This research describes a new method called SWDD (Klopman, Witteveen+Bos, 2018b), which can obtain information on wave propagation directions from the surface elevations at a set of positions. The primary intention of the method is to separate multiple incoming wave components, i.e. wave heights, phases and directions. The goal is to obtain the incoming wave conditions, that can among others be used in the design of (coastal) structures and assessment of moored ship response. The novelty of this method is that a large number of incoming wave directions is prescribed, equally distributed around a circle. For each of these many incoming wave conditions, the wave amplitude and phase are the unknowns (while the directions are known). The main advantage is that this makes the problem linear and in that aspect easier to solve. The disadvantage is that, most often, the resulting system becomes ill-posed (having more unknowns than equations). This problem is solved by using Tikhonov regularization (Tikhonov and Arsenin, 1977) together with the L-curve method (Hansen, 1992; 2000). The main differences with other common deterministic directional wave-analysis methods are: the SWDD method is free of user-checks after each analysis, the directional resolution is higher, the computation time is faster and a wave field reconstruction after the directional wave-analysis is possible. The applicability of the SWDD method has been tested using synthetic wave signals for (the sum of) monochromatic long-crested waves, prescribed wave patterns – containing wave-crest curvature and wave amplitude variation – and model results of a mild-slope wave model (WIHA). Multiple sensitivity analyses have been applied to check the sensitivity of the SWDD method to: various physical phenomena (e.g. diffraction and wave amplitude variation), domain variations (e.g. slopes) and input parameter variation. The study shows that the SWDD method is able to analyse irregular wave-fields using an array configuration containing a low number of gauges and a dense grid containing many gauges. Based on the findings an advisory flowchart is presented on how to determine the optimum radius of the array setup for using the SWDD method in practice, both for the analysis of data from phase-resolving numerical wave models and from measurements. The study shows that the SWDD method is a robust and reliable method to analyse (complex) wave fields on a (near) homogeneous bathymetry. The incoming wave direction(s) and associated wave height(s) are graphically depicted in a polar plot or a directional spectrum.

During the design process of the new sea lock in IJmuiden the design wave conditions were described by a bimodal wave spectrum. With a spectral calculation method it was observed that a small low frequency component leaded to a large influence in the force spectrum. This observation served as the starting point for this thesis, where different design methods were validated for the non-breaking wave load of bimodal wave spectra on a vertical wall. The design methods under consideration were the formulae of Sainflou, Goda, the linear wave theory and the spectral calculation method. These methods were validated by the phase-resolved numerical model SWASH. First, the characteristic wave force for different shapes of spectra was addressed. In addition, the probability distribution of wave force was compared with the Rayleigh distribution. It turned out that the large influence of a low frequency component in a bimodal wave spectrum may cause underestimations of the traditional design formulae. The spectral calculation method performed accurate for all considered wave conditions.

Near IJburg a new Island named Strandeiland is being build to create living area. On the eastern part of this island an inlet is situated. In this research the wave penetration in this inlet is simulated using the numerical models SWAN and SWASH. With the results of the simulations the verticall walls which surround the inlet are dimensioned. Furthermore a comparison between the used models is made.

Durban is the third largest city of South-Africa, located in the province of KwaZulu-Natal. The city suffers from severe floods from time to time, finding its cause in both the Indian ocean as well as the Umgeni river. The eThekwini municipality wishes a better insight in the occurrence of these floods and searches for a structural solution to protect the coastline. The eThekwini municipality has models in operation to predict the hydraulic characteristics in the ocean and the river. However, the existing models don’t represent the reality sufficiently, since the interaction between the Indian ocean and the Umgeni river is not modelled properly yet. An analysis on the area of interest has been executed. The conclusion was drawn that the Umgeni river delta was (partly) tide-dominant, meaning that the Indian ocean imposes the downstream water level. Furthermore, the wave climate was observed, as well as a look into present coastal protections. The link between the Indian ocean and the Umgeni river has been modelled using Delft3D. Since the Indian ocean imposes a downstream boundary condition (in terms of a water level) for the Umgeni river, a backwater curve might occur. First, the link is made by extending the Delft3D-model which was present for the Indian ocean only. The model has been extended all the way up to the Inanda dam. The part of the river included in the new model is approximately 32 푘푚 long. When comparing the models output at the river mouth, at the same location as a measurement point, similar behaviour can be observed. The same phase (lag) is observed, contrary to the tidal range. The tidal range in the model differs from reality, but this is due to a lack of calibration in the amplitudes of the different tidal constituents taken into account. Hence, the renewed model seems to work, but more validation still has to be done. This was not possible yet, as there is a lack of measurement stations along the river. Next to an extension of the Delft3D model, a script has been written in Python. This script is based on the empirical fit of Bresse and shows an elegant function. The results from the function in Python and the model in Delft3D are similar in a qualitative and a quantitative way. Both the models show an influence of the Indian Ocean, reaching easily to about 12 푘푚 upstream of the river mouth. This can be explained by the mild bed slope in this part. A structural solution for the flooding on the promenade at the height of North Beach was found in the form of a seawall. The most important design demand is to protect against a high water level of a 200 year return period combined with a 50 year return period wave height. These storm conditions are input for the ocean-river model, which delivers wave characteristics at the beach front, linking the structural design to the ocean-river model. After a pre-selection on design options, a Multi Criteria Analysis is carried out for the remaining eight design options. Grading is done based on criteria, representing the viewpoints of the many stakeholders involved and leading to a highest grading of a seawall in combination with an emergency barrier. Following, the water-retaining height for a vertical wall is determined. Given the the ground level height of the promenade to be 푀푆퐿 + 2.2 푚 and a total water-retaining height of 푀푆퐿 + 2.944 푚 this leads a practical construction height of 0.80 푚. Due to the limited height a reinforced concrete seawall is designed with emergency barriers for the beach entrances. The emergency barriers are designed of pinewood. Additionally, in order the fit properly in the surroundings, an integrated design is added with features like benches, thatch umbrellas and plants to disguise the construction and protect the Golden Mile in style.

Flotsam lines may arise on coastal dikes after a storm surge. These lines are generated when material due to debris accumulation on the foreshore has been transported onto the dike surface by wave run-up. Hydraulic engineers who used flotsam line measurements, interpreted a flotsam line as a line which is marking the highest wave run-up. In the past, flotsam lines were used to assess the safety of coastal dikes along the Wadden Sea. Currently, models (SWAN and WAQUA) fulfil this function and this may result in losing the value of flotsam lines. This study aims to rediscover the value of flotsam lines. The objective of this study was to shed light on the value of flotsam lines. Using the spatial information obtained from flotsam levels it is investigated whether flotsam levels can be used to assess the quality of models (SWAN and WAQUA). This was done by calculating flotsam lines using a sequence of models and wave run-up formulas and then compare to measured flotsam lines. This study showed that the upper side of the flotsam line marked the maximum wave run-up in case of a small layer of flotsam. Besides, a relative thick layer of flotsam was able to absorb the force of the wave run-up and remained in position. This means that the amount of flotsam can disturb the wave run-up and eventually flotsam levels. It also was determined that the analysis of (calculated) flotsam lines gives an indication of the performance of the applied set of models (SWAN and WAQUA) and wave run-up formulas, provided that a systematic comparison between modelled and measured data is performed. A large database of detailed flotsam lines with corresponding storm conditions (water level, wave conditions, wind, etc) can provide valuable information to low costs. This database can be used to detect spatial variations which might give more insight in certain processes during storm conditions

Numerieke modellen worden alsmaar belangrijker om voorspellingen te doen in de waterbouwkunde. Het is namelijk veel eenvoudiger en goedkoper om proeven numeriek te simuleren dan om deze uit te voeren in een laboratoriumopstelling. De numerieke modellen moeten echter wel worden gevalideerd aan de hand van metingen. In dit rapport wordt de bruikbaarheid van het model SWASH getest voor simulaties van golfoverslag op dijken met een keermuur. Hierin worden zowel monochromatische regelmatige golven als onregelmatige golven beschouwd. Numerical models are incresingly important for predictions in Hydraulic Engineering. They are easier and cheaper to employ than physical scale models. However, these numerical models need to be validated to measurements. In this report the usability of the SWASH model is investigated for dikes with crown walls. Both monochromatic regular waves and irregular waves are taken into account.