Kazuki Oda

Numerical modeling of the initial stages of dam-break waves

In this paper, we present a numerical investigation of dam-break waves during the initial stage. The numerical model is based on the Reynolds Averaged Navier-Stokes (RANS) equations with a k-e turbulence closure model (J. Fluid Mech. 359, 1998, 239). Numerical results are compared with existing experimental data (J. Fluid Mech. 374, 1998, 407) as well as the new experimental data. Good agreements are observed. The effects of the water depth in front of the dam and the pull-up motion of dam on the generated waves are then investigated. The turbulence associated with the dam-break waves is also discussed.

Modelling population dynamics of the pelagic larval shrimp Metapenaeus ensis in the Osaka Bay estuary

Aiming at providing numerical tools useful to assess the impacts of coastal development pressures on marine life, a Lagrangian model for population dynamics of pelagic eggs and larvae of the greasyback shrimp, Metapenaeus ensis, in Osaka Bay was developed and improved based on laboratory experiments. The model was combined with a 3-D Eulerian numerical model that predicts physical and biological conditions of the habitat. A series of numerical experiments was done to investigate their transport processes from the spawning grounds, and the concentration process of full-grown larvae towards the mouth of Yodo River that flows into the innermost basin. Model results revealed, as a general tendency, that the early larval developmental stages through nauplius to zoea continue to drift like a passive tracer, and begin to concentrate at the river mouth area after the mysis stage, mainly avoiding low saline environment in the surface layer. This suggests that the full-grown larvae may be favored with chance to take advantage of the river-induced gravitational circulation that dominates the innermost estuarine basin. In addition, it was found that tidal condition around the spawning period also exerts a considerable influence upon the fate of pelagic larvae.

SHIP WAVES IN SHALLOW WATER AND THEIR EFFECTS ON MOORED SMALL VESSEL

This report will update the coastal zone practitioner on the National Flood Insurance Program (NFIP) as it affects the implementation of manmade changes along the coastline. It is our intent to place in proper perspective this fast-changing and often difficult to interpret national program. Readers will achieve an overall understanding of the NFIP on the coast, and will be in a position to apply the programs requirements in their efforts. We will begin with a history of the application of the NFIP to the coastal zone. The history of the problems encountered will lead into current regulations, methodologies, and the changes the Federal Emergency Management Agency plans for the future.The spatial variability of the nearshore wave field is examined in terms of the coherence functions found between five closely spaced wave gages moored off the North Carolina coast in 17 meters depth. Coherence was found to rapidly decrease as the separation distance increased, particularly in the along-crest direction. This effect is expressed as nondimensional coherence contours which can be used to provide an estimate of the wave coherence expected between two spatial positions.Prediction of depositional patterns in estuaries is one of the primary concerns to coastal engineers planning major hydraulic works. For a well-mixed estuary where suspended load is the dominant transport mode, we propose to use the divergence of the distribution of the net suspended load to predict the depositional patterns. The method is applied to Hangzhou Bay, and the results agree well qualitatively with measured results while quantitatively they are also of the right order of magnitude.

An attempt to restore suitable conditions for demersal fishes and crustaceans in the Port of Sakai-Semboku, north Osaka Bay, Japan

Hypoxia and/or anoxia developed in the summer of 1995 and 1996 in the lower water layer in the Port of Sakai-Semboku, north Osaka Bay, causing an increase in sulfide content and a decrease in the redox potential of the bottom sediment. As a result, the number of benthic animal species was reduced and in the innermost part of the port no benthic animals were found. A jet stream pump system was installed at the Dejima Fishing Port, the innermost part of the Port of Sakai-Semboku to improve the oxygen conditions in the bottom waters. This led to an increase in percentage saturation of oxygen (ca. 10% increase) of the lower seawater layer along with an increase in richness and abundance of benthic fishes and crustaceans in the summer. These findings indicate that dissolved oxygen is a crucial environmental factor in the functioning of the port as a habitat for various benthic animals in north Osaka Bay. Based on the results of field surveys, the possibility of restoration of the benthic fauna by using a jet stream pump system is also discussed.

DEVELOPMENT OF A NUMERICAL SIMULATION METHOD FOR PREDICTING THE SETTLING BEHAVIOR AND DEPOSITION CONFIGURATION OF SOIL DUMPED INTO WATERS

A special reflecting wall 12 m long and 2.1 m high was built off the beach at Reggio Calabria, and 30 wave gauges were assembled before the wall and were connected to an electronic station on land. It was possible to observe the reflection of wind waves generated by a very stable wind over a fetch of 10 Km. The experiment aimed to verify the general closed solution for the wave group mechanics (Boccotti, 1988, 1989), for the special case of the wave reflection.Significant features on Wadden Sea wave climate are evaluated in respect of the state of the art. Main emphasis was laid on an analysis of the governing boundary conditions of local wave climate in island sheltered Wadden Sea areas with extensions being sufficient for local wind wave growth. Explanatory for significant wave heights a reliable parametrization of local wave climate has been evaluated by using generally available data of water level and wind measurements.

DEVELOPMENT OF A NEW TYPE OF REEF BREAKWATER THEORETICAL AND EXPERIMENTAL STUDY

Detailed studies have been undertaken to assist in the design of major extensions to the port of Haifa. Both numerical and physical model studies were done to optimise the mooring conditions vis a vis the harbour approach and entrance layout. The adopted layout deviates from the normal straight approach to the harbour entrance. This layout, together with suitable aids to navigation, was found to be nautically acceptable, and generally better with regard to mooring conditions, on the basis of extensive nautical design studies.Hwa-Lian Harbour is located at the north-eastern coast of Taiwan, where is relatively exposed to the threat of typhoon waves from the Pacific Ocean. In the summer season, harbour resonance caused by typhoon waves which generated at the eastern ocean of the Philippine. In order to obtain a better understanding of the existing problem and find out a feasible solution to improve harbour instability. Typhoon waves measurement, wave characteristics analysis, down-time evaluation for harbour operation, hydraulic model tests are carried out in this program. Under the action of typhoon waves, the wave spectra show that inside the harbors short period energy component has been damped by breakwater, but the long period energy increased by resonance hundred times. The hydraulic model test can reproduce the prototype phenomena successfully. The result of model tests indicate that by constructing a jetty at the harbour entrance or building a short groin at the corner of terminal #25, the long period wave height amplification agitated by typhoon waves can be eliminated about 50%. The width of harbour basin 800m is about one half of wave length in the basin for period 140sec which occurs the maximum wave amplification.Two-stage methodology of shoreline prediction for long coastal segments is presented in the study. About 30-km stretch of seaward coast of the Hel Peninsula was selected for the analysis. In 1st stage the shoreline evolution was assessed ignoring local effects of man-made structures. Those calculations allowed the identification of potentially eroding spots and the explanation of causes of erosion. In 2nd stage a 2-km eroding sub-segment of the Peninsula in the vicinity of existing harbour was thoroughly examined including local man-induced effects. The computations properly reproduced the shoreline evolution along this sub-segment over a long period between 1934 and 1997.In connection with the dredging and reclamation works at the Oresund Link Project between Denmark and Sweden carried out by the Contractor, Oresund Marine Joint Venture (OMJV), an intensive spill monitoring campaign has been performed in order to fulfil the environmental requirements set by the Danish and Swedish Authorities. Spill in this context is defined as the overall amount of suspended sediment originating from dredging and reclamation activities leaving the working zone. The maximum spill limit is set to 5% of the dredged material, which has to be monitored, analysed and calculated within 25% accuracy. Velocity data are measured by means of a broad band ADCP and turbidity data by four OBS probes (output in FTU). The FTUs are converted into sediment content in mg/1 by water samples. The analyses carried out, results in high acceptance levels for the conversion to be implemented as a linear relation which can be forced through the origin. Furthermore analyses verifies that the applied setup with a 4-point turbidity profile is a reasonable approximation to the true turbidity profile. Finally the maximum turbidity is on average located at a distance 30-40% from the seabed.

EXPERIMENTAL STUDY ON GENERATION AND DISSIPATION MECHAMISIMS OF TURBULENCE INCIDE AND IN THE VICINITY OF POROUS MEDIA

A measuring method of fluid motion inside and in the vicinity of porous media made of silicon spheres is presented. Sodium iodide solution is used as the refraction index matching fluid. In order to capture pictures, a CCD camera and YAG laser are used. The velocity datum are obtained by analyzing the pictures using the superresolution PIV method. Some experimental results on the velocity field and turbulence kinematic energy are presented. Structure of the flow filed inside and in the vicinity of the porous media is discussed. Moreover generation and dissipation mechanisms of the turbulence are discussed.

SHIP-BRIDGE-PIER PROTECTIVE SYSTEMS

Parameter Identification (PI) algorithm is an optimization procedure that systematically searches the parameters embedded in a mathematical model. These parameters are not measurable from a physical point of view. The optimization is based on the minimization of a selected norm of the differences between the solution of the mathematical model and scattered observations collected from the system. Parameter identification (or inverse problem) has been studied in groundwater systems extensively for the past decade (15), and it has also drawn many researchers in the fields of open-channel flow and estuarine modeling since 1972 (1,2,9,17). All the past estuarine PI works in the literature are confined to the one-dimensional case, and hydrodynamics and transport equations are treated separately. This study deals with PI in a two-dimensional vertically-averaged estuarine salinity model. The salinity transport equation is coupled with the hydrodynamics equations. The coupled relationship introduces extra density terms in the hydrodynamics equations, which must be solved simultaneously with the transport equation. One of the most difficult problems in PI is the collection of needed observations from the system which is being modeled. With limited exception, the currently available data from the prototype estuaries are not adequate for the purposes of developing a PI algorithm. This is usually critical in quantity (the number of stations and/or the period of time) and in quality (noise of data). However, if an operational hydraulic model is available, the data could then be obtained economically and accurately under an ideally controlled environment. The large amount of data that can be collected from a hydraulic model of an estuary will provide a sufficient number of observations and the required initial and boundary conditions for the development of a PI algorithm. The use of the estuary hydraulic model could provide a better source of prototype data than would be available from the real estuary. It will be much easier to distinguish between the inadequacy of the mathematics and the inadequacy of our understanding of the prototype. Thus, it will give us an idea of how well we could expect to mathematically model the real estuary if we had an unlimited amount of prototype data. Additionally, when these types of data are used in PI, parameters can be optimally identified and the mathematical model can then be used conjunctively with the hydraulic model for prototype applications, provided that the mathematical model is consistently formulated. How well a hydraulic model simulates the prototype estuary is not considered in this study.The problem of buoyant surface jet (BSJ) is relevant from the practical standpoint to the discharge of cooling water of power plants into the receiving water bodies. The buoyant surface jet has extensively been studied by numerous investigators both theoretically and experimentally. Most studies have been concerned with the problems of BSJ discharged horizontally into a surface of a deep ambient water with or without cross current. From a practical standpoint, however, the design engineers are often confronted with the design of thermal outfalls in the coastal regions which are frequently shallow and have the boundary effects. Few investigators have studied the problem of BSJ discharged horizontally over slopping bottom into quiescent receiving water (1), (2), (4), (5), (6), and (7). However, no information on the foregoing problem with moving ambient water is available. The purpose of this paper is (a) to present the experimental results of BSJ which is discharged over slopping bottom into moving ambient water, and (b) to see the degree of error which is introduced by applying the deep water integral models to the case of a buoyant surface jet with a bottom boundary.This study deals with the statistical properties of the group formation of random waves determined by the zero-up-cross method. Probability distributions about (1) the run of high waves (2) the total run (3) the run of resonant wave period are derived theoretically providing that the time series of wave height and wave period form the Markov chain. Transition probabilities are given by the 2-dimensional Rayleigh distribution for the wave height train and the 2-dimensional Weibull distribution for the wave period train. And very good agreements between data and the theoretical distributions have been obtained. Then the paper discusses those parameters which affect the statistical properties of the runs and shows that the spectrum peakedness parameter for the. run of wave height and the spectrum width parameter for the run of wave period are the most predominant.One of the characteristics of the North Sea between the British Isles, the Netherlands, Germany and Denmark is the occurrence of heave storm surges especially in autumn and winter with heights of about 4 m above spring highwater. Coastal areas and especially the estuaries of the tidal rivers are hit by these storm surge events. The mean tidal range at the German coast comes to about 3 m with relatively low daily and semimonthly inequalities of less than 0.5m. Within the framework of long-term developments of the navigation channels of the estuaries as well as of the storm surge protection works, physical model tests had to be carried out in order to predict the influences of such measures on the storm surge heights to be expected.A two-dimensional laboratory investigation of sediment transport, induced by shallow-water waves, showed that the sediment motion over suspension-dominant asymmetric ripples is closely related to the development of eroding beaches. High-speed motion picture analysis revealed that vortices, formed over this type of ripple, play a crucial role in transporting the sediment to the offshore region. A relation for net offshore sediment flux was formulated for sand 0.02 cm in diameter. A simple model for eroding beaches was proposed and its validity was checked by using two existing data sets for 0.02-cm sand beaches; the model could predict fairly well profile and shoreline changes in the early stages.Queenslands Beach Protection Act (1968-1974) resulted, inter alia in the formation of the Beach Protection Authority, which is responsible for investigating coastal erosion, planning remedial works, recording and evaluating results of investigations, and various other functions. Control of windblown sand and retention of vegetated and naturally stable coastal sand dunes are valuable means of decreasing coastal erosion and because of this the Authority implements a broad research program into the management of coastal dunes in Queensland. Field trials are carried out at the Authoritys Dune Management Research Station on South Stradbroke Island to determine methods of repairing, stabilizing and managing coastal dunes. The research program conducted so far consists of fifteen separate field trials within four general areas of investigation:- (a) Dune Forming Fences Two trials were installed in blown-out sections of the frontal dune to compare different types of semi-permeable fences (eg. wooden slats) and brush matting (a surface mulch of tree branches) on the basis of their ability to accumulate windblown sand and initiate dune formation. (b) Dune Stabilization Techniques Three trials were installed on bare dunal areas to evaluate methods of temporary sand surface stabilization (organic mulches and spray-on materials) as an aid in establishing dune vegetation. (c) Dune Vegetation Two trials were conducted to produce and compile information on the performance of important or potentially useful dune plants. (d) Plant Nutrition Eight trials using different combinations and rates of fertilizer were used to study methods of improvement of establishment and early growth of dune stabilizing plants, particularly sand spinifex grass (Spinifex hirsutus). Good establishment and rapid early growth is required in order to accelerate, improve, and decrease the costs of, the stabilization process.Construction of the Jebel Ali Port complex, 35 km southwest of Dubai, in the United Arab Emirates, has included the disposal of 110 Million cubic metres of excavated spoil. Disposal of dredged carbonaceous breccia raised particular problems due to the high proportion of fines generated and which, unless properly controlled, could cause wide scale environmental damage in the coastal zone. At the same time it was necessary that acceptable reclamation should be created. An extensive data collection exercise was carried out in order to monitor the geotechnical, hydraulic, meteorological, marine climate and marine biology aspects of the operation.Tung-Kang Fishing Harbor, which is about 16 km to the south of Kaohsiung Harbor, is a river harbor on the south-west coast of Taiwan. This harbor is located at the estuary of the Niu-Pu River, which meets the Tung- Kang River and the Kao-Ping River on the north side, (see Fig. 1) The original north and south jetties were constructed in 1959. Because the entrance is located at the meeting of the three rivers and the water depth at the entrance is shallower than that in the breaking zone, the entrance is easily chocked with sand during the summer season when the south-west wind and waves are strong. Therefore, dredging is always necessary to maintain the required depth. On. the other hand, because of the increasing number of fishing boats and deeper draft, the port cannot function effectively. There-fore, how to keep the required water depth at the entrance and to obtain a wider and stable water basin is an urgent problem with this harbor. Based on the sounding of 1973, the littoral drift is mainly from the south. In the next year the construction of a 176 m long new south jetty was begun to protect the entrance and to facilitate the sedimentation study. In 1975, the Taiwan Fisheries Consultants was appointed to undertake the investigation and long-term planning work. This project includes littoral process study, planning, model test and design. Finally it is recommended that an adequate layout of south and north jetties can solve the problem of accretation of the harbor entrance. The purpose of this paper is to describe some aspects with emphasis on how to prevent the shoaling of the entrance channel located at the meeting of the rivers.

Protection of Maritime Structures against Ship Collisions

A significant portion of the damage by hurricanes is the storm surges. The National Weather Service has developed a dynamical-numerical model to forecast hurricane storm surges. The model is used operationally for prediction, warning, and planning purposes. The model requires fixed oceanographic and real time meteorological input data. The oceanographic data were prepared for the Gulf and East coasts of the U.S. and are stored as an essential part of the program. Meteorological data for any tropical storm are supplied by the forecasters or planners using the model. The model was applied to hurricane Camille 1969. Comparison between the observed and computed surges for Camille was satisfactory for prediction purposes.The main consideration in harbor master planning is to maximize the amount of time that the harbor can be used. The potential level of harbor utilization can be evaluated by analyzing vessel performance during harbor operations in terms of the range of imposed environmental conditions. The harbor utilization level is expressed statistically as the probable amount of time that the harbor can be used as planned.The design and construction of a major ocean outfall and diffuser system for disposal of wastewater effluents is a complex process involving an interplay of requirements originating from various disciplines. These include, among others, considerations of physical oceanography, mixing and dispersion, treatment processes, regulatory requirements, marine geology, economics and construction. The recently completed Sand Island Outfall and the newly designed Barbers Point Outfall are both on the southern coast of the island of Oahu, Hawaii, and are designed for treated sewage effluents from the densely populated portion of the City and County of Honolulu. In this paper, some design considerations of these outfalls will be examined. The emphasis in this paper is on the hydrodynamics, although other design aspects are also discussed briefly.The height of dikes and other coastal structures can only be calculated after determination of the wave run-up. Several formulas for the calculation of wave run-up are developed after model tests as a rule. But the influences of scale effects and natural wind conditions are practically unknown. To clear these questions further investigations and especially field measurements should be carried out. By measuring the markerline of floating trash on the slope of the seadikes the maximum wave run-up could be found out after four storm surges in 1967 and 1973In two graphs it will be shown that on the tidal flats the run-up depends on the waterdepth. The run-up was higher than it could be expected after model tests of 1954. With a newly developed special echo sounder the run-up could be measured in January 1976. The waves and the run-up could be registrated synchronously during two severe storm surges. As shown in Fig. 9 it was found a logarithmic distribution of the wave height, wave period and the higher part of the wave run-up. The found wave run-up is considerably higher than estimated before. The measured 98 % run-up is found about twice the computed value. That is an interesting and important result of the first synchronous recording of wave run-up on sea dikes.In March 1972 the authors firm in association with two Portuguese firms of consulting engineers, Consulmar and Lusotecna, were appointed by the Portuguese Government agency Gabinete da Area de Sines to prepare designs for the construction of a new harbour at Sines on the west coast of Portugal. The location is shown in Figure 1. The main breakwater, which is the subject of this paper, is probably the largest breakwater yet built, being 2 km long and in depths of water of up to 50 m. It is exposed to the North Atlantic and has been designed for a significant wave height of 11 m. Dolos units invented by Merrifield (ref. 1) form the main armour. The project programme required that studies be first made of a wide range of alternative layouts for the harbour. After the client had decided on the layout to be adopted, documents were to be prepared to enable tenders for construction to be invited in January 1973. This allowed little time for the design to be developed and only one series of flume tests, using regular waves, was completed during this period. Further tests in the regular flume were completed during the tender period and a thorough programme of testing with irregular waves was commenced later in the year, continuing until August 1974 when the root of the breakwater was complete and the construction of the main cross-section was about to start. The model tests, which were carried out at the Laboratorio Nacional de Engenharia Civil in Lisbon, were reported by Morals in a paper presented to the 14th International Coastal Engineering Conference in 1974. (ref. 2)Estuaries may be sequentially classified into highly stratified, moderately mixed and vertically homogeneous. An important difference between moderately stratified or vertically homogeneous estuaries, and highly stratified estuaries (salt wedges) is that, in the former, tidal currents are sufficient to cause turbulent mixing of fresh water and sea water over the full depth of the estuary. In the latter, a distinct interface or interfacial layer exists which separates the two nearly homogeneous layers. The vertical advectlon of salt in this two-layer flow is the dominant process in maintaining the salt balance. This paper presents an analytical model describing this process. Experiments have been conducted in the laboratory to compare with the developed theory.

STUDIES OF THE NAVIGATION BUOY FOR STRONG TIDAL CURRENTS AND LARGE WAVES

The data for the spectra of wind-generated waves measured in a laboratory tank and in a bay are analyzed using the similarity theory of Kitaigorodski, and the one-dimensional spectra of fetch-limited wind waves are determined from the data. The combined field and laboratory data cover such a wide range of dimensionless fetch F (= gF/u ) as F : 10 ~ 10 . The fetch relations for the growthes of spectral peak frequency u)m and of total energy E of the spectrum are derived from the proposed spectra, which are consistent with those derived directly from the measured spectra.A solution of finite amplitude long waves on constant sloping beaches is obtained by solving the equations of the shallow water theory of the lowest order. Non-linearity of this theory is taken into account, using the perturbation method. Bessel functions involved in the solution are approximated with trigonometric functions. The applicable range of this theory is determined from the two limit conditions caused by the hydrostatic pressure assumption and the trigonometric function approximation of Bessel functions. The shoaling of this finite amplitude long waves on constant sloping beaches is discussed. Especially, the effects of the beach slope on the wave height change and the asymmetric wave profile near the breaking point are examined, which can not be explained by the concept of constancy of wave energy flux based on the theory of progressive waves in uniform depth. These theoretical results are presented graphically, and compared with curves of wave shoaling based on finite amplitude wave theories. On the other hand, the experiments are conducted with respect to the transformation of waves progressing on beaches of three kinds of slopes ( 1/30, 1/2.0 and 1/10 ) . The experimental results are compared with the theoretical curves to confirm the validity of the theory.Measurements of drift were made in a wind and wave facility at different elevations below the mean water level. The drift profiles were obtained for reference wind speeds, Ur = 3.1, 5.7 and 9.6 m/sec. The measurement technique involved tracing the movement of small paper discs which were soaked in water to become neutrally buoyant at the elevation of release. A logarithmic drift profile is proposed. The water shear velocity, U*w, predicts a surface stress, TS = pw U*S, in agreement with that obtained from the wind shear velocity, s = Pa U*li where pa and pw refer to air and water densities, respectively.The paper describes a procedure for obtaining field data on the mean concentration of sediments in combination of waves and currents outside the breaker zone, as well as some results of such measurements. It is assumed that the current turbulence alone is responsible for the maintenance of the concentration profile above a thin layer close to the bottom, in which pick-up of sediments due to wave agitation takes place. This assumption gives a good agreement between field data and calculated concentration profiles.A section of beach on the south coast of England has been under surveillance for five years, from March 1966 until March 1971. During this period, two permeable groynes of the Makepeace Wood type were constructed. Beach cross sectional areas and rates of accretion were compared before and after groyne construction. The groynes caused a buildup in beach levels updrift.The results of model tests, carried out to evaluate the stability of submarine slopes under wave action are presented. A Bentonite clay was sedimented in a glass walled tank 6 feet long by 0.5 feet wide by 2.5 feet deep. The sedimentation and consolidation processes were studied and sediment densities were measured at various depths in the profile. Vane shear strength profiles were also measured afvarious average degrees of consolidation. Plastic markers were placed in the sediment adjacent to a glass wall so that the soil movements under both gravity and wave induced slides could be documented by photography. Dimensional similitude is discussed and the model test data are presented in a dimensionless form. All instabilities were observed to be of the infinite slope type. Analysis of the data shows that wave action is instrumental in initiating downslope mass movements in gently to steeply sloping off-shore sediments. General lack of agreement between the model test results and published theoretical analyses was found but there was close similarity in the depths and form of failure under wave action and under gravity stresses alone. The loss of stability under wave action is analyzed on the concept that failure is gravity controlled and the soil strength is reduced to a value commensurate with gravity sliding by the cyclic shearing stresses imposed by progressive waves. A method of evaluating the stability of prototype slopes using a model test correlation and field vane strength measurements is proposed. INTRODUCTION Instabilities in submarine slopes have been observed or have been inferred over a wide range of slope angles from less than half a degree up to about 30°. These subaqueous landslides are believed to have caused rupture of submarine cables and to have generated many of the geomorphological features on the ocean bottom. There are numerous records describing these landslides but very few publications discuss the application of the principles of soil mechanics to the analysis of the stability of submarine slopes. Associate Professor of Civil Engineering, Queens University at Kingston, Canada 2 Soils Engineer, Geocon Ltd., Toronto, Canada 3 Associate Professor of Civil Engineering, Cornell University, Ithaca, N.Y.Several mathematical models have been lately presented which describe the tidal wave propagation within an estuary. The existing models derived from the method for damped co-oscillating tides are based on sinusoidal wave profile. Meanwhile a tidal wave which moves upstream, generally exhibits a progressive deformation which tends to unbalance the length of time between flood and ebb tides. The actual profile is therefore no longer sinusoidal. Our investigation uses the potential method, and takes into account the wave amplitude which is usually neglected compared with the water depth. Finally, the velocity potential is obtained explicitely, using a double iterative method. Tidal elevation, particle velocities and trajectories are given by the same computer programmed algorithm. Our study shows that l) the phenomenon can be clearly visualized on the theoretical curves and 2) the magnitude of this deformation is inversely proportional to the water depth, becoming significant when the ratio f|/h reaches the critical value of 1/10. Damping and geometrical effects are also considered and the theory was applied to the St.Lawrence Estuary. A partial positive reflection of the incoming tidal wave is assumed at the narrow section near Quebec, whereas a complete negative reflection is assumed at the entrance to Lake St.Peter. The calculated and observed wave profiles, velocity distributions, and phase shifts are in good agreement.A numerical model is presented to describe the hydromechanics of lagoons connected to the ocean by relatively narrow inlets. Because special attention is given to the flushing, all second order terms in the hydrodynamic equations are retained. The study is restricted to lagoons with a onedimensional flow pattern and water of uniform density. In designing a numerical solution to the equations, the inlet equations are regarded as implicit boundary conditions to the equations describing the flow in the lagoon proper. The advantages of this approach are: (1) the size of the computational grid in the lagoon can be chosen independently of the relatively small dimensions of the inlets and (2) the flow at branching inlets (an inlet connecting a lagoon to the ocean such that branching of the inlet flow can occur) still can be described by a one-dimensional tidal model. The predictive capability of the numerical model is confirmed by favorable comparison between measured and computed particle paths and net transport for a series of laboratory experiments. In the experiments a canal of uniform width and depth is freely connected to a tidal basin at one end and at the other end is connected to the same basin by a submerged weir.