Neural network modelling of wave overtopping at coastal structures

A method has been developed to estimate wave overtopping discharges for a wide range of coastal structures. The prediction method is based on Neural Network modelling. For this purpose use is made of a data set obtained from a large number of physical model tests (collected within the framework of the European project CLASH, see e.g. [Steendam, G.J., Van der Meer, J.W., Verhaeghe, H., Besley, P., Franco, L. and Van Gent, M.R.A. (2004). The international database on wave overtopping. World Scientific, Proc. 29th ICCE, vol. 4, pp. 4301–4313, Lisbon, Portugal.]). Moreover, a method was developed to obtain confidence intervals for the overtopping predictions of the neural network.     

Numerical investigations of wave overtopping at coastal structures

Under the numerical modelling work package of the EU funded CLASH project, the time accurate, free surface capturing, incompressible Navier–Stokes solver AMAZON-SC has been applied to study impulsive wave overtopping at Samphire Hoe, near Dover in the United Kingdom. The simulations show that the overtopping process on this vertical, sheet pile, seawall is dominated by impulsive, aerated, near vertical overtopping jets. In order to perform the simulations AMAZON-SC has been extended to incorporate an isotropic porosity model and for validation purposes the solver has been applied to study overtopping of a low crested sea dike and a 10:1 battered wall. The results obtained for the battered wall and Samphire Hoe tests are in good agreement both with predicted overtopping discharges calculated using the UK overtopping manual and with available experimental results.     

Effects of new variables on the overtopping discharge at steep rubble mound breakwaters — The Zeebrugge case

This paper describes on the one hand parametric tests on wave overtopping for a steep rubble mound breakwater in Zeebrugge, Belgium. On the other hand the comparison between prototype measurements at the breakwater and their scale reproductions in two laboratories is dealt with. The objective is to gain information on possible scale and model effects for wave overtopping from this comparison. The prototype measurements are described together with the resulting dataset of 11 storms where wave overtopping occurred. Scale models and the laboratory measurements are described into detail mentioning similarities and differences to the prototype. Several model effects are identified and special attention is given to wind effects and to the placement pattern of the armour units, respectively. Monte Carlo simulations have been performed to get an idea about the influence of selected model uncertainties. Finally, scale effects are discussed and the influence of model and scale effects for the performed tests is quantified. Recommendations on how to treat these effects are presented.     

Numerical simulation of wave overtopping of coastal structures using the non-linear shallow water equations

A one-dimensional high-resolution finite volume model capable of simulating storm waves propagating in the coastal surf zone and overtopping a sea wall is presented. The model (AMAZON) is based on solving the non-linear shallow water (NLSW) equations. A modern upwind scheme of the Godunov-type using an HLL approximate Riemann solver is described which captures bore waves in both transcritical and supercritical flows. By employing a finite volume formulation, the method can be implemented on an irregular, structured, boundary-fitted computational mesh. The use of the NLSW equations to model wave overtopping is computationally efficient and practically flexible, though the detailed structure of wave breaking is of course ignored. It is shown that wave overtopping at a vertical wall may also be approximately modelled by representing the wall as a steep bed slope. The AMAZON model solutions have been compared with analytical solutions and laboratory data for wave overtopping at sloping and vertical seawalls and good agreement has been found. The model requires more verification tests for irregular waves before its application as a generic design tool.     

Combined classifier–quantifier model: A 2-phases neural model for prediction of wave overtopping at coastal structures

A 2-phases neural prediction method for wave overtopping is developed. The ‘classifier’ predicts whether overtopping occurs or not, i.e. q = 0 or q > 0. If the classifier predicts overtopping q > 0, then the ‘quantifier’ is used to determine the mean overtopping discharge. The overtopping database set up within the EC project CLASH (De Rouck, J., Geeraerts, J., 2005. CLASH Final Report, Full Scientific and Technical Report, Ghent University, Belgium) is used to train the networks of the prediction method.     

Three-dimensional investigations of wave overtopping on rubble mound structures

To study the influence of wave obliquity and directional spreading on wave overtopping of rubble mound breakwaters a total of 736 three-dimensional model tests were carried out at Aalborg University. The results of these tests are presented and analysed in this paper yielding a new empirical reduction factor to describe the influence of wave obliquity and directional spreading on the average wave overtopping discharges. The study shows that perpendicularly incident, long-crested waves result in conservative values of the overtopping discharge for the tested cross-section.     

A synchronously coupled tide–wave–surge model of the Yellow Sea

A coupled wave–tide–surge model has been established in this study in order to investigate the effect of tides, storm surges, and wind waves interactions during a winter monsoon on November 1983 in the Yellow Sea. The coupled model is based on the synchronous dynamic coupling of a third-generation wave model, WAM-Cycle 4, and the two-dimensional tide–surge model. The surface stress generated by interactions between wind and waves is calculated using the WAM-Cycle 4 directly based on an analytical approximation of the results obtained from the quasi-linear theory of wave generation. The changes of bottom friction factor generated by waves and current interactions are calculated by using simplified bottom boundary layer model. The model simulations showed that bottom velocity and effective bottom drag coefficient induced by combination of wave and current were increased in shallow waters of up to 50 m in the Yellow Sea during the wintertime strong storm conditions.     

Simulation of wave propagation over a submerged bar using the VOF method with a two-equation k– turbulence modeling

A two-equation k– turbulence model is used in this paper to simulate the propagation of cnoidal waves over a submerged bar, where the free surface is handled by the volume-of-fluid (VOF) method. Using a VOF partial-cell variable and a donor–acceptor method, the model is capable of treating irregular boundaries, including arbitrary bottom topography and internal obstacles, where the no-slip condition is satisfied. The model also allows the viscous sublayer to be modeled by a wall function approximation implemented in the grid nodes that are immediately adjacent to a wall boundary. The numerical model applied to the propagation of cnoidal waves over a submerged bar can produce results that are in general agreement with some laboratory measurements. Some remarks arising from the comparison between the computational and experimental results are presented.