Coastal Engineering 1978

This paper gives examples of the separate and combined efforts of Physics and Mathematics in coastal engineering with particular reference to the possibilities in the future. It points to the fact that physical thinking is necessary as an inspiration to mathematical and numerical work.

While there is relatively little duplication of work (among the various institutions) of a purely theoretical character, the same statement does not apply to numerical models. One may hope that the future will produce more coordination in this respect.

There are two disciplines where the establishment of high quality numerical models will require a particularly strong combination of basic research, numerical expertise and field work: three-dimensional mixing processes and sediment problems. It would seem that no single institution has available both the integrated expertise and the capital investment required. Hence, a close cooperation among several institutions is almost mandatory.

There is a growing need for instrumentally-measured wave data, but it is not easy to discover what measurements, if any, may have been made in any particular area To try to alleviate the situation the Institute of Oceanographic Sciences is establishing an international reference centre which will create and maintain an inventory of such data. It is appealing for volunteers world-wide to help in identifing locations where waves have been measured.

It will be operated through the U.K. Marine Information and Advisory Service at the Wormley Laboratory of the Institute.

This paper discusses the statistical properties of long-term ocean and coastal waves derived from analysis of available data. It was found from the results of the analysis that the statistical properties of wave height and period obey the bi-variate log-normal probability law. The method to determine the confidence domain for a specified confidence coefficient is presented so that reliable information in severe seas where data are always sparse can be obtained from a contingency table. Estimation of the extreme significant wave height expected in the long-term is also discussed.

This paper presents the results of recent investigations at three sites where waves have been monitored simultaneously by two commonly used deep-water wave recorders, over a total period of 16 sensor-years. The study confirms earlier statements that there are relative differences between the wave parameters and statistical values calculated from the measurements of the two instruments. However, the large amount of data has enabled the authors to quantify the results in engineering terms and to assess the implications for extreme value analysis, spectral analysis and wave climate operational planning.

This paper presents an analysis of data collected in a hurricane wave research program. The data were collected with a synthetic aperture radar (SAR) during five aircraft flights into hurricanes in August and September, 1976. These data are the first collected on the directional distributions of waves throughout the region of active generation.

The wave patterns in all of the storms are similar and show a marked radially asymmetry. The dominant waves propagate ahead of the storm in a broad arc that has an apparent center in a region of confused sea to the right and rear of the hurricane eye. The asymmetry in the wave patterns is attributed to the forward motion of the storms. The wave directions throughout the storms do not show a sensitive dependence on the forward speed of the storms or on their maximum wavespeeds. However, there is an increase in peak wavelength with increasing windspeed and forward velocity.

Analysis is made of 89 records of surface waves for the joint distribution of the heights and periods of zero up-crossing waves. Records are classified into five groups according to the rank of the correlation coefficient between individual wave heights and periods, and the data of the joint distribution are presented for five groups separately. In comparison with the present data, the theory of Longuet- Higgins for a narrow band spectrum can describe the joint distribution in its upper portion with high waves when the spectral width parameter is fitted to the marginal distribution for wave periods, although the joint distribution in the lower portion with low waves shows deviation from the theory. Another theory by a group of C.N.E.X.O. based on the distribution of positive maxima can describe the general pattern of observed distribution better than the former theory, but the agreement remains qualitative. The present data also suggests that the joint distribution of wave periods and heights may be parameterized with the correlation coefficient between wave heights and periods.

Water level deflections μ (t) have been measured synchronously at some positions in a beach profile on the isle of SYLT / North Sea during severe storm surge conditions as well as at attenuating wave action.

A steadily increasing wave period $\overline{\text{T}}$_z in the upbeach direction, turning out from strip chart evaluations, is in accordance with the result of FOURIER syntheses. Near shore wave deformation is explained by ANOMALOUS dispersion of the frequency components.

Nearshore sediment is actively reworked during major storms,often significantly altering the nearshore morphology. It has been suggested that infragravity waves with wave periods 30-300 seconds are very important in the formation of major nearshore features.

A field study to further understand the nature of infragravity waves was carried out in Martinique Beach, Nova Scotia. Velocity measurements were taken using three electromagnetic flowmeters. Incident conditions varied from calm to swell and wind waves generated by hurricane Belle. Spectral analysis of the low tides revealed a sharp increase in the infragravity band energy associated with the storm. Throughout the storm the spectra of all three instruments were dominated by a strong 100 second peak which remained constant in frequency despite significant changes in the incident wave field. This peak is found to satisfy edge wave theory. A frequency selection mechanism based on longshore topographic trapping of edge waves is suggested.

In many applications there is a great need for a correct description of the natural, irregular three-dimensional sea and its reproduction in physical and numerical models. Because of the tremendous difficulties inherent in the nonlinearities, the science of coastal engineering is still very far from this ultimate goal.

Indeed, the scope of this paper is comparatively very modest: To describe and reproduce natural, irregular two-dimensional waves, i.e. waves propagating in one direction in a flume. In addition, this scope is fulfilled only by assuming linear superposition of Fourier terms.

As opposed to the usual spectral description, the deterministic description presented here does not eliminate the phase information in the wave train recorded. Because of the nonlinearities, however, the linear deterministic description invariably degenerates with the distance travelled by the waves. It appears though from the present paper that the degeneration is fairly slow even for rather steep waves.

Fundamental properties of random waves determined by the zero-upcross method are discussed. Firstly, the wave length and the wave velocity are treated. Experiments are carried out with some supplemental definitions such as the spatial zero-up-cross method in a laboratory wave tank. Average values of K (= a ratio of measured wave length to theoretical one L_e/L_th) and R (= a ratio of measured wave velocity to theoretical one C_e/C_th) are very close to unity though data are considerably scattered. But the relations between L_e~T_e and C_e~T_e are slightly different from the theoretical ones where T_e is the measured wave period. Secondaly , breaking characteristics on sloping beaches are treated. The wave height H_b, the wave length L_b and the water depth h_b are measured at a breaking point. Breaking characteristics of random waves are considerably different from those of periodic waves. The measured wave height-water depth ratio H_b/h_b is plotted against the water depth-wave length ratio h_b/L₀ about 30~40% below the breaker inception curve for periodic waves.

Large waves in a series of random ocean waves are considered in the design of ocean structures. When random structural vibrations can be ignored, periodic wave theories are used to predict the water particle kinematics for a design wave even though the real wave is irregular. This paper presents the authors’ first attempt to quantify the validity of using periodic wave theory for random waves. Measurements of maximum horizontal and vertical velocities were made in laboratory generated periodic and random waves. They compared favorably with predictions from periodic wave theories (even with Airy theory) particularly for the large waves in a series. Since the design wave concept is applied to the largest waves, the conclusion is that periodic wave theory may be adequate, providing an appropriate factor of safety is used to account for the differences between the actual maximum wave kinematics in nature and those in the predictive theory.

The theoretical dimensionless frequency response functions for the wavemaker stroke spectrum, Q_S(ω), and for the wavemaker dynamic pressure moment spectrum, Q_M(ω), were verified experimentally in the Oregon State University-Wave Research Facility (OSU-WRF) from random waves which were simulated from two types of two-parameter theoretical design wave spectra. The random motions of the wavemaker were first digitally simulated by a unique inverse stacked FFT algorithm which were then used to drive the wavemaker through digital-to-analog converters (DAC). The dimensionless frequency response function for the hydrodynamic pressure moment spectrum was not measured directly but was computed from the dynamic covariance equations for a hinged wavemaker of variable-draft by linear combinations of related dimensionless frequency response functions and cross-spectral estimates. The measured estimates were found to agree reasonably well with the analytical approximations, and these measured stochastic hydrodynamic pressure moment estimates on a hinged wavemaker of variabledraft are believed to be unique.

A numerical method for determining the characteristics of waves generated by a hinged inclined-plate wave generator operating in a constant depth channel is discussed. The analysis is in reasonably good agreement with experimental results. The results indicate the sloping generator operating under certain conditions is completely inefficient, i.e., for a given stroke and depth-to-wave-length ratio, very small waves are produced; for other wave periods for the same conditions significantly larger waves are generated.

In this paper we describe an experimental study on changes in height of short gravity waves on long waves.

Experiments were conducted by making mechanically generated long waves superpose on mechanically generated short waves in a wave flume of 30m long and lm wide.

Exact solution by Longuet-Higgins and Stewart explained our experimental results,but approximate expression a’= a₁(l+P) which is widely accepted seemed to be inadequate to explain our results.

The simulation of short wave propagation, including refraction, diffraction, partial reflection and all other such features, is made possible by a new version of the System 21, Jupiter. The Systemgenerated models can describe any bathymetry and topography with any time-varying mean flow, correctly accounting for wave and current interactions, wave-thrusts or radiation stresses, longshore currents and other “second order” effects. The models work with irregular waves just as well as with regular waves. Radiation boundary modules are also provided so that models can be cut-out in any desired region and new features introduced without invalidating the field-study-determined boundary data. As models are system-generated, they can be constructed and run in a few hours, starting from charts, a lay-out of the proposed engineering works and the available boundary data. The development and testing of the System is briefly described, followed by an account of its applications in coastal engineering practice.

The dissipation of wave energy by various bottom mechanisms plays an important role in the spectral transformation of waves as they propagate from deep to shallow water. Three bottom dissipation mechanisms are discussed. The bottom friction mechanism is investigated in detail and a method for calculating the friction coefficient is proposed. The method is tested by comparison with field measurements. Dissipation due to percolation and bottom motion are also discussed. The magnitude of dissipation rates induced by the different mechanisms are compared under various wave and bottom conditions.

The ideal theory for the prediction of wave-induced phenomena should be sufficiently accurate in all relative water depths, easy to apply and extensively tabulated. No available theory meets all these requirements. Vocoidal theory has been developed for application in all water depths. An extensive evaluation against experimental data proves that this theory meets the above requirements.

This study focuses upon four elements of breaking wave behavior:

1. Relative breaking depth criteria
2. Breaking wave classification
3. Evaluation of the plunge distance
4. Breaking wave height prediction

Waves in the surf zone are a highly nonlinear process which is evident by the appearance of secondary waves. The secondary waves appear as strong peaks in the period PDFs corresponding to the first harmonic of the peak of the wave spectrum. The strong first harmonic period peak is also reflected in the highly correlated height and velocity PDFs. Due to the high probability of the secondary waves, the mean wave period for breakers is a poor descriptor of the average period of the offshore incident waves.

The joint probability density functions for periods and heights of the breaking waves show high correlation (0.60-0.80) which says that greater wave periods are associated with larger breaker heights. The joint PDFs of period and particle velocity, and velocity and height, suggest that the maximum onshore particle velocities are correlated with both the wave periods and wave heights.

The equations describing conservation of mass, momentum and energy in a turbulent free surface flow are derived for a controle volume extending over the whole depth. The effect of the turbulent surface oscillations are discussed but neglected in the following analysis, where the equations are applied to the energy balance in a surf zone wave motion. This leads to results for the wave height variation and the velocity of propagation. The results cannot be reconciled completely with measurements and the concluding discussion is aimed at revealing how the model can be improved.

A possibility to estimate the water particle velocity of breaking wave on beaches by giving only the values of the beach slope i and the deep-water wave steepness H₀/L₀ is investigated. The data of the water particle velocity and profile of breaking wave on the beaches measured by Iwagaki, Sakai, Tsukioka and Sawai(1974) are used for this purpose. A method of using empirical curves relating the coefficients of Dean’s stream function to i and H₀/L₀ does not give good results. The relations between the asymmetric breaking wave profile, i and H₀/L₀ are examined. As well as the front face of the profile, the slope behind the crest above some level is found to become steep when H₀/L₀ becomes small. The breaking wave profiles are reproduced by using the empirical curves relating the parameters characterizing the breaking wave profile to i and H₀/L₀. The velocity of Dean’s stream function calculated from the reproduced profile explains the measured velocity better than that of Stokes waves. It is therefore possible to estimate the water particle velocity of breaking wave on beaches by giving only the values of i and H₀/L₀.

A description is given of a model developed for the prediction of the dissipation of energy in random waves breaking on a beach. The dissipation rate per breaking wave is estimated from that in a bore of corresponding height, while the probability of occurrence of breaking waves is estimated on the basis of a wave height distribution with an upper cut-off which in shallow water is determined mainly by the local depth. A comparison with measurements of wave height decay and set-up, on a plane beach and on a beach with a bar-trough profile, indicates that the model is capable of predicting qualitatively and quantitatively all the main features of the data.

The transformation of waves crossing a coral reef in Hawaii including the probability density function of the wave heights and periods and the shape of the spectrum is discussed. The energy attenuation and the change of height and period statistics is examined using spectral analysis and the zero up-crossing procedure. Measurements of waves at seven points along a 1650 ft transect in depths from 1 to 3.5 ft on the reef and 35 ft offshore were made.

The heights were tested for Rayleigh, truncated Rayleigh and Wei bull distributions. A symmetrical distribution presented by Longuet-Higgins (1975) and the Weibull distribution were compared to the wave period density function. In both cases the Weibull probability density function fitted with a high degree of correlation. Simple procedures to obtain Weibull coefficients are given.

Fourier spectra were generated and contours of cumulative energy against each position on the reef show the shifting of energy from the peak as the waves move into shallow water. A design spectrum, with the shape of the Weibull distribution, is presented with procedures given to obtain the coefficients which govern the distribution peakedness. Normalized non-dimensional frequency and period spectra were recommended for engineering applications for both reef and offshore locations.

A zero up-crossing spectrum (ZUS) constructed from the zero upcrossing heights and periods is defined and compared with the Fourier spectrum. Also discussed are the benefits and disadvantages of the ZUS, particularly for non-linear wave environments in shallow water. Both the ZUS and Fourier spectra are used to test the adequacy of formulae which estimate individual wave parameters.

Cross spectra analysis was made to obtain gain function and squared coherency for time series between two adjacent positions. It was found that the squared coherency is close to unity near the peak frequency. This means that the output time series can be predicted from the input by applying the gain function. However, the squared coherency was extremely small for other frequencies above 0.25 HZ.

Conventional wave diffraction diagrams often yield erroneous estimation of wave heights behind breakwaters in the sea, because they are prepared for monochromatic waves while actual waves in the sea are random with directional spectral characteristics. A proposal is made for the standard form of directional wave spectrum on the basis of Mitsuyasu’s formula for directional spreading function. A new set of diffraction diagrams have been constructed for random waves with the proposed directional spectrum. Problems of multi-diffraction and multi-reflection within a harbour can also be solved with serial applications of random wave diffraction.

Diffraction calculations for breakwaters are often based on SOMMERFELDs solution, which is mathematically exact for thin full-reflecting walls. For breakwaters with low reflecting frontsides, and if guidewalls are used, commonly a modified solution is applied, reducing the second term of the solution- formula proportional to the degree of reflection.

It could be shown that this approach is not sufficient in the region just behind the breakwater, especially for small angles of wave attack.

Regarding the exact solution for wedges it was possible to determine a special weighing factor for the second term of the SOMMERFELD solution, dependent on the degree of reflection and the wave direction, which leads to a better agreement between model tests and theoretical results.

The paper deals with a mathematical method to calculate wave heights in harbours caused by diffraction and reflection. Using the complete SOMMERFELD-solution for a semi-infinite breakwater, a linear superposition method is applied. The reflections of the harbour boundary are taken into account using a geometric mirroring principle.

The computer-programme allows the phase-correct superposition of any number of wave systems and, therefore, also the consideration of re-reflections which can be important in the presence of vertical walls. For the presentation of results (K’-lines) an interpolation-plot-programme is used.

The computer-programme has been applied to the harbour Greenville extension (Liberia) (BURKHARDT, 1977). Hydraulic model tests were performed to check the programmes, especially with respect to the influence of harbour reflections and the layout of the breakwater head.

By superimposing solutions due to Sommerfeld, a calculation was made to obtain the wave height distribution around permeable breakwaters in a constant water depth. The cases dealt with were a semi-infinite breakwater, a single relatively large gap in a long breakwater and a single detached breakwater all with incident waves normal to the breakwater. Some cases were verified through experiments in a shallow water basin.

The finite element method and boundary integral equation method are general approximation processes applicable to a wide variety of engineering problems. After a brief description of the combined method, several examples are given for water waves problems : tides, harbour oscillations and waves diffraction and refraction.

Conservation of wave crests and wave action is introduced to yield the new wave length L₂ and new wave height H₂ as a wave train of plane incidence crosses a shearing current; refraction angle a is determined by Snell's law. Input parameters are water depth h (assumed constant), absolute wave period T_a, angle of incidence α₁, current velocities U₁ and U₂ (see Fig 1), and initial wave height H₂. Solution domains are also given, analytically and graphically. The numerical results for L₁, L₂, α₂, and H₂ are presented non-dimensionally in a number of figures, with dimensionless input parameters. As a direct illustration of the effect of the shearing current, a sequence of graphs are presented, showing in dimensional form the variation of L₂, α₂, H₂, and steepness S₂ = H₂/L₂ with U₂ for fixed values of h, α₁, U₁, T_a, and H₁. Large positive and negative currents can increase the steepness significantly. The variation of S₂/S₁ with Ta and h is finally depicted, demonstrating the "filtering" effect of a shearing current on waves.

A numerical example shows how simple it is to calculate accurately quantities L₁, L₂, α₂, and H₂.

This paper presents some experimental results of wind waves generated on currents in a wind-wave channel with a water circulation pump system. The waves were measured at fetches less than 27.8 m by using resistance-type wave gauges. Surface velocities as well as velocity profiles in water were also measured elaborately and true frequency wave spectra were obtained from observed apparent spectra which were modified by the doppler effect of current.

Significant wave heights H_1/3 computed from $\stackrel{-}{{\eta }^2}$ and peak frequencies of true specyra f_0m were examined with emphasis. It was inferred from the variation of true spectra that the most prominent effect of water current is to change the effective fetch length. Then an idea of equivalent fetch length was proposed to express the current effect on the development of total wave energy.

By using the equivalent fetch F’ in place of the natural fetch it is shown that H_1/3 and f_0m measured under various current conditions can be represented by the non-dimensional fetch relations, respectively, which were originally obtained in the case of no current.

Simultaneous measurements were made of the offshore directional spectra of gravity waves, and longshore currents within the surf zone. The goal was to test theories which suggest a direct relationship between mean longshore currents ($\overline{\text{V}}$ ) in the surf zone and offshore values of the offaxis component of radiation stress (S_XY). Seventeen minute averages of both S_XY and $\overline{\text{V}}$ showed considerable temporal variation, and little or no tendency to vary together. There was also considerable longshore spatial variability of the longshore" current. Attempts to measure gradients of S_XY in the surf zone failed because of small errors in instrument orientation. The measurements suggest that considerable temporal and spatial averaging will generally be required to obtain a representative picture of longshore currents, even if no rip currents are present, due to the presence of “eddy” motions or long edge waves.

Nodal lines normal to the shoreline of infragravity low mode edge waves in the nearshore zone were observed with eleven wave staffs simultaneously with the nearshore current spatial velocity field on a gently sloping beach. About five peaks were found in the energy spectrum and their frequencies agreed well with cut-off mode edge waves [Huntley(1976)]. Based on the above observation, conceptual models of nearshore current patterns for the infragravity domain are proposed and general current patterns for the three domains are discussed by combining the horizontal patterns of Harris(1969) and the vertical patterns of Sasaki et al.(1976).

Results from a two-dimensional numerical model for nearshore circulation induced by waves and wind are compared with observations made during two storms at a beach on Lake Michigan. Model-input data include bathymetry, offshore wave characteristics, wind histories, and local water-level changes. The predicted locations of the breaker zone are in rough accord with those observed during the storms. Data for comparison with model results consist of wave and current observations across the surf zone, especially those acquired by using a towed, instrumented sled. The comparisons show that the model often predicts peak currents near the breaker zone quite well, but underestimates the decay of wave height and the strength of longshore currents across the surf zone. Wave breaking on the bar-trough beach structure prevalent in this study apparently is not well represented by the model. An improved breaking criterion, treatment of breaking waves as traveling bores, and inclusion of horizontal mixing of momentum might add to better simulation of surf-zone currents.

Mass, momentum and wave action conservation laws, including the radiation stress, are used to obtain a rip current spacing as an eigenvalue. A coastal region is divided into two parts: offshore region and surf zone separated by a breaker line. Only the case of normal incidence of the waves is considered. From the matching conditions of the two horizontal velocity components at the breaker line, we can obtain rip current spacing as a function of a nondimensional parameter characterizing the surf zone, for an arbitrary value of a parameter indicating the strength of horizontal mixing.

A systematic experiment to study the wind-induced flow phenomena was conducted in a laboratory tank. The results are related to the wind friction velocity and subsequently scaled for applications at various fetches under different wind velocities. The wind-stress coefficients are found to be well scaled by the Froude number. The bottom friction is measured with an effective shear gauge. The ratios between the bottom stress and the wind stress are obtained. The complete profiles of wind drift current are measured under various wind velocities. A tentative distribution of drift currents in the whole water depth is proposed. The results from the experiment are used to examine the wind-induced flow phenomena in a closed basin.

The drift speed of small floating objects subjected to periodic waves was investigated experimentally. Although data scatter is evident, the results show reasonably good agreement between Stokes third order mass transport drift speed and the drift speed of small surface floats, for the lower wave amplitudes. For the steepest waves there is good agreement between the data and recent developments of Longuet-Higgins. Surprisingly, the objects of deeper draft, such as a small spar-type buoy, drifted faster than the Stokes drift speed in the lower amplitude wave region of the tests. In the steepest waves the deeper buoys drifted a bit slower than the small objects.

A vertical current profile has been measured with three acoustic meters 60 cm, 100 cm and 200 cm from the sea bottom. The depth at the measuring site was 84 metres. The profile is found to depend on the time scale of the water particle motion. An Ekman-like turning of the current is also observed, and the thickness of friction layers is estimated. Comparison of the current data with wave measurements indicates that the vertical transfer of surface wave energy is 30-50 per cent less than first order wave theory prescribes.

This paper considers a method of deriving the probability of occurrence of extreme sea levels by combining the probability functions of surge and tide. As a result the quantity of data required is less than with traditional methods. The philosophy of the method is discussed and the conditions under which the theory can be applied are examined. Finally the technique is applied to a number of ports in the United Kingdom and the results are compared with known estimates of extreme levels.

Along the south coast of England, series of observed annual maximum sea levels, ranging from 16 years to 125 years have been analysed for each of 10 ports. The Jenkinson¹ method of analysis was used to compute the frequency of recurrence of extreme levels. For a number of these ports the series of annual maxima are shown to have significant trends of the same order as those for mean sea level. The Jenkinson method can be simply adjusted to cope with maxima having a component linear trend, making it possible to allow for such trends in computing the frequency of recurrence of extreme levels. If a trend in the annual maxima varies throughout the sample of observations it is shown that difficulties arise in using the Jenkinson method to compute acceptable statistics. It is also shown that for certain ports having long series of observed annual maxima it may be necessary to restrict the sample size of observations in order to compute estimates of the recurrence of extreme levels within reasonable return periods.

The North Sea as a very shallow sea with high wind set-up effects is acting highly as extremely sensitive measuring equipment for climatic changes, especially for surge producing weather conditions. The flood disaster in the Netherlands 1953, in Germany 1962, the Adolph-Bermpohl-Orkan (1967), with mean wind speed of 37 ra/sec. over 5 hours, the strong continental storm with high damages in the forests from France till Poland in November 1972, a series of 6 heavy floods in November/ December 1973 and two extreme floods in January 1976 with the highest water levels ever registrated in the German bight are indications for some changes in meteorological conditions.

The authors suggest a storm tide forecasting method that allows high water predictions for a coastline 3 to 4 hours in advance with an accuracy of ± 30 min in time and ± 20 to 30 cm in height. It is based on actual (not on predicted) data, i.e. exact wind velocity and direction data from a reference station and tide data from two gauges. The method was developed by analysing storm surge curves and wind data of those 50 storm tides that occurred since 1965 in the German Bight. Another 50 storm tides back to the year of 1930 were taken into account, though without exact wind data.

The present state of the development of an operative storm surge prediction system in Germany is described. It is based on numerical models of the atmosphere and the North Sea. First simulations of the storm surge on Jan. 3, 1976 yield the result, that the observed water levels along the North Sea coasts can be recalculated quite well using a meteorological input derived from observations, Whereas the forecasted water levels, using the predicted geostrophic winds of the atmospheric model, are too low since the pressure gradients are too weak.

A series of storm surge recalculations with observed and predicted meteorological data shall answer the question, wether parameter fits, applied to the predicted wind stress, lead to satisfying results, suitable for practical applications.

First results of a wave investigation program in the Outer Weser (German Bight of the North Sea) point out, that under storm conditions higher waves than computed by the normal prediction methods are possible in the exterior estuary. In the interior estuary higher waves occur mainly as a sort of swell. The influence of bad weather conditions on the probability of runs of waves with H*> H 1/3 is shown in two examples in comparison with a theoretical investigation.

Coastal flooding in developed areas can be catastrophic. As an essential element in coastal water level prediction, a two-dimensional numerical model of long period wave behavior is presented. The time dependency is treated implicitly for cost-effective simulation of coastal flooding from hurricane surges or other hydrodynamic phenomena such as extratropical storm surges, tides, tsunamis, etc.

An important feature of the model is use of a coordinate transformation in the form of a piecewise exponential stretch. Such a technique permits simulation of a complex landscape by locally increasing grid resolution and/or aligning coordinates along physical boundaries.

The model is applied to Galveston Bay, Texas, for storm surge and coastal flooding from Hurricane Carla 1961. Verification for the Galveston area was accomplished by using physical model data from simulations of free gravity waves (tide and design surge). Subsequent hindcasting of Carla produced good agreement between observed and computed surges with a mean absolute error of 0.18 m for peak elevations.

This paper describes how a two-dimensional numerical model of the North Sea was used to determine optimum positions for the deployment of off-shore tide gauges during the JONSDAP '76 oceanographic exercise.

A three-dimensional model of the North West European Shelf is also described. Using this model the three-dimensional distribution of the M₂ tidal current over the shelf has been computed. This model has also been used to compute the wind induced circulation of the North Sea for the INOUT period of JONSDAP '76.

Numerical modelling of rivers, estuaries and shallow seas has attracted increasing interest over the last two decades. The models have developed from one dimensional (ID) applications to tidal propagation and flood routing through two and, finally, three dimensional applications to motions ranging from “pseudo-turbulence” to annualmean residual flows. The present account describes the development, over the last five years, of the modelling studies carried out by the author concerning the hydrodynamics of the southern North Sea and River Thames. The objective is to identify those major points which have emerged that may have a wider significance.

A three-dimensional morphodynamic model of sequential beach changes Is presented. The model Is based on variations in breaker wave power generating a predictable sequence of beach conditions. The spectrum of beach conditions from fully eroded-dissipatlve to fully accreted-reflective is characterised by ten beach-stages. Using the breaker wave power to beach-stage relationship the model Is applied to explain temporal, spatial and global variations In beach morphodynamlcs.

A mathematical model for long term shoreline evolution is developed. The combined effects of variations of sea level, wave refraction, wave diffraction, loss of sand by density currents during storms, by rip currents and by wind, bluff erosion and berm accretion as well as effects of man-made structures such as long groin or navigational structures and beach nourishment are all taken into account. A computer program is devloped with various subroutines which permit modification as the state-of-the-art progresses. The program is applied to a test case at Holland Harbor, Michigan.

Field observations of beach and inshore morphology and of surf and inshore current spectra using an array of pressure transducers and low-inertia bidirectional flow meters interfaced with an in-field mini-computer/logging system have been replicated on several beaches in southeastern Australia under a range of energy conditions. Two broad extremes of beach conditions are distinguished spatially and temporally: (1) reflective systems In which much of the incident wave energy Is reflected from the beach face; and (2) dissipative systems with wide surf zones and high turbulent viscosity. Reflectivity increases as the ratio of wave steepness to beach (or bed) steepness decreases. Compared to steep, unbarred reflective beaches which are common in deeply indented or partially protected compart-, ments, the topography of exposed dissipative systems is more complex and varied: six time-and-environment-dependent morphologic types with different bar patterns and bar-beach relationships are recognized. The greatest total dissipation prevails In regions of most abundant inshore sediments or during and immediately after severe storms. Between the reflective and dissipative extremes there is a hierarchy of observed resonant frequencies with the highest frequency resonance occurring in the most reflective cases. Results indicate that near the beach face, motions associated with resonance at periods greater than incident wave periods exhibit strong net seaward resultants and are probably important sources of beach erosion. Reflective beaches are sensitive to resonant excitations over a wider range of frequencies and under lower energy conditions than are dissipative beaches. Hence, although reflective beaches represent the accretive end point of a “beach cycle” they are also more delicately poised with a higher potential for erosion.

High rates of weathering, abundant rainfall, and high discharge rates combine to supply large volumes of sediment to the coastal zone of eastern Nicaragua. This terrigenous sediment is confined to a narrow section of the inner shelf (<30 km wide) due to the circulation pattern within a coastal boundary layer. Sediment transport within the inner shelf and shore zone is to the south. This simple transport pattern is considerably modified by variations in wave-energy levels that are a function of shelf width, bottom friction, and wave sheltering. In northern sections, the shelf is up to 200 km wide but narrows to less than 20 km in the south. A direct result is that wave-energy levels at the shoreline are of the order of three times greater in the south. In the north the Rio Coco delta is prograding seaward in a fluvially dominated environment, whereas the Rio San Juan delta in the south has a wave-dominated morphology characterized by deflected distributaries. Other major accumulation features have developed where wave-shadowing is produced by offshore reefs and cays. Alongshore a spatial variation was recorded, with straight beaches and simple linear bars in the north that change to rhythmic beach topography and crescentic nearshore bars as wave-energy levels increase toward the south.

Sediment dispersal patterns in tidal inlets within the German and the Georgia Bights are found to be controlled by three major environmental factors: (1) the tide range, (2) the nearshore wave energy, and (3) the geometry of the backbarrier bay. Both embayments chosen for study are characterized by high wave energies and low tide ranges on their flanks, and low wave energies and high tide ranges in their centers. The spatial variability in inlet morphology, therefore, contains information on the relative role of tides and waves in inlet sediment dispersal. The paper concludes by proposing a simple model for inlet morphologies for successively greater relative role of tidal currents in the sediment dispersal.

The Atlantic Coast of Delaware consists of four separate but continuous segments including (from north to south): (1) a northward-projecting spit complex (Cape Henlopen); (2) eroding Pleistocene headlands; (3) a linear coastal washover barrier; and (4) an area of migrating inlets with associated modern and relict ebb and flood tidal deltas. Coastal process studies show that continuing coastal erosion is accompanied by longshore transport of sand eroded from headlands, offshore transport to the nearshore marine area, and overwash processes transporting sand landward across the barrier. Studies of the adjacent nearshore marine area show that the barrier and its various geomorphic elements lay at the outer edge of the continental shelf approximately 12,000 years ago, and migrated landward and upward to the present position as the Holocene marine transgression continued. The sequence of coastal sediments of the barrier system consist of (landward to seaward) tidal marsh fringe, lagoonal muds and sands, barrier sands (including washover, dune, and beach deposits), and shallow nearshore sand and gravel. Drill-hole studies provide information on the subsurface configuration of the barrier from which the three-dimensional structure and stratigraphy of coastal sedimentary environmental lithosomes may be defined.

In planning and operating coastal harbors subjected to shoaling, it is imperative that the characteristics and regime of the sediments which deposit in the harbor entrance be quantified to the maximum extent possible in order that the economic impacts of the channel shoaling and along adjacent shores may be evaluated.

This paper presents a brief progress report on the study of a coastal harbor in an area subjected to shoaling. This study represents the input of many engineers and researchers in the United States.

Studies were undertaken to document the past and present characteristics and trends of Delaware’s two major tidal inlets, Roosevelt and Indian River Inlets.

It was found that both inlet complexes are effective sediment traps causing considerable downdrift erosion. The major mechanism by which sand enters Indian River Inlet is by overtopping the impounded south jetty. At Roosevelt Inlet sediments are readily transported past the severed steel sheet pile jetties.

The results of a one-dimensional hydraulic model, as well as field measurements, predict the presence of a mean southerly flow through the canal and bay system which connects these two inlets. This flow is shown to have a substantial effect on the behavior and stability of these entranceways, causing major assymmetries on the depositional patterns at each location. Roosevelt Inlet was found to have a strong tendency to trap sediment within its throat; whereas, Indian River Inlet, on the opposite end of the system, was found to retain large quantities of sand on its developing ebb tidal shoal.

A spatially integrated one-dimensional numerical model of inletbay hydraulics has been combined with a simple sediment transport model to investigate selected tidal inlet-bay system characteristics. A parametric study has been performed using the models to determine the effect of various factors on the net direction and order of magnitude of inlet channel flow and sediment transport. Factors considered include astronomical tide type, storm surge height and duration, variation in bay surface area, time-dependent channel friction factor, and the addition of a second inlet connecting the bay and sea.

Fast-response electromagnetic flowmeters were used in a marginal flood channel of an ebb tidal delta to assess the importance of wave contributions to the flood dominance of these channels. Measurements were made at a single point in the channel in both ebb and flood currents. The oscillatory motion of waves was a very significant feature of the velocity records, and its magnitude was comparable with the mean flow at all stages of the tide. This observation shows that flowmeters capable of responding accurately to wave velocities are needed to obtain accurate values of mean flow. Some earlier measurements made with slow response flowmeters are probably unreliable. Wave contributions to the mean flow were assessed by looking at the correlation between the low frequency (> 17.5s) oscillations of the along-channel current and the low frequency envelope of the wave velocities. Surprisingly little correlation was found for any time lag, suggesting that wave effects were not important in the mean tidal currents in the channel studied. However, close to low tide on the ebb, conditions existed which appear to have been favourable for the “wave pump” mechanism suggested by Bruun andViggisson (1973). Significant correlation between the wave envelope and low frequency fluctuations was observed at this time. It is therefore suggested that wave effects can be important to the mean flow in marginal channels with rapidly converging and shoaling mouths which are oriented towards the dominant incident wave direction.

The edge wave hypothesis for periodic inshore morphology and circulation is tested for five beaches and is supported by resulting wave-current spectral and cross-spectral data. Beach types range from a reflective, narrow surf zone, case through various dissipative medium to high energy beaches including some with inshore bar-trough morphology and one broad surf zone troughless one. In all cases beachface reflectivity is moderately high (E < 2.5) and inshore resonance occurs, indicated by strong spectral peaks at lower than incident frequency with wave-current co-peaks being 90° out of phase. Several different edgewave frequency and mode combinations are indicated. The reflective beach shows an n = 0 subharmonic edgewave (i.e. at half incident wave frequency) which Guza and Davis (1974) predict as the most likely case, viz. the (0,0) triad. The troughless dissipative case shows a (1,0) edgewave triad; the same occurs in some bar-trough dissipative cases but in other cases is supplanted by the (0,0) sub-harmonic wave and/or by a lower subharmonic wave at ¼, incident frequency. The likelihood of a given edge .waveset appears to be regulated by surf friction, and a change of edge wave set appears likely to explain observed changes of inshore circulation.

Beach cusps are very common, concave-seaward cuspate patterns at the shoreline of a beach, which tend to occur with a regular longshore spacing, but which can have a wide range of longshore wavelengths from a few centimeters to several kilometers or more. Edge waves, resonant waves trapped at the shoreline by refraction, have been suggested as the cause of beach cusps but it has proved difficult to establish a definitive link on natural beaches. This paper describes field measurements of nearshore velocities, in all three orthogonal directions, that show the presence of edge wave motion just before the formation of beach cusps of the corresponding wavelength, and thus provides convincing evidence that edge waves are responsible for beach cusps. The magnitude of the observed edge wave oscillatory and drift velocities are found to be large and apparently well able to form cusps of the observed size. The observed edge waves are at the subharmonic of the incident wave frequency and thus are the field equivalent of the laboratory observations of Guza and Inman (1975) and Guza and Bowen (1977). It is not clear, however, whether the developing cusp topography enhanced or suppressed the edge wave motion.

Bakker (1974) developed a mathematical model concerning the sand concentration and velocity distribution in an oscillatory turbulent flow, with or without resultant current.

The flow is assumed to be uniform in horizontal direction. The present paper reports on an experimental verification of this theory. Furthermore, the numerical accuracy of the model has been investigated and diagrams are presented which enable the computation by hand of global velocity profiles.

This paper evaluates, through the use of a stepwise multiple regression procedure, whether parameters descriptive of the surf-zone wave field adequately explain the variability in longshore current velocities, or if the inclusion of additional physical environmental parameters could significantly improve the ability to predict such currents. The data set consists of 250 LEO — observations, collected on a seasonal basis over one year, at Debidue Island beach, South Carolina.

A regression analysis was performed both on linear combinations of all measured wave parameters, and on nonlinear parameter combinations proposed in various semiempirical predictive equations. Invariably, in all the regression analyses, the longshore component of the wind velocity proved to be the independent variable explaining most of the observed variance in the current velocity. Therefore, the statistical data analysis presented in this paper strongly suggests that wind stress can be a most significant factor in surf-zone current generation.

By use of a synchronized camera system, multiband black-andwhite photographs and conventional color photographs were taken respectively with the purposes of testing filters available for shallow-water photographic bathymetry, and of checking the availability of low-cost process imagery for the study of coastal processes. Kodak Wratten filters 29, 58, and 90 were employed for the multiband photography. A Wratten 90 filter provided the best correlation between water depth and the photographic density. The low-cost imagery, obtained in a laboratory from the color photographs by applying ordinary filters without using any expensive image processing devices, proved to be useful.

Underwater bars, the characteristic features of oceans and lakes occur singly or in a series along the coast. Nearest bar to the shore, namely the break-point bar moves shoreward in summer, joins the coast and is replaced by another bar in its original place. The other seaward bars are storm bars, more or less permanent though they may shift slightly in orientation, position and shape depending upon the wave climate and state of the coastal processes. With the sediment and bottom profiles changing constantly with differing wave characteristics and beach exposure, a rigorous mathematical analysis for long range variability of profiles and therefore coastal processes in not possible. Therefore, the concept of medium depth and steepness characteristics is introduced to distinguish the profiles and their major dimensions.

Onshore-offshore sediment motion is sometimes far in excess of longshore transport mostly confined in the breaker zone. When submarine bars are present, such motion is considerable mainly as a result of the hydrodynamic reaction between the rotating eddies generated over the bars and the bar surface. By means of dimensional analysis, it is possible to relate the quantity of onshore-offshore motion to the bar dimensions, wave period, water depth and transport direction by profile steepness characteristics.

The above two concepts are then applied to the Nile Delta coastal processes with satisfactory results.

A theoretical model is developed for the movement of loose sediments in oscillatory flow with or without a net current. In the present formulation the model is two-dimensional, but may readily be extended to three dimensions.

It is assumed that all movement of sediments occurs in suspension, and exact analytical solutions are given for the time variation of the concentration profile, the instantaneous sediment flux and the net flux of sediment over a wave period. The model requires as empirical input a diffusion coefficient e and pick-up function p(t), for which experimental data are presented. Two examples are discussed in detail, illustrating important aspects of the onshore-offshore sediment motion.

A sediment entrainment parameter is used to calculate maximum water depth for intense bed agitation by shoaling linear waves of given height and period. Calculated limit depths agree with available laboratory measurements of water depth at an erosive wave cut into slopes of quartz and other fine sediments. Ignored variables have small effects on the agreement between calculations and laboratory measurements. On natural seasonal beaches, available measurements of seaward limit to appreciable sand level changes agree with limit depths calculated for extremely high waves expected 12 hours per year. The apparent accuracy and lack of scale effect in the calculated limit depth justify several applications in field and laboratory projects.

A coring technique employed during wave action allowed accurate measurement of the depth of vertical mixing bm of fluorescent sand tracer grains within the surf zone of a gently sloping Pacific Ocean beach (beach slope tangent s = 0.012). The depth bm is the distance from the sediment surface to the lower limit of observed tracer grains within the inner portion of the core. Although this definition is only strictly applicable to a rectangular distribution of tracer concentration with depth, the bm results were quite similar to those using concentration-weighted depth averages of Crickmore (1967). For one winter regime experiment, vertical cross-sectional contour maps of tracer concentration normalized by the local core maximum were drawn with concentrations computed for each 0.4cm slice. Trends present are (1) in the onshore-offshore direction the maximum concentration is at the bed surface shorewards of the mid-surf position and 0.4 cm to 1.2 cm below the bed seaward of the mid-surf position, and (2) in the longshore direction (at the mid-surf position) the maximum concentration lies 0.4 cm to 1.6 cm below the bed surface. For spilling breaker heights Hb between 75 cm and 150 cm, histograms of bm were clearly different for spring/summer and fall/winter experiments: the mean and standard deviation (in parenthesis) are 0.5 cm (0.5 cm) and 1.1 cm (0.5 cm), respectively. These results are substantially less than both the 3.0 cm and the 20 cm to 40 cm disturbance depths per 100 cm of Hb reported by King (1951) and by Otvos (1965) and Williams (1970). The discrepancy with Otvos and Williams is due to the much different breaking process; in their experiments small breakers (Hb = 5 cm to 30 cm) plunged directly onto steep beach slopes (s = 0.1) causing large bm- The tracer grain’s longer exposure to bottom stresses of passing surf bores may explain King’s greater disturbance depths. Her sampling interval was one semi-diurnal tidal period T versus the span 0.02 T to 0.32 T in this study.

The scale relation for modeling natural beach profiles in the laboratory and selecting size of model sediments is examined. The results are shown for relating scale law to the dimensionless fall velocity and the model law for selecting sand size is proposed.

This paper describes an experimental study of sand motion on the seabed caused by surface water waves. The observations were made close to a beach, but outside the breaker zone and in a location where steady currents were small. Measurements of water velocity components were made at various heights above both rippled and flat beds, together with measurements of the pressure gradients at the seabed, in order to examine the threshold of motion of the natural coarse sand (D_so≈1.4mm). This motion was monitored with an underwater television system. The flow conditions were predominantly laminar and no flow separation occurred above the lee slopes of the ripples.

Sediment motion was of ’bed load’ type and was confined to the crests when the bed was rippled. This motion has been found to be caused by waves having an orbital velocity amplitude (measured in the free stream flow) of about one half of that required to cause motion on a flat bed of the same material. Wherever possible the threshold measurements have been compared with results obtained in the laboratory.

The relative importance of forces on the seabed induced by velocity and pressure gradients has been assessed. It appears that the latter effects are of little or no importance in situations of the kind described, as suggested elsewhere in the literature.

The distributions of longshore and on-offshore sediment transport rates in a surf zone were measured by an apparatus which was able to separately record both components of the sediment transport rate. The characteristics of their distributions were discussed from the bottom shear stresses which were measured by the shear meter under the same wave conditions as the laboratory experiment of the sediment transport.

The maximum bottom shear stress took place at the depth between the breaking depth of waves and the depth where the velocity of the longshore current showed a maximum. On the other hand, the maximum onoffshore and longshore sediment transport rates occured at the depth slightly shallower than the depth where the maximum bottom shear stress took place. What’s more, the longshore sediment transport rates were represented by the longshore current velocity and the bottom shear stress generated by waves and the longshore current. However, the distribution of the on-offshore sediment transport rates showed more complicated profile than that of the longshore sediment transport rates because there were no eminent unidirectional flow in the direction normal to the shore line. Therefore, the on-offshore sediment transport rates could not be formulated by the bottom shear stresses.

A technique is proposed for calculating sediment load, the mass concentration of sediment in motion, under combinations of waves and currents. The technique is based on the unidirectional flow method of Ackers and White, Ref. 1. The calibration of the technique against measurements of sediment load under waves has only just begun.

Water velocities and shear stresses have been determined for a laminar boundary layer of a progressive wave travelling over a regular series of ripples. The Lavrentiev variational method was used to transform conformally the water area with ripples into a strip with flat bottom, while the Lin approach permitted solution of the boundary layer equation.

The theoretical prediction of the bed friction was verified experimentally with a new mechanical apparatus.

By coupling the theoretical shear stress at the rippled bed with laboratory data for ripple parameters one can expose the friction conditions that control the growth and decay of ripples. If waves develop higher values of shear stress, the rippled bed becomes gradually washed out. Eor known shear stresses, basing on the Erijlink-Bijker formula one can compute sediment transport rates. In the respective diagram, a curve of s.t. rate versus bottom friction consists of two branches. The stages of the growth and decay of ripples are reflected in the lower and upper branches of the curve. For identical ripple height there are two values of s.t. rate, for two different wave intensities, likely to differ by as much as 25 per cent.

Three-dimensional ripples have been analyzed with regard to bed friction and compared with two-dimensional conditions.

Alongshore sediment transport rate was studied in a 3-dimensional mobile bed coastal model and was found to depend on the beach profile and rate of wave energy dissipation in addition to the normal wave and sediment parameters. Alongshore sediment transport rate was found to be strongly related to the surf similarity parameter, a single parameter simplistically describing beach profile and breaker type.

To examine the longshore transport processes of beach gravels under wave action, a field experiment was performed by tracing the dacite blocks injected on Fuji Coast, Shizuoka Prefecture, Central Japan.

The mean dislocating velocity of the tracer was 2 to 3 m/day under normal sea conditions, while under storm conditions it reached about 400 m/day. This velocity was fairly proportional to the longshore component of incident wave energy flux.

The longshore variations of the size and shape of beach gravels were mainly resulted from the progressive attrition and impact breakage of beach gravels rather than from the selective transport.

A major drawback of all existing tracer techniques for monitoring shingle movement, except that of labelling with radioactive isotopes, is that tracer recovery rates are invariably low, (commonly less than 15% of the total injected) because recovery is limited to the beach surface. Investigations were made into the possibilities of developing a new tracer that might overcome this problem.

The paper describes the results of, and the conclusions drawn from two trial field experiments carried out using metal tracer pebbles. These had specific gravities, size and shape similar to the indigenous beach pebbles, and were recovered both on and beneath the beach surface using metal detectors. By assessing the relative merits and drawbacks of the technique it was concluded that the use of metal pebbles as tracers for shingle beaches is more practical than other methods for most tracing purposes. At present the technique is best suited to investigations ranging in length from a few days to a few months and requiring small to medium-scale injections of 5000 tracer pebbles or less. The considerable scope for the further development and application of the technique is discussed.

We introduce here a numerical two dimensional model for sediment transport which permits to compute the impact of a coastal structure on the bottom evolution.

The introduction of current disturbance and some assumptions using difference of time scale between current and bottom evolutions permits to obtain a propagation equation driving the bottom evolution. The model has been calibrated in the case of the local scour around a jetty. At last, it has been applied to the bottom evolution in the vicinity of the new port of Dunkerque.

Suspended sediment concentration was measured in approximately 250 breaking waves on undeveloped beaches near Price Inlet, South Carolina, U.S.A., using portable in situ bulk water samplers. As many as 10 instantaneous 2-liter water volumes were obtained in each wave for a total of 1500 samples. Concentrations of suspended sediment were determined at fixed intervals of 10, 30, 60 and 100 cm above the bed for various surf zone positions relative to the breakpoint. The majority of waves sampled during 22 days in June and July, 1977 were relatively long crested, smooth, spilling to plunging in form, with breaker heights ranging from 20 to 150 cm. Surf zone process variables measured included breaker height and depth, breaker type, wave period, surface longshore current velocity, wind velocity and direction.

The present paper is an attempt to determine a single curve for the prediction of the length of ripples forming due to wind waves in shallow waters. The curve is revealed by normalising the field and laboratory data supplied by various authors. The concept of the unified plot embodied by the single curve mentioned is developed by using dimensional methods and by considering the fact that the specific weight and the density of the cohesionless bed material do not affect the length of ripples in a detectable manner. It is shown that the present formulation of the length of ripples due to waves satisfies the requirement of transition into the corresponding formulation of the unidirectional flow ripples when the period and the amplitude of the oscillatory motion increase indefinitely, while their ratio (implying “the velocity”) remains finite.

Three numerical models representing shoreline response are desscribed and applied to a number of problems of coastal engineering interest. Included are: (1) a one-line explict model, (2) a one-line implicit model, and (3) a two-line explicit model. Simplified refraction and diffraction schemes are incorporated into the models. The models allow grid elements to be activated and deactivated as sand is initially deposited in or the last sand removed from a grid at a jetty inclined to the shoreline. The one-line explicit model and twoline explicit model are similar to those described by Bakker, Breteler and Roos(3). The one-line implicit model offers the advantage of stable computations for much longer time steps.

In 1972, a beach nourishment scheme was to delay the steady coast erosion near Westerland (Germany). Morphologic investigations state the development of the fill and its effects to adjacent beaches, and yield recommendations for another nourishment scheme in 1978.

The morphologic analyses are related to two different profile areas. They show that the effects of the nourishment were quite confined in space and time. Particularly the island base and the bar remained unaffected by the fill.

The analysis becomes more instructive and perhaps easier by the use of special means, such as the differential morphometric characteristic and the mean profile depth instead of mass computations or mass balances. The standard mean depth in the morphologic system of the investigation area is found to be NN-4,1 m.

Beach nourishment models commonly employed by the U.S. Army Corps of Engineers compare textural properties of native beach and dissimilar borrow sediments to determine overfill and renourishment requirements for beach fill projects. It is assumed for these comparisons that the texture of borrow sediments is unchanged by dredging and handling operations but investigations have shown that significant handling losses do, in fact, occur.

This paper presents results from four field studies that document textural changes caused by dredging and sediment handling at Rockaway Beach, NY, and at New River Inlet, NC. Errors associated with calculating volumes of sediment dredged and lost using standard surveying and production methods are discussed and an alternate method is presented as a handling-loss model that compares bottom and dredged sediment texture to determine volumes lost.

Coastal defense up to the present has employed seawalls, groynes and renourishment, all of which do not tackle the basic problem of lack in sediment supply from upcoast. The need is for sufficient sand to be continually available for the formation of the defensive offshore bar. If means are provided for this material to be returned directly on shore by subsequent swell, a stable situation 'ensues. Such normal re-deposition occurs within bays formed between headlands which have reached equilibrium shape or nearly so. Comparisons are made between various stabilization procedures. The influence of sand characteristics in renourishment is discussed.

Stabilization of coasts has been carried out over many decades. The remedies have taken three major forms, namely, seawalls, groynes, and in more recent times sand renourishment. Whilst shapes and orientation of these structures have been varied in order to optimise protection, engineers in the main have relied upon bigness for greater reliability. Investment in dredging to supply sediment “temporarily” to beaches is growing prodigiously. It is now time to sit back and reassess the situation, so as to determine a change of outlook, be it only slight, that may effect greater long term economies.

A method is presented, and illustrated with examples, for calculating planforms for a class of “pocket” beaches. This type of pocket beach is formed of mobile sediment due to waves diffracting through an opening in erosion resistant material, for example behind a break in a revetment or behind closely spaced offshore breakwaters. The opening is considered as a series of sources with circular wavelets radiating landward from each element. The height and phasing of each wavelet is varied depending on whether the depth at the element limits the wave height and on the wave direction relative to the opening, respectively. Based on reasonable, but not complete, considerations of sediment transport, the equilibrium bathymetry is considered to exist when the wave front is everywhere tangent to the local bottom contours. A differential equation is developed for the local orientation of the contours; this equation is solved numerically starting from a reference transect and extending the contour until it intersects the line defining the opening.

Examples are presented illustrating the method for the following cases: (1) normally incident waves diffracting through a single relatively narrow opening, (2) obliquely incident waves diffracting through a single relatively narrow opening and (3) spiral bays which are contained by two relatively widely spaced headlands. In addition, a procedure is suggested for applying the results to the case of normally and obliquely incident waves diffracting through the openings formed by a series of offshore breakwaters.

The suspension and transportation of fluid muds in the nearshore zone by shallow-water, solitary-like waves has been investigated along the coast of Surinam, South America. Accumulations of fluid mud which front the coast at a spacing of 30-60 km affect incoming swell by changing the wave profile from sinusoidal to solitary-like and by preventing wave breaking except for occasional spilling. Simultaneous time-series measurements of wave height and period, fluid-mud density, and tide elevation, along with results of suspended-sediment measurements, indicate that in cases when the bulk density is less than 1.20 g/cm³ and where water depths are less than 5 m fluid mud is suspended from the bottom in two frequency modes: wave-by-wave suspension (~10 sec) and tiderelated suspension (~12.4 hr). Surface-water suspensate concentrations exceed 3.4 x 10³ mg/1 as up to 0.5 m of fluid mud is periodically removed from the bottom.

Processes and sediment transport were investigated in a salt marsh drainage system at Kiawah Island, South Carolina. A general survey of the tidal current was done in the major tidal channel (Bass Creek) for a 10 tidal cycle period in August, 1977. Detailed determinations of current velocity, discharge, and suspended load were conducted during 15 tidal cycles in March, 1977 and again during 8 tidal cycles in July-August, 1977. For each of these periods, mass budget for the total suspended load were computed.

The tidal currents have a pronounced time velocity asymmetry with the maximum current velocity occurring nearer high slack water and the peak ebb velocity being 20 – 30% stronger than the flood. Suspended load transport is significantly affected by the time velocity asymmetry. Peak current occurring nearer high slack water causes a net displacement of suspended material in an ebb or seaward direction under normal conditions. This process is enhanced by the stronger ebb currents. Mass budgets reflect the ebb dominance of the system showing a net export of combustible (organic) material during the March sampling period and a net export of both noncombustible (inorganic) and combustible material during the July-August period. Also important to suspended load transport in marsh systems are stressed meteorological conditions. High winds or heavy rains increase suspended load concentration and can cause significant import or export of fine-grained material.

Stability studies of natural tidal basin system demand a regime-oriented analysis and a characteristic quantification of the morphological values. Hence it was necessary to create relative form parameterization dependent on the location by means of a two-dimensional system of natural coordinates (z =elevation, s = gully length coordinate).

The harbor of Gros-Cacouna on the South shore of the St.Lawrence Estuary has been silting at the rate of 31 cm/yr. since it was dredged at the depth of 14 meters in 1968. Measurements of temperature, salinity, turbidity, current speed and direction were carried out as well as bottom sampling and reflection seismic profiling. A model of suspended sediment transport combines the tidal volumes and the current profiles at the harbor entrance.

During a period of high turbidity (Spring) in the St.Lawrence Estuary, 54.2 tons of suspended sediments entered the harbor during the flood phase, while 41.1 tons were carried out during the ebb phase of a semi-diurnal tide, leaving 13.1 tons of sediments in the harbor. The transfer coefficient is 0.24 indicating that one quarter of the suspended sediment load settles in the harbor during one tidal cycle. In September, the turbidity is low in the Estuary and the suspended sediment budget in the harbor is 4 times smaller but the ratio of deposited sediments versus the total quantity of sediments transported in suspension is the same.

Field observations are analyzed to determine the primary factors governing the distribution of sediments suspended by clam-shell bucket dredge operations. These data show the plumes produced under typical estuarine conditions to be relatively small scale features having maximum longstream dimensions of approximately 700 m. Plumes can be considered to consist of three contiguous zones: an initial mixing zone, a secondary zone and a final mixing zone. The initial mixing zone immediately adjacent to the dredge has dimensions governed by bucket induced mixing and suspended material concentrations determined by dredge efficiency. Observations indicate that dimensions can be reasonably estimated using wake theory and that efficiencies result in the introduction of 2-4% of the sediment mass contained in each bucket load. Resultant concentrations range between 200 and 400 mg/l. Progressing downstream into the secondary mixing zone concentrations decay rapidly due primarily to gravitational settling. The observed decay rates indicate an average settling velocity of 4.7cm/sec well in excess of values based on the grain size characteristics of the dredged sediment. The behavior suggests significant particle agglomeration within this area. At the downstream limit of this zone distributions become essentially exponential in character and remain so through the final mixing zone. In this area concentrations progressively approach the upstream background levels and variations are governed primarily by diffusion. In each of these zones the observed distributions appear amenable to relatively straightforward modeling.

Oscillations of ground-water table were measured in perforated piezometers distributed across the Baltic beach at the coastal research station of Lubiatowo, Prom spectral and correlation analysis it appears that the most pronounced wind-wave oscillations having a period of about 6 seconds have not been detected in the beach, while longwave oscillations, dominant in the beach spectrum, correlate well with nearshore long waves. Among the longwave oscillations, it is only those having periods about or slightly longer than 100 seconds that obey the Boussinesq law. However, some longer waves may also be generated by the interaction of shorter waves. Oscillations with periods from 50 to 100 s are very coherent throughout the beach. In the absence of stochastic noise and variety of inputs, low values of coherence for other periods indicate presence of nonlinear effects. More light should be shed on the origin of this nonlinearity and theoretical tools should be tried to complement the Boussinesq model.

Coastal structures have caused significant impacts to adjacent shorelines, especially when these shorelines are composed of sand. Many times, these shoreline impacts have not been expected due to improper planning prior to the design and construction of these structures. Consequently, excessive erosion and/or deposition of sediment as a result of these structures has necessitated costly, and in some cases, continuous maintenance operations.

This paper reviews the expected shoreline effects for an offshore pier-trestle and breakwater system for an LNG marine terminal. Coastal structures originally proposed for the LNG marine terminal consisted of a 4,600-foot-long pile supported “T” head pier/trestle system and a 1,000-foot-long detached rubble-mound breakwater. This investigation involved field and historical aerial photographic examination of 30 structures in the Southern California Bight and a literature review of similar structures in other environments. Also, a review of theoretical and physical model studies applicable to structures within the coastal marine environment was conducted.

A seawater intake had to be constructed for a diamond mine on the coast of Namibia just north of Oranjemund. The solution adopted consisted of a piled jetty with a dolos island on its seaward end protecting the pump chamber which was built of closely spaced concrete piles.

This paper deals experimentally with combinations of the pneumatic breakwater and other type breakwaters in order to increase the effectiveness of wave damping.

Firstly, a submerged breakwater is picked up, and the wave damping effect of this combined type breakwater is examined. Results obtained in this experiment show that some improvements on the wave damping are found for low frequency waves that cannot be damped by the pneumatic breakwater only. The reason of appearence of the combination effect is explained that a part of energy of the transmitted waves over the submerged breakwater transfers to shorter period waves.

Secondly, a floating breakwater is combined with the pneumatic breakwater. Experiments show that the transmission factor for high frequency waves becomes smaller than that of the pneumatic breakwater only, while there is not so much wave damping effect for low frequency waves even when the floating breakwater is combined. In addition, a guide plate is set below the bottom of the floating breakwater in order to increase the horizontal flow velocity for a given air discharge. It is found that the velocity of horizontal surface flow by using the guide plate increases as much as about 1.3 times that in the case of the pneumatic breakwater only. As a result, a little improvement on the wave damping due to the guide plate is also found.

It has been found that certain sequences of waves, such as occurring within well defined wave groups, can cause greater damage to rubble mound structures, than equally high individual waves dispersed throughout a wave train. It has therefore been necessary to develop a new wave synthesizing technique, which allows control of the phasing of the wave frequencies, so that a similar degree of wave grouping can be produced in the laboratory as is expected to occur at a particular location in the prototype.

Also, during the course of this investigation, an attempt was made to simulate the strength of concrete armour units to the correct model scale. The breaking of armour units, due to their rocking or being displaced, resulted in a much higher percentage of damage, than would have been possible to predict from tests with commonly used model armour units.

Accuracy and compatibility of measuring and testing techniques are discussed briefly and a plea is made for standardization to avoid, as far as possible, deviations in test results of different laboratories. One of the main causes of these differences is inconsistency in Dolos packing densities and corresponding layer thicknesses or shape factors. In an attempt to alleviate this problem three placing densities, namely ‘light’, ‘mean’ and ‘dense’ have been defined and their physical properties determined. Flume tests with regular waves, and Dolos armour units at these packing densities, showed very little difference in stability and, considering practical limitations during construction, it is suggested that the ‘mean’ packing density be used for a ‘first design’, followed by proper model tests. The results of tests with model Dolosse using three different unit densities were inconclusive and further tests using a wider range of densities are underway.

Tests on 100 gm model dolos units on the bed of an open-channel under steady state turbulent flow reveal that the dolos unit has no inherent interlocking property that would make it preferable to ordinary armour stone of the same weight in resisting movement. However interlocking can occur when dolos units are placed on a slope since the natural angle of repose of dolos units is much greater than that of ordinary armour stone, thus accounting for the enhanced K_D of dolosse in a breakwater situation.

For the design of the storm surge barrier in the Eastern Scheldt, a study has been carried out on wave impacts against coastal and marine structures. First a review was made of relevant literature, including both wave impacts on coastal structures and slamming of sea-going vessels. From this, the so-called Bagnolds piston model emerged as most appropriate to describe the wave impacts caused by standing waves against protruding elements. This model was then further elaborated to include both adiabatic and isothermal compression of the air cushion and to allow for the compression of the water. Moreover, amodel was developed to determine the spatial pressure distribution. Finally, experiments were performed, the results of which were in satisfactory agreement with the mathematical models. Based upon the results of these studies, a scaling law is presented here, from which the pressure magnitude and the time history of the impact in nature may be determined.

For severe storm waves with periods of 7.0 sec to 14.0 sec and heights of 6.3 m to 9.0 m, it was proved that the resultants of the maximum simultaneous pressures exerted by breaking waves on the slittype breakwaters with the optimum relative chamber width of 1/L = 0.05 to 0.07 were in most cases less than 70 per cent of those exerted on the conventional composite-type breakwaters.

This paper describes the dynamic behavior of a fixed cylindrical pile due to both the in-line or longitudinal force and lift or transverse force in regular waves. Resonant response of the pile due to the lift force in the direction normal to the wave propagation direction is discovered at the period ratios of T_w/T_n=2,3,4,5 and 6 (T_w : the wave period, T_n : the natural period of the pile). Furthermore, the resonant responses in the wave propagation direction due to the in-line force also appear at the same period ratios, in addition to the well known resonance point of T_w/T_n=l. Moreover, dynamic displacements of the pile in the direction normal to the wave propagation direction are longer than those in the wave propagation direction when the period ratio is longer than 1.6 and Keulegan-Carpenter number is larger than 6.

Next, for the purpose of the ocean structural design,the methods of estimating the dynamic displacements in both directions and of estimating the dynamic displacements considering both are derived by using Morison’s equation and lift force equation formulated bythe authors. The displacements calculated are compared exactly with the experimental results to investigate the validity of the proposed method.

In order to examine the irregular wave forces on a small diameter cylinder, laboratory experiments have been conducted on water particlen velocities and wave forces with various kinds of irregular waves.

In order to determine wave forces on a row of three cylindrical piles (Figure 2), a numerical computation procedure was applied using a solution of the Helmholz equation, in which the scattered wave field is described as the result of a series of singular sources located along the circumference of the pile [Berkhoff, 1976, reference 1]. Results of the computations were verified by means of model experiments, using both regular and irregular waves.

It is shown that for the two pile geometries, included in the study, strong mutual interference will occur, resulting in transverse forces which are much higher than those found for single piles.

Cooling water from a power generating station in Eastern Canada ispumped to an outfall and distributed into the ocean through discharge ports in the sidewalls of a diffuser cap. The cap is essentially a shell-type structure consisting of a submerged circular cylinder 26.5 ft in diameter and 14 ft high. It is located in 25 ft of water at low water level and 54 ft at high water level. Horizontal forces, vertical forces and overturning moments exerted by waves on a 1:36 scale model of the diffuser cap were measured with and without cooling water discharging from the outfall. Tests were run with regular and irregular waves producing both non-breaking and breaking wave loads on the diffuser cap.

The overturning moments measured on the diffuser cap were up to 150 percent greater than those on a solid submerged cylinder sealed to the seabed. Unlike sealed cylinders, all of the wave loads measured on the relatively open structure reached maximum values at approximately the same time. The largest wave loads were measured on the diffuser structure when it was subjected to spilling breakers at low water level. For a given wave height, the spilling breakers caused wave loads up to 100 percent greater than those due to non-breaking waves.

This paper describes a simple but elegant concept developed for the construction of offshore pile-supported structures in strong current. This tripod concept was developed during design studies for the Carajas Project which required an iron ore terminal at Ponta da Madeira, Sao Marcos Bay, in northern Brazil for mooring ships up to 300,000 DWT in up to 6 knot tidal currents. Experience during the construction of the Immingham oil terminal on the Humber River in England in 1968 had shown that cylindrical steel piles were susceptible to vortex-induced in-line and cross-flow vibrations. The cross-flow vibrations were particularly dangerous and occured mainly during the construction phase when the individual piles could vibrate as cantilevers.

The length of the coastline of Japan is very long, and it exceedes 31000 kilometers. In which, about 19000 kilometers are remained as natural coast, but 8000 kilometers are protected by the seadikes(inclusive of seawalls).

Before 1965, there were about 5900 kilometers of seadikes. Then, we have constructed more than 2100 kilometers of seadikes during the past ten years.

In Japan, sea and shore are all under the control of the Government, and 8000 kilometers of coastal structures have been constructed or improved as the Public Works. Before 1945, however, most of seadikes, though their length were not so long in that age, were constructed as reclamation works by private, and after the War, these private reclamation seadikes were changed to the government management and have been improved as the public works. These former seadikes were almost for the storm surge.

In this paper, the general features and mechanism of scouring at the toe of a seawall due to tsunami invasion are discussed based upon the results of two-dimensional experiments. The effects of the various slopes, bed material, water depth and wave conditions are separately investigated. After some consideration of the scouring mechanism, a critical condition for the occurrence of scouring is given in terms of two important parameters, namely, the rate of return flow from the land and water layer thickness in front of the seawall. These findings lend perspective towards the quantitative prediction of the total amount and pattern of scouring.

In this paper, a description is given on the mixing processes of heated water discharged into the surf zone, based on the field investigations.

In accordance with the flow characteristics observed, the flow region can be classified into three parts, namely the jet flow region, nearshore current region and coastal current region. In the jet flow region, the flow characteristics are expressed well by the two dimensional turbulent jet flow model and strongly influenced by the cuspate bottom configuration formed under the interaction between the jet flow and nearshore currents. It is realized that the dacay of plume centerline temperature is slower than the other cases owing to the influence of bottom slope, water depth and the direction of jet axis. By the dye tracer studies, in the nearshore current region the variance increases approximately with time at a power of 1.72 for longitudinal and of 1.95 for lateral respectively, while the diffusion coefficient increases with diffusion scale at a power of 1.43 for longitudinal and of 1.71 for lateral respectively. In the coastal current region, the representative isotherms are mainly in appearance either of the southerly alongshore or northerly stretch, possibly caused by some fairly long period waves.

The cloud of heated water was always confined within a certain strip of nearshore zone, likely in response to the existence of a turbulent boundary layer phenomena appeared in parallel to the coastline. Quantitative modelling of this resulting plume is then made. In addition, some pulsation patterns of isotherms were also observed. Finally, a graphical representation of the functional relationship between the relative temperature difference and the area within the specified isotherm is shown.

Two approaches for developing outfall diffusion models for the coastal zone are discussed. The statistical model combines a simple Gaussian analysis with the time-series records of flow measurements to elucidate the dispersion patterns in a shore-parallel, a current-reversal, and stagnation flow regimes. The deterministic model explores the more complex characteristics of a plume in an advection-dominant situation. The cases of Fickian diffusion, shear diffusion, and inertial subrange hypothesis are studied. It is shown that a previously derived semi-empirical relationship produces an agreement at least as good as the optimized results of these theoretical models. These models are quite useful for site specific evaluation of potential continuous discharges of effluents into the coastal zone.

The applicability of oceanic mixed-layer models to the case of wind mixing in a coastal region dominated by river runoff is explored. Two-dimensional effects and the propagation of internal-inertial waves out of the mixed layer are seen to be extremely important. Modification of the boundary conditions changes the appearance of the solutions as well. Further field work will be necessary to determine if additional terms, ignored in the oceanic models, might become important in the coastal region.

Ocean Thermal Energy Conversion, called OTEC, is presently getting much serious support for continued studies. Presently, there are potential OTEC sites off Punta Tuna, Puerto Rico; West Coast of Florida; New Orleans, Louisiana; and Keahole Point, Hawaii, the latter of which is the theme of this paper. The paper gives a summary of the early history of OTEC and its present status at Keahole Point, Hawaii, including design criteria. Any OTEC plant must operate throughout the normal environment, i.e. operational design sea state, including winds, waves and currents. The plant must be designed for the extreme environmental conditions, such as associated with hurricanes. The selection of an OTEC site depends on the availability of the resource, particularly associated with the temperature difference between the surface waters and the deep water. The change in the environmental parameters, and the consequences of any anticipated changes, are subjects of an environmental impact statement, the subject of which has been studied but is not reported here as part of this paper.

Three-dimensional modelling of the Irish Sea has led to the determination of regimes of residual elevation and current due to wind, density and sea-surface gradient. These regimes are superimposed, along with tidal residuals from two-dimensional modelling, to yield first estimates of mean sea level distribution and long-term residual circulation.

The circulation pattern in the northern Arabian Sea is presented for the well defined wind fields, which are classified as the South-West Monsoon and the North-East Monsoon. To check the reproduction ability of the model, first tidal waves are computed. The results shows a good agreement with the known values given in literature.

A 2-year study of the currents and salinity (density) fields has been conducted on the broad, shallow Miskito Bank of the eastern coast of Nicaragua.

Observations across the Bank show a southward-flowing low-salinity, seaward-thinning wedge of highly turbid water trapped against the coast within the first 25-40 km offshore. This so-called coastal boundary layer grades seaward into a northward-flowing shelf current of opensea salinity that is essentially free of suspended sediment. Detailed transects across the coastal boundary layer show the salinity (density) structure to be closely coupled to the high-speed jet of south-flowing water.

Velocity and density measurements from the coastal boundary layer allow quantitative evaluation of each of the terms in the momentum balance equation and of the effect that each has on the circulation dynamics. The Coriolis force, the baroclinic and barotropic pressure gradient forces, and the internal friction force make important contributions to the on-offshore force balance. In the longshore balance, only the baroclinic pressure gradient force was found to be insignificant. A marked difference in this balance of forces was observed in the upper and lower layers of the water column in both the alongshore and on-offshore balances.

This report concerns with investigations into the three dimensional mechanism of flow motion in the sea water of Mikawa Bay for the purpose of elucidating the effect of wind, tidal current and topographical features on oceanic environmental fluctuations among factors related to the diffusion process in the bay.

On the assumption that dynamics of the bay water would be affected by the tidal currents and the flow caused by the wind, a numerical simulation analysis of the flow motion phenomenon in the bay water was conducted on the basis of the meteorological and oceanographical observation data collected at the points in the investigated sea region, so as to examine the circulation mechanism of the bay water caused by the above mentioned factors.

The salt wedge has been observed by ultrasonic method at estuaries of the Ishikari, Shiribetsu and Rumoi River in Hokkaido, Japan. According to the records of the longitudinal profile of the salt wedge, behavior of the interface of salt and fresh water is strongly influenced by configurations of the water course and the river, bed. Therefore, in this paper, a distance from the front of the salt wedge to the river mouth is divided into two or three sections in accordance with behavior of the interface, and the salinity distribution in the upper layer is estimated in each section.

By solving the differential equation of two dimentional salinity diffusion, the distribution is represented by terms of flow velocity, diffusion coefficients, depth of the upper layer and salinity at the boundary. Where, diffusion coefficients are determined by comparing evaluated longitudinal distribution of surface salinity with observed one.

By estimating the rate of salinity entrainment into the upper layer, the entrainment coefficient E at the interface is evaluated as E = 0.4 x 10^-5 ˜ 0.8 x 10^-3 at three estuaries.

The friction factors at the interface in a two-layered stratified flow have been studied experimentally in a closed rectangular duct with freshwater flowing over a quasi-stagnant salt water. The analysis of the flow was based on the application of the one-dimensional mass and energy equations for each layer. It was found that the interfacial friction coefficient, f̄_i ,is best correlated with the dimensionless number R_eF², where R_e and F are some non-densimetric Reynolds and Froude numbers of the flow,and with the relative density difference of the two layers Δρ/ρ. Good agreement has been obtained with results of previous laboratory investigations and field data.

The stratification and salinity structure of the water mass in the lower portions of tidal estuaries are important factors of the general circulation and local water quality. In natural conditions an equilibrium can be observed in each estuary and depends on the geometry of the estuary, the motion of tides inside the estuary and the freshwater discharge.

Extensive studies of the salinity structure in the estuaries of the La Grande and Grande Baleine rivers have shown that water of high salinity content will be expected along the total length of the estuary, for the discharge expected during the fill up period.

Sand-bars being present in several transverse sections in these estuaries, it is of the greatest importance to verify if the saltwater introduced upstream of these bars by a provisionnal modification in the freshwater discharge would not be definitely present.

This paper presents the relevant parameters, the theoretical formulation and the results obtained for the above mentioned estuaries.

A harbour, connected to a tidal river, will affect the salt intrusion in the river. To study the interaction between harbour and river a systematic investigation has been carried out in the tidal salinity flume of the Delft Hydraulics Laboratory (Fig. 1a). The investigation included measurements of the density distribution in harbour and river and measurements of the exchange phenomena in the harbour entrance. The study was executed as part of a long-term basic research program on salt intrusion in tidal rivers, commissioned to the Delft Hydraulics Laboratory by the Rijkswaterstaat (Dutch Government Public Works Department).

A numerical model utilizing a fully time-centered implicit (ADD computational algorithm is used to investigate the effects of distortion of the laboratory model of the Tromsø sound where advective accelerations are important. The numerical model is used to study the individual effects of bottom and side resistance in order to obtain a better understanding of the dynamics and energetics of the tidal flow. Bottom friction is modeled by Chezy’s formula. Correspondingly, a lateral viscosity proportional to the local velocity is used to obtain a realistic representation of turbulent lateral momentum exchange. Deviations between the results of the models and field observations are found to be within the natural variability from one tidal cycle to the next, indicating that the laboratory simulation is not seriously affected by distortion.

With the enlargement of industrialization in the 19th century and the growth of world trade the sea navigation increased considerably. The sea routes had to be improved. This development continued very fast in the last 30 years. The capability of extension in the particular estuary (for example: Elbe, Weser, Jade, Ems) is limited. The improvements include not only the deepening of navigational channels, but also groins, training-walls, fixation of bars, partial or total damming up from by-channels, new localization of main navigational channel lines, new ports etc. The tidal low water is falling and the tidal high water rises, the tidal lift and the tidal volume increase and the flood-as well as the ebbcurrent is floating more powerfully through the tidal estuary. This shows the effect of constructions.

The influence of tidal cycles with neap and spring tides or of storm surge events on the distribution of temperature increases caused by heat injection in an estuary was investigated in a thermal-hydraulic model. The results of the model tests have shown, that under natural tidal conditions as of the Elbe River during tidal cycles as well as storm surge events in the far field region no higher temperature increases occurred than under mean tidal conditions.

It has been extensively recognized from many past studies, that the interfacial Froude number must be unity at a river mouth, under the condition of a salt wedge existing inside the river. However, there seems no study having paid efforts to clarify how its numerical values distribute horizontally, inside or outside the river mouth. This problem has come to mind very important for the present authors, in order to obtain better understandings on the dynamical structure of the density current.

The river mouth has been thought to be an extremely singular place, from many field observations and laboratory experiments, because it forms a boundary between two quite different phases in flow pattern, inside and outside. For example, abrupt changes in velocity, thickness and mixing occur for the fresh water, at the river mouth. In order to solve its essential behavior, the transient motion of the fresh water, when it passes through the river mouth, was analysed based on some ideal conditions.

A simplified steady state multilayered (horizontally homogeneous) thermal model is described and applied to assess the effects of the cold water discharge created by a proposed liquid natural gas (LNG) regasification facility. The model, similar to ones developed for predicting average cooling pond performance, accounts for advection and diffusion between layers, atmospheric and solid boundary heat exchange, and heat exchange due to tidal and density currents. For the configuration in which both the intake and discharge were located in a dredged turning and docking basin, recirculation created thermal deficits from -8°C to -17°C. Adverse environmental effects on migrating species (particularly various life stages of shrimp) and the benthic community and costs associated with auxiliary seawater heating suggested that other alternatives (such as a separate intake basin or an offshore diffuser) would be more appropriate.

Criteria for the design of outlet arrangements from hydroelectric power stations, necessary to prevent ice formation in fjords in the winter months, are presented. The initial entrainment of seawater to the fresh water discharge has been investigated by means of laboratory models. A numerical model of the fjord dynamics, as well as a simplified analytic model, is used to study the estuarine circulation and entrainment in the fjord. Heat loss to the atmosphere is parametrized using small modifications of well known empirical formulas.