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Showing papers in "Journal of Waterway Port Coastal and Ocean Engineering-asce in 1995"


Journal ArticleDOI
TL;DR: In this paper, a numerical code based on Nwogu's equations is developed, which uses a fourth-order predictor-corrector method to advance in time, and discretizes first-order spatial derivatives to fourthorder accuracy, thus reducing all truncation errors to a level smaller than the dispersive terms.
Abstract: The extended Boussinesq equations derived by Nwogu (1993) significantly improve the linear dispersive properties of long-wave models in intermediate water depths, making it suitable to simulate wave propagation from relatively deep to shallow water. In this study, a numerical code based on Nwogu's equations is developed. The model uses a fourth-order predictor-corrector method to advance in time, and discretizes first-order spatial derivatives to fourth-order accuracy, thus reducing all truncation errors to a level smaller than the dispersive terms retained by the model. The basic numerical scheme and associated boundary conditions are described. The model is applied to several examples of wave propagation in variable depth, and computed solutions are compared with experimental data. These initial results indicate that the model is capable of simulating wave transformation from relatively deep water to shallow water, giving accurate predictions of the height and shape of shoaled waves in both regular and irregular wave experiments.

546 citations


Journal ArticleDOI
TL;DR: In this article, the authors derived a relation for the fluid motion through thin porous structures in addition to the conventional governing equation and boundary conditions for small-amplitude waves in ideal fluids.
Abstract: Diffraction of water waves by porous breakwaters is studied based on the linear potential wave theory. The formulation of the problem includes a newly derived relation for the fluid motion through thin porous structures in addition to the conventional governing equation and boundary conditions for small-amplitude waves in ideal fluids. The porous boundary condition, indirectly verified by collected experimental data, is obtained by assuming that the flow within the porous medium is governed by a convection-neglected and porous-effect-modeled Euler equation. A vertically two-dimensional problem with long-crested waves propagating in the normal direction of an infinite porous wall is first solved and the solution is compared with available experimental data. The wave diffraction by a semiinfinite porous wall is then studied by the boundary-layer method, in which the outer approximation is formulated by virtue of the reduced two-dimensional solution. It is demonstrated that neglect of the inertial effect of the porous medium leads to an overestimate of the functional performance of a porous breakwater.

280 citations


Journal ArticleDOI
TL;DR: In this article, a variable grid finite-differences approximation of the characteristic form of the shallow-water wave equations without artificial viscosity or friction factors was presented to model the propagation and runup of one-dimensional long waves, referred to as VTCS-2.
Abstract: We present a variable grid finite-differences approximation of the characteristic form of the shallow-water-wave equations without artificial viscosity or friction factors to model the propagation and runup of one-dimensional long waves, referred to as VTCS-2. We apply our method in the calculation of the evolution of breaking and nonbreaking waves on sloping beaches. We compare the computational results with analytical solutions, other numerical computations and with laboratory data for breaking and nonbreaking solitary waves. We find that the model describes the evolution and runup of nonbreaking waves very well, even when using a very small number of grid points per wavelength. Even though our method does not model the detailed surface profile of wave breaking well, it adequately predicts the runup of plunging solitary waves without ad-hoc assumptions about viscosity and friction. This appears to be a further manifestation of the well-documented but unexplained ability of the shallow water wave equatio...

251 citations


Journal ArticleDOI
TL;DR: In this paper, the applicability of a neural network to analyze model test data of the stability of rubble-mound breakwaters is examined, and the predicted damage levels predicted by the neural network, calibrated by using a part of Van der Meer's 1988 experimental data, agree satisfactorily well with the measured damage levels of another part of the data source.
Abstract: This paper examines the applicability of a neural network to analyze model test data of the stability of rubble-mound breakwaters. The neural network is an information-processing system, modeled on the structure of the human brain, that is able to deal with information whose interrelation is not clear. Seven parameters concerning the stability of rock slopes are used: the stability number, the damage level, the number of attacking waves, the surf-similarity parameter, the permeability parameter, the dimensionless water depth in front of the structure, and the spectral shape parameter. The damage levels predicted by the neural network, calibrated by using a part of Van der Meer’s 1988 experimental data, agree satisfactorily well with the measured damage levels of another part of the data source by Van der Meer 1988 and by Smith et al.’s 1992 data. The agreement between the predicted stability numbers by the neural network and the measured stability numbers is also good.

128 citations


Journal ArticleDOI
TL;DR: In this article, the influence of oscillatory flow conditions on the porous flow friction coefficients have been implemented in new expressions for porous flow coefficients, which can be used both to study scale effects in small-scale physical models and for the implementation in numerical models simulating porous flow.
Abstract: Permeability measurements were carried out in a U-tube tunnel to study flow through coarse granular material. The results are of importance for studying the flow in permeable structures such as rubble-mound structures and gravel beaches. The contributions of laminar and turbulence friction terms have been determined as well as the importance of inertial resistance. Differences between stationary flow and oscillatory flow conditions have been studied. The influence of oscillatory flow conditions on the porous flow friction coefficients have been implemented in new expressions for porous flow friction coefficients. These can be used both to study scale effects in small-scale physical models and for the implementation in numerical models simulating porous flow.

120 citations


Journal ArticleDOI
TL;DR: In this article, the vertical and temporal variations of the instantaneous sediment concentration and transport velocity from which the sediment-transport rate per unit width was obtained were measured based on individual particles.
Abstract: Experiments on sediment transport under sheet-flow conditions were conducted by tracing individual and grouped light plastic particles. The measurements based on individual particles yielded the vertical and temporal variations of the instantaneous sediment concentration and transport velocity from which the sediment-transport rate per unit width was obtained. In addition, moving areas of painted particle groups were measured to estimate instantaneous sediment transport rates per unit width directly. Measured local sediment-transport rates were the largest at one or two particle diameters above the initial bed surface. Instantaneous sediment-transport rates per unit width exhibited a π/6 phase lead relative to the free-stream velocity. The measured sediment-transport rates averaged over a half-cycle were compared with forcing functions Shields and mobility parameters. The present data as well as most available existing data in terms of the normalized transport rate without the settling velocity were well arranged by the mobility number to the power of 1.5.

82 citations


Journal ArticleDOI
TL;DR: In this paper, the effect of macrocystis kelp forest on the propagation of surface gravity waves was measured over a 67-day period at four locations around a 350m-wide kelp bed off Carlsbad, California.
Abstract: The effect of a Macrocystis kelp forest on shoreward propagating surface gravity waves was measured. Observations were made over a 67-day period at four locations around a 350-m-wide kelp bed off Carlsbad, California. Instruments were located directly offshore and onshore of the kelp bed at depths of 13 m and 8 m, respectively, and at control stations at the same depths, but displaced 750 m alongshore, away from the kelp bed. The bathymetry between the offshore and onshore sites was gently sloping and featureless. The measured spectra, significant wave height, mean wave direction at peak frequency, and total radiation stress differed only slightly between the offshore kelp and control stations and were similar at the onshore sites. The similarity of the wave field at the onshore kelp and control sites shows that this typical southern California kelp bed, with an average density of about 10 plants per 100 m 2 , does not have a significant effect on waves. These measurements can be used to place upper bound...

73 citations



Journal ArticleDOI
TL;DR: In this paper, a model for the decay of random waves in the surf zone that requires transformation of only one representative wave height [root-mean square (RMS)] without making any assumption about the shape of the probability density function is presented.
Abstract: A model for the decay of random waves in the surf zone that requires transformation of only one representative wave height [root-mean square (RMS)] without making any assumption about the shape of the probability-density function is presented. The breaker decay model proposed by Dally is used as a starting point in the derivation of the new model. It is assumed that random wave properties in the surf zone may be obtained by individually transforming a large number of waves across shore and adding together the effect from each single-wave component. In deeper water, outside the surf zone, where wave breaking is negligible, a Rayleigh distribution is employed to characterize the randomness of the sea. This semianalytic model is compared with a complete Monte Carlo–simulation approach for different beach profile shapes, including barred profiles, and macrofeatures of wave height and energy flux transformation across the surf zone are similar for the two approaches. Comparisons are made in the paper with labo...

52 citations


Journal ArticleDOI
TL;DR: In this article, a technique for the estimation of root-mean-squared velocity parameters associated with irregular waves that have been reflected by coastal structures is presented. But it is not suitable for the case of smooth impermeable plane sloping revetments and permeable rubble-mound cross sections.
Abstract: This paper provides a technique for the estimation of root-mean-squared velocity parameters associated with irregular waves that have been reflected by coastal structures. A previously published first-order expression for estimating root-mean-squared water velocities beneath normally incident and reflected nonbreaking irregular waves by Hughes has been empirically augmented so that estimates can be made for the case of smooth impermeable plane sloping revetments and permeable rubble-mound cross sections. Empirical relationships for reflection coefficient and reflection phase were developed based on measurements obtained during laboratory experiments. These relationships, when used in the theoretical formulations, gave reasonable estimates of RMS velocity compared to measured laboratory data. The procedure given in this paper can be applied with a minimum of computational effort, and it provides realistic estimates of irregular wave kinematics near coastal structures. The capability to make these velocity estimates, particularly near the seabed, provides practicing engineers with an improved tool for addressing such problems as scour potential at structure toes and design of suitable scour blankets.

51 citations


Journal ArticleDOI
TL;DR: In this article, a three-dimensional physical model study of wave diffraction around a semi-infinite breakwater was conducted using a directional spectral wave generator, where both regular and irregular waves with narrow and broad frequency and directional spreading were simulated.
Abstract: A three-dimensional, physical model study of wave diffraction around a semi-infinite breakwater was conducted using a directional spectral wave generator. Both regular and irregular waves with narrow and broad frequency and directional spreading were simulated. Surface elevations were measured in the lee of the breakwater, within a radius of three wavelengths of the tip. Comparisons with regular and irregular wave prediction methods indicate the strengths and limitations of the methods for various wave conditions, and the importance of directional spreading. Data are given to assist other investigators in testing numerical models.

Journal ArticleDOI
TL;DR: In this article, a suspended pipe breakwater was designed specifically for fishery/pleasure-craft harbors where moderate wave agitations in the harbor basin are admissible, which consists of a row of closely spaced pipes mounted onto a frame and suspended between the support piles spaced far apart.
Abstract: A suspended pipe breakwater was designed specifically for fishery/pleasure-craft harbors where moderate wave agitations in the harbor basin are admissible. The present breakwater consists of a row of closely spaced pipes mounted onto a frame and suspended between the support piles spaced far apart. Experimental studies conducted to determine the wave transmission characteristics indicate that by suspending a row of closely spaced pipes (with a gap to diameter ratio of 0.22 and draft to water depth ratio of 0.46), a 50% reduction in incident-wave height can be achieved. The cost and performance of conventionally adopted pile breakwater (involving a row of closely spaced piles driven on the seabed) were compared with the present system. The comparison revealed that the present system can reduce the investment cost by about 40% and can attenuate waves with the same efficiency as that of a row of closely spaced piles.

Journal ArticleDOI
TL;DR: In this article, the authors analyzed the response of an evolving beach nourishment project and the causative forces in terms of sediment-transport rates and gradients in Perdido Key, Florida.
Abstract: Field data from Perdido Key, Florida, describing the response of an evolving beach nourishment project and the causative forces are analyzed in terms of sediment-transport rates and gradients. Numerical models for planform and profile evolution are applied and tested against the field data. Commonly applied concepts within the coastal engineering community regarding the “depth of closure,” profile “equilibration,” and the best-choice coefficient for use in a predictive equation for longshore sediment transport rate are discussed. The results indicate that the beach planform may be described qualitatively by an analytical solution, and a one-line numerical model gives a reasonable quantitative description of the longshore sediment transport. The depth to which longshore sediment transport gradients affect the profile appears to be much less than the depth to which profile changes are observed, illustrating the importance of cross-shore sediment transport. An existing profile-response model, slightly modified, yielded good results immediately following nourishment, but poorer results as the beach profile approached a more natural configuration.

Journal ArticleDOI
TL;DR: In this article, the stability of three-dimensional physical models of low-crested, detached rubble-mound breakwaters were built, with their individual sections representing the following components of the breakwater: front slope, crest, back slope, total section (combination of the three previous sections), front head, and back head.
Abstract: Three-dimensional physical models of low-crested, detached rubble-mound breakwaters were built, with their individual sections representing the following components of the breakwater: front slope, crest, back slope, total section (combination of the three previous sections), front head, and back head. The stability of the armor units in each of these sections was assessed, for different freeboards, using irregular waves. In a 1992 paper, Vidal et al. presented the stability criteria for the different trunk sections of this model breakwater. This paper focusses on test results from the head sections. A comparison between the stabilities of the head and trunk sections is also discussed. The stability of the back head (BH) section is found to be highly freeboard-dependent. For fully submerged conditions, the back head is one of the most stable sections of the breakwater. On the other hand, when the breakwater is nonovertopping, it is the least stable section. The front head (FH) section's behavior is similar...

Journal ArticleDOI
TL;DR: In this paper, a new wave parameter based on the distribution of large wave heights was proposed to characterize breakwater stability, which also accounts for the duration of the test and the variability in the results of breakwater tests.
Abstract: The description of a sea state just by its variance spectral density and duration is not enough to analyze the stability of rubble- mound breakwaters, since it does not include an adequate characterization of the large waves in that sea state. Numerical simulation has been used to demonstrate that different time domain characteristics result from the simulation of a sea state solely defined by its spectrum and its duration. As a result, it is possible to obtain drastically different damage values on a given breakwater. A relationship between the groupiness factor and some extreme wave- height parameters such as H1/20 has also been illustrated by this numerical simulation. Because of these results, arguments for the use of a new wave parameter, which is based on the distribution of large wave heights, to characterize breakwater stability are made. This new parameter also accounts for the duration of the test. This paper may be helpful in explaining some of the variability found in the results of breakwater tests carried out by different laboratories.

Journal ArticleDOI
TL;DR: In this article, a model for the migration of submerged mounds constructed offshore of the day-to-day surf zone but within the depths disturbed by waves during storm events is developed.
Abstract: A model for the migration of submerged mounds constructed offshore of the day-to-day surf zone but within the depths disturbed by waves during storm events is developed. The model considers net shoreward sand transport due to the velocity asymmetry of finite-amplitude waves, and is based on Bagnold’s bed-load–sand transport equation with Stokes’ second order wave theory. Conservation of sand considerations lead to an equation that indicates mounds will behave according to a nonlinear convection-diffusion model. The “convection coefficient”–like parameter, which is based on the wave and sand-transport models only, is proposed as an estimate of the migration rate for submerged mounds. The expected value of mound movement in different depths can be estimated with site-specific wave-climate data. The full sediment-transport equations successfully simulate the migration of a mound at Silver Strand State Park, California, in 1989. The expected value of the mound-movement parameter gives results that agree reasonable well with measured migration rates both at Silver Strand and offshore of Mobile, Alabama.

Journal ArticleDOI
TL;DR: In this article, a method is developed whereby the delays of a set of interdependent locks may be calculated, by incorporating interdependencies into benefit calculations of lock-improvement projects.
Abstract: As with much of the nation's infrastructure, the inland waterway system is in critical need of expansion and repair. Many of the inland waterway lock and dam facilities have become major constraints to navigation due to increased traffic and facility deterioration, leading to costly delays. Because funds for lock and dam improvements are severely limited, comprehensive analysis methods are necessary to ensure efficient allocation of resources among the many proposed improvement projects. Unfortunately, locks and dams are often treated as independent facilities with regard to operations when in fact there are likely to be significant interdependencies among many of them. An analysis technique is needed that accounts for interdependencies between locks when considering lock improvements. In this paper, a method is developed whereby the delays of a set of interdependent locks may be calculated. By incorporating interdependencies into benefit calculations of lock-improvement projects, a more comprehensive ass...

Journal ArticleDOI
TL;DR: In this paper, a wave load-response model was proposed to simulate the reshaping process of the seaward slopes of dynamic coastal structures such as berm breakwaters and gravel beaches.
Abstract: Wave interaction with berm breakwaters is studied by means of a physical model and a numerical model. The physical-model tests have been used to verify the wave motion as calculated by the numerical model. The numerical model based on finite-amplitude shallow-water wave equations is capable of simulating the wave motion both on and inside the structure. This model for normally incident waves has been extended with a new morphological model for cross-structure transport, which resulted in a wave load-response model capable of simulating the reshaping process of the seaward slopes of dynamic coastal structures such as berm breakwaters and gravel beaches. The combined wave-morphological model has been verified with small-scale laboratory tests and with prototype data. Trends observed in physical model tests, such as the influence of wave height, wave period, and stone diameter on the reshaped seaward slopes, are also reproduced properly.

Journal ArticleDOI
TL;DR: In this article, the authors considered the equations required to analyze the three-dimensional steady-state configuration of an underwater cable system, and the equations used to simulate the cable configuration were given.
Abstract: This paper considers the equations required to analyze the three-dimensional steady-state configuration of an underwater cable system. Both towed systems and autonomous remotely controlled systems are considered, and the equations used to simulate the cable configuration are given. A sea-buggy example, originally considered by De Zoysa in 1978, is given to demonstrate the solution of the resulting two-point boundary-value problem by a shooting method. The results correct those of Wang et al. in 1993. An example of a towed system using a stranded cable demonstrates the inclusion of cable lift. A simplified analysis of the dependence of the cable tension on the cable length is also given. The optimum length of cable required to product the minimum force on the vehicle is between three and six times the direct range of the vehicle from the ship, for a range of vehicle positions.

Journal ArticleDOI
TL;DR: In this article, a numerical model that simulates the sediment transport due to plunging breaking waves has been developed, where a plunging breaker is simulated by superimposing a jet on a non-breaking wave.
Abstract: A numerical model that simulates the sediment transport due to plunging breaking waves has been developed. A plunging breaker is simulated by superimposing a jet on a nonbreaking wave. The hydrodynamics are described by applying a discrete vortex model based on the mixed Eulerian-Lagrangian description of the cloud-in-cell method. Rotation is introduced in the flow where the jet impinges on the surface and in the boundary layer along the bottom. A combined diffusion-convection procedure provides a Lagrangian description of the suspended sediment. The pickup and initial suspension event in the boundary layer is simulated by a diffusion process, while the transport in the outer flow domain is simulated by convection, using the flow field provided by the hydrodynamic module. The bed-load transport is calculated by a conventional formula that relates the transport rate to the Shields parameter. A simulation over a complex bottom topography is compared to the full-scale laboratory experiments performed by Dett...

Journal ArticleDOI
TL;DR: In this paper, an expansion for small oblique wave-incidence angles is used to derive an approximate relationship between measured array cross-spectra and a small number of parameters that describe the incident-wave properties and the reflectivity of the structure.
Abstract: A new method is presented for estimating the reflection of a random, multidirectional sea from a coastal structure. The technique is applicable to an array of wave gauges of arbitrary geometry deployed seaward of the reflector. An expansion for small oblique wave-incidence angles is used to derive an approximate relationship between measured array cross-spectra and a small number of parameters that describe the incident-wave properties and the reflectivity of the structure. Model tests with simulated array data demonstrate that the gross properties of incident and reflected waves can be accurately estimated for wave-incidence angles less than about 30°. The new method is applied to array data acquired offshore of a permeable, rubble-mound breakwater in Monterey Bay, California. The estimated reflection coefficients decrease approximately linearly with increasing frequency. Whereas the observed reflections depend only weakly on the incident-wave energy, the fraction of the incident-wave energy flux transmitted through the breakwater decreases with encreasing wave energy, suggesting that dissipation is enhanced with large-amplitude waves.

Journal ArticleDOI
TL;DR: In this paper, the authors describe a surge discharge at the transition of flow from ebb to flood, which generates the bore, which is possible only in rivers where the summation of the phase lead and delay angles exceeds a threshold.
Abstract: In a tidal river, the peak value of the discharge occurs earlier than the peak value of the tidal elevation. The high water level of a tidal wave moves faster than the low water level, and as a result the slope of the wave-surface profile, in the direction of propagation, increases from high water to low and decreases from low water to high. This differential slope causes retention of tidal flux during ebb, which in turn elevates the low water level and introduces a delay in the occurrence of the low water phase. This delay causes the flood discharge, at the transition of flow from ebb to flood, to start with an initial value. During the passage of tides of large amplitudes, the delay angle and consequently the initial value of the flood discharge at the transition of flow from ebb to flood becomes large and generates a surge. This surge discharge, at the transition of flow from ebb to flood, generates the bore. This is possible only in rivers where the summation of the phase lead and delay angles exceeds...

Journal ArticleDOI
TL;DR: In this article, the inceptive condition for wave breaking over a submerged horizontal plate is proposed, which depends on the ratio of the wave celerity over the plate to that of the incident wave and also on the relative length of the plate relative to the incident wavelength.
Abstract: The inceptive condition for wave breaking over a submerged horizontal plate is proposed. The incident wave parameter I =gH0/C2h, which reduces to the relative wave height for long waves and is proportional to the wave steepness for deepwater waves, is used as the breaking index. Waves break over the plate when I is greater than a critical value I c , which depends on the ratio of the wave celerity over the plate to that of the incident wave and also on the relative length of the plate to the incident wavelength. The establishment of the breaking inceptive condition is based on an empirical formula for partial standing waves breaking in uniform water depth. To determine the relation between the local waves over the plate and the incident wave, linear analysis is employed, and a modification is then made to take into account the nonlinear effect. A laboratory experiment is carried out to verify the semiempirically established breaking condition, and satisfactory agreement between the semiempirical predictio...

Journal ArticleDOI
TL;DR: In this paper, the effects of water table manipulation on beach erosion/accretion is studied, and the effectiveness of the drain for a range of wave climates is also addressed The model study identified an important scale effect pertaining to the infiltration characteristics of the model beach face.
Abstract: The experimental study of the effects of water-table manipulation on beach erosion/accretion is meant to help engineers design and operate beach drain systems The initial position of the drain and expected flow rates through the drain system are key design parameters Whether or not drain systems can be used in both nontidal and tidal coastlines is discussed The effectiveness of the drain for a range of wave climates is also addressed The model study identified an important scale effect pertaining to the infiltration characteristics of the model beach face, which reduced the effectiveness of the model drain The drain was effective for both accretive, and slightly erosive wave climates and for both tidal and nontidal situations; the beach face steepens with the drain operating compared to the no-drain situation This indicates that a drain system should be operated under a wide spectrum of wave conditions Drain flow rates are dependent on wave climate and relative position of the drain

Journal ArticleDOI
TL;DR: In this paper, the evolution of nearshore bars at three sites is examined using a mathematical model to simulate wave-bed interactions induced by progressive wind-generated surface waves, and the model is used to simulate bar development from an initial plane shoreface slope (equivalent to the mean slope at each site) using peak wave periods for moderate and severe storms observed in the region.
Abstract: The evolution of nearshore bars at three sites is examined using a mathematical model to simulate wave-bed interactions induced by progressive wind-generated surface waves. The wave dynamics are described by nonlinear, dispersive, shallow-water theory; the wave-induced flux of sediment is calculated using an associated mass-transport velocity; and the bed topography is described using a continuity equation. The resulting coupled system of nonlinear partial differential equations is simplified using a modal decomposition of the surface wave and is approximated numerically. The model is used to simulate bar development from an initial plane shoreface slope (equivalent to the mean slope at each site) using peak wave periods for moderate and severe storms observed in the region. Predictions of bar number and spacing show good correlation with measured bathymetric profiles. The model provides a physical explanation for the observed correlation of bar number and spacing to basin dimensions and nearshore slope i...


Journal ArticleDOI
TL;DR: In this paper, a 3D wave basin and a 2D wave flume were tested in parallel, and it was found that the time scales for morphological development are adequately modeled in the 2D flume and that there are some differences in the resulting beach profile shapes.
Abstract: Scale effects are always a major concern in mobile-bed hydraulic-model studies. These scale effects can be minimized by using large models (i.e., almost prototype size), but large models require large and costly modeling facilities. Several large “super flumes” have been built for two-dimensional (2D) testing, but right now a comparable large “super basin” does not exist. Thus, beach processes can be tested in large 2D models, but not yet in three-dimensional (3D) models. The research in super flumes assumes that 2D-wave-flume experiments are representative of the 3D prototypes. Two aspects of that assumption are tested in this paper. Six sets of parallel tests were performed in both a 3D wave basin and a 2D wave flume. It was found that the time scales for morphological development are adequately modeled in the 2D flume, and that there are some differences in the resulting beach profile shapes. The 3D profiles correspond closely with the prototype observations; the 2D profiles are affected by exaggerated...

Journal ArticleDOI
TL;DR: In this article, a theoretical solution for oblique-wave diffraction by a segmented offshore breakwater system consisting of an infinite array of equally spaced vertical barriers oriented at an arbitrary angle to the line joining their centers is presented.
Abstract: A theoretical solution is presented for oblique-wave diffraction by a segmented offshore breakwater system consisting of an infinite array of equally spaced vertical barriers oriented at an arbitrary angle to the line joining their centers. The solution is obtained by a Green's function approach. The geometrical periodicity of the breakwater system reduces the problem to that of a singular integral equation for the potential difference across a single breakwater element. Zero-order reflection and transmission coefficients are defined in terms of the amplitudes of the asymptotic (propagating) diffracted waves traveling in the opposite direction to or the same direction as the incident waves, respectively. Numerical values of these coefficients are presented for a range of angles of wave incidence and breakwater orientation, for various breakwater geometric configurations. For certain parameter combinations, significant wave reflection can be achieved using this type of breakwater system.

Journal ArticleDOI
TL;DR: In this paper, the authors proposed a method to estimate the equilibrium planform of pocket beaches similar to the previous work of Hsu and Evans (1989) but depending on only one calibration parameter.
Abstract: Ille FIG. 6. R/Ro versus 13/0 for Platja de Sant Pol 0.10+.5-.--0'.6-~0..,.1-~-a.r8~-a.r9~---lt.a tive to describe the bay planform. However, the discussers have found in their field analysis that linear expressions can also give reasonable results to reproduce the planform of some hayed beaches. In the example just presented, the fit using a first-order polynomial (linear fit) gives r 2 = 0.99. This linear approach, however, can only he used when the upcoast headland does not permit the development of the most curved part of the bayed heach, which appears to be a very common case in nature, at least for the stretch of Mediterranean coast considered. Moreover, the authors, like many others researchers [e.g., Hsu and Evans (1989)], suggest that their adjusted coefficients have an universal value hecause the pattern of wave energy redistribution on the beach of any hay is nearly independent of its dimensions. At the same time, they consider that variations in the material forming the heach do not affect the shape of the heach, and that the same coefficients can he applied. With respect to this point, Fig. 6 shows the application of the authors' method andHsu and Evans' method to predict the planform of another bayed beach (Sant Pol, Catalonian coast). Also included in the figure is the empirical fit to a parabolic curve. As with the previous example, this heach has all the requisites to satisfy the static-equilihrium concept. The angle 13 hetween the dominant incident waves and the control line is 50° and the same as before. In this case, the The authors propose a method to estimate the equilibrium planform of pocket beaches similar to the previous work of Hsu and Evans (1989) but depending on only one calibration parameter. The standpoint is that in the neighborhood of the control point the tangent to the beach is parallel to the wave crest of the incident waves. From this, the authors derive a secondorder polynomial equation for R/Ril in terms of 13/8 to describe the planform of bayed beaches [(4)]. After imposing the conditions at the control point, the authors found that their expression depends on one parameter, 0'. This expression must fit a bayed beach in a way similar to the original parabolic method, although improving the fit at the control point, because now they take into account the local properties at this location. The adjusted coefficients obtained by Hsu and Evans (1989) do not satisfy the condition C, + C 1 + C2 = I at the downcoast control point. However, analyzing the example presented by the authors in Fig. 3, the fitted curve departs from Hsu and Evans' bay planform in the extreme opposite of the control point. Theoretically, this curve should improve the fit at the control point, but far away from this point the fit should be similar. To see if this behavior is due to the selected example, in which the authors reproduced the bay planform using Hsu and Evans' coefficients, the proposed method has been applied to several bayed beaches of the Catalonian coast (northwest Mediterranean Sea, Spain). For illustration, Fig. 5 shows the relation between R/Ril and 13/8 for one of the beaches considered (called Platja del Castell) as predicted by the authors' method and Hsu and Evans' method. Also shown is the empirical fit of the bay planform to a parabolic beach (second-order polynomial) by the least-squares method. This beach is located in a small hay, in such a way that at the extremes the condition of zero transport can be reasonahly assumed, and there is no river inside the hay. Under these conditions, it can he assumed that the planform of the beach is in static equilihrium and the method can he applied. The empirical fit of the heach gave an r 2 value of 1.00, and the coefficients ohtained were Cll = ~0.1O, C = 1.61, and C2 = ~().51.

Journal ArticleDOI
TL;DR: In this article, an experimental study of plunging-wave impacts on flat vertical walls suspended just above the still water level has been presented, where simultaneous pressure measurements are examined in conjunction with video records.
Abstract: An experimental study of plunging-wave impacts on flat vertical walls suspended just above the still water level has been presented. Simultaneous pressure measurements are examined in conjunction with video records. From the results, impact conditions have been found to vary from one associated with a rising water mass and a progressively steeper wavefront during wave action to one with a well-developed plunging jet and significant air entrapment at impact. Pressure distributions and impact force time histories have also been presented to elucidate the spatial and temporal variations of the impact loads. For the plunging wave examined in the study, the highest horizontal force is found to be about two times higher than that on a surface-piercing wall over the zone above still water level. Dominant force oscillations immediately after the occurrence of peak force have also been found. Such oscillations, with amplitudes as high as nonimpact force levels, can have significant influence on the dynamics and st...