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This paper presents the results of an experimental study of the seabed liquefaction beneath standing waves. Silt (with ) was used in the experiments. Two kinds of measurements were carried out: pore water pressure measurements and water surface elevation measurements. These measurements were synchronized with video recording of the liquefaction process from the side. The ranges of the various quantities in the experiments were wave height , wave period , and water depth . The experiments show that the seabed liquefaction under standing waves, although qualitatively similar, show features different from that caused by progressive waves. The pore water pressure builds up (or accumulated) in the areas around the node and subsequently spreads out toward the antinodes. The experimental results imply that this transport is caused by a diffusion mechanism with a diffusion coefficient equal to the coefficient of consolidation. The experiments further show that the number of waves to cause liquefaction at the nodal section appears to be equal to that experienced in progressive waves for the same wave height. [ABSTRACT FROM AUTHOR]

Landslide-generated impulse waves are considered a severe danger for humans and infrastructure. Design formulas following intensive laboratory research allow for a quick assessment of potential slide-event wave features. Unfortunately, prototype data are rare except for underwater slide deposits often corresponding to the only traces of a past event. If past events could be back-analyzed based on in situ scanned underwater slide deposits, the existing assessment approaches could be supported. Video recordings of 41 slide-generated impulse wave tests in a two-dimensional (2D) wave channel were analyzed regarding the underwater slide dynamics and their final deposition patterns. The underwater slide propagation process is described for three specifically selected tests. Correlation equations are presented for underwater slide front propagation and velocity, which are also useful for numerical modeling purposes. In addition, correlation equations are given for slide deposit features, including length and thickness, allowing for their estimation based on initial slide parameters. [ABSTRACT FROM AUTHOR]

Breakwaters can be broadly classified into overtopping and nonovertopping structures. In the case of a nonovertopping breakwater, either the crest level is designed in consideration with the maximum run-up level or a concrete crown wall is provided at the crest on the ocean side of the breakwater to avoid or minimize overtopping. It is essential to understand the wave-induced dynamic and uplift pressures exerted on the vertical face and base slab of the crown wall to incorporate this information in the design. The recently introduced armor block KOLOS, a modified version of DOLOS, is considered for detailed investigation of its hydrodynamic characteristics. Empirical relations have been proposed for the wave-induced pressures caused by regular waves on the crown wall fronted by KOLOS through a comprehensive experimental program. The overall results, compared with a breakwater fronted by natural rocks, indicate that the KOLOS armor layer offers better wave energy dissipation and results in minimal pressures induced on its crown wall. [ABSTRACT FROM AUTHOR]

The current study proposes prediction formulas both for random wave runup and mean overtopping discharge at seawalls constructed on land or in very shallow water. Although several existing formulas for runup and overtopping use the incident wave characteristics at the toes of seawalls, this study adopts the equivalent deepwater wave characteristics and an imaginary seawall slope for easy application of the formulas, especially in relation to seawalls constructed on land. The prediction formulas for overtopping use the predicted runup values. For the wave runup prediction formulas two sets of experimental data are used; i.e., a new set of data and the data obtained in a previous study. For the wave overtopping prediction formulas, the experimental data measured in a previous study are used. Comparisons with measurements show good performances of both new prediction methods. [ABSTRACT FROM AUTHOR]

The channel analysis and design evaluation tool ( CADET) is a numerical program to determine the optimum dredge depth for the offshore portions of entrance channels. A brief description of the theoretical basis and risk assessment in CADET is presented. Validation comparisons between CADET predictions and field measurements of wave-induced vertical motions at Ambrose Channel, New York, are presented. Prototype ship motions were measured with a differential global positioning system in April 1998 along three 488-m-long reaches. Comparisons were made with six ships, three tankers and three containerships, during inbound and outbound transits. In general, the CADET predictions matched the field measurements reasonably well, especially considering the wave heights were relatively small during the measurement period. [ABSTRACT FROM AUTHOR]

About 6,300,000 pressure head waves beneath the sea surface were recorded by an array of 26 transducers aligned orthogonally to the coastline of Reggio Calabria, Italy. The data set covered spectra from very narrow unimodal to very broad multimodal and waves from shallow to deep waters. Herein, the quasi-determinism (QD) theory is proven to be very effective in predicting the probability of large-wave heights as well as the period and particle acceleration of these waves both on deep and shallow waters. In addition, the Tayfun model for predicting the probability of large-wave heights is also proven to be highly effective. [ABSTRACT FROM AUTHOR]

The relative contributions of sea-level rise (SLR) and increasing extratropical storminess to the frequency with which waves attack coastal features is assessed with a simple total water level (TWL) model. For the coast of the U.S. Pacific Northwest over the period of wave-buoy observations (approximately 30 years), wave height (and period) increases have had a more significant role in the increased frequency of coastal flooding and erosion than has the rise in sea level. Where tectonic-induced vertical land motions are significant and coastlines are presently emergent relative to the mean sea level, increasing wave heights result in these stretches of coast being possibly submergent relative to the TWL. Although it is uncertain whether wave height increases will continue into the future, it is clear that this process could remain more important than, or at least as important as, SLR for the coming decades, and needs to be taken into account in terms of the increasing exposure of coastal communities and ecosystems to flooding and erosion. [ABSTRACT FROM AUTHOR]

Experiments on a large pipeline and a small pipeline in a piggyback configuration under regular and irregular waves are carried out. A comparison of the wave forces on the large pipeline and the small pipeline is made. The nondimensional force coefficients for the drag, inertia, and lift are obtained based on the Morison equation. The effects of the Keulegan-Carpenter (KC) number and the spacing ratio between the two pipelines on the force coefficients for the large pipeline, small pipeline, and piggyback pipeline system are investigated. The experimental results indicate that the variation tendencies of the drag coefficients and inertia coefficients with the KC number or the spacing ratio for the large pipeline, small pipeline, and piggyback pipeline system are similar. The variation tendency of the lift coefficient with the spacing ratio for the large pipeline is opposite to that for the small one. [ABSTRACT FROM AUTHOR]

Extensive knowledge is available on the overtopping behavior of traditional smooth impermeable sea defense structures, such as mildly sloping dikes and vertical walls, both typically featuring a high crest freeboard to reduce wave overtopping. A particular design application emerges in the development of wave energy converters of the overtopping type, where maximization of wave overtopping is required, i.e., smooth impermeable steep sloping structures with low crest freeboards subjected to nonbreaking waves. To date, relatively limited knowledge is available on the overtopping behavior of those structures. In this study, the average overtopping rate obtained from new experiments has been analyzed and compared with existing prediction methods. This study contributes to a better knowledge on the overtopping behavior of the steep low-crested structures, which is positioned in between that of mildly sloping dikes and vertical walls and that of structures with zero crest freeboards and relatively large crest freeboards. The existing prediction methods seem unable to predict the significant effects of the slope angle and small relative crest freeboards on the average overtopping rate accurately. Therefore, a new set of prediction formulas is proposed based on the new experiments combined with existing data from literature. These formulas include wave overtopping at vertical walls subjected to nonimpacting waves and at structures with zero crest freeboard. [ABSTRACT FROM AUTHOR]

Vessel-generated waves have the potential to erode the shoreline where there is regular commercial and recreational boat traffic in otherwise low-energy estuarine and fetch-limited environments. Whereas it is well established that vessel-generated waves are capable of resuspending significant quantities of bottom and bank sediment, there are limited field data showing how and when sediment is resuspended by the wake and the direction of net transport. This paper presents the results of an instrumented field study to measure sediment resuspension and transport in response to wakes generated by supercritical pilot boats and subcritical container ships at the mouth of the Savannah River in Georgia. Suspended sediment concentrations increase with the turbulent kinetic energy of the supercritical pilot-boat wake. The amount of sediment resuspended dependent on the available supply of sediment on the upper-foreshore. Whereas sediment is transported landward by the individual waves of the group, net transport is offshore in response to a low-frequency oscillation similar to a second-order group-forced current. In some cases, the direction of net transport is reinforced or reversed depending on the timing of the pilot-boat wake with the seiche forced by a passing container ship. In contrast to the pilot boats, sediment transport by subcritical container ships tends to be landward, but can also be weakly offshore depending on the timing of the wave group with the low-frequency drawdown and surge. [ABSTRACT FROM AUTHOR]

An experiment was conducted in a wave flume to examine the processes of gravel beach profile evolution under irregular waves. Two erosion tests were performed on a steep slope of 1/2 with two different significant wave heights. An accretion test was conducted on a mild slope of 1/5 until its profile became quasi-equilibrium. Another test was initiated with a gravel bar constructed at the toe of the equilibrium profile. The bar migrated onshore and resulted in the seaward shift of the equilibrium profile. Quasi-equilibrium profiles observed after 18 or 36 bursts of 400-s wave action were similar but affected by the differences in the wave height and initial profile. A numerical model developed for damage progression of stone armor layers is shown to predict the profile changes of the two erosion tests. The bed load formula used in the model is adjusted to better predict the onshore bar migration and the accretional change on the mild slope. More extensive comparisons of the numerical model with data will be required before it can be applied to gravel and cobble beaches. [ABSTRACT FROM AUTHOR]

The viscous, two-dimensional, free-surface flow induced by the propagation of nonlinear water waves over a rigid rippled bed was simulated numerically. The simulations were based on the numerical solution of the Navier-Stokes equations subject to fully nonlinear free-surface boundary conditions and appropriate bottom, inflow, and outflow boundary conditions. The equations were properly transformed so that the computational domain became time-independent. A hybrid scheme was used for the spatial discretization with finite differences in the streamwise direction and a pseudospectral approximation with Chebyshev polynomials in the vertical direction. A fractional time-step scheme was used for the temporal discretization. Over the rippled bed, the wave boundary layer thickness increased significantly, while vortex shedding at the ripple crest generated alternating circulation regions over the ripple trough. The velocity of the Eulerian drift profile was opposite to the direction of wave propagation far above the ripples, whereas close to the bed, its magnitude was influenced by the ripples up to a height of about six times the ripple height above the ripple crest. The amplitude of the wall shear stress on the ripples increased with increasing ripple steepness, whereas the amplitude of the corresponding friction drag force on a ripple was insensitive to this increase. The amplitude of the form drag force attributable to the dynamic pressure increased with increasing ripple steepness; therefore, the percentage of friction in the total drag force decreased with increasing ripple steepness. The period-averaged drag forces on a ripple were very weak, while the influence of form drag increased with increasing ripple steepness. [ABSTRACT FROM AUTHOR]

During nine small-scale laboratory experiments simulating combined wave overtopping and storm surge overflow on a trapezoidal levee, time series measurements of flow thickness and velocity were acquired at a location on the levee crest and at a location on the landward-side slope. Flow thickness and velocity were combined to estimate time series of the instantaneous discharge. Comparisons of the calculated overtopping discharge time series at the two locations revealed that the time series of instantaneous discharge was the same at both locations with the only difference being a short phase lag. Individual peaks of the discharge time series were examined, and an empirical expression was determined for the root-mean-squared discharge peak. The largest discharge peaks were overestimated by the Rayleigh distribution. For locations on the landward-side slope where the friction slope is approximately the same as the levee slope, it is possible to derive a stream power probability density function based on the overtopping discharge cumulative exceedance probability. The stream power probability density function may be a useful tool for assessing erosion potential of overtopped earthen levees. [ABSTRACT FROM AUTHOR]

To gain a better understanding of the wave forces that led to the failure of numerous causeway-type coastal highway bridges along the U.S. Gulf coast, a series of experiments was conducted on a realistic, 1:5 scale reinforced concrete bridge superstructure. The experimental setup is unique compared to other wave-in-deck studies in that the stiffness of the horizontal support system can be varied to represent different dynamic properties of the bridge system. The bridge specimen is subjected to a wide range of regular and random wave conditions at multiple water levels. In addition to measuring pressures and forces, the experiments measure the dynamic response of the bridge specimen using strain gauges, displacement sensors, and accelerometers. This paper presents the innovative experimental setup, and a preliminary analysis of the data showing the effect of wave height, wave period, and water level, on the forces experienced by the bridge superstructure. [ABSTRACT FROM AUTHOR]

Velocities and sand concentrations measured along 20 transects at the Field Research Facility (FRF) at Duck, North Carolina during October 16–23, 1997 are analyzed to examine the cross-shore and longshore suspended sand transport in the FRF pier depression. The suspended sand volume Vs per unit bottom area remains large outside the surf zone in the depression. The depth-integrated offshore and longshore suspended sand transport rates are shown to be estimated as a, UVs and VVs, respectively, where the empirical parameter a is in the range of 0.1–0.4 in the depression, U is the cross-shore current and V is the longshore current. The offshore suspended sand transport rate at the end of the pier is estimated to be as large as 3.5 m3/h/m at the peak of a storm with an offshore significant wave height of 3.5 m. The sand transported offshore appears to have been supplied by the longshore sand transport toward the pier depression. [ABSTRACT FROM AUTHOR]

An experimental study has been undertaken within the U.K. Coastal Research Facility (CRF), located at HR Wallingford Ltd. Detailed measurements were made to examine the on–off shore spreading of a solute, mostly inside the surf zone, for shore normal waves combined with a longshore current. The results show that the on–off shore mixing is significantly increased by almost 70 times, when compared to current-only conditions. A theoretical advection–dispersion mixing mechanism has been postulated. Using suitable estimates for the turbulent diffusion and on–off shore wave-induced velocity, a theoretical approximation to the overall mixing within the surf zone can be obtained. This theoretical analysis suggests that the on–off shore mixing in the surf zone is proportional to Hb3/2, where Hb is the breaker wave height. It is demonstrated that within the surf zone, the on–off shore mixing is dominated by the effects of the on–off shore velocity. Some previous experimental studies to determine the magnitude of the mixing within the surf zone have been performed. However, the mechanisms responsible for generating the mixing were neither fully investigated nor reported. The previous studies, together with the results obtained from the CRF, are compared to estimates for the theoretical description of mixing developed within this present study. A good agreement exists. [ABSTRACT FROM AUTHOR]

Nonlinear effects for wave groups in bimodal sea states are investigated. The linear free surface displacement is obtained by applying the quasi-determinism theory of the highest waves, with the spectrum given by the superposition of two JONSWAP spectra. Linear groups are modeled as the sum of two groups produced by each unimodal spectrum. Nonlinear effects are given as second-order contribution to the linear free surface displacement. The structure of wave groups is then analyzed for some bimodal spectra. The linear component of wave groups shows a strong variation with respect to the classical structure with unimodal spectra, particularly in mixed seas. It is observed that the nonlinearity gives small contributions for swell dominated seas. For wind dominated sea states, the main nonlinear contribution is given by the wind wave spectral components. For mixed sea states, the interaction among the components of the wind wave spectrum and the components of the swells could give a meaningful contribution to the nonlinear profile. The strongest nonlinear effects occur when the two peaks of the spectrum are close to each other. Finally, the results are validated by means of Monte Carlo simulations of nonlinear sea waves. [ABSTRACT FROM AUTHOR]

The present study is to parameterize the influence of regular progressive waves on the diffusion of a neutrally buoyant turbulent round jet experimentally. The jet, located at the middepth, discharges into the wave field horizontally in the direction against the wave propagation. The particle image velocimetry technique and the laser induced fluorescence technique were used to measure the velocity field and examine the jet cross-sectional profile. Three different wave periods with a range of wave amplitudes in each wave period were tested to investigate the effect of waves on jet diffusion. The wave conditions cover both the shallow water and deep water, whereas the wave slopes range from linear to weakly nonlinear. The results showed that the width of the jet was significantly affected by the waves. The wave dispersion enhanced the jet diffusion, especially for a larger wave slope and a shallower water depth. The results also showed that the wave-to-jet momentum ratio is the most important parameter to characterize the effect of waves to the diffusion of jet. [ABSTRACT FROM AUTHOR]

The present work is a numerical investigation on waves generated by a pressure disturbance moving at constant speed in a channel with a variable cross-channel depth profile. The channel profile, which is uniform in the along-channel direction, has a deep trench located along the centerline of the channel, and shallow banks near the channel walls. Characteristic features upstream and downstream of the moving pressure disturbance are related to the parameters of the pressure disturbance and the cross-channel profile. Our numerical investigation is based on the COULWAVE long wave model. [ABSTRACT FROM AUTHOR]

Offshore wave setup generated by wave breaking during coastal storms can create significant flow through tidal inlets and increase bay flooding. However, these flow contributions are not always considered when determining coastal flooding risk for engineering studies. This paper describes the wave-driven flow process at tidal inlets and demonstrates its impact on bay flooding on Long Island, New York. Numerical simulations using a coupled hydrodynamic and wave model are presented to show contributions to bay water level by wave-driven flow with respect to those by wind surge. These simulations include two major historical coastal storms and a small nor’easter in 2003, during which the model was validated using field measurements of water level. Finally, an approach is introduced for estimating wave-induced flow contributions to bay flooding as a function of inlet and storm characteristics, including tidal prism and wave conditions. The findings of this study indicate that wave-induced flow contributions make up 15–35% of the total storm surge, where the wave-induced flow contribution increases with increased inlet efficiency. [ABSTRACT FROM AUTHOR]

This investigation deals with the changes in the mean velocity associated with a bichromatic wave train in a steady current. The Eulerian-mean velocity model originally developed for monochromatic waves is applied to the calculation of the mean horizontal velocity for bichromatic waves. Instantaneous two-dimensional velocity components for waves following or opposing a current were measured to examine the turbulent intensities and wave-current Reynolds stress. The experimental data suggest that wave direction is an important factor to change the vertical profile of mean velocity based on the logarithmic law. The predicted shape of the mean velocity shows quantitative agreement in the whole depth with the experimental data for various conditions such as irregular waves. [ABSTRACT FROM AUTHOR]

The semicircular breakwater (SBW) is a composite breakwater consisting of a semicircular caisson resting on a rubble mound. The SBW function as a barrier dissipates the incident wave energy and creates tranquility on its leeside. The dynamic pressures due to random waves exerted on seaside perforated SBWs with 7, 11, and 17% of its exposed surface area with perforations were measured. The measured pressures are compared with experimental results of SBW without perforations. In addition, the forces exerted on the caisson alone are measured. The reflection coefficient, runup characteristics, measured total forces, and dynamic pressures in a dimensionless form are presented as a function of relative water depth. The tests were conducted for surface piercing conditions. The effect of the water depth, perforations, and rubble mound height on the above stated variables are brought out, the details of which are reported in this technical note. [ABSTRACT FROM AUTHOR]

This paper compares the output from four methods used to predict the mean overtopping discharge at the root of the South Breakwater of Póvoa de Varzim Harbour (Portugal): two numerical models AMAZON, based on solving the nonlinear shallow-water equations, and COBRAS-UC, based on the Reynolds averaged Navier–Stokes equations, Pedersen’s empirical formula, and the neural network tool NN_Overtopping. Output from the methods is considered alongside data from two-dimensional (2D) physical model tests. The results show that rather accurate predictions can be obtained with COBRAS-UC. Agreement between the data and the AMAZON output depends principally on the impact of porosity on overtopping: agreement is very good when the impact is limited (for high overtopping discharges) and it worsens as porosity plays a more important role (for small discharges). NN_Overtopping estimates the mean discharges with a degree of accuracy similar to AMAZON. Pedersen’s results are those which deviate more from the data, substantially overpredicting the mean discharges for the conditions analyzed. [ABSTRACT FROM AUTHOR]

In this study, we present comparisons of wave height estimates using data from acoustic Doppler wave gauges in ten coastal and estuarine environments. The results confirm that the agreement between significant wave height estimates based on spectral moments (Hm0) versus zero-crossing analysis (H1/3) is linked to the underlying narrow band assumption, and that a divergence from theory occurs as spectral width increases with changes in the wave field. Long-term measurements of the maximum to significant wave height ratio, Hmax/H1/3, show a predictable dependence on the site-specific wave climate and sampling scheme. As an engineering tool for other investigators, we present empirically derived equations relating Hm0/H1/3 and H1/3/m0 to the spectral bandwidth parameter, ν, and evaluate two procedures to predict Hmax from the spectrum when the surface elevation time series is unavailable. Comparisons with observations at each site demonstrate the utility of the methods to predict Hmax within 10% on average. [ABSTRACT FROM AUTHOR]

This study employs an existing finite-difference model based on the hyperbolic form of the modified mild slope equation (MMSE) to investigate wave reflection near bathymetric depressions such as dredged borrow pits and nearshore canyons. First, the model is tested for numerical limitations on the higher order bottom slope and curvature terms using idealized cases of a simple depth transition and a symmetric trapezoidal trench, with comparisons of the MMSE to both the traditional mild slope equation (MSE) solution and a shallow water analytic solution. It is demonstrated that the model gives accurate solutions on slopes as steep as 1:1, and that the solutions from all three models agree in the shallow water region. However, for waves in intermediate depths, predicted wave reflection from nearshore depressions is shown to differ significantly between the MMSE and MSE models. Next, geometrical data from a wide range of existing and proposed borrow pits and a submarine canyon are gathered and analyzed for whether wave reflection is an important process near realistic nearshore depressions. The geometric data show that realistic nearshore depressions lie within the tested range of the MMSE model and that borrow pits are generally not in shallow water, which means it is important to use a MMSE-type model to calculate reflection from these features. In addition, storm conditions on average lead to a 50% increase in reflection coefficient in comparison to the mean wave conditions, due to the increase in wave period. Finally, the results also indicate borrow pit design criteria that can be used to ensure minimal reflection. [ABSTRACT FROM AUTHOR]

This paper describes nonintrusive optical techniques to measure large-scale O(10 m×10 m) flows in a laboratory wave basin. Numerous drifters with weak positive flotation are tracked discretely and automatically using a video camera mounted near the laboratory ceiling. Processed drifter tracks are used for dense estimates of mean surface currents over the visible area. Examination of the drifter tracks also shows that waves are imaged and therefore basic wave properties may also be estimated, although this requires some further assumptions. These video based flow observations are presumed to have less precision than in situ measurements; however, the density of measurements from the video far exceeds that which can be obtained using fixed instruments, providing the method’s major advantage. [ABSTRACT FROM AUTHOR]

Solitary wave interaction with porous breakwaters is studied by using a two-dimensional numerical model. In this model, flows outside of porous media are described by Reynolds-averaged Navier-Stokes equations. For porous flows, the spatially averaged Navier-Stokes equations, in which the effect of porous media is considered by including additional inertia and drag forces, are derived and implemented. The drag force is modeled according to Morison’s equation assuming uniform spherical particles within porous media. The corresponding drag force coefficient is expressed as the function of Reynolds number and hence the proposed porous flow model is valid in a wide range of porous flow regimes, i.e., laminar (linear friction), transitional, and turbulent (nonlinear friction) flows. The numerical model is validated against available theories and experimental data for both long wave and solitary wave interaction with porous breakwaters. The model is then employed to study solitary wave interaction with fully emerged rectangular porous breakwaters with different length and particle size. Based on the results, the characteristics of wave reflection, transmission and energy dissipation are discussed. Additional numerical tests are conducted to study the effects of depth of submergence and porosity of breakwaters on wave transformation. The scale effects in small scale and large scale model tests are also discussed by performing numerical experiments in the reduced and enlarged numerical wave flumes. [ABSTRACT FROM AUTHOR]

Experiments were conducted in a wave flume to investigate wave seepage and overtopping of permeable stone slopes with wide crests. The numerical model based on the time-averaged continuity, momentum, and energy equations is extended to include the landward water flux due to wave seepage and overtopping. The measured wave runup distributions are fitted to the Weibull distribution whose shape parameter increases with the increase of the wave overtopping probability. The wave overtopping rate normalized by the wave-induced water flux at the still water shoreline is shown to depend on the wave overtopping probability and the horizontal number of stones above the maximum wave setup. A simple formula for the seepage rate is proposed by analyzing the seepage flow driven by the wave setup on the seaward slope. The extended numerical model is shown to be in agreement with the measurements of the free surface elevation, cross-shore velocity, wave runup, and seepage and overtopping rates but will need to be evaluated using more extensive data sets. [ABSTRACT FROM AUTHOR]

A numerical model based on the time-averaged continuity, cross-shore momentum, longshore momentum, and energy equations is developed to predict the cross-shore variations of the mean and standard deviation of the free surface elevation and depth-averaged cross-shore and longshore velocities under obliquely incident irregular breaking waves. The suspended sediment volume per unit horizontal area is estimated using the computed energy dissipation rates due to wave breaking and bottom friction. The longshore suspended sediment transport rate is estimated as the product of the longshore current and suspended sediment volume. The developed model is compared with limited field and laboratory data. The calibrated model is in fair agreement with the data. The longshore suspended sediment transport rate is shown to be approximately proportional to the square of the longshore current. The developed model appears promising but will need to be evaluated using extensive data sets. [ABSTRACT FROM AUTHOR]

The paper presents the results of model scale experiments for the study of wave attenuation by horizontal interlaced, multilayer, moored floating pipe breakwater. A review of some significant floating breakwater models proposed by earlier investigators is included. For a floating breakwater the transmission coefficient (Kt) is influenced by relative width of the breakwater (W/L). Nondimensional graphs indicating the variation of Kt with respect to W/L (with Hi/L as a parameter for different Hi/d values) and Kt versus Hi/L (for a range of d/L values from 0.09 to 0.24) have been plotted. Further variation of Kt with relative depth d/L for different W/L values is also studied. From the experimental study and results obtained, it is found that the transmission coefficient decreases with an increase in relative breakwater width W/L and wave steepness Hi/L for all Hi/d values. In the present study it was observed that performance was better for breakwater configurations of W/L>=0.7 when compared with configurations of W/L<0.7. Further, the experimental results obtained were compared with the output of a mathematical model. From the comparison for Hi/L=0.04, values of Kt obtained from the present experiments were in agreement with those obtained from the mathematical model. [ABSTRACT FROM AUTHOR]

Estimation of a wave spectrum from specified values of significant wave heights and average zero cross periods is traditionally made through empirical equations like those of Pierson–Moskowitz and Jonswap. This technical note discusses an alternative scheme based on artificial neural network. Wave spectral distribution over various wave frequencies was obtained for given values of significant wave height and period using feedforward back-propagation network. The rider buoy data at a site off the United States coast monitored by the National Data Buoy Center was used as a basis for network development. Qualitative as well as quantitative comparisons of the network-yielded spectra with target spectra indicated that the developed network could model the wave spectral shapes in a better way than commonly used theoretical spectra. [ABSTRACT FROM AUTHOR]

The accuracy of using high-order Boussinesq-type models as compared to the typical order models is examined in this paper. The high-order model used is the two-layer model of Lynett and Liu in 2004, which captures both linear and nonlinear wave evolution up to kh≈6. The physical situations examined all involve nearshore breaking, and an eddy-viscosity type breaking model is adopted for the two-layer model. One-horizontal dimension setups are the focus of this paper. It is shown that high-order models show significant benefit very near to the breaker line. For regular incident waves, the overshoaling seen in the one-layer (“fully nonlinear” extended Boussinesq) model is due to rapid increase of energy in the fifth and higher harmonics. These high-order nonlinear components are captured well in the two-layer model. The two-layer model also exhibits a noticeable accuracy increase for cnoidal waves breaking on a slope. For regular wave evolution over a bar, the high-order models are in good agreement with experiment, correctly modeling the free short waves behind the step. Under irregular wave conditions, it is likewise shown that high-order nonlinearity is important near the breaker line and the outer surf zone. Using SwashX field data, spectral comparisons are made and discussed. [ABSTRACT FROM AUTHOR]

The characteristics of impulse waves generated in reservoirs by the impact of variable density mass flows were assessed using two-dimensional model experimentation. Particle image velocimetry (PIV) was applied within the wave generation area at the slide impact location and the water wave profiles were measured by seven successive capacitance wave gages. The maximum relative wave amplitude and the normalized wave amplitude of the propagating wave train were correlated with the dimensionless slide quantities and the relative propagation distance, respectively. The impact Froude number was identified as the dominant parameter for slow impacting slides, whereas the water depth and the slide thickness governed the maximum possible wave amplitude for large impact Froude numbers. Four wave types were distinguished due to three different levels of wave nonlinearity associated with variable impact Froude numbers, relative slide densities, and characteristic slide geometries: nonlinear transient bore, transition wave, oscillatory wave, and nonbreaking solitary wave. Moreover, the density effect on the wave generation process was investigated with small impact Froude numbers using sequential PIV velocity vector fields. [ABSTRACT FROM AUTHOR]

Short-crested waves are three-dimensional waves that may be generated through a reflection of a two-dimensional Stokes wave on a seawall. Thus, they are more likely to be observed near ports or any consequent marine structure. Two numerical methods are used to compute three-dimensional surface gravity short-crested waves on deepwater. The first method is an asymptotic procedure and the second computes a direct numerical solution. One of the main properties is the four-wave resonance. Such resonance introduces nonuniqueness with several solution branches connected through a turning point. We show that both computational methods are reliable for nonresonant waves, but that the direct numerical method converges faster. For resonant waves, the direct method is more appropriate because all solution branches can be obtained. The asymptotic method computes only one branch of solutions for any given parameter values, and is uncertain around and past any turning point. Stability analysis of the branches shows that, although sporadic, an instability associated with harmonic resonance is more likely to appear for one branch in the vicinity of the turning point. Consequently this could amplify the unstable resonant mode. The nonuniqueness of the solution requires careful attention in every study on the impact of surface waves on marine structures. It is shown here that the wave force exerted on a seawall may change drastically from one branch of solution to another. [ABSTRACT FROM AUTHOR]

A video technique has been developed to study the motion of individual sediment particles under waves. The technique was developed for moveable bed conditions under waves in the Davidson Laboratory’s large wave tank. Experiments were conducted with grain sizes of 1, 2, and 3 mm. All runs were applied to a modified Shields diagram and accurately predicted the region of motion and no motion. This proves that shear stress is an accurate predictor of grain movement initiation for a flat bed. The individual particle velocities were also measured. An ensemble average of particle velocity with respect to wave phase compared well with Sleath’s expression for instantaneous bed load transport. [ABSTRACT FROM AUTHOR]

An approximate analytical assessment of long wave development due to nonlinear shoaling is obtained and verified against wave-flume experiments. The phase averaged equation for the nonlinear evolution of shoaling waves by Agnon and Sheremet serves as a starting point. Their shoaling interaction function J is significantly simplified through the mild slope assumption. Results, which may be used to assess the long wave input for engineering applications such as harbor resonance studies, are given. [ABSTRACT FROM AUTHOR]

We investigate the drift of small bodies (bodies which do not significantly disturb the fluid) in waves. We begin with the slope sliding models of Rumer and Marchenko, and we establish that the models are different and that the correct model is due to Marchenko. We then investigate the slope sliding model when we have linear wave forcing of constant frequency (for which the differences between the two models vanish). We establish that the drift velocity, for this case, is independent of initial position, which contradicts published results in which drift velocity was shown to depend on initial position. The reason for the error in previous results was the slow decay of the transient motion. For this reason we present a numerical method to calculate the drift velocity, which avoids the problems associated with the slow decay of the transient motion. Some results for the drift velocity are given. [ABSTRACT FROM AUTHOR]

The complex dynamics of the Venice tidal barrier subjected to broadbanded wave spectra are investigated by applying empirical orthogonal function (EOF) analysis to experimental data sets. Space and frequency patterns of the natural modes of the barrier are reconstructed and satisfactorily compared with the recent theory of Li and Mei. The results indicate that when broadbanded wave spectra are considered, natural modes with the longest spatial wavelengths seem more likely to be excited than those with shorter wavelengths. [ABSTRACT FROM AUTHOR]

Predictions of wave action on slopes, and various wave- and depth-induced processes in the surf zone rely on two principal parameters: Wave steepness and surf parameter. For irregular waves, the theoretical distributions of these parameters are not known. Some studies suggest that wave steepness is described well by the Weibull and lognormal probability distributions. These distributions and thus their predictive utility depend on two key statistics, namely the mean and root-mean-square values of wave steepness. This study develops approximate theoretical forms of these statistics for narrow-band long-crested waves. For waves with steepness less than a Miche–Stokes type upper limit, comparisons with measurements from two severe storms show that the theoretical forms so derived and the resulting lognormal law in particular describes empirical data well. These results then permit the distribution of surf parameter to be approximated in a lognormal form also. Consequently, the nature and implications of such an approximation, resulting statistics and their plausible applications to breaker heights and types on slopes are explored. [ABSTRACT FROM AUTHOR]

A new numerical model based on the incompressible, nonhydrostatic Navier-Stokes equations for free surface flow is developed. The equations are transformed vertically to the σ coordinate system and laterally to an orthogonal curvilinear system and solved in a fractional step manner in which the pressure is split into hydrostatic and nonhydrostatic components. The model treats the nonhydrostatic term implicitly and uses a collocated grid and pressure interpolation to prevent checkerboard solutions that occur when the velocity and pressure become decoupled. Advection and hydrostatic pressure terms are integrated explicitly with a second-order accurate predictor-corrector scheme. The corrector utilizes fluxes that are computed in a Godunov-based manner by solving a Riemann problem at each cell face. Flow variables are reconstructed at each cell face to obtain second-order spatial accuracy. Numerical simulations of Stokes, cnoidal, and solitary waves with the proposed method and a reference method in which the hydrostatic pressure is implicitly integrated are compared with analytical solutions and experimental data. [ABSTRACT FROM AUTHOR]

This work compares the spectral analysis of ocean wave fields performed from nautical radar and waverider buoy measurements. The data were taken by a radar station located in the northern coast of Spain and by a buoy that was moored close to the area covered by the radar for its calibration. In this area the sea states are mainly dominated by the presence of northwest swells coming from storms originating in the North Atlantic Ocean. In this order, the radar calibration and the comparisons of different spectral parameters and scalar spectra from both sensors are presented. [ABSTRACT FROM AUTHOR]

Recent advances in the Boussinesq modeling of nearshore hydrodynamics offer a platform for the study of wind effects on wave transformation and breaking-generated nearshore circulation. The paper documents: (1) the new parameterization of the momentum flux transferred from the wind to surface gravity waves in the coastal region on the basis of the field observations; (2) the implementation of the parameterized wind stress into phase-resolving Boussinesq wave models; (3) the development of empirical breaking criteria with the wind effect based on the existing laboratory data; and (4) the tests of the extended Boussinesq model against field observations and empirical results with respect to wind drag coefficients over shoaling waves and wave growth on a shallow lake. Fairly good agreement between the model results and measurements is observed. The methodology for the parameterization of the wind stress as a function of wave steepness and wind speed as well as the extended Boussinesq model incorporating the wind forcing can be used as a tool to improve our understanding of wind effects on nearshore wave propagation and horizontal circulation. [ABSTRACT FROM AUTHOR]

Hunt’s equation provides a simple means of estimating the runup of breaking waves. However, breaking waves also induce setup on a slope. A modification to Hunt’s equation is advocated which accounts for the presence of wave setup. Support for the modification is provided by data from model tests involving random waves approaching smooth, impermeable slopes of 1:5, 1:10, 1:20, and 1:30. Coefficients to be used in the modified equation are given which allow the significant runup and other characteristic values to be estimated. [ABSTRACT FROM AUTHOR]

A new parameter is proposed to characterize the tail spreading performance of extremal distribution functions as defined by the ratio of the 50-year return wave height to the 10-year height, and it is called the spread parameter. Extreme data sets of annual maximum wind speed and peaks-over-threshold significant wave heights have been analyzed for best-fitting distribution functions, for which the spread parameter is evaluated. The observed values of the spread parameter are in good agreement with the predicted values based on the coefficient of variation of an extreme data sample. Formulas are given to derive the scale and location parameters from a given value of the spread parameter. Some typical values of the spread parameter are presented for promotion of performance-based design of maritime structures in the world. [ABSTRACT FROM AUTHOR]

A hydrodynamic analysis has been conducted to assess the potential impact of the sea state on cargo transfer operations in simultaneous sea and swell waves incident from distinct directions. An interactive tool has been developed that allows parameter variation and provides an immediate graphical presentation of the data. This note presents some typical results for relative vertical velocity between two of the vessels in the form of surface and polar plots. These graphical representations clearly display the effects of shielding and other complex hydrodynamic interactions among the vessels in a seaway. [ABSTRACT FROM AUTHOR]

An improved curvilinear grid model based on fully nonlinear Boussinesq equations is used to simulate wave propagation in Ponce de Leon Inlet, Fla. We employ the nearshore bathymetry of Ponce de Leon Inlet and generate a stretched curvilinear grid that can resolve shortwaves in the nearshore region and fit the complex geometry. Simulations of 18 cases with monochromatic input waves and Texel-Marsden-Arsloe spectral waves are carried out on the same scale as in the 1:100 scale physical model conducted at the U.S. Army Engineer Research and Development Center. Wave height comparisons, time series comparisons of surface elevation for monochromatic wave cases, and comparisons of power spectrum for spectral wave cases are made between numerical results and laboratory measurements. Comparison is also made between the probability distribution of surface elevation and skewness and asymmetry measures for both the measured data and the Boussinesq model results. It is shown that for the computations of nonlinear wave transformation over irregular bathymetry, the Boussinesq model is able to predict nonlinear wave features and is thus a more accurate model than some conventional models in shallow water. [ABSTRACT FROM AUTHOR]

This paper summarizes a part of the work carried out in the framework of the European research program MAST III-PROVERBS. It deals with the evaluation of pressure distribution and forces acting on the different faces of a perforated caisson breakwater. Various 2D model tests were performed at LeHavre and Caen Universities, and field measurements were made on the Dieppe breakwater. The aim of the study was to improve common knowledge and design of this type of dissipative monolithic breakwater. A new method for the calculation of maximum horizontal wave forces is proposed. The method is tested for more than 120 force estimates derived from various experimental sources, and it proves to be fairly good and reliable for engineering applications. [ABSTRACT FROM AUTHOR]

A 3D numerical solution was derived to determine the wave field in a physical wave tank equipped with a porous wave absorber of variable width and draft. The solution was achieved by applying the boundary element method. The model was applied to analyze the effect of the geometry and material of wave absorbers on wave reflection to eventually equip a wave tank with a proper wave absorber. The results show that absorber geometry has a complex, often surprising and nonintuitive effect on wave reflection. A more pronounced effect on wave reflection possesses physical and hydraulic properties of the material used to build a wave absorber. A reduction of wave reflection can usually be achieved by increasing absorber length and simultaneously decreasing its slope, and often a reduction of wave reflection can be achieved by increasing absorber draft or width. Moreover, a reduction of wave reflection, often substantial, can be achieved by increasing porosity and the damping coefficient. The results and additional analysis show that a reasonable wave reflection level can already be achieved for fairly short absorbers, and the model can be applied to select an optimal wave absorber for any prespecified conditions. Theoretical results are in reasonable agreement with experimental data. [ABSTRACT FROM AUTHOR]

In the design of oil and gas terminals, six degrees of freedom (SDF) models are often used to calculate the motions of the moored ship and forces in mooring lines and fenders. Although the SDF simulation programs have been used for more than 20 years, there is still little verification of the results with prototype measurements. This paper includes the results of a verification of one of these SDF models using prototype measurements as reference data. The prototype measurements consisted of mooring line loads of liquefied natural gas (LNG) carriers at berth for periods during which environmental conditions were recorded. A study was carried out to simulate these conditions in the model and to compare the model results with the measurements. In addition to mooring line loads, the computed vessel motions have been analyzed. For the studied berth situation, the yaw motion resulting from swell waves is quite dominant and is causing large breast line forces. An empirical expression has been derived to calculate the yaw motions of the moored LNG carrier in swell waves. This expression is a first step in defining a general expression to estimate maximum yaw motions and mooring forces to be used in preliminary harbor design. [ABSTRACT FROM AUTHOR]

Beach-profile evolution, along with measurements of waves, currents, and sediment concentration, under spilling and plunging breakers of similar height were studied in the three-dimensional Large-Scale Sediment Transport Facility at the U.S. Army Engineer Research and Development Center. Unidirectional irregular waves were generated over a fine-sand beach. Beach-profile shape reached equilibrium after 1,330 and 280 min of spilling and plunging wave actions, respectively. Near the main breaker line, the profile evolved differently under plunging and spilling breakers. Across most of the midsurf zone dominated by surf bores, the equilibrium profile shapes were similar. Uniform energy dissipation per unit volume at equilibrium, as assumed in the Dean 1977 model and often used in cross-shore sediment-transport modeling, was measured for both cases across most of the surf zone except at the main breaker line, where a much greater rate of dissipation occurred. The bar/trough formation and maintenance were closely related to the local patterns of sediment suspension and bed scour at the plunging point. [ABSTRACT FROM AUTHOR]