Bernard Le Mehaute

Dynamic Interaction of Intense Rain with Water Waves

Abstract A theory for determining the dynamic effect of intense rain on water waves is established, based on momentum exchange. The theory takes into account the rain intensity, angle of incidence and fall velocity, and the wave amplitude, frequency and water depth. It is found that the rain induces a uniform increase of pressure in the water column and a uniform mass transport in a thin boundary layer affected by the momentum exchange. The rain also induces a fluctuating pressure and shear stress on the free surface. For vertical or near vertical rainfall, these fluctuating free surface forces are responsible for a non-negligible wave amplitude decay, particularly in the high frequency range. In the case of high winds, the rain horizontal velocity component is large and the corresponding stress on the free surface is nearly in phase with free surface slope. Then instead of causing a decay, the rain adds its effect to the wind and enhances the growth of high frequency waves. It is concluded that this effe...

Effect of dispersion on impulsive waves

The generation and propagation of surface waves resulting from suddenly created disturbances over water surfaces is investigated. The initial boundary conditions defining the disturbance are given either by a velocity of the free surface, an initial elevation of the free surface or a pressure impulsively applied on the free surface. It is shown that the corresponding three forms of solutions are related by a simple time derivative. Linear solutions are obtained in the cases where the wave motion is assumed to be nondispersive, mildly dispersive and fully dispersive, as well as in the case where the motion is given by the method of stationary phase. Criteria are established to indicate the limit of validity of each method.

Cavities, domes and spikes

A general formulation for surface deformation generated by a initial localized free surface disturbance is established in double integral form. The initial condition characterizing the localized disturbances can be 1) a movement of the free surface characterized by a velocity distribution, 2) a static departure of the free surface from the still water level, or 3) an impulse on the free surface. Solutions are obtained for a number of cases in which the initial disturbances are mathematically defined, allowing a first integration by Hankel transform. Closed form solutions are obtained in the nondispersive mode, while numerical solutions are obtained in the general cases. It is found that the initial disturbances result in nonoscillatory movements at the origin. Also, the wave motions are little affected by dispersion. The oscillations which are known to exist at a distance are only the results of linear dispersion in deep and intermediate water depth. Also the vertical rebound following the collapse of cav...

CRITERION FOR STABILITY OF SHORELINE PLANFORM

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.

Breaking wave characteristics on a plane beach

Abstract The determination of parameters describing a wave at the point of breaking is considered. The desired characteristics are the wave height, wave length, angle of wave crest with shoreline and water depth. The problem is solved for the simplified situation of a plane sloped beach by introducing a new hybrid approach which uses cnoidal wave height transformation and linear wave length transformation. The approach yields results which compare favorably with existing experimental data on breaker angle and breaker height.

Original surface disturbances from wave records

The general formulation of water waves generated by an instantaneous axisymmetric free surface disturbance on an initially quiescent body of water is recalled. The initial conditions characterizing the localized original disturbances are defined by the sum of a static departure of the free surface from the still water level and a free surface velocity distribution. A general solution is presented in the form of Fourier integrals which are solved by the fast Fourier transform in preference to the more limited method based on the stationary phase approximation. Based on this theoretical approach, the inverse problem is defined, allowing the determination of the initial disturbances from the wave records taken at a distance from the origin. The method is applied to explosion generated water wave records in shallow water. Analytical linear disturbances are defined as an equivalent mode of generation to the complex nonlinear dissipative physical process resulting from underwater explosion. A predictive mathematical moel is presented in a parametrized form, which could be related to the explosion yield, depth of burst and water depth.

Advances in impulsively generated water waves

Some recent development on the analysis of surface water waves generated by locally impulsive disturbances is presented in this paper While the classical Cauchy-Poisson approach to the problem has various practical applications, the theoretical analysis has been limited to either leading wave or the trailing wave solution in the farfield. Direct numerical integration except for very simple form of disturbance has difficulties due to the highly oscillatory kernel function of the Cauchy-Poisson integral. The new development shows that the method of Fourier transform may remove all the difficulties which have been faced either analytically or numerically and the solution is uniformly valid for both leading and trailing waves, deep and shallow water and for either near or far field within the linear definition. An inverse application of this method may also determine the infield initial disturbances at the origin. Nonlinear approximate solution to the same problem in the nearfield where linear solutions are not exactly valid is presented. Appropriate KdV equation in radial coordinate system are solved linearly using Fourier transform techniques but nonlinear corrections are added using implicit finite difference scheme. Wave data from experiments of TNT explosion and plate dropping in shallow water are presented. Substantiation of the theory is demonstrated by comparing the theoretical calculation with the experimental results.

LIMIT WAVES ON HORIZONTAL SEA FLOOR

More than 150 tests have been analyzed in order to describe the dynamically stable profiles of rock slopes and gravel beaches under wave attack. Relationships between profile parameters and boundary conditions have been established. These relationships have been used to develop a computer program. This program is able to predict the profiles of slopes with an arbitrary shape under varying wave conditions, such as those found in storm surges and during the tidal period.This paper investigates the utility of winds obtainable from a numerical weather prediction model for driving a spectral ocean-wave model in an operational mode. Wind inputs for two operational spectral wave models were analyzed with respect to observed winds at three locations in the Canadian east coast offshore. Also, significant wave heights obtainable from the two spectral models were evaluated against measured wave data at these locations. Based on this analysis, the importance of appropriate wind specification for operational wave analysis and forecasting is demonstrated.