Wave transformation of regular waves was measured in a laboratory model of a fringing reef with a steep face and an outer reef-top slope gradually decreasing in the landward direction. Data was obtained for various wave conditions and water levels. A nonlinearity parameter, Fco = g1.25Ho0.5T2.5/hc1.75, based upon one proposed by Swart and Loubser (1979), is proposed as a suitable parameter for classifying wave transformation regimes on this reef. In particular, when Fco > 150, waves plunge on the reef edge and the amount of wave energy reaching a shore or structure is small ⩽ 16%. When Fin co ⩽ 100, waves spill on the reef-top but the greater part of their energy is transmitted over the reef-top. The maximum values of the wave height to water depth ratio on the reef-top were found to be consistent with Nelson's analyses for laboratory and field data which indicate that the maximum stable wave height to depth ratio H/d on a horizontal bottom never exceeds 0.55 for shallow water waves (Fc > 500). The experimental data confirms that the maximum value of H/d decreases when Fc decreases but that it also increases when the bottom slope increases.
The Haringvliet estuary is part of the Dutch Delta coast. Since 1950, several large coastal engineering projects have been carried out in the Haringvliet area. The most important of these is the closure of the estuary by the construction of a dam with sluices (finished in 1970). Land reclamation projects of the Maasvlakte (1964–1976) and the so-called Slufter (1986–1987) have also been carried out. These projects have profoundly affected the hydrodynamics and therefore the morphology of the area. New interventions are under discussion and to be able to predict their impact on the morphology, it is necessary to understand the morphological developments caused by the past interventions. In this study, the development with time of the sand volume in the Haringvliet estuary after closure has been studied using bathymetric measurements of the years 1970, 1972, 1979, 1980, 1986 and 1990 until 1999. The changes in sand volume above NAP (Dutch Ordnance Level) −10 m relative to 1970 have been determined. The area in which these volumes have been calculated had to be chosen very carefully to diminish the effects of all other human interventions. As was expected, the estuary shows sedimentation. It could be concluded that the adaptation time scale is about 11 years and that the equilibrium volume has almost been reached in the year 2000.
Erosion of the southern Gold Coast beaches (SE Queensland, Australia) was exacerbated after the extension of the Tweed River training walls in the early 1960s. To achieve the objective of restoring and maintaining beach amenity, significant nourishment works have been undertaken in Coolangatta Bay over the past 30 years. Particularly, under the Tweed River Entrance Sand Bypassing Project (TRESBP) since 1995, a number of nourishment campaigns and the implementation of a permanent sand bypass system in 2001 have resulted in significant changes of Coolangatta Bay morphology. The present case study investigates the influence of both wave climate and nourishment works on the area extending from the updrift Snapper Rocks area to downdrift Kirra Beach. SWAN spectral wave model is implemented at Coolangatta Bay area and forced by the global wave model WW3 to estimate wave forcing and the potential natural longshore drift entering in Coolangatta. Specific transects extracted from accurate bathymetric surveys are used to investigate and quantify Coolangatta Bay sedimentation for the period 1987–2005. A network of Argus video stations provides high sample rate information on the shoreline evolution. Results show that, over the past 10 years, Coolangatta Bay has infilled rapidly. Sedimentation reached up to 6 m in some areas between 1995 and 2005, with beach width increasing by 200 m at Kirra Beach. Rapid seaward shoreline migration is consistent with the intense over-pumping of sand relative to the natural potential to move sand alongshore. The nourishment strategy used during this project has successfully delivered large amounts of sand to the southern Gold Coast embayment, although it has been up to now controversial from many community perspectives. The artificial sand bypassing process proved to be much more efficient than depositing the dredged sand in the nearshore area which requires a significant period of low energy condition in order for the deposited sediment to migrate shoreward and weld to the shore. This case study confirms that, when carefully undertaken, sand bypassing is a sustainable and flexible soft engineering approach which can work in concert with natural processes.
Existing methods for solving 1D morphodynamical systems have been reviewed and new, improved approaches have been identified. Usually the flow equations and the bed-updating equation are solved at separate time steps, using a quasi-steady approach. In this paper we have investigated the simultaneous (or coupled) solution of the equations. The schemes tested are the Lax–Wendroff and the Roe schemes, both with and without flux-limiting methods. Furthermore the discretisation of source terms has been investigated and has shown to be important.
The transformation of irrotational surface gravity waves in an inviscid fluid can be studied by time stepping the kinematic and dynamic surface boundary conditions. This requires a closure providing the normal surface particle velocity in terms of the surface velocity potential or its tangential derivative. A convolution integral giving this closure as an explicit expression is derived for linear 1D waves over a mildly sloping bottom. The model has exact linear dispersion and shoaling properties. A discrete numerical model is developed for a spatially staggered uniform grid. The model involves a spatial derivative which is discretized by an arbitrary-order finite-difference scheme. Error control is attained by solving the discrete dispersion relation a priori and model results make a perfect match to this prediction. A procedure is developed by which the computational effort is minimized for a specific physical problem while adapting the numerical parameters under the constraint of a predefined tolerance of damping and dispersion error. Two computational examples show that accurate irregular-wave transformation on the kilometre scale can be computed in seconds. Thus, the method makes up a highly efficient basis for a forthcoming extension that includes nonlinearity at arbitrary order. The relation to Boussinesq equations, mild-slope wave equations, boundary integral equations and spectral methods is briefly discussed.
In the recent paper by J.P. Le Roux [Coastal Engineering 54 (2007) 271–277], the author provides a simplified approach to calculating the depth, length, and height of waves at the onset of depth-induced breaking (i.e. at the breaker line). However, the proposed methodology and the comparisons to other methods suffer from a large number of inconsistencies and basic calculation errors. In addition, there are a number of erroneous physical interpretations and many of the conclusions are based on erroneous data. The remaining conclusions are either not new or based on circular logic, such as to render them moot. In the following, we will not attempt to point out all the errors or inconsistencies that we found, instead we focus on major points of contention.
A two-dimensional (2D) numerical model of wave run-up and overtopping is presented. The model (called OTT-2D) is based on the 2D nonlinear shallow water (NLSW) equations on a sloping bed, including bed shear stress. These equations are solved using an upwind finite volume technique and a hierarchical Cartesian Adaptive Mesh Refinement (AMR) algorithm. The 2D nature of the model means that it can be used to simulate wave transformation, run-up, overtopping and regeneration by obliquely incident and multi-directional waves over alongshore-inhomogeneous sea walls and complex, submerged or surface-piercing features. The numerical technique used includes accurate shock modeling, and uses no special shoreline-tracking algorithm or shoreline coordinate transformation, which means that noncontiguous flows and multiple shorelines can easily be simulated. The adaptivity of the model ensures that only those parts of the flow that require higher resolution (such as the region of the moving shoreline) receive it, resulting in a model with a high level of efficiency. The model is shown to accurately reproduce analytical and benchmark numerical solutions. Existing wave flume and wave basin datasets are used to test the ability of the model to approximate 1D and 2D wave transformation, run-up and overtopping. Finally, we study a 2D dataset of overtopping of random waves at off-normal incidence to investigate overtopping of a sea wall by long-crested waves. The data set is interesting as it has not been studied in detail before and suggests that, in some instances, overtopping at an angle can lead to more flooding than at normal incidence.
As a gridless particle method, the MPS (Moving Particle Semi-implicit) method has proven useful in a wide variety of engineering applications including free-surface hydrodynamic flows. Despite its wide range of applicability, the MPS method suffers from some shortcomings such as non-conservation of momentum and spurious pressure fluctuation. By introducing new formulations for the pressure gradient and a new formulation of the source term of the Poisson Pressure Equation (PPE), and by allowing a slight compressibility, we have proposed modified MPS methods for the prediction of wave impact pressure on a coastal structure. The improved performance of the modified methods is shown through the simulation of numerous wave impact problems (including the impacts by a dam break flow, a flip-through and two cases of slightly-breaking waves) in comparison with the experimental data.
A class of compound mathematical models of transient morphological evolutions in shallow water is discussed, based on commonly applied horizontally two-dimensional formulations of the water and sediment motion in the coastal zone. Three major aspects of the composition of such models are considered, viz. the specific adequacy of the constituent models, the balance of the total model and the possibility of spurious interactions. The lacunae in the knowledge and the tools needed to judge a proposed model at these points are indicated.Examples of spurious interactions are described in further detail and techniques to trace and avoid them are given. These examples, concerning morphological evolutions without the influence of waves, show that the advective acceleration terms in the flow model play an essential part in the bottom evolution and its interaction with the current and that incorporation of the bottom slope effects on the sediment transport is indispensable in models with a local transport formulation.
In this paper, a hybrid scheme based on a set of 2DH extended Boussinesq equations for slowly varying bathymetries is introduced. The numerical code combines the finite volume technique, applied to solve the advective part of the equations, with the finite difference method, used to discretize dispersive and source terms. Time integration is performed using the fourth-order Adams–Bashforth–Moulton predictor–corrector method; the Riemann problem is solved employing an approximate HLL solver, a fourth-order MUSCL-TVD technique is applied. Five test cases, for non-breaking and breaking waves, are reproduced to verify the model comparing its results to laboratory data or analytical solutions.
The state-of-the-art in depth-averaged mathematical modelling of 3-D coastal morphology is described for the medium-term morphodynamic model type, in which constituent models of waves, currents and sediment transport based on first physical principles are linked together to describe the time-evolution of the bed topography. Various aspects of the combined system of equations are discussed, such as its mathematical character, its inherent stability and its equilibrium state. The results of an intercomparison of different models are shown for two test cases and the potentials and limitations of the model concept are discussed.
The present study aims to analyze the effects of different submerged bars nourishment strategies using a 2DV process-based morphodynamical model. A two-barred beach profile typical of the French Mediterranean micro-tidal storm-dominated coastline is chosen as a reference profile. Two different kinds of modified beach profiles are considered. (i) Only the outer bar is nourished, the inner bar being unchanged (ii) both bars are nourished. Three typical wave forcing regimes are considered. The behavior of the natural profile is first investigated under the 3 wave forcing regimes. Then the behavior of the various nourished profiles is analyzed in terms of wave dynamics and bars behavior. On the basis of the model results, the outer bar only nourishment strategy appears to be preferable.
In this paper, infragravity (IG) waves, forced by normally and obliquely incident wave groups, are studied using the quasi-3D (Q3D) nearshore circulation model SHORECIRC [Van Dongeren, A.R., I.A. Svendsen, 1997b. Quasi 3-D modeling of nearshore hydrodynamics. Research report CACR-97-04. Center for Applied Coastal Research, University of Delaware, Newark, 243 pp.], which includes the Q3D effects. The governing equations that form the basis of the model, as well as the numerical model and the boundary conditions, are described. The model is applied to the case of leaky IG waves. It is shown that the Q3D terms have a significant effect on the cross-shore variation of the surface elevation envelope, especially around the breakpoint and in the inner surf zone. The effect of wave groupiness on the temporal and spatial variation of all Q3D terms is shown after which their contribution to the momentum equations is analyzed. This reveals that only those Q3D coefficients, which appear in combination with the largest horizontal velocity shears make a significant contribution to the momentum equations. As a result of the calculation of the Q3D coefficients, the IG wave velocity profiles can be determined. This shows that in the surf zone, the velocity profiles exhibit a large curvature and time variation in the cross-shore direction, and a small — but essential — depth variation in the longshore direction.
A quasi-3D model for suspended sediment transport based on an asymptotic solution of the convection-diffusion equation is developed for currents and waves. The influence of waves on the sediment concentration is included through the diffusion analogy and the boundary condition near the bed. The flow velocity profile is assumed to have a logarithmic shape. An extensive sensitivity analysis concerning the influence of wave and current parameters on the suspended adjustment phenomenon shows that the presence of waves considerably enlarges the suspended load and its adjustment time and length scales. Validity analysis of the quasi-3D formulation results in restrictions for the suspension parameter (modified for waves) and for the time and length scales of changes in hydraulic conditions. The presence of waves eases all the above restrictions and thus enlarges the validity area of the model considerably.The model is compared with 2DV and 3D numerical solutions of the convection-diffusion equation with good agreement and verified with existing measurements.
Existing concepts of wave-induced nearshore current models, in the cross-shore vertical plane (2DV) and depth-integrated (2DH), are combined to a quasi-3D mathematical model. This combination is tested for reproducing correct results in 2DV and 2DH situations. The importance of the various contributions to the wave-induced secondary circulation in the vertical plane is investigated for realistic parameter ranges, which leads to the conclusion that both the non-breaking and the breaking fraction of a random wave field in the surf zone generate important secondary currents.Additional computations show the relevance of a 3D-approach of nearshore currents, even in seemingly simple situations like a plane sloping beach with obliquely incident waves.
A background knowledge of marine dynamics helps harbour managers to control pollution and to manage dredging and traffic operations. This contribution studies the hydrodynamic conditions within Bilbao Harbour, which is enclosed by the Nervión Estuary (in the Basque Country, Spain). The results obtained from hydrographical surveys are compared with numerical simulations obtained using the Regional Ocean Modelling System (ROMS). Hydrodynamic modelling was carried out to determine the inner harbour currents for a specific period in which data were available. Then, numerical experiments were designed in order to quantify the importance of different driving mechanisms in the harbour hydrodynamics. The results show that, in addition to the strong tidal influence on water circulation, the wind forcing and freshwater discharge also have a non-negligible influence on the currents. The computational domain is complex due to the presence of harbour infrastructures (i.e. breakwaters and piers). As a result, topographic eddies are therefore observed in the results. The freshwater influence of the Nervión river can also be observed in residual currents. This paper presents an improvement to the application of numerical modelling to a complex geometry domain, contributing to our understanding of the behaviour of the marine systems in meso-tidal harbours. This can be used to deal with harbour engineering and management problems.
A two-dimensional phase-resolving wave transformation module is combined with an intra-wave sediment transport module to calculate the two-dimensional sediment transport rates. The wave module is based on the Boussinesq equations extended into the surf zone. Two hydrodynamic modules are developed for the calculation of the vertical variation of the eddy viscosity and the currents. The intra-wave sediment concentrations and sediment transport rates are also calculated. The model was verified against several test cases, and a sensitivity analysis was performed. Both hydrodynamic modules produced close results for the mean currents. The two models also produced close results for the sediment transport rates with larger differences observed at the locations with a stronger undertow. The model results showed that for irregular breaking waves, the mean sediment concentration cannot be calculated directly from the mean eddy viscosity.
This study presents wind wave fields' characteristics over the Baltic Sea obtained with the WAM model and their verification against observations. This is a part of the HIPOCAS research project funded by the European Union with an objective to obtain a 44-year hindcast of wind, wave, sea-level, and current climatology for European waters and coastal seas for application in coastal and environmental decision processes. A reasonable agreement between the modelled and observed both in-situ and satellite wave data was obtained. A high-resolution homogeneous wave data set generated with the hindcast system created within HIPOCAS provided a large number of possibilities to examine the long-term statistics and variability of the wind wave fields over the Baltic Sea.
Nowadays, many efforts are leading to use the high potential offshore wind energy resources. A detailed assessment of the offshore wind resources arises as a first-rate requirement. Most of such assessment is based on extreme offshore wind atlas generated mainly from global reanalysis and satellite data. Both sort of data show certain shortcomings related, among others, to coarse spatial resolution and time inhomogeneity issues, respectively. This snag seems to be crucial over areas such as the Mediterranean Basin, which is characterized by a complex land–sea distribution and a significant orography. The HIPOCAS Mediterranean long-term (1958–2001) wind database comes to overcome the aforementioned reanalysis shortcoming and provides a Mediterranean wind data set useful to perform extreme wind analysis. This contribution also deals with a statistical extreme wind analysis over the whole Mediterranean offshore areas. Extreme return periods and levels are obtained from annual maxima using a number of distributions. Additionally, an alternative regional statistical method based on regional L-moment statistics is also proposed. The regional technique is applied to reduce uncertainty and allows a higher number of measurements to be included in the analysis, using data from a homogeneous region instead of from a single location. The herein performed extreme wind analysis provides a detailed assessment of high wind offshore areas over the Mediterranean and constitutes a subject of great interest for evaluation of wind resources.
The subject of the investigation was the multiyear hindcast of the sea level elevations and currents over the Baltic Sea. The approach follows to the HIPOCAS project conception and contained the 3D hydrodynamic model using boundary conditions from the atmosphere and catchment for 44-year period referring to the second half of the 20th century.The sea level fluctuations and current hindcast were performed by the M3D_UG model based on the POM. The evaluations of hindcast accuracy were done by comparison of the modelled simulations to field observations. Their results were presented as statistical measures cored on the mean and integral square errors. The model results compared to the observed data agreed well and confirmed usefullness of the used model for hindcast.Except for the hindcast quality evaluations, both observed and modelled sea level elevations were analyzed by the spectral and principal component analysis methods for singling out the components of its variability. The research proved at least two opposite trends — decreasing at the northern coast and increasing in the southern ones. Moreover, three temporal components of their variability were revealed. Due to vectorial and modular average of currents, annual circulation patterns in the Baltic Sea have been obtained. Using of long term sequences of the current fields, inter annual changes of averaged velocity and their increasing trend were evaluated.
This paper describes the development of tsunami scenarios from the National Seismic Hazard Maps for design of coastal infrastructure in the Pacific Northwest. The logic tree of Cascadia earthquakes provides four 500-year rupture configurations at moment magnitude 8.8, 9.0, and 9.2 for development of probabilistic design criteria. A planar fault model describes the rupture configurations and determines the earth surface deformation for tsunami modeling. A case study of four bridge sites at Siletz Bay, Oregon illustrates the challenges in modeling of tsunamis on the Pacific Northwest coast. A nonlinear shallow-water model with a shock-capturing scheme describes tsunami propagation across the northeastern Pacific as well as barrier beach overtopping, bore formation, and detailed flow conditions at Siletz Bay. The results show strong correlation with geological evidence from the six paleotsunamis during the last 2800 years. The proposed approach allows determination of tsunami loads that are consistent with the seismic loads currently in use for design of buildings and structures.
As a part of the MAST2 G8-M Coastal Morphodynamics project, the predictions of four sediment transport models have been compared with detailed laboratory data sets obtained in the bottom boundary layer beneath regular waves, asymmetrical waves, and regular waves superimposed co-linearly on a current. Each data set was obtained in plane bed, sheet flow, conditions and each of the four untuned numerical models has provided a one-dimensional vertical (1DV), time-varying, representation of the various experimental situations. Comparisons have been made between the model predictions and measurements of both time-dependent sediment concentration, and also wave-averaged horizontal velocity and concentration. For the asymmetrical waves and for the combined wave-current flows, comparisons have been made with vertical profiles of the cycle-averaged sediment flux, and also with the vertically-integrated net sediment transport rate. Each of the turbulence diffusion models gives an accurate estimate of the net transport rate (invariably well within a factor of 2 of the measured value). In contrast, none of the models provides a good detailed description of the time-dependent suspended sediment concentration, due mainly to the inability of conventional turbulence diffusion schemes to represent the entrainment of sediment into suspension by convective events at flow reversal. However, in the cases considered here, this has not seriously affected the model predictions of the net sediment flux, due to the dominance of the near-bed transport. The comparisons in this paper are aimed not only at testing the predictive capability of existing sediment transport modelling schemes, but also at highlighting some of their deficiencies.
A cylindrical tumbling mill apparatus is used to provide weight loss and shape change data on rock fragment abrasion from four experiments Weight loss data for the four limestone samples confirm the reproducibility of the test conditions and of the abrasion resistance index value which had been reported previously for this rock type Progressive shape changes of subsamples are analysed using recently developed automated image analysis techniques and computer methods based on Fourier and Fractal shape descriptors.A theoretical relationship between weight loss, revolutions in the mill and surface roughness is developed. A single shape descriptor is chosen to account for the role played by shape and roughness in changing the rate of weight loss. The experimental data is consistent with the theory when the single descriptor is the Fourier Asperity Roughness Factor as defined in this paper.Weight loss-time, and asperity roughness-time relationships are determined and their application to armourstone rounding is discussed. Examples from a hard and a soft limestone are given to illustrate the use of the tumbling mill aggregate abrasion test in the prediction of wear of armourstone after a certain number of years in service.
A theoretical solution for the reflection of linear shallow-water waves from a vertical porous wave absorber on a horizontal bottom is presented. Periodic solutions are matched at the front face of the absorber by assuming continuity of pressure and mass. The friction term describing the energy loss inside the absorber is linearized and, by using Lorentz principle of equivalent work, the reflection coefficient is determined as a function of parameters describing the incoming waves and the absorber characteristics.
The objective of the present work is to discuss the implementation of an active wave generating–absorbing boundary condition for a numerical model based on the Volume Of Fluid (VOF) method for tracking free surfaces. First an overview of the development of VOF type models with special emphasis in the field of coastal engineering is given. A new type of numerical boundary condition for combined wave generation and absorption in the numerical model VOFbreak2 is presented. The numerical boundary condition is based on an active wave absorption system that was first developed in the context of physical wave flume experiments, using a wave paddle. The method applies to regular and irregular waves. Velocities are measured at one location inside the computational domain. The reflected wave train is separated from the incident wave field in front of a structure by means of digital filtering and subsequent superposition of the measured velocity signals. The incident wave signal is corrected, so that the reflected wave is effectively absorbed at the boundary. The digital filters are derived theoretically and their practical design is discussed. The practical use of this numerical boundary condition is compared to the use of the absorption system in a physical wave flume. The effectiveness of the active wave generating–absorbing boundary condition finally is proved using analytical tests and numerical simulations with VOFbreak2.
A computational model is developed to demonstrate the behavior of a set of multilayer porous media which are installed in front of a solid wall. The purpose of the model is to investigate their efficiency in wave absorption, with the aim of providing guidance for the design of a wave absorber which can not only absorb waves effectively but also occupies less space.Generally speaking, a single-layer porous medium with proper thickness can be used to give a very low reflection coefficient for waves of a particular wave period, but not for many other wave periods. It is found that this disadvantage can be improved by adopting a set of multilayer porous media. In other words, the multilayer structure can reflect a smaller wave for a wider range of wave periods.In comparison with a single-layer porous medium, the two-layer ones provide a lower reflection coefficient with a thinner structure. The same phenomeon is found in comparing both the three-layer with the two-layer and the four-layer with the three-layer. Therefore, special attention is paid to the four-layer porous media. With a thickness of 3.2 times water depth, the four-layer porous media can provide a reflection coefficient of 0.08 for . It was found that the larger number of layers the media had contained, the better function it would provide, and the less space it would occupy.
A new method of implementing, in two-dimensional (2-D) Navier–Stokes equations, a numerical internal wave generation in the finite volume formulation is developed. To our knowledge, the originality of this model is on the specification of an internal inlet velocity defined as a source line for the generation of linear and non-linear waves. The use of a single cell to represent the source line and its transformation to an internal boundary condition proved to be an interesting alternative to the common procedure of adding a mass source term to the continuity equation within a multi-cell rectangular region. Given the reduction of the source domain to a one-dimensional region, this simple new type of source introduced less perturbation than the 2-D source type. This model was successfully implemented in the PHOENICS code (Parabolic Hyperbolic Or Elliptic Numerical Integration Code Series). In addition, the volume of fluid (VOF) fraction was used to describe the free surface displacements. A friction force term was added to the momentum transport equation in the vertical direction, in order to enhance wave damping, within relatively limited number of cells representing the sponge layers at the open boundaries. For monochromatic wave, propagating on constant water depth, numerical and analytical results showed good agreements for free surface profiles and vertical distribution of velocity components. For solitary wave simulation, the wave shape and velocity were preserved; while, small discrepancy in the tailing edge of the free surface profiles was observed. The suitability of this new numerical wave generation model for a two source lines extension was investigated and proven to be innovative. The comparisons between numerical, analytical and experimental results showed that the height of the merging waves was correctly reproduced and that the reflected waves do not interact with the source lines.
The effect of acceleration skewness on sheet flow sediment transport rates is analysed using new data which have acceleration skewness and superimposed currents but no boundary layer streaming. Sediment mobilizing forces due to drag and to acceleration (∼ pressure gradients) are weighted by cosine and sine, respectively, of the angle φτ · φτ = 0 thus corresponds to drag dominated sediment transport, , while φτ = 90° corresponds to total domination by the pressure gradients, . Using the optimal angle, φτ = 51° based on that data, good agreement is subsequently found with data that have strong influence from boundary layer streaming. Good agreement is also maintained with the large body of U-tube data simulating sine waves with superimposed currents and second-order Stokes waves, all of which have zero acceleration skewness. The recommended model can be applied to irregular waves with arbitrary shape as long as the assumption negligible time lag between forcing and sediment transport rate is valid. With respect to irregular waves, the model is much easier to apply than the competing wave-by-wave models. Issues for further model developments are identified through a comprehensive data review.
Near-bed oscillatory flows with acceleration skewness are characteristic of steep and breaking waves in shallow water. In order to isolate the effects of acceleration skewness on sheet flow sand transport, new experiments are carried out in the Aberdeen Oscillatory Flow Tunnel. The experiments have produced a dataset of net transport rates for full-scale oscillatory flows with varying degrees of acceleration skewness and three sand sizes. The new data confirm previous research that net transport in acceleration-skewed flow is non-zero, is always in the direction of the largest acceleration and increases with increasing acceleration skewness. Large transport rates for the fine sand conditions suggest that phase lag effects play an important role in augmenting positive net transport. A comparison of the new experimental data with a number of practical sand transport formulations that incorporate acceleration skewness shows that none of the formulations performs well in predicting the measured net transport rates for both the fine and the coarser sands. The new experimental data can be used to further develop practical sand transport formulations to better account for acceleration skewness.
This paper presents a study of the siltation process in an access channel to a port through analysis of environmental data, viz. waves, tidal currents, sediment characteristics, silt concentration and siltation at site. A rational methodology has been presented to co-relate environmental data and siltation quantity, judiciously applying the various theories available to wave propagation, littoral current, sediment transport and its trapping. The efficacy of the method is then tested to simulate the observed siltation in different phases of its development in terms of widening and deepening of the channel. It is observed that estimation of the representative environmental parameters is very important as the data collected over a long period show wide variation since sediment transport formulae available are very sensitive to these parameters. An attempt has been made in this paper to understand the mechanism of siltation in the approach channel to the port.
The paper focuses on the numerical simulation of erosion of plane sloping beaches by irregular wave attack in three wave flumes of different scales. One of the prime objectives of the tests was to provide a consistent data set for the improvement of numerical beach profile models. A practical application of this research with wave attack on plane sloping beaches is the erosion of the plane beaches after nourishment. Three models (CROSMOR, UNIBEST-TC and DELFT3D) have been used to simulate the flume experimental results focusing on the wave height distribution and the morphological development (erosion and deposition) along the beach profiles. Overall, the model predictions for wave heights show consistent results. Generally, the computed wave heights (Hrms and H1/3) are within 10% to 15% of the measured values for all tests (under-prediction of the largest wave heights close to the shore). The three models can simulate the beach erosion of the wave flume tests (erosive tests) reasonably well using default values of the sand transport parameters. The model performance for the accretive tests is less good than that for the erosive tests. A practical field application of this research is the erosion of nourished beaches, as these beaches generally have rather plane beach slopes immediately after nourishment. Various graphs are given to estimate the beach erosion of nourished beaches.
The mild-slope equation is a vertically integrated refraction-diffraction equation, used to predict wave propagation in a region with uneven bottom. As its name indicates, it is based on the assumption of a mild bottom slope. The purpose of this paper is to examine the accuracy of this equation as a function of the bottom slope. To this end a number of numerical experiments is carried out comparing solutions of the three-dimensional wave equation with solutions of the mild-slope equation.For waves propagating parallel to the depth contours it turns out that the mild-slope equation produces accurate results even if the bottom slope is of order 1. For waves propagating normal to the depth contours the mild-slope equation is less accurate. The equation can be used for a bottom inclination up to 1:3.
A Corrected Incompressible SPH (CISPH) method is proposed for accurate tracking of water surface in breaking waves. Corrective terms are derived based on a variational approach to ensure the angular momentum preservation of Incompressible SPH (ISPH) formulations. The proposed CISPH method is applied to solve the Navier–Stokes equation for simulating the breaking and post-breaking of solitary waves on a plane slope. The enhanced precision (compared to the ISPH method) of the CISPH method is confirmed through both qualitative and quantitative comparisons with experimental data. The introduction of corrective terms significantly improves the capability and the accuracy of the ISPH method in the simulation of wave breaking and post-breaking.
A numerical scheme for solving the class of extended Boussinesq equations is presented. Unlike previous schemes, where the governing equations are integrated through time using a fourth-order method, a second-order Godunov-type scheme is used thus saving storage and computational resources. The spatial derivatives are discretised using a combination of finite-volume and finite-difference methods. A fourth-order MUSCL reconstruction technique is used to compute the values at the cell interfaces for use in the local Riemann problems, whilst the bed source and dispersion terms are discretised using centred finite-differences of up to fourth-order accuracy. Numerical results show that the class of extended Boussinesq equations can be accurately solved without the need for a fourth-order time discretisation, thus improving the computational speed of Boussinesq-type numerical models. The numerical scheme has been applied to model a number of standard test cases for the extended Boussinesq equations and comparisons made to physical wave flume experiments.
Several theoretical and numerical aspects concerning the highly accurate Boussinesq-type equations of Madsen et al. (2003, 2006); Jamois et al. (2006) are discussed. A re-derivation of the model recently presented by Bingham et al. (2009) is outlined. This provides a more general framework for the model establishing the correct relationship between a velocity formulation and a velocity potential formulation and correcting previous errors in the potential formulation. A new shoaling enhancement operator is introduced which enables the derivation of new models which differ from the existing ones at O(Δh). The performance of the new formulation is validated using computations of linear and nonlinear shoaling problems. The behaviour on a rapidly varying bathymetry is also checked using linear wave reflection from a shelf and Bragg scattering from an undulating bottom. A new stable discretization scheme around structural corners within the fluid domain is also presented.
The use of acoustics to measure sediment transport boundary layer processes has gained increasing acceptance over the past two decades. This has occurred through the development of increasingly sophisticated measuring systems and theoretical developments, which have enabled flow and suspended sediment parameters to be obtained from acoustic data with a high degree of accuracy. Until relatively recently, separate acoustic systems were used to measure flow and suspended sediment concentration. Over the past few years, however, the technology has become sufficiently advanced so that flow and sediment measurements can be integrated into a single system. This integration provides, quasi-instantaneous, non-intrusive, co-located, high temporal-spatial resolution measurements of benthic flow and sediment processes. Here the development of such an instrument, the Acoustic Concentration and Velocity Profiler (ACVP) is described. The theory underpinning its application is outlined, new approaches to velocity de-aliasing and suspended sediment inversion instabilities using multi-frequency capabilities are presented and the application of the system to sediment transport processes over a sandy ripple bed is illustrated. The observations clearly show the value of such instrumentation for studying the dynamical interaction between the bed, the flow and the sediments at and within the bottom boundary layer.
The oceanographic tower Acqua Alta was constructed in early 1970 in the Adriatic Sea some 20 km from Venice. The main objective was to obtain information about the meteomarine conditions off the Venice lagoon, where the old town is threatened by ever more severe floodings. The paper describes the tower and its instrumentation, and summarizes the experience and results of activities relevant to coastal engineering. This encompasses modelling of wind field, storm surge and wind generated waves. Various types of models have been applied to and validated for the Adriatic Sea and in particular for the coastline of the Venice lagoon. This includes application of long-term statistics of extreme wave heights. Specific studies of the influence of bottom friction and wind gustiness on waves are presented as well as measurements of kinematics of wind generated waves. Further, a short discussion of white capping is included. Finally, some information about the management of the tower is given.
This paper reviews recent advances that have been made in the numerical modelling and measurement techniques of the surf zone. The review is restricted by the assumption of a long and uniform coastline case. Therefore, the frame of reference is the 2DV case, but including tree-dimensional processes important for this topic. During the last two decades, new measurement techniques have become available (e.g. Laser Doppler Anemometry (LDA) and Particle Image Velocimetry (PIV)), which have successfully been applied in numerous laboratory experiments. These methods have enabled detailed measurements of, for instance, the production, transport and dissipation of turbulence and have made a valuable contribution to our understanding of the processes in the surf zone. The first models that were developed were primarily based on assumptions directly derived from such observations. Since the development of the first numerical models in the mid-eighties, much research effort has been put into trying to improve these wave-averaged models because they can be applied at relatively low computational cost. The improved understanding of the surf-zone processes has also led to the development of more advanced intrawave models such as the Boussinesq-based models as well as the use of Navier–Stokes solvers. These new modelling techniques give a detailed description of the processes in the surf zone.
Longshore currents were measured during a storm in a barred surf zone in the Great Lakes. Mean beach slope was 0.015, with three bars ranging up to 0.5 m in height. Comparisons with theoretical predictions revealed the effects of the bars on the horizontal structure of these currents and the degree of lateral mixing: (1) perturbations in currents are localized spatially but increase with bar relief; (2) currents are lower and higher respectively in the outer and inner surf zone than expected for a plane beach. The predictions of Longuet-Higgins (1972) provide a reasonable approximation where relief is low; (3) in the inner surf zone a plane beach solution suggests bars increase lateral mixing () by increasing the velocity gradients; (4) the barred slope model of Ebersole and Dalrymple (1981) most closely resembles the prototype; (5) use of planar beach equivalents for P or N in models for barred beaches, results in under-prediction of the appropriate eddy viscosity.
Numerical models have been developed to estimate the wave forces acting on a three-dimensional body on a submerged breakwater. These models combine the VOF model and porous body model to simulate the nonlinear wave deformation including wave breaking and its interaction with a porous structure. One model is two-dimensional and is associated with empirical wave force formulae, like the Morison equation. The other one is three-dimensional and does not require any empirical formula or coefficients. Comparison of estimated and measured wave forces shows good agreement, both in two- and three-dimensional model cases, and the present estimation methods are revealed to be powerful tools for estimation of wave force acting on a three-dimensional body, even for breaking wave condition.
Among all environmental loads usually considered in the design procedure, the most critical problem in determining a vertical stability of a submarine pipeline buried in permeable soils under progressive surface-water-wave loading is the prediction of the wave-induced cyclic pore-pressure response of a seabed in the vicinity of a submarine pipeline. A study of the hydrodynamic (i.e., wave-induced) uplift force acting on a submarine pipeline buried in sandy seabed sediments is presented, under the assumption of different compressibility models of the two-phase seabed/pore-fluid medium. Introducing an uplift-force perturbation ratio, the question of perturbation effects affecting the wave-induced pore-pressure field by the presence of a stiff and impermeable body of the submarine pipeline is analysed thoroughly.
Description of the wave action on and in coastal structures can lead to a prediction of flow properties and forces on elements of those structures. For permeable structures several aspects concerning the interaction between the external flow and the internal flow have to be described accurately to predict for instance velocities and run-up levels. The P.C.-model ODIFLOCS, developed at Delft University of Technology within the framework of the European MAST-Coastal Structures project, describes the wave motion on and in several types of structures. This structure can be an impermeable or a permeable structure. For instance dikes, breakwaters and submerged structures can be dealt with. The model is a one-dimensional model based on long wave equations. The program takes various phenomena into account such as reflection, permeability, infiltration, seepage, overtopping, varying roughness along the slope, linear and non-linear porous friction (Darcy- and turbulent friction), added mass, internal set-up and the disconnection of the free surface and the phreatic surface. Satisfactory results were obtained with modelling of run-up, surface elevations and velocities. Other applications show more possibilities of the model.
Laboratory experimental data on sediment threshold conditions for fine to coarse sands, under the combined action of waves and currents are presented. Higher flows are needed to satisfy threshold under short period waves than for longer period waves. The combined threshold velocities indicate that under the shorter (5 s) period waves, the oscillatory and steady flows are independent of each other, but interact to a greater extent as the wave period increases. The derived threshold flow conditions are converted into threshold shear stress values using existing linear and non-linear models. The performance of the models for various periods of oscillation is then examined in view of the assumption that a unique threshold value exists for a particular grain size. All models suggest that the critical stress of a particular grain is higher under shorter period waves, for the range of grain sizes presented. Using different models for waves, of different periods, appears to remove the effect of wave period upon the data. It is suggested that theories used by the existing models are insufficient to fully describe the interaction of the steady and oscillatory flows during the experiments.
The ability of a 1.2-MHz Acoustic Doppler Current Profiler (ADCP) to measure suspended sediment concentration (SSC) and particle size variation in a mud-dominated environment has been investigated. Experiments were conducted in the Bay of Banten, Indonesia, where clays and silts in the range of 3–55 μm are prevalent. The ADCP backscatter depends both on SSC and on the size of the scatterers. Over the time span of several separate deployments, which lasted 20 days at most, SSC was found to be proportional to the acoustically normative grain size squared. Using this relation, the ADCP could be calibrated to yield depth profiles of SSC. The obtained calibrations, however, were spatially and seasonally dependent. Differences between the calibrations could not be completely ascribed to variation in grain size distributions, due to the largely unknown influences of aggregates and organic scatterers. The ADCP backscatter measurements provided insight into diurnal events of erosion and subsequent deposition. An increase or decrease of SSC generally coincided with a raise or decline of the average grain size in the sediment suspension (respectively).
A three-dimensional PC-based hydrodynamic model, Bachom-3, is developed using an Alternating Direction Implicit (ADI) finite difference scheme. The model is tested for a uni-nodal standing wave in a rectangular basin. The model results for the surface elevation and the velocities coincide with the analytical results. To verify the field applicability of the model, the model is applied to Suyoung Bay in Pusan, Korea. The numerically predicted velocity fields during the spring tide show good agreement with field measurements. Computed velocity fields show the expected phase difference between the velocities in the surface layer and those in the bottom layer. Subsequently, when applied to wind-driven currents, the model also yields encouraging results.
Numerical modeling of a beach nourishment project is conducted to enable a detailed evaluation of the processes associated with the effects of nearshore dredge pits on nourishment evolution and formation of erosion hot spots. A process-based numerical model, Delft3D, is used for this purpose. The analysis is based on the modification of existing bathymetry to simulate “what if” scenarios with/without the bathymetric features of interest. Borrow pits dredged about 30 years ago to provide sand for the nourishment project have a significant influence on project performance and formation of erosional hot spots. It was found that the main processes controlling beach response to these offshore bathymetric features were feedbacks between wave forces (roller force or alongshore component of the radiation stress), pressure gradients due to differentials in wave set-up/set-down and bed shear stress. Modeling results also indicated that backfilling of selected borrow sites showed a net positive effect within the beach fill limits and caused a reduction in the magnitude of hot spot erosion.
The continuity equation for mean longshore current velocity, V = gmT sin 2θb, agrees with selected field and laboratory data covering a wide range of conditions. Agreement between continuity equation and data is improved by eliminating those laboratory data which imply deep-water wave crests at angles near or greater than 90 degrees to the shoreline. Agreement between continuity equation and data is further improved by adjusting breaker angles to account for convection of the breaker point by the longshore current. Breaker point convection increases breaker angle by an amount predictable from the analysis developed here. This increase in angle is significant in those laboratory experiments with breaking wave crests at high angles to the shoreline.In the continuity equation, m is bottom slope, T is wave period, and θb is breaker angle, but breaker height does not appear. According to radiation stress theory, mean velocity does depend on breaker height, but only weakly. Consistency between the two approaches would require a dimensionless velocity, Cb/gT, to be relatively constant, which it is. (The same dimensionless velocity appears in the analyses of breaker point convection.) The continuity equation is functionally independent of friction and mixing, in keeping with its derivation from simple conservation of mass considerations. The equation has no adjustable coefficients. The degress of agreement with data and the internal consistency of the analysis suggests that it is a good predictor of mean velocity in ordinary longshore currents.
The prevention of flooding inside the Venice lagoon requires a system to disconnect the North Adriatic sea and the lagoon hydraulically in order to control the water level. This requires the definition of extreme design wave conditions for the various structures. This paper describes numerical modelling using a parametric wave prediction model to derive the design wave conditions outside the inlets to the lagoon. This includes a description of a verification study using buoy measurements and a sensitivity study into the effect of uncertainty in the model parameter settings.
Novel laboratory experiments and numerical modelling have been performed to study the advection scales of suspended sediment in the swash zone. An experiment was designed specifically to measure only the sediment picked up seaward of the swash zone and during bore collapse. The advection scales and settling of this sediment were measured during the uprush along a rigid sediment-free beach face by a sediment trap located at varying cross-shore positions. Measurements were made using a number of repeated solitary broken waves or bores. Approximately 25% of the pre-suspended sediment picked up by the bores reaches the mid-swash zone (50% of the horizontal run-up distance), indicating the importance of the sediment advection in the lower swash zone. The pre-suspended sediment is sourced from a region seaward of the shoreline (still water line) which has a width of about 20% of the run-up distance. An Eulerian–Lagrangian numerical model is used to model the advection scales of the suspended sediment. The model resolves the hydrodynamics by solving the non-linear shallow water equations in an Eulerian framework and then solves the advection–diffusion equation for turbulence and suspended sediment in a Lagrangian framework. The model provides good estimates of the measured mass and distribution of sediment advected up the beach face. The results suggest that the correct modelling of turbulence generation prior to and during bore collapse and the advection of the turbulent kinetic energy into the lower swash is important in resolving the contribution of pre-suspended sediment to the net sediment transport in the swash zone.
New laboratory and field data are presented on fluid advection into the swash zone. The data illustrate the region of the inner surf zone from which sediment can be directly advected into the swash zone during a single uprush, which is termed the advection length. Experiments were conducted by particle tracking in a Lagrangian reference frame, and were performed for monochromatic breaking waves, solitary bores, non-breaking solitary waves and field conditions. The advection length is normalised by the run-up length to give an advection ratio, A, and different advection ratios are identified on the basis of the experimental data. The data show that fluid enters the swash zone from a region of the inner surf zone that can extend a distance seaward of the bore collapse location that is approximately equal to half of the run-up length. This region is about eight times wider than the region predicted by the classical swash solution of Shen and Meyer [Shen, M.C., Meyer, R.E., 1963. Climb of a bore on a beach. Part 3. Runup. Journal of Fluid Mechanics 16, 113–125], as illustrated by Pritchard and Hogg [Pritchard, D., Hogg, A.J., 2005. On the transport of suspended sediment by a swash event on a plane beach. Coastal Engineering 52, 1–23]. Measured advection ratios for periodic waves show no significant trend with Iribarren number, consistent with self-similarity in typical swash flows. The data are compared to recent characteristic solutions of the non-linear shallow water wave (NLSW) equations and both finite difference and finite volume solutions of the NLSW equations.