the dredger capacity required for closing tidal gaps with sand as the only building material.

The method is based essentially on a relation between parameters describing the flow of the water and the resulting sand transport.

Empirically determined coefficients are used to approximate the effects of the non-stationary flow in the gap and the supply of suspended material at the dumping site.

The experiences gained at a number of closure operations are discussed and compared with the computations.

Sediment transport In the vicinity of inlets and coastal regions depends on the combined bottom shear stresses due to both currents and waves. The modeling of the movement of bedload is controlled by the Froude law, bottom shear stress, wave steepness, and friction factor. Assuming Einstein's theory of bedload function can be applied to this study, an analysis was performed after conducting experiments in the flume and model basin. A series of results obtained from the flume tests is to Insure the relationship between the fluid characteristic and the movement of bedload. The final results concerning the longshore sediment transport appeared satisfactory with the estimated curves. The bottom configurations in the inlet after each test were also shown satisfactorily similar. The sedimentologlcal time scale for the three bed materials were not in satisfactory agreement, however, more discussion of the results was presented in this paper.

Studies were conducted on San Francisco Bar in June 1971 and February 1972 to monitor dredge material disposal. The purpose of the study was to determine the effects of dredging and material disposal on the physical and biological environment and to develop dredging procedures and disposal sites to mitigate possible adverse effects. This paper presents the results of the material dispersion portion of the study including bottom deposition, current measurements and aerial photography. The biological studies and water quality monitoring are not presented.

Gross longshore transport rates for 11 long-term field measurements are predicted reasonably well by the empirical relation, Q=2H², where Q is longshore transport rate in 100,000 yd³/yr, and H is a mean breaker height in feet. A physical explanation of this empirical relation assumes: (1) most littoral drift is transported in suspension; (2) longshore current velocity is predicted by V-gmTsin2θ_b; (3) the empirical relation is an equation for conservation of suspended sediment in the longshore current.

A rational design of coast protection works requires a knowledge of the behaviour of beach under natural conditions. The estimation of the littoral drift rate is thus a necessary preliminary to the analysis of the cause of beach erosion and the evaluation of the effect of projected remedial measures.

This study presents a method for estimating the rate of littoral drift along sandy beaches. The derived method is based on the use of fluorescent tracer, and observing the tracer concentration reaching the different profiles along the study zone, as function of location and time of sampling. Steps followed in estimating the rate of littoral drift, using the derived formula, are included in this paper.

The objective was to obtain quantitative data on the movement of shingle under wave action in water depths of about 10 to 20 m by tracking pebbles tagged with radioactive material.

The paper describes the method of tagging, the method of position fixing, and the development of an underwater detection vehicle with a wide field of view. The field tracer tests demonstrated both increased mobility with decreasing depth and the existence of a small landward movement of shingle inshore of a depth of 12 m. Existing predictive data on the threshold of movement under waves, based on the results of previous work in the laboratory, was confirmed.

A review of laboratory and field studies on suspended sediment under waves shows that although about five analytical or semi-empirical approaches have been attempted to predict the vertical distribution of suspended sediment, none of the approaches has had its general validity proven. This is mainly due to the lack of knowledge about the characteristics of turbulence of the wave boundary layer and to the lack of a suitable suspended sediment measuring technique for use in waves. Six different suspended sediment measuring techniques have been used in the studies reviewed. Although none of them gives completely reliable laboratory or field measurements, an optical system appears to show promise in obtaining information on the mechanics of suspension under waves.

The reanalysis of longshore sediment transport data and tests of the relationships Q = A₁E_a, ${\text{Q = A}}_{\text{2}}{\text{E}}_{\text{a}}^{\text{B}}$, and I_l = A₃E_a, where Q is volume transport rate in cubic yards per day, E_a is longshore component of wave energy flux in lbs per day per foot of beach and I_l is immersed weight transport rate in lbs per day, for different subsets of data and using the method of least squares, showed that a single set of A₁, A₂ and B does not fit all subsets of data with minimum average percentage deviation of observed values from those predictable by the relationships. The subset of data consisting of all but the observations with light weight sediments can be described by the line of fit, Q =1.93 X 10⁻⁴E_a, with the observed data differing from the predicted ones by 74 percent on the average.

The wave-induced sand transport alongshore is investigated by an energy principle approach. Although the energy approach has been used before, this is the first application to comparing theory and measurements of the distribution of littoral transport along a line perpendicular to the beach. Bed load transport equations are formulated for outside and inside the surf zone. Sand transport data were collected in the field using bed load traps. Wave, tide, wind, and current information was collected simultaneously in order to verify the derived predictive equations for longshore current and sediment transport. Quite reasonable predictions are obtained for the relative distribution of bed load transport, both inside and outside the surf zone.

In excess of 800 suspended sediment samples were collected from stations along the City Pier, Ventnor, New Jersey and Jennettes Pier, Nags Head, North Carolina using a tractor-mounted pump sampler. Most samples were collected within the surf zone at the Ventnor site. At the Nags Head site, sample collections included the surf zone, but generally extended over a wider range of the nearshore zone. Average sampling time was 3 minutes. Nozzle elevation varied from 3 inches above the bottom up to a maximum about mid-depth, generally not greater than 2.5 feet above bottom. Maximum concentrations at Ventnor ranged up to 2.6 ppt by weight and at Nags Head were about 4.0 ppt. Median size at Ventnor ranged from 0.12 to 0.15 mm and averaged about 0.20 mm in depths of 4 feet and less at Nags Head. Results are summarized in a series of scatter plots which relate suspended sediment concentration to nozzle height, wave height, water depth and sampling distance from an observed wave-breaker-line. Results are compared to CERC laboratory data, to two excerpted concentrations from unidirectional flow tests and to the CERC TR-4 design curve of longshore wave energy versus longshore transport.

With financial support by the German Research Association (Deutsche Forschungsgemeinschaft) an instrument for automatic long-term measurement of suspended matter has been developed by the authors. It works on a settling method. A sample of 20 1 of water is pumped into a conical settling bottle every hour. The suspended sediments settling in a measuring tube at the bottom of the bottle are recorded by a camera. The device called "Silt Gauge" is intended for long-term measurements in shallow coastal water.

The paper describes a procedure for obtaining field data on the mean concentration of sediments in combination of waves and currents outside the breaker zone, as well as some results of such measurements. It is assumed that the current turbulence alone is responsible for the maintenance of the concentration profile above a thin layer close to the bottom, in which pick-up of sediments due to wave agitation takes place. This assumption gives a good agreement between field data and calculated concentration profiles.

The Lower Fraser River, being continually developed for better navigation and larger port- facilities, is an area of active sedimentation. The dynamic processes influenced by river discharge, tides and winds are probably the most important factors in the transport and deposition of sediments in the estuary. The main part of the Fraser Estuary is vertically homogeneous (non-stratified) and the sediments are transported progressively seaward and are accumulated near the limit of net landward flow. The lower estuary is stratified and coarse sediments are trapped near the toe of the salt wedge while the fine sediments are carried seaward with the outflowing river water.

The hydrometric and sediment survey of the lower Fraser River are described. Survey results are used in determining the sediment balance of the river reach. In the budget analysis, the river and estuary are divided into four consecutive reaches, the sediment discharges are subdivided to represent about 10 particle size ranges and the balance is then determined for each reach and particle size range.

Conclusions are drawn with respect to the sediment transport and depositional characteristics, annual variations, and the agreement between the sediment entering the estuary and the sediment dredged.

Experiments to determine the length, height and steepness of bed forms generated by wave action have been conducted in a laboratory wave flume and an oscillating water tunnel. The effects of a wide range of oscillatory flows were examined on polystyrene (specific gravity 1.05, diameter 1.54 mms), bakelite (specific gravity 1.60, diameter 0.52 mms), bakelite (specific gravity 1.51, diameter 0.67 mms) and sand (specific gravity 2.68, diameter 0.36 mms).

From the results of the experiments design curves were plotted which make it possible to predict the length and height of bed form that will develop on any specified sediment bed for given conditions of fluid oscillation.

A model design method is suggested which is based on the principles of the theory of dimensions and which is evaluated by experimental relations for the geometric properties of dunes. The model is distorted and, in general, non Froudian. The geometrically similar model dunes are reduced in vertical model scale. The scale of the flow velocity is derived from a generalised friction equation which takes into account the influence of both skin friction and form drag. The application of the method is illustrated by a numerical example. This example indicates that a practicable set of scales is obtained if the model bed is formed by a light weight material.

Experiments with wave motion over asymmetrical "ripple-like" forms show that the difference between a net sand transport in a down-wave versus an up-wave direction is related to a subtle phase dependent mechanism associated with the intensity of vortex formation in the lee of the form. Artificial roughness modules have been developed, consisting of arrays of asymmetrical forms resembling natural ripples. The asymmetry of the forms causes an intense vortex to form in the lee of the steep face. This vortex traps and suspends sediment, which when the orbital motion reverses its phase, is lifted above the roughness element and carried in the new direction. Thus, the direction of the net sand transport is dependent upon the relation between the steep face of the roughness element and the phase of the orbital velocity; the net transport being in the direction of the orbital velocity that is out-of-phase with the maximum vortex formation.

A rational basis for the design of wave models with a mobile bed is presented. The discussion is of a preliminary nature and further model analysis, underway at present at Queen's University, should introduce a sounder basis for model design.

Hydraulic model studies were conducted to aid in ascertaining the technical feasibility and optimum design factors of the perched beach concept. Among these were two-dimensional, movable-bed studies to determine an estimate of the amount of sand which would be lost seaward over the submerged toe structure by normal and storm wave action, the optimum elevation of the submerged toe structure, and the length of a stone blanket required to reduce seaward migration of sand to a minimum. The model beach was subjected to test waves until equilibrium was reached for a wide range of wave conditions for both the existing beach and the perched beach. Test results indicate that (a) little or no beachfill material will be lost seaward of the toe structure for normal wave conditions but the larger storm waves may cause erosion of the perched beach, (b) the installation of a stone blanket shoreward of the toe structure will reduce the amount of beach erosion, (c) if the beach fill is extended a sufficient distance seaward, the toe structure serves no useful purpose, and (d) a three-dimensional movable-bed model study is feasible and is necessary to determine the final design features of a perched beach.

In the design of mobile bed coastal models it is inherently assumed that prototype beach processes may be modelled using lightweight sediment. At the Queen's University Coastal Engineering Research Laboratory, a long range project is currently in progress to determine scaling laws and scale effect for mobile bed coastal models. A large portion of this program is directly concerned with beach profiles and in this paper preliminary work is reported, in which a comparison is made between two dimensional laboratory beach profiles obtained from controlled "prototype", undistorted model and some distorted model tests.

Laboratory studies were conducted in an attempt to find out a relationship between beach and wave characteristics when equilibrium conditions are reached in beach wave interaction for the simple case of regular waves acting normal to the beach. Experimental results indicate the existence of stable points on beach profiles where the coordinates of the profile do not change with time when waves of constant characteristics act on the beach. Erperical relationship between the wave and beach properties are proposed. A new criterion for classification of beach profiles is indicated.

Hawaii's beaches are of great economical and social value; they serve a variety of purposes and are valuable both to residents and tourists alike. Like in many other parts of the world, many of Hawaii's beaches are in a state of erosion and measures of improvement must be designed to cope with this problem. Although in the past several studies have been undertaken to evaluate Hawaii's beach systems and to analyze possible measures of improvement, this study aims at an in-depth analysis of the physical factors at work in the coastal zone. A thorough understanding of these processes, it is felt, is indispensable for the application of sound and economic measures in stabilizing and maintaining Hawaii's beaches. This paper describes some preliminary results of field studies conducted in Waikiki Beach. The latter beach was chosen because of the pressing need for improvements and because of its convenient location. In order to project this study against the proper background, a short review of the general characteristics of Hawaiian beaches precedes the results of the Waikiki Beach study.

Frequent measurements of beach profiles have been made at sixteen areas between Maine and Long Island since September 1965 by members of the Coastal Research Center of the University of Massachusetts. This research effort has resulted in the accumulation of approximately 2000 beach profiles along the New England coastline.

The coast line of Kouchibouguac Bay, New Brunswick, within the southern Gulf of St. Lawrence coastal province, consists of a barrier island system of sand beaches and low dunes. It is a relatively low energy system in a protected location with the important waves entering the bay through a narrow fetch window from the northeast. The behaviour of these wave trains and their refraction patterns within the S. Gulf of St. Lawrence and Kouchibouguac Bay were simulated by the construction of a series of refraction diagrams, from which it is possible to obtain a realistic appraisal of wave conditions at the shore. Waves entering the bay from N and NE directions are concentrated on the southern part of the barrier island system, and those entering from the ENE and E are concentrated on the northern part. In greater detail, a series of wave refraction diagrams, based on former conditions of nearshore bathymetry at Richiboucto Inlet, help to explain the changes which have occurred there in the past 80 years. The simulation of wave behaviour in Kouchibouguac Bay has provided useful additional information which helps to explain the recent evolution of the barrier island system.

Starting from a provisional hypothesis, presented by the author at the 11^th Conference on Coastal Engineering, this paper deals with the further development of our knowledge about dune erosion during storm conditions. Results of measurements in the prototype are mentioned. Some speculations about the occuring processes during storms are given. However, the problem has not yet been solved. Further measurements in the prototype will be necessary.

Several types of beach features seem to have a rather regular, longshore pattern. This pattern may indeed he sufficiently uniform to be described in terms of a recognisable longshore wavelength. A likely explanation for such features lies in the motion of edge waves, surface waves trapped by refraction to the shoreline. These waves, by themselves or by interaction with the normal, incoming surface waves breaking on the beach, can generate longshore features having a wavelength equal to or half the edge wave wavelength.

If a broad spectrum of edge wave modes were present any longshore variation should appear rather irregular. The existence of regular features therefore suggests that a particular edge wave mode is often dominant, the characteristics of the dominant mode depending on the geometry of the nearshore area and the width of the surf zone.

Any new, artificial structure stretching seawards provides new boundary conditions, almost certainly altering the characteristic of the edge wave spectra. This is particularly obvious in the case of a regularly spaced structure such as a set of groynes. A deeper understanding of the edge wave processes is needed so that the induced changes in the edge wave spectra are the least deleterious or, an intriguing possibility, advantageous.

A mathematical model is described that is capable of predicting changes in the plan shape of a beach following the construction of sea defences or an alteration in the wave climate. The rate of change is calculated. The technique is illustrated by comparing model predictions with results from experiments carried out in a wave basin. The importance of the method in estimating coastal changes due to offshore dredging is mentioned, and the future development of the mathematical approach is outlined.

The theory of wave-induced longshore currents is applied to problems of beach erosion. An erosion equation is derived, relating the local erosion (or deposition) rate to the form of the beach and to the characteristics of the incoming wave field. A numerical integration technique of the erosion equation is discussed and a specific example is examined: that of a linear coast line which is gradually eroded into a spiral-shaped beach in the lee of a headland.

Crenulate shaped bays are the rule rather than the exception on coastal margins of oceans, inland seas or lakes where sedimentary beaches exist between headlands. They have a particular orientation to the swell or resultant wave energy vector, such that the straight tangent section is downcoast and the curved portion upcoast. The latter is a logarithmic spiral at all stages of development of the bay. When fully stable, that is no littoral drift taking place, the constant of the log-spiral equation has a specific relationship to the approach angle of the waves to the headland alignment. In this condition it is shown that diffraction and refraction are involved when waves sculpture the curved beach in the lee of the upcoast headland. A further ratio to identify stable bays appears to be the ratio of indentation length to clearance between headlands. The application of crenulate shaped bays to stabilization of a reclaimed shoreline suffering strong littoral drift on Singapore Island is described.

An annotated bibliography on groins, compiled by Balsillie and Bruno (1972), has provided the background for this paper. A review of functional design criteria is presented including groin length, height, spacing, permeability-adjustability, and orientation. A discussion of coastal processes and their relationship to groin design and effectiveness is also given.

This paper demonstrates the results of the comparison between the calculated alignment of the beach's plan view and the actual alignment that resulted from the natural wave action.

A new groin system was designed to replace an existing one. The new groin system and spacing was designed to hold the beach fill at the required width during average wave conditions as well as changing storm wave conditions. The system was designed for Las Tunas Beach, a beach near Los Angeles, California.

In other words, the energies are tabulated for all storm conditions, and the beach alignment is recalculated for changing storm conditions. As the beach plan view alignment rotates back and forth with changing storm directions, it must always meet the minimum beach width requirements. This may entail changing the groin lengths, heights and spacing several times before the design complied with all requirements.

Surveys from 1929 to 1970 showed that the beach did not have long periods., periods of several years, of constant erosion or constant accretion. If there are no major man made changes, it is safe to assume that nature will provide an adequate send supply.

Last, but not least, the calculated beach alignments check with the empirical information gathered from years of surveying.

A section of beach on the south coast of England has been under surveillance for five years, from March 1966 until March 1971. During this period, two permeable groynes of the Makepeace Wood type were constructed. Beach cross-sectional areas and rates of accretion were compared before and after groyne construction. The groynes caused a build-up in beach levels updrift.

The Nile Delta Coast on the Mediterranean Sea was formed through many centuries. The two existing main branches of the River Nile, i.e. Rosetta and Damietta, succeeded over the ages in forming two peninsulas or protrusions in the sea. By the end of the 19th century erosion started at several important points of the coast, causing damages to the national economy, either directly or indirectly. This erosion has increased tremendously during the last decade.

Several field and laboratory studies were carried out during the last few years, concentrating on the severely attacked areas, such as Ras-El-Bar, Burullos, Rosetta, Maadia.

Based on the quick field and laboratory studies, remedial constructions are designed for the locations of severe erosion. Groins for Ras-El-Bar with artificial sand feeding and stone pitching and a wall for the Damietta estuary. A large groin for Burullos outlet which developed some advantageous changes even before finishing its execution, and sea wall for Maadia. All the above projects are discussed and explained.

A long term study project was started early in 1971 to collect the data necessary for a better understanding of the problem. The aims of this project are as follows: (1) To determine the historical formation of the Delta and forecasting future changes; (2) Study the Meteorology and the Hydrodynamics of the area; hindcasting and starting a new forecasting technique for them; (3) Planning and design of protective constructions for the coast is to be gained.

All the above will be based on an extensive field data collection programme, mathematical models and hydraulic scale models.

The SouthWest coast of India is subjected to severe erosion due to attack by waves and tidal overflow. Through the years the problem has intensified as beach front areas have become more extensively developed and subject to greater damage from the force of the sea. More than 300 kms of the coast is subjected to severe erosion due to constant attack by waves and tidal overflow, resulting in continuous recession, loss of valuable property and affecting many aspects of its economy. The paper presents the problem at the proper perspective. It describes the various physical factors of the Southwest coast of India, namely the geomorphology, winds, waves, tides and currents, littoral drift, material characteristics, shore line and shore depth changes, effects of inlets and mudbanks. The study, evolution and development of different coastal defense works and their behaviour and effectiveness is also presented.

Results concerning the artificial nourishment of Copacabana Beach (Brazil) with sand are described. The beach, 4.2 km long, was formerly about 55 m wide. After an artificial nourishment with 3.5 million c.m. of sand, a mean width of about 140 m was reached. From that total of sand, 2.0 million c.m. were dumped offshore and the remaining amount stockpiled on the foreshore. Prototype and model results agree quite well. Comments are made on the efficacy of the offshore dumping method and recommendations concerning its use in future cases are presented.

Several artificial beach nourishments were completed during the last twenty years on the German North Sea coast. Investigations made it possible to settle different problems connected with artificial beach nourishment and to gain additional information and experience. At present beach nourishments at Langeoog and Sylt will be realized in a way which is expected to bring the highest effectiveness. The hydrodynamic processes in connection with these beach nourishments and their change in shape will be subject to the paper.

Interruption of sand transport is the most persistent worldwide coastal problem. Wave action produces sand transport which is not a problem in some areas but in others results in coastal erosion, obstruction of harbor entrances, and permanent loss of sand. Conflict between saving sand and bypassing it is caused by a lack of methods to manage this valuable resource. Separate elements of control have been used with varying degrees of success; now it is proposed to incorporate subsystems into an integrated system for management of the littoral transport. A coastal sand management system is to be evaluated using three principal subsystems: (1) a mobile jet pump for use with a crater sink and fluidization accessories; (2) interlocking inertial modules which simulate structural materials because of high intergrain stresses; and, (3) the tactical deployment of phase dependent roughness elements to direct (or reverse) the net transport of sand.

A coherent sand management system promises to make a start toward true control of littoral sand transport. In addition, there is the prospect of eventually establishing the first self maintaining harbors.

It is attractive to consider systems which would be operative within reasonable cost, which may be entirely submerged, and which are capable of operating without regard to surface seakeeping problems.

Some aspects of the system indicate possible use of the mobile jet pump as a means for estimating longshore transport in the field, use in archaeology, and as a dredging and maintenance tool for small nations whose investment capital could not support massive dredging operations.

The results of model tests, carried out to evaluate the stability of submarine slopes under wave action are presented. A Bentonite clay was sedimented in a glass walled tank 6 feet long by 0.5 feet wide by 2.5 feet deep. The sedimentation and consolidation processes were studied and sediment densities were measured at various depths in the profile. Vane shear strength profiles were also measured at various average degrees of consolidation. Plastic markers were placed in the sediment adjacent to a glass wall so that the soil movements under both gravity and wave induced slides could be documented by photography. Dimensional similitude is discussed and the model test data are presented in a dimensionless form.

All instabilities were observed to be of the infinite slope type. Analysis of the data shows that wave action is instrumental in initiating downslope mass movements in gently to steeply sloping off-shore sediments. General lack of agreement between the model test results and published theoretical analyses was found but there was close similarity in the depths and form of failure under wave action and under gravity stresses alone. The loss of stability under wave action is analyzed on the concept that failure is gravity controlled and the soil strength is reduced to a value commensurate with gravity sliding by the cyclic shearing stresses imposed by progressive waves. A method of evaluating the stability of prototype slopes using a model test correlation and field vane strength measurements is proposed.

Stability tests on the Europoort breakwaters, situated on a shallow foreshore, clearly demonstrated the effect of the foreshore configuration on the overall stability. The present article gives a description of the stability experiments and the interpretation leading to general conclusions regarding foreshore effects in combination with hydraulic conditions such as wave period, water depth and wave height. Both regular and irregular waves have been used. The experiments, carried out in commission of the Netherlands Government Department of Public Works (Rijkswaterstaat) were of an applied nature and were not directed primarily to the systematic study of foreshore effects.

Near surface sea floor sediments were obtained by the tracked underwater vehicle RUM from four locations on the floor of the La Jolla Canyon. The sediments were clayey silts of high plasticity. The engineering properties of the sediments, including grain size, index properties, strength and compressibility, were determined.

The commercial mining of sand at coastal locations along California has been a continuing activity at some sites, sporadic at others and altogether discontinued at still other sites. This mining activity includes all methods of sand mining (dragline, self-propelled bottom-dump scrapers, diesel shovels, etc.) and may be classified by littoral zone location as (1) mining from a beach foreshore or backshore area wetted by the normal tidal range, (2) mining within a river mouth or other estuary upstream from the ocean but still within the tidal zone, and (3) mining from bluff or dune areas not wetted by the normal range of tides but still within the littoral system. Processing of the sand thus mined takes place when the material is transported from the mining site, usually by end dump trucks or belt conveyor to either a fixed or a portable plant.

Commercial uses of the sand thus mined fall into two general categories, (1) construction and (2) special purposes. Construction usage includes aggregate for concrete, asphalt, mortar, plaster and stucco, base material in road construction, and fill and structural backfill. Specialty uses include sand blasting and filtration material, foundry and engine sands, and raw material for manufacture of glass and ceramics.

The Florida Legislature passed a law in 1971 requiring the establishment of coastal construction setback lines on a county basis along the sand beaches of the State of Florida fronting on the Atlantic Ocean and the Gulf of Mexico.

Florida's beach areas (valued in $ billions) are being developed at an accelerated rate, however the coastline is in a general state of serious erosion. These factors combine to make implementation of the above law extremely urgent.

The Coastal and Oceanographic Department of the University of Florida has a contract with the Florida Department of Natural Resources to furnish a comprehensive engineering study of the various coastal counties of Florida in order to provide the technical information and make recommendations for the establishment of such setback lines.

A typical coastal county study is described. The study included historical data related to shoreline stability, field measurements, computations and evaluation of all pertinent factors. Some factors considered were dune elevations, foreshore-offshore slopes, erosion trends, storm surge, vegetation bluff line, wave setup, uprush, coastal structures and upland development.

Analysis of the pertinent factors resulted in formulation of criteria that were applied in recommendation of the setback line. The criteria-application is described along with adoption procedures as required by law.

Although the phenomenon of saltation of sand grains in a sand storm is very complicated, there exists the successive saltation defined by the authors. The height and distance of saltation of sand grains in successive saltation by wind are compared with the theory of successive saltation proposed by the authors. The concentration of sand grains and velocity profile in a saltation layer are theoretically investigated with the aid of the results of experiment.

A solution of two-dimensional long waves on a beach of uniform slope is connected with that in water of constant depth, in order to yield an approximate solution for standing waves in front of a sloping dike. Wave motions are expressed in the Lagrangian description.

The highest possible standing waves as well as the reflection coefficient are calculated according to the Miche's conception. Theoretical results show a good agreement with the experimental results of Murota and Yamada.

It is also predicted that there is a relationship between the wave overtopping quantity and the quantity of water of standing waves above the crest height of the dike.

As for the wave pressure of standing waves, a simple formula in the Eulerian description is derived for relative-dike length l/L < 0.16 by allowing 6% error.

This paper is concerned with the study of wave pressures exerted upon breakwaters of the vertical type from overtopping waves.

The formulae for maximum wave pressure upon vertical walls and the wave crest elevation for overtopping waves are suggested by the author. The phase interval method for the maximum wave pressure is also given.

Multiple linear regression analysis is applied to predict horizontal velocities and acceleration of water particles subjected to waves. Furthermore it was used to predict the coefficient of drag for circular piles. The mean value functions of the parameters are calculated and the assumption of their lognormal distribution reasonably well verified. The method used here is free from theoretical assumptions about wave mechanisms and, hence, explains the behavior of experimental results.

Using Monte Carlo simulation these regression relations were then utilized to generate the distribution functions of wave forces. Using the Morison force equation, in this simulation, the distribution function for the drag and the inertial components of the force are determined separately. A linear superposition of those time varying processes was performed to obtain the distribution of the total maximum force. Finally a probabilistic wave height-wave force relationship was developed for the purpose of creating a force distribution function given a random sea state.

This is a presentation of the analyses of data obtained from a laboratory investigation of horizontal forces produced by oscillatory waves on submerged pipes. The research program was planned to help solve design problems for pipe lines located on or below the bottom in the oceans or the Great Lakes. The project was financed by the National Science Foundation.

A continuous record of wave height and horizontal force was obtained for pipes of four diameters, for three wave heights and three wave lengths. Forces were measured at four locations below the water surface, the lowest position being as near the bottom as possible. Other tests were conducted with the pipes located in various positions within trenches of several different shapes. The actual pipe diameters, wave heights and wave periods used in the laboratory tests were such that on the basis of a scale ratio of 1 to 75 the range of prototype parameters would include pipe diameters varying from 8 to 15 feet, wave heights varying from 8 to 23 feet and wave periods in the range from 6 seconds to 12 seconds. Results are presented in the form of coefficients of inertial resistance and drag which can be used with the Airy equations to compute forces.

The solution of wave scattering by a vertical elliptical cylinder is applied to calculate the wave forces exerted upon it. The wave forces in the directions of long and short axes of ellipsis are shown in nondimensional forms as the functions of the angle of wave approach, the diameter-to-wavelength ratio, and the aspect ratio of ellipsis. The results of wave force computed are also shown in terms of the virtual mass coefficients associated with the reference volume of the circular cylinder the diameter of which is approximately equal to the apparent width of the elliptical cylinder observed from the direction of wave approach.

Theory is further applied for the wave forces acting upon a vessel moored tight at offshore dolphins and the forces transmitted to the dolphins through the vessel. The vessel is approximated with the fixed elliptical cylinder having the same width-to-length ratio. The computation with directional wave spectra shows that a tanker of 200,000 D.W.T. may exert the force of about 1,400 tons at the one-third maximum amplitude to each breasting dolphin when the tanker is exposed to the incident waves of H_1/3=1.0m and T_1/3 =10 sec from the broadside.

Up to the present time, some researches have been done about hydrodynamic forces and tensile forces on mooring cables and configuration of cables in uniform and ununiform currents.⁽¹⁾ Recently, the dynamic problems on the mooring system of buoy in waves are being studied by means of analytical and numerical methods. Authors have studied about a large navigation buoy exposed to strong tidal currents and large waves by means of model tests in an open channel and a wave tank.

Observation of hurricane damage along the Mississippi Gulf Coast has stimulated studies of wave action on structures which permit the waves to pass beneath the floor or bottom surface. This paper reports a laboratory study which compares relative drag and lift forces on a structure with a plane, horizontal bottom surface to those on a structure with a ribbed bottom surface, for various conditions of relative wave height and relative clearance of the structure above the stillwater surface. Also, the effects of relative depth of ribs, relative spacing of ribs, and end webs or diaphragms are noted. The study was limited to the condition for which the bottom ribs were transverse to the general direction of wave motion. The results, which are presented in graphical form, clearly show the effects of the ribs.

The force exerted by a liquid on a moving body always depends on the preceding velocity and acceleration of the body.

The Basset-Lai equation, derived from the linearized equation of motion, gives the force on spheroids when convective acceleration of the water particles may be ignored. Examples prove that the history integral it contains accounts for a large portion (even all) of the force. Measured forces on a cylinder anchored in accelerating water show that history is equally important when convective accelerations are large. An important unanswered question is whether history terms that will fit a range of motions can be invented for simple non-linear problems.

For non-linear repetitive motion, such as the force exerted on piles by regular waves, no explicit history term is needed. The usual division of force into inertia and velocity portions is possibly less sound than a suggested alternative form from dimensional analysis.

One cannot expect to unravel the hydrodynamics of irregular wave forces, but he may use similarity principles to predict their probability distribution from measurements made elsewhere. Irregular waves will be statistically similar, altho mean heights may differ greatly, if the probability distributions of suggested characteristics of the gage records are alike. Given similar waves and structures scaled to the waves, the probability distributions of dimensionless wave forces also will be alike, and the forces at one place can be predicted from measured forces at another.

A mathematical model is presented which portrays the physical system of a large axially symmetric structure in a flow field of finite water depth, large amplitude wave and strong current. The flow field, which enters as the input, is derived from a velocity potential similar to that of the cnoidal wave of Keulegan and Patterson. The inclusion of a uniform velocity in the derivation of velocity potential results in a cross interference term in addition to the well known Doppler shift effect.

The numerical results are compared with experiments on a bridge pier (Ref. 6) which is partially cylindrical with base diameter equivalent to 100 feet in prototype; close to the surface, where the wave action is greatest it is conical. These results are also compared with theoretical calculations based on linear wave theory and fifth-order wave theory. It is concluded that the results based on the modified cnoidal wave theory come closest to the experimental value.

In the light of tests on breakwater armor units conducted at Laval University on behalf of the Department of Public Works of Canada, a discussion on various factors involved in model tests on breakwater armor units is presented in comparison with previous studies made on the subject. Tests have been carried out on natural stones, tetrapods and mainly dolosse.

Various factors whether they pertain to waves or to the structure are analysed in view of the factors resulting from the interaction of both of them, that is stability of the armor units, damage to the structure or run up of the facing. These factors are the ones for which model tests are conducted. The interpretation of results for the given test conditions should not be evaluated without considering possible scale effects.

From the analysis of test results presented by different investigators, a need for the standardization of test results became apparent. Recommendations are made concerning the presentation of results for their future use in engineering design. A standard weight of 100 grs with a standard length of 100 cms for model values are proposed to present the results on a diagram showing significant wave height versus damage, where damage should be expressed in terms of the number of units displaced in the area between ± the wave height giving 1% damage.

A theory is derived to predict ocean wave reflection and transmission at a permeable breakwater of rectangular cross section. The theory solves for a damped wave component within the breakwater and matches boundary conditions at the windward and leeward breakwater faces to predict the reflected and transmitted wave components. An approximate solution to conventional rubble mound breakwater designs is formulated in terms of an equivalent rectangular breakwater with an additional consideration for wave breaking. Experimental and theoretical results are compared and evaluated.

Effects of characteristics of incident waves and of the thickenss of structure on wave reflection by and transmission through a porous structure were studied. Use of an idealized porous structure which is a lattice composed of circular cylinders was made. The relative thickness of structure B/L was found to have appreciable effects on reflected and transmitted wave energies.

The reflection coefficient Kr reaches to a maximum of it for B/L of about 0.2 to 0.25, then decreases as B/L increases, and remains approximately uniform for B/L larger than about 0.6. The transmission coefficient Kt, however, decreases nearly exponentially as B/L increases.

Measurement of wave height within structure revealed a pattern of standing waves having a loop at the front face and a node at the rear face of it. That relates to the trend of Kr.

Analytical approaches to predict the transmitted wave height, and wave heights before and within porous structures are found to be useful.

In conducting model tests of wave transmission through permeable rubble-mound breakwaters, it is impossible to satisfy simultaneously the Froude and Reynolds criteria for dynamic similarity. The common practice has been to scale the wave parameters and breakwater dimensions in accordance with the Froude Number, and to use large models.

This study represents an attempt to develop theoretical expressions for the coefficients of reflection and transmission as functions of the effective porosity of the breakwater structure, as influenced by the Reynolds-dependent boundary layer growth an the pores. These expressions use linear wave theory and boundary layer theory to estimate the effective decrease in pore diameter due to growth of the displacement boundary layer thickness in the pore.

The theoretical expressions were compared with experimental results from a series of three model tests with breakwaters having vertical faces and using gravel with diameters of 1.37 in., 0.762 in., and 0.324 in. respectively. The prototype to model ratios (using the largest model as the prototype) were 1/1.80 and 1/4.23 respectively.

The experimental results show clearly the existence of scale effects in both coefficients of reflection and transmission. The theoretical expressions were found to overestimate the scale effect in reflection and to underestimate it in transmission.

Wave motion in a rockfill embankment is solved by a finite element approach. Lagrangian coordinates are used to trace the movement of fluid particles on the free surface.

The rubble-mound seawalls, groins, breakwaters and ripraps around oceanfall pipelines are still the most common type of shore-protection structures currently in use. Major reasons include: easiness to construct and repair, flexible with respect to settlement, favorable wave-energy dissipation, fitness for any water depth and any foundation, and because of its economical nature if rubble-stones are readily available. However, the importance of a filter system in the stability of such structures must be emphasized. More recently, the submerged rubble-mound structures have become very popular due to aesthetic reasons. A filter system is considered a must to protect such a structure against erosion as a result of wave overtopping.

Following a brief review of the problems, general discussions are made of the specific causes of failures including piping, overtopping, and nonstability. The physical factors that would affect the filter design are discussed in detail. Methods for design of filter system is presented including those applicable to the gradation of filter layers and to the plastic filters. The design procedure involves (a) making mechanical analysis of the backfill and base material, (b) estimating sizes of voids in the rubble-stones, (c) designing filter by Terzaghi criteria as revised by U.S. Army Waterways Experiment Station.

A sample design of graded filter system behind rubble-mound seawalls is given.

The procedure for the selection of plastic filters is also included.

A comparison of the merits and demerits of these two types of filter systems will be made. This comparison will take into account the model test results conducted in the Look Laboratory. However, the readers are cautioned about the scale effects of the scour characteristics particularly on those tests with light-weight model sediments.

This paper is intended as a general guideline for practicing engineers who will be responsible for design and construction of rubble-mound marine structures.

A group of piles in a specific geometric pattern may represent a part of a foundation supported by multiple pilings or a porous sea wall or other type of porous coastal structure. "Wave characteristics" of such a structure will include not only the wave transmission but also wave reflection characteristics.

Most of the experiments in the past on pile groups were mainly concerned with wave transmission characteristics as a function of wave height and period. The main purpose of these previous studies was to evaluate the absorption characteristics of pile groups, and wave reflections were generally not measured, or evaluated.

Variables in this study included wave characteristics such as wave height and length and three types of symmetric pile arrays, two providing clear spacing in the direction of the wave between pile rows and one with a staggered arrangement.

The results presented in dimensionless form show the effect of pile geometry and wave steepness on the coefficient of reflection and transmissibility.

Wave height at a point on vertical cylinders is measured as a function of the orientation angle, α, between the normal from the point on the cylinder and the direction of travel of a single periodic train of waves. The wave height distribution, H(α), has a broad maximum around α = 0° (facing into the waves) and a more restricted maximum at α = 180° . The maximum at α = 0° increases with wave height in all cases, and the superelevation has about the magnitude of the velocity head in the wave crest. In 21 different H(α) for which it is possible to determine the axis of symmetry by a simple objective test, 14 H(α) have axes of symmetry within ± 3° of the direction of wave travel. Most of the variation in H(α) is due to variation in crest elevation; trough elevation remains relatively constant for the 360° range of a. The shape of H(α) depends more on height and cylinder cross section than on period, although the variation in H(α) as a function of cross section is significantly less than the extreme variations in tested cross sections. Applications of these results to wave direction measurement and to interpretation of wave records from surface-piercing wave gages are discussed.

The quantitative relationships among run-up, overtopping and reflection of waves are presented in this paper. In addition, the authors have proposed several empirical relationships to calculate the height of wave run-up and the quantity of wave overtopping in the region of standing waves.

Energy losses in breaking irregular waves are estimated on the assumption that a wave, while breaking, loses only that portion of its height which would be in excess of the breaker height for the given wave period and the mean local depth. This leads to expressions for the magnitude of the radiation stresses as a function of the distance offshore. From this the variations in mean water level and the longshore current velocity are calculated with existing methods. Laboratory measurements of set-up in two-dimensional irregular waves are described. The data appear to some extent to be internally inconsistent; this may be due to enclosed air bubbles.

The quantifiable determination of important coastal parameters remotely rather than by in situ measurements combined with automatic data reduction and analysis will result in a greatly increased understanding of the parameters being studied. This paper gives a progress report on joint Corps of Engineers-National Aeronautics and Space Administration (NASA) efforts to apply remote sensing in coastal studies. The devices used were multiband photography, the infrared scanner, the Side Looking Airborne Radar and various image enhancement and processing devices.

This paper reviews the important coastal engineering applications of aerial remote sensing techniques and provides a current state of the art summary of the utilization of aerial remote sensors in coastal engineering studies. The sensors discussed include conventional black and white aerial photographs, black and white infrared aerial photographs, color and color infrared aerial photographs, multispectral aerial photographs, satellite photographs, infrared imagery, multispectral imagery, and radar imagery.

The field of coastal engineering is considered in a broad context to include all important applications of aerial remote sensing that relate to coastal engineering problems. The use of remote sensors to monitor coastal changes, study coastal landforms, examine storm effects, map coastal areas, determine nearshore hydrography, and monitor the environmental effects of coastal engineering projects, a topic of considerable current concern, is described.

The important characteristics of the various aerial remote sensors are described briefly. The advantages and limitations of the aerial remote sensing techniques for different coastal engineering studies are noted. The review and state of the art summary of the applications of the aerial remote sensors can be used by coastal engineers as guidelines in employing the sensors in future coastal engineering investigations.

This paper describes the Earth Resources Technology Satellite (ERTS) placed in orbit in July 1972 and the ERTS simulation high altitude aircraft flights which have been flown for approximately one year. The ERTS satellite and simulation programs conducted by the National Aeronautics and Space Administration (NASA) have been developed to demonstrate the techniques for efficient management of the earth's resources. To achieve this objective the ERTS-A satellite provides for the repetitive acquisition of high resolution multispectral data of the earth's surface on a global basis. Two sensor systems have been selected for this purpose: a four-channel multispectral scanner (MSS) subsystem for ERTS-A and a three-camera return beam vidicon (RBV) system. Systematic repeating earth coverage under nearly constant observation conditions is provided for maximum utility of the multispectral images collected by the ERTS satellite, which operates in a circular sun synchronous nearly polar orbit at an altitude of 494 nautical miles. It circles the earth every 103 minutes completing 14 orbits per day and views the entire earth in 18 days. The orbit has been selected so that the satellite ground trace repeats its earth coverage at the same local time every 18-day period within 20 nautical miles. A number of data output products are available from this satellite which include 70 mm products for precise location of topographic features, 9.5 inch positive or paper prints and also computer compatible tapes or punched cards.

Also described are the results of the ERTS-A simulation flights flown at an altitude of 65,000 feet as related to coastal studies. Simulations of both the RBV and MSS in coastal areas are presented.

Once-through cooling water systems for thermal power plants offer an economical means of dissipating the differential energy of modern-day turbines.

Before the decision to proceed with the design of a once-through cooling water system is made, a considerable study effort must be undertaken in order to determine that no harmful effects will accrue to the environment from the plant's operation.

The ocean provides enormous capacity for dispersion and assimilation of human and natural wastes. Indeed marine ecosystems depend on such terrestrial sources for their nutrient supplies. It is incumbent on man to cause minimal disruption and, if possible, beneficial effects from dispersing his wastes in the sea. The Southern California Bight receives the most intense exposure to discharged sewage of any exposed region along the Pacific coast of North America. Evidences of significantly altered chemical and biological conditions in southern California hare been demonstrated. Elevated concentrations of certain metals occur in sediments near some large sewage outfalls. Pesticide residues were extremely high in sand crabs from southern California. Beds of giant kelp decreased near some, but not all, sewage outfalls. Correctional measures are discussed. Ecological surveys are currently used to provide early warning of potential biological problems near some southern California outfalls. A survey near an outfall removed from service indicated most changes in fish and macroinvertebrate populations occurred within a few months after the discharge oeased.

The Capital Regional District of British Columbia, Canada, is implementing for the Greater Victoria area, a major sewerage plan based mainly on marine discharge by submerged outfalls. To assess effects on the receiving ecosystem, a thirty month monitoring program has been carried out at the site of a newly constructed 6000 foot marine outfall. Of the standard water quality parameters, several were established during the pre-discharge period as "gross sewage field indicators" at beach outfalls: nitrite, phosphate, total and fecal coliform bacteria, Secchi depths, Forel colour and salinity. The remaining parameters were not sensitive to the presence of effluent: temperature, dissolved oxygen, nitrate, silicate and chlorophyll. In the water surrounding the diffuser of the extended outfall, only total coliform values showed the presence of effluent once discharge was diverted from the beach outfall. Profiling techniques were employed for measuring chlorophyll, turbidity and Rhodamine dye. A method was developed for mapping coliform bacteria in the sediment surrounding the diffuser, as an index of the ability of the receiving water to assimilate effluent loads being discharged into it. It is stressed that monitoring programs should be included in plans for any major coastal operation.

The in former years nearly exclusively agriculturally structured coastal areas of Lower Saxony recently undergo an increasing industrialisation. This process was introduced by the settlement of a Titandioxyd factory at the Weser estuary, which releases acid sewage. The problems, connected with the discharge of this sewage are discussed, as well as the tests performed in order to prevent a possible overstrain of the Weser water. The hitherto gained results are described and preliminarily interpreted. The recent, partly surprising biological development cannot be traced back to a measurable ecological change in the Weser estuary and therefore is inducement to think over critically the applied procedure.

The authors consider the derivation of an expression for ealinity distribution in an estuary, from an instantaneous mass balance equation for a solute in a continuum. The expression is compatible with existing field instrumentation and limited economic resources. Details are given of a prototype survey which included continuous monitoring of the salinity distribution of the Firth of Tay, an estuary subject to a wide range of fluvial and marine influences. The survey results enabled an apparent dispersion coefficient to be evaluated and an estimate to be made of the net mixing.

To optimise dispersion from marine outfalls multiport diffusers have been developed. The addition of mixing tubes to such outlets can create an ejector action and so cause pre-mixing before discharge to the receiving mass of water. The characteristics of such water jet-pumps in this submerged condition have been derived elsewhere, but are applied herein to the dilution of effluents. For a range of jet to mixing tube area ratios optimisation has been carried out on a computer, thus indicating the densimetric Froude numbers and depth ratios at which dilution exceeds that for the plain jet. Even for a stagnant ambient medium dilution in experiments exceeds that predicted, possibly because of macro-turbulence not accounted for in the theory available. Turbulons developed in a mixing tube are larger than any emerging from a plain smaller jet and may thus promote better mixing from its exit to the sea surface. Mixing tubes have obvious applications in shallow water and where an effluent is particularly obnoxious.

Due to increased environmental pressures, there is a rapidly growing tendency to shift from traditional land disposal of dredged material to offshore or ocean disposal. The quantities of such materials are quite large, resulting in a very serious disposal problem. For example, maintenance dredging alone produces approximately six million cubic yards of material annually in Charleston Harbor. Existing techniques are reasonably adequate to describe the transport and settling characteristics of coarse, sandy dredge materials discharged from barges or hopper dredges at sea. However, such approaches need to be modified to describe the transport of fine-grained clay and silt materials. This material constitutes a significant portion of the dredged material resulting from both new harbor and channel construction and maintenance dredging along the coast of the Carolinas and Georgia. These fine-grained materials are subject to many additional physical forces as well as chemical phenomena, e.g., flocculation, salinity and temperature variations, etc. A hydrodynamic model for fine-grained dredged material has been developed which considers many of these forces. It is also applicable for describing the transport mechanisms associated with barge disposal of wastewater sludges from municipal and industrial sources. The results of the model indicate what discharge strategies are necessary for placing the sludge at a desired location or depth with a predetermined concentration.

This paper describes the results of a numerical modeling study of the Lower Biscayne Bay system in southeast Florida. The purpose of the study is to predict the effects of cooling water intake and discharge associated with the Turkey Point Power Plant facility, which comprises two fossil-fueled units and two nuclear units. When completed the system will generate 2450 megawatts. One of the original (but since abandoned) operating plans considered would require intake by the plant ranging from 4250 to 10,600 cfs of Bay water for cooling and dilution purposes to be returned via a six-mile canal to the Bay system.

The Lower Biscayne Bay system comprises several bodies of water of 6 to 10 ft. depth which are connected over shallow limestone and mud sills. The numerical model incorporates an area of approximately 36 by 12 nautical miles divided into grid squares of 2 nautical miles on each side.

Available field data are used to calibrate the model. The results of the calibration and predictions of the effects of the plant withdrawal and discharge on the natural bay system flows are presented.

The primary features of interest of the study include: 1) the effect of the plant cooling water requirements on the Bay hydromechanics, including recirculation and flows through small inlets connecting the Bay to the Ocean; and 2) the concentration distributions of conservative constituents in the Bay system as affected by advective and dispersive processes. The numerical procedure consists of a non-dispersive and a dispersive model which are employed sequentially.

A numerical model is presented to describe the hydromechanics of lagoons connected to the ocean by relatively narrow inlets. Because special attention is given to the flushing, all second order terms in the hydrodynamic equations are retained. The study is restricted to lagoons with a one-dimensional flow pattern and water of uniform density. In designing a numerical solution to the equations, the inlet equations are regarded as implicit boundary conditions to the equations describing the flow in the lagoon proper. The advantages of this approach are: (1) the size of the computational grid in the lagoon can be chosen independently of the relatively small dimensions of the inlets and (2) the flow at branching inlets (an inlet connecting a lagoon to the ocean such that branching of the inlet flow can occur) still can be described by a one-dimensional tidal model.

The predictive capability of the numerical model is confirmed by favorable comparison between measured and computed particle paths and net transport for a series of laboratory experiments. In the experiments a canal of uniform width and depth is freely connected to a tidal basin at one end and at the other end is connected to the same basin by a submerged weir.

A long term time-dependent mathematical model has been developed for predicting the salinity distributions in the upper York River System, including the tidal portions of the Mattaponi and Pamunkey Rivers.

The method of calculating the longitudinal dispersion coefficient is discussed in detail. The study area and field project are described. The downstream boundary condition was found from a scheme combining a semi-explicit technique and linear extrapolation. The mass-balance equation, averaged over a tidal cycle and solved numerically by the implicit finite difference scheme, provided a reasonable solution and afforded economy in computer time. Field data were compared with the corresponding model results, indicating the general accuracy of the methodology.

A one-dimensional numerical model of a 340 mile section of the St. Lawrence River has been formulated to study tidal propagation. For a more detailed study of the flow distribution in a localised section of the river a two-dimensional model was used. A half mile square grid was used to schematise an area of approximately 20 miles long by 15 miles wide. This two-dimensional model was embodied within the one-dimensional model to permit a free interaction of flow across the boundaries.

For the one-dimensional case, a comparison of model and prototype results is included for both elevation and velocity. For the two-dimensional model a comparison of flow distribution was made by using field results obtained from photographing ice movement and from drogue movement.

To interpret the results of the two-dimensional model into a simple method of flow visualisation, use was made of animation techniques. A movie film was made that demonstrates both tidal rise and fall and the associated horizontal velocities. Elevation was reproduced by use of varying shades of coloured paper to simulate contours, velocities were represented by simulating drogue movement to produce smoke streaks.

A mathematical model is developed using analytical techniques to determine the longitudinal and vertical distributions of velocities and salinities, averaged over a tidal period, for mixed but partially stratified estuaries. The flow is assumed laterally homogeneous and the estuary width and depth are assumed to be functions of the longitudinal coordinate only. Required inputs to the model include the salt intrusion length, the ocean boundary salinity, the distribution of the depth-averaged salinity and the freshwater discharge.

The governing equations included in the model are the vertical and longitudinal equations of motion, continuity, salt conservation and an equation of state. The key assumption is made that the longitudinal salinity gradient is independent of depth. This decouples these equations and thus permits an analytical solution to be found.

Using data from laboratory flume tests and field surveys the model solutions are used to find correlations for the mean vertical transfer coefficients of mass and momentum with gross characteristics of the estuary. These correlations, plus the results from a one-dimensional numerical model, permit this analytical model to be used as a predictor of the velocity and salinity profiles in estuaries and to relate changes in freshwater discharge to possible changes in the location of shoaling zones.

The convection and dispersion of pollutants in a deltaic estuary system are calculated using several interfaced computer programmes. The basic programme is a Dronkers type one dimensional hydrodynamic model, which is interfaced with a model of the salt water intrusion in the seaward reach.

The importance of Pitt Lake, a large fresh water but highly tidal lake, is discussed, inasmuch that it integrates water quality changes over long periods of time.

The salt wedge analysis reveals the nature of the interfacial stress which is not a function of velocity or velocity squared. It is shown that the interfacial stress is a function of entrainment, rather like a Reynolds stress, and plots are given of interfacial stress against local Richardson number multiplied by local upper layer velocity.

The paper describes a method of choosing scales for the correct representation of convective spread in a hydraulic model involving densimetric phenomena. Although most prototype spreads are non-viscous in nature it is possible for small scale laboratory spreads to become affected by viscous influence when the spreading density front is remote from the outfall. This must be avoided if correct representation is to be achieved and the scales for the model must be chosen with this in view. It is often impossible to avoid viscous influence in a natural scale model of reasonable size and distortion of the vertical scale must then be employed.

A large tidal model of the St. Lawrence River covering the region from Montreal to lie du Bic is connected directly to a mini computer for data acquisition and control of the tidal boundary. Some of the more important concepts for the design and operation of a computer based system for this application are described. Details of an adaptive feedback controller for diurnal tides are given.

A 16 mm film (N.R.C.-Division of Mechanical Engineering, film no. HYP 620, same title) describes the instrumentation and operation of the model. A report (N.R.C.-Division of Mechanical Engineering, Report No. MH-110, same title) provides further details of this system.

Several mathematical models have been lately presented which describe the tidal wave propagation within an estuary. The existing models derived from the method for damped co-oscillating tides are based on sinusoidal wave profile.

Meanwhile a tidal wave which moves upstream, generally exhibits a progressive deformation which tends to unbalance the length of time between flood and ebb tides. The actual profile is therefore no longer sinusoidal.

Our investigation uses the potential method, and takes into account the wave amplitude which is usually neglected compared with the water depth.

Finally, the velocity potential is obtained explicitely, using a double iterative method. Tidal elevation, particle velocities and trajectories are given by the same computer programmed algorithm.

Our study shows that 1) the phenomenon can be clearly visualized on the theoretical curves and 2) the magnitude of this deformation is inversely proportional to the water depth, becoming significant when the ratio η/h reaches the critical value of 1/10.

Damping and geometrical effects are also considered and the theory was applied to the St.Lawrence Estuary. A partial positive reflection of the incoming tidal wave is assumed at the narrow section near Quebec, whereas a complete negative reflection is assumed at the entrance to Lake St.Peter. The calculated and observed wave profiles, velocity distributions, and phase shifts are in good agreement.

A systematical comparison between experiments in hydraulic models and numerical computations for the case of the propagation of tidal waves in schematic estuaries is carried out. It is the aim of the investigations to present the advantages and disadvantages, the possibilities and limitations of the two models. The results show, generally, a fair agreement between measured and computed quantities even in the case of the occurence of horizontal eddies within the fluid.

Investigations have been undertaken to predict the tidal amplitudes and current patterns at the mouth of the Caño Macareo in Venezuela to the Atlantic Ocean. These studies were undertaken as part of a more comprehensive feasibility study sponsored by the Corporacion Venezolana de Guayana for location and orientation of a 60-foot deep navigation channel and for the design of related channel appurtenances. In the analysis, three simulation methods were employed conjunctively. These included one- and two-dimensional mathematical models and an electro analogical model. Model results have been supplemented with prototype data and other information based on field observations.

Analyses provided for determination of tidal hydraulics, first, to establish baseline conditions as they presently exist, and second, to evaluate the effects of various proposed channel alignments. The two-dimensional mathematical model and the electro analogical model both provided for inclusion of a pronounced longshore sea current which plays an important role in determining current patterns at the mouth of the Macareo. In addition, the use of a berm to modify the sea current in the vicinity of the channel entrance was investigated.

The Bundesanstalt für Wasserbau (BAW) was charged to investigate an estuary tidal model of the Elbe-river (North Sea). The model, fitted with a movable bed, serves for special research with regard to suitable actions for the enlargement and maintenance of the main navigable channel in the sea area.

Because in tidal estuaries the interaction of fluid and solid material is extremely unknown, the investigation was undertaken to find out the arising morphological changes, only caused by tidal currents, considering structure or dredging works present or planned in prototype. The procedure seems advantageous and a better way as speculative interpretations of sediment movements, derived from flow velocities in a fixed bed model.

The horizontal scale of the model is 1:800, the vertical scale 1:100. After basic considerations as similarity, hydrology, morphology, respectively, specifications of the modelling technique are given and finally some test results are discussed.

Results are presented for a laboratory study Investigating the effectiveness of using a small-scale laboratory model to predict tidal flushing patterns in small-boat marinas. Laboratory results are compared with field measurements taken in an existing small-boat harbor.

Model limitations are indicated, but it is concluded that simple, small-scale models can constitute an effective, economical tool in the evaluation of designs of small, enclosed basins where water quality problems associated with circulation patterns in the basin are important. Some implications are made concerning the effect of basin planform upon circulation patterns.

Nearshore water transport in the vicinity of Birch Bay and Cherry Point, Washington was investigated during the spring of 1971. The techniques used were: surface floats with variable depth drags, dye patches, streams of paper sheets, wind direction and velocity data, infrared and color aerial photography, and salinity and temperature readings from water samples. Birch Bay flood tide transports water into the bay, and ebb tide carries it out. The latter water either eddies off Point Whitehorn or moves out into the Strait of Georgia. Flood tide at Cherry Point transports water to the Point Whitehorn eddy or into Birch Bay, while on the ebb tide water moves from Cherry Point toward the vicinity of Neptune Beach and Sandy Point.

Simultaneous measurements of horizontal wind velocity above the water surface, air and water temperature difference, and water level were made during the summer of 1971 at an exposed field site off the northwest coast of Florida. Three identical vertical arrays of six-cup anemometers were used; they were located in the surf zone, in the area between the inner and the outer bars, and on the outer slope of the outer bar. The distances of these three stations from the mean shoreline were approximately 30, 130, and 230 m. Mean water depths were 1.5, 4.3, and 5.0 m.

Analysis of the profile data under adiabatic and onshore wind conditions indicates that better than 90 percent of the valid wind profile measurements are logarithmic. It was found from the nearly fifteen hundred 15-minute logarithmic wind profiles that the shear velocity U_* was not a linear function of wind speed, as is usually assumed in coastal applications, but had a functional relationship with velocity at 10 m or U_10m (from 0.5 to 8.5 m/sec), such that U_* = 0.37 U_10m^2/3.

Comparison with similar investigations in deeper water and oceanic regions was also made.

An attempt to clean beaches without the use of dispersants was undertaken in Chedabucto Bay, Nova Scotia, following a spill of Bunker C oil from the tanker "Arrow" in the spring of 1970. Sand beaches account for less than 2% of the coast of Chedabucto Bay and those which were polluted were cleaned manually using peat moss, rakes, and shovels. Most sand beaches can be cleaned with relative ease, as oil does not permeate the sediments, and the angle of sand beaches is generally low so that mechanical methods can be applied without large-scale removal of beach sediments. Oil deposited on gravel beaches permeates below the surface layer and cleaning by mechanical methods involves excavation of beach sediments to depths of one metre or more. This method endangers the stability of a beach, particularly if the sediment supply is limited. Also this method was found to be ineffective in removing all contaminated sediments.

Field observations were carried out for a period of 20 months on the seashores of Chedabucto Bay, following the spillage of 108, 000 barrels of bunker C oil in the bay by the tanker Arrow in February 1970. The main factors that control the natural cleaning of seashores are as follows:

The hydrodynamics of oil slick containment are examined. It is shown that containment is only possible when a densimetric Froude number based on flow velocity and depth and the oil density is less than a critical value. Experiments confirmed that an oil slick was unable to maintain a stationary front when the Froude number exceeded the critical value.

It is also shown that viscous effects ultimately limit the thickness and therefore the length and volume of any real slick. Expressions are derived which enable these limits to be determined.

A linear theory is presented for waves generated by an arbitrary bed deformation (in space and time) for a two-dimensional and a three-dimensional fluid domain of uniform depth. The resulting wave profile near the source is computed for both the two and three-dimensional models for a specific class of bed deformations; experimental results are presented for the two-dimensional model.

The growth of nonlinear effects during wave propagation in an ocean of uniform depth and the corresponding limitations of the linear theory are investigated. A strategy is presented for determining wave behavior at large distances from the source where linear and nonlinear effects are of equal magnitude. The strategy is based on a matching technique which employs the linear theory in its region of applicability and an equation similar to that of Korteweg and deVries (KdV) in the region where nonlinearities are equal in magnitude to frequency dispersion. Comparison of the theoretical computations with the experimental results indicates that an equation of the KdV type is the proper model of wave behavior at large distances from the source region.

Recreational surfing has been studied in Hawaii to develop criteria for the preservation, enhancement and design of surf sites. The criteria will aid in planning compatible uses of the coastal zone. Surfing characteristics and wave transformations were studied in the field and related to ocean bottom features at prime surf sites. A small scale, three-dimensional, hydraulic model study was conducted to determine the effect that a given bottom feature had upon the surfing wave. A concept of a multiple-purpose surfing shoal to be compatible with several varied interests in the coastal zone was hypothesized from field, analytic, and model studies.