Quantification of changes in current intensities induced by wave overtopping around low-crested structures

The phenomenon of overtopping is traditionally studied for well-emerged harbour structures and often focuses on safety and stability. In this paper laboratory tests are presented and analysed to sharpen the hypothesis that overtopping is capable of changing the horizontal circulation pattern around low-crested structures. A unique data set from laboratory experiments was acquired in the wave basin at Delft University of Technology. The experiments were performed using an emerged impermeable low-crested structure (three freeboards and three different wave conditions for each freeboard) and yielded nine different combinations of set-up and overtopping driving forces. Using this information it was possible to quantify the changes in cross-shore and longshore velocity induced by the overtopping and the set-up changes under the different freeboard and wave conditions described. It is found that overtopping enhances the outgoing flows (longshore velocities parallel to the structure) away from the lee side of the structure and dampens the water level gradient driven flow towards the structure.     

Spatial distribution of wave overtopping water behind coastal structures

Spatial distribution of random wave overtopping water behind coastal structures was investigated using a numerical model based on Reynolds-Averaged Navier-Stokes solver (RANS) and Volume of Fluid (VOF) surface capturing scheme (RANS-VOF). The computed spatial distributions of wave overtopping water behind the structure agree well with the measurements by Pullen et al (2008) for a vertical wall and Lykke Andersen and Burcharth (2006) for a 1:2 sea dike. A semi-analytical model was derived to relate spatial distribution of wave overtopping water behind coastal structures to landward ground level, velocity and layer thickness on the crest. This semi-analytical model agrees reasonably well with both numerical model results and measurements close to coastal structures. Our numerical model results suggest that the proportion of wave overtopping water passing a landward location increases with a seaward slope when it is less than 1:3 and decreases with a seaward slope when it gets steeper. The proportion of wave overtopping water passing a landward location increases with landward ground level and overtopping discharge. It also increases with the product of incident wave height and wavelength, but decreases with increasing relative structure freeboard and crest width. We also found that the extent of hazard area due to wave overtopping is significantly reduced by using a permeable structure crown. Findings in this study will enable engineers to establish the extent of hazard zones due to wave overtopping behind coastal structures.     

Wave overtopping and piling-up at permeable low crested structures

The paper aims at providing a simple model for evaluating piling-up, overtopping, filtration and rip currents for low crested structures. The model is essentially based on mass and momentum balance and on resistance laws that relate piling-up and mass fluxes. A procedure is suggested and validated against 2D and 3D experimental data. This procedure is innovative with respect to existing formulations since it applies both to emerged and submerged structures and it simultaneously accounts for structure permeability, return flow through gaps and dissipative effects.     

Numerical simulation of wave overtopping at coastal dikes and low-crested structures by means of a shock-capturing Boussinesq model

In this paper, a shock-capturing numerical model, based on the combined solution of Boussinesq and nonlinear shallow water equations is applied to the simulation of wave runup, overtopping and wave train propagation over impermeable, emerged and low-crested, structures. In order to improve the performances of the scheme at wet–dry interfaces, a numerical treatment is introduced to provide well-balancing of advective fluxes and source terms. One- and two-dimensional test cases are presented to validate the performances of the model under both regular and irregular wave conditions.     

Wave overtopping and induced currents at emergent low crested structures

This paper deals with wave overtopping associated to low emergent detached breakwaters. It starts presenting the various mechanisms which define the functional behaviour of detached breakwaters which are frequently overtopped. The emphasis is on the role played by overtopping and how this contributes to the wave pumping in the area around the structure. The paper then reviews the available formulations for predicting overtopping, considering the sensitivity of various equations to climatic drivers and their suitability for low crested coastal structures. The paper then analyzes nearshore circulation models and how overtopping discharges can be included. This is illustrated with a sample Q-3D model by analyzing the differences obtained with/without overtopping. The emphasis is on the implications for the functional design of the structure and its morpho-hydrodynamic impact. The main conclusion is the sensitivity of the functional design of such structures to the underlying hydrodynamics processes and the importance to explicitly include overtopping for numerical simulations of the morpho-hydrodynamic behaviour of low crested breakwaters.     

Wave transmission and reflection at low-crested structures: Design formulae,oblique wave attack and spectral change

A part of the DELOS research focused on wave transformation at low-crested structures, called LCS. This paper gives a summary of all results. Wave transmission on rubble mound structures has been subject for more flume tests in the DELOS programme and simultaneously an existing database has been increased extensively by receiving data from other researchers in the world. This new database consists of more than 2300 tests and has been used to come up with the best 2D wave transmission formula for rubble mound LCS, although not necessarily new as existing ones have been evaluated. Oblique wave attack on LCS was a second objective within DELOS. Results were analysed leading to new empirical transmission formulae for smooth LCS and to conclusions on 3D effects for both rubble mound and smooth LCS. The spectral shape changes due to wave transmission and this change has been subject of analysis for all new test data described above. Although analysis has not been finished completely, former assumptions on spectral change were more or less confirmed. Finally, some analysis was performed on reflection at LCS and a first formula was derived to take into account the effect that wave overtopping or transmission reduces reflection and must be dependent on the crest height of the structure.     

Wave run-up and overtopping on smooth and rough slopes of coastal structures

A series of hydraulic model tests has been carried out in a glass wave flume to investigate the influences of wave height, wave period, wave steepness, surf similarity parameter, roughness, layer thickness and porosity on wave run-up and overtopping of 1:2 sloped impermeable and permeable breakwaters fronted by a 1:10 gentle, smooth beach slope. The analysis of results involves the correlation between the overtopping energy transfer with the relative wall height and the relationship between wave run-up and overtopping rate. Further, measured wave run-up and overtopping rates are compared with the results given in the Shore Protection Manual (1984), Automated Coastal Engineering System (1992)and results of other investigators.     

Wave upwelling effects in TLP and semisubmersible structures

Mutual hydrodynamic interaction effects between closely spaced large columns can cause substantial increases in local wave height and in other kinematic quantities. This phenomenon of upwelling is here analysed theoretically, by using a high order hybrid element technique. Results are presented as contour plots and isometrics of local free surface amplitudes in regular waves; linear transfer functions of wave amplitude at a point; mean square wave amplitudes in long crested random seas; and local components of horizontal velocity in regular waves. It is suggested that wave upwelling is an important phenomenon which should be considered in design.     

Wave drift enhancement effects in multi column structures

A theoretical assessment is made of mean wave drift forces on groups of vertical circular cylinders, such as the columns of a floating offshore platform. A complete analytical solution is obtained for two cylinders extending from seabed to free surface, and a long wave approximation is found to provide reliable predictions of the drift force in line with the waves at low frequencies. For moderate separation between the two cylinders, this force is found to tend at low frequencies to a value four times the force on an isolated cylinder.A numerical method is employed to study two surface piercing cylinders truncated below the free surface, and an arrangement of four vertical cylinders characteristic of a floating offshore platform. The mean vertical drift force is found to be reasonably well approximated, over the frequency range of practical interest, by the force on an individual cylinder considered in isolation multiplied by the number of cylinders in the group. Interaction effects, however, have a profound influence on the total horizontal drift force. At low frequencies this force is found to tend to the force on an isolated cylinder multiplied by the squate of the number of cylinders in the group.     

Water Wave Refraction and Diffraction over Frictional Topography

- This paper considers the effects of wave energy dissipation induced by sea-bottom friction on the computational results of water wave refraction and diffraction with the parabolic equation method. The presented results show that the friction factor formula adopted in this paper is of higher numerical accuracy than that introduced by Dalrymphe (1984), and it can be used to compute wave propagation over large open areas.     

An ecological perspective on the deployment and design of low-crested and other hard coastal defence structures

Coastal areas play a crucial role in the economical, social and political development of most countries; they support diverse and productive coastal ecosystems that provide valuable goods and services. Globally flooding and coastal erosion represent serious threats along many coastlines, and will become more serious as a consequence of human-induced changes and accelerated sea-level rise. Over the past century, hard coastal defence structures have become ubiquitous features of coastal landscapes as a response to these threats. The proliferation of defence works can affect over half of the shoreline in some regions and results in dramatic changes to the coastal environment. Surprisingly little attention has been paid to the ecological consequences of coastal defence. Results from the DELOS (Environmental Design of Low Crested Coastal Defence Structures, EVK3-CT-2000-00041) project indicate that the construction of coastal defence structures will affect coastal ecosystems. The consequences can be seen on a local scale, as disruption of surrounding soft-bottom environments and introduction of new artificial hard-bottom habitats, with consequent changes to the native assemblages of the areas. Proliferation of coastal defence structures can also have critical impacts on regional species diversity, removing isolating barriers, favouring the spread of non-native species and increasing habitat heterogeneity. Knowledge of the environmental context in which coastal defence structures are placed is fundamental to an effective management of these structures as, while there are some general consequences of such construction, many effects are site specific. Advice is provided to meet specific management goals, which include mitigating specific impacts on the environment, such as minimising changes to surrounding sediments, spread of exotic species or growth of nuisance species, and/or enhancing specific natural resources, for example enhancing fish recruitment or promoting diverse assemblages for eco-tourism. The DELOS project points out that the downstream effects of defence structures on coastal processes and regional-scale impacts on biodiversity necessitate planning and management at a regional (large coastline) scale. To effectively understand and manage coastal defences, environmental management goals must be clearly stated and incorporated into the planning, construction, and monitoring stages.     

A Unique Solvable Higher Order BEM for Wave Diffraction and Radiation

- For the discretization of higher order elements, this paper presents a modified integral domain method to remove the irregular frequencies inherited in the integral equation of wave diffraction and radiation from a surface-piercing body. The set of over-determined linear equations obtained from the method is modified into a normal set of linear equations by superposing a set of linear equations with zero solutions. Numerical experiments have also been carried out to find the optimum choice of the size of the auxiliary domain and the discretization on it.     

Wave diffraction by large offshore structures: an exact second-order theory

An exact second order theory has been formulated in this paper to calculate the wave forces on offshore structures. Lighthill's method for deep water waves has been extended to shallow water waves. Exact expression for linear velocity potential applicable to the circular cylindrical strcutures for shallow water waves have been used in these calculations. These results have been verified with those obtained by direct perturbation technique reported recently by Rahman and Heaps. It is interesting to note that both the methods yield identical results.     

Wave Diffraction from A Vertical Cylinder with Two Uniform Columns and Porous Outer Wall

—Based on a linear model of the pressure difference between two sides of a porous wall and thefluid velocity inside it.an analytic solution is established for wave diffraction from a cylinder with an outerporous column and an inner solid column.Numerical experiments are carried out to examine the effects ofthe wave force on a porous low-column cylinder and the wave elevations outside and inside the cylinderdue to the porous character of the outer column and the ratio between the radii of the inner and outer col-umns.The numerical results show that the increase in the coefficient of porosity of the outer column of adouble column cylinder will reduce the wave elevation around the cylinder and the wave load on it.The ra-dius of the inner column does not affect too much the wave elevation around the cylinder and the totalforce on the cylinder.     

Erosional equivalences of levees: Steady and intermittent wave overtopping

Present criteria for acceptable grass covered levee overtopping are based on average overtopping values but do not include the effect of overtopping duration. This paper applies experimental steady state results for acceptable overtopping to the case of intermittent wave overtopping. Laboratory results consisting of velocities and durations for acceptable land side levee erosion due to steady flows are examined to determine the physical basis for the erosion. Three bases are examined: (1) velocity above a threshold value, (2) shear stress above a threshold value, and (3) work above a threshold value. The work basis provides the best agreement with the data and a threshold work value and a work index representing the summation of the product of work above the threshold and time are developed. The governing equations for flow down the land side of a levee establish that the flows near the land side levee toe will be supercritical. Wave runup is considered to be Rayleigh distributed with the runup above the levee crest serving as a surrogate for overtopping. Two examples illustrating application of the methodology are presented. Example 1 considers three qualities of grass cover: good, average, and poor. The required levee elevations for these three covers differ by 1.8 m. The results for Example 1 are compared with the empirical criteria of 0.1 liters per second per meter (l/s per m), 1.0  l/s per m, and 10.0  l/s per m. It is found that the required crest elevation by the methodology recommended herein for the “poor” cover is only slightly lower than for the criterion for average overtopping of q=10.0  l/s per m but significantly lower than for the overtopping criterion of 1.0 and 0.1 m/s per m. Example 2 considers two durations of the peak surge with the result that the longer duration peak surge requires a levee that is higher by approximately 0.8 m.     

Wave impacts on structures with rectangular geometries: Part 1. Seawalls

This paper considers steep wave impact on seawalls of various geometries. A simple analytical model for the pressure impulse due to a wave of idealized geometry and dynamics is developed and applied to the following geometries: (a) vertical seawall with a berm, (b) vertical seawall with a ditch at its base and (c) vertical seawall with a block missing (damaged condition).The method uses eigenfunction expansions in each of the rectangular regions that satisfy some of the rigid surface conditions and a simplified free-surface condition. Their unknown coefficients are determined from the impact boundary condition, rigid wall conditions and by matching the values and the horizontal derivatives of the solutions in each rectangular region at their mutual boundary. The method yields the pressure impulse throughout the entire region. The overall impulse and moment impulse on the seawall and a simple model for the uprush of the spray jet after the impact are also presented. The effects of different impact regions and different geometries can therefore be quickly estimated and used to show trends in the results. It is shown that berms generally have a beneficial effect on reducing the impulse, moment impulse and uprush, but not the maximum pressure impulse on the seawall, whereas ditches are generally and sometimes strongly detrimental for all effects except uprush. A missing block in the seawall gives an almost constant or linearly decreasing value inside the gap (depending on the boundary condition applied at the rear of the gap being hard or soft respectively); the soft case can affect the pressure impulse on the front face of the seawall, thereby affecting the impulse and moment impulse.     

Wave enhancement due to blockage in semi-submersible and TLP structures

An exact analytical method is described to solve the diffraction problem of a group of truncated vertical cylinders. In order to account for the interaction between the cylinders, Kagemoto and Yue's exact algebraic method is utilised (Kagemoto, H., Yue, D.K.P., 1986. Interactions among multiple three-dimensional bodies in water waves: an exact algebraic method. J Fluid Mech, 46, 129–139). The isolated cylinder diffraction potential is obtained using Garret's solution and evanescent mode solutions are derived in a similar manner (Garret, C.J.R., 1971. Wave forces on a circular dock. J Fluid Mech, 46, 129–139).Free surface elevations are calculated for an array of four cylinders and compared with experiments. Comparisons show good agreement.     

MBACI sampling of an episodic disturbance: stormwater effects on algal epifauna

Whilst it has been well established that stormwater and associated contaminants negatively impact the quality of recipient waters, the ecological effects of individual stormwater pulses in marine environments are relatively unknown. In this study, the impacts of stormwater outfalls upon water quality and epifaunal invertebrates inhabiting the alga Sargassum linearifolium are assessed through an MBACI sampling program. Water quality and the abundance of mobile algal epifauna were recorded at three control sites and three impact sites every 10-12 weeks during dry weather and opportunistically within 24h of large rain events (>50 ml rainfall in 24h) and again 4d after the rain event. Sampling took place during two periods over two separate years and this included four large rainfall events. Following rainfall, salinity dropped rapidly at impact sites close to stormwater outfalls, whilst turbidity increased. Declines in salinity at control sites were slight and turbidity did not differ to 'before' periods. The abundance of epifaunal gastropods and polychaetes were reduced at impact sites 24h after rain events, but not control sites. The abundance of copepods, amphipods and ostracods, however, were reduced at both control and impact sites for up to 4d following rainfall. Reductions of these taxonomic groups could not be attributed to stormwater outfalls. Whilst short-term impacts of stormwater runoff were identified for some faunal groups, impacts were not identified for the majority. Instead, effects were harbour-wide (i.e. at control and impact sites), probably in response to the physical disturbance of heavy seas associated with large rain events.     

A Fully Nonlinear HOBEM with the Domain Decomposition Method for Simulation of Wave Propagation and Diffraction

A higher-order boundary element method (HOBEM) for simulating the fully nonlinear regular wave propagation and diffraction around a fixed vertical circular cylinder is investigated. The domain decomposition method with continuity conditions enforced on the interfaces between the adjacent sub-domains is implemented for reducing the computational cost. By adjusting the algorithm of iterative procedure on the interfaces, four types of coupling strategies are established, that is, Dirchlet/Dirchlet-Neumman/Neumman (D/D-N/N), Dirchlet-Neumman (D-N), Neumman-Dirchlet (N-D) and Mixed Dirchlet-Neumman/Neumman-Dirchlet (Mixed D-N/N-D). Numerical simulations indicate that the domain decomposition methods can provide accurate results compared with that of the single domain method. According to the comparisons of computational efficiency, the D/D-N/N coupling strategy is recommended for the wave propagation problem. As for the wave-body interaction problem, the Mixed D-N/N-D coupling strategy can obtain the highest computational efficiency.