· · · Institutional Repository

Part I: On the time scales of wave processes. To systematically improve the SWAN model a study on the wave physics in a tidal inlet was carried out. The third-generation SWAN model was used to compute the wave processes in a tidal inlet for storm conditions. The computed wave processes are propagation (shoaling, refraction and frequency shifting), generation (wind input), non-linear wave-wave interactions (quadruplet wave-wave interactions and triad wave-wave interactions), dissipation (white capping, depth induced breaking and bottom friction), and the work done by the currents against the radiation stresses. The results were normalised, which resulted in the time scales of all wave processes. The time scales were of the order 100s – 1,000s, except for the work done by the currents against the radiation stresses, which is of the order of 1,000s – 10,000s. Part II: Depth-induced breaking: A comparison of the performance of three models. Depth-induced breaking is a subject that has been widely studied, resulting in many scalings on the Battjes and Janssen model. The Battjes and Janssen model, the biphase scaling and the Nelson scaling were selected to compare results in terms of significant wave height. The parameter of interest is the model coefficient . The models were tested with the SWAN model on three different test cases; two reef cases and one sloping bottom profile. The wave period appeared to have a strong influence on the prediction of the significant wave height, in particular on the biphase scaling. The best model over the three test cases statistically is the Nelson scaling.

Part I Probabilistic aspects. An overview is given of literature on the statistics of breaking waves in open ocean. New approximations of the fraction of breaking waves and the distribution of breaking wave heights are presented and compared with results found in literature. Part II Observed breaking wave statistics. This part is dedicated to the results of the field observations. In this experiment visual observations of breaking waves passing a waverider buoy are carried out. The statistics of breaking waves are investigated from wave records of this buoy in which visually observed breaking waves are labelled. Part III ontbreekt.

The present report describes some of the results obtained during experiments in the Large Wave Flume of the Fluid Mechanics Laboratory of the Delft University of Technology. The experiments are part of the PhD-work of M. Boers. They follow on the LIP llD-experiments, carried out in the Delta Flume of Delft Hydraulics in spring 1993. During the LIP 11D-experiments much information was obtained about physical parameters in the surf zone such as wave heights, wave set-up and velocities. The experiments have the following objectives: To add measuring data to the LIP llD-data To obtain data which can reconstruct the mass, momentum and energy balances To obtain detailed information about regions with steep gradients of wave heights and wave set-up (onshore slope of breaker bar and toe of foreshore) To obtain information about the breaking behaviour of waves To measure bed shear stresses To measure turbulence motions The objective of this report is to distribute the results of the measurements among researchers working in the field of coastal engineering. Further, it gives information about the accuracy of the measuring data. The results of the experiments are described in two reports. Report 1 (the present report) describes the experimental set-up [Chapter 2], wave height measurements and the video recordings of the wave breaking [Chapter 3]. The results of velocities and shear stress measurements are described in Report 2 [Boers, 1996]. Some of the results are already published by Boers and Van de Graaff [1995]. The results of the analysis of the measurements is presented in many figures. Data are also available in files [Enclosure A].

The present report gives the results of a study on bedforms and undertow in the surf zone. It is the objective of this study to get a better insight into the physical processes in the surf zone. In this study, we make use of the data obtained during the LIP llDexperiments (Arcilla et al. [1994] and Roelvink and Reniers [1994]). We derive the characteristics of bedforms from measured profiles. We relate these bedform characteristics to the hydraulic conditions and analyse if they can be predicted with present prediction methods. Further, we develop an inverse modelling technique, which is based on the mass and momentum balance equations. With this technique we derive values of important physical parameters, like eddy viscosity, shear stresses, friction factors, bed roughness and mass flux. The derived physical parameters are compared with present methods to describe these parameters.

It is well known (see Divoky et al., 1970, for a review) that on gentle slopes (slope S < 1:30, say) the wave height after breaking does not decay in proportion to the mean depth. The curve H/Hb vs h/hb is concave upwards (for plane bottom). The concavity increases with decreasing S and with increasing Ho/Lo (Nakamura et al., 1966). The often-used hypothesis H(x) = gamma h(x), gamma = const. for given (S, Ho/Lo)' does not incorporate the effects mentioned above. Its success in the prediction of set-up can perhaps be ascribed Co the fact that it has been tested mainly on plane and relatively steep slopes, where indeed it is in reasonable agreement with the data. The hypothesis H = gamma h is not applicable in regions where the depth is constant or increasing in the propagation direction, such as in a bar-trough profile. Visual observations of the latter situation cannot fail but to give the impression that the immediate post-breaking behavior is governed primarily by the characteristics at breaking, with its own imposed length scale. The bottom slope is believed to affect this behavior only if it is sufficiently steep, so that the rate of change of wave height due to changes in depth ("shoaling" with either increasing or decreasing depth) is comparable to that due to breaking.

In many coastal, engineering problems the sediment transport plays a part. A transport gradient causes accretion or erosion. Various models, such as that of Bijker, Engelund and Hansen (van de Graaff and van Overeem, 1979) and Nielsen (1985) are available to estimate the sediment transport rate if the hydraulic and environmental conditions (wave height, current velocity and direction, sediment size) are known. Since reliable data under field conditions are extremely scarce, the reliability of these models is not known, while also no understanding of the basic relations between the sediment transport, current velocity and wave height can be obtained. To extend the knowledge of the basic phenomena, a laboratory study was carried out. Fluid velocities and sediment concentrations have been measured in case of irregular non-breaking waves alone, and in combination with following or opposing currents.

Investigation to sediment transport rate in case of waves and currents, tests executed in the wave-current flume of the laboratory of Fluid mechanics of TU Delft. Sediment transport was measured using sand of 100 micron; comparison to similar tests with 200 micron sand.

Much research has been done on the stability of stones in breaking waves, but up to now, most of these studies were based on experiments with slopes varying from 1: 1 to 1:7. The stability of stones on mild slopes, slopes not steeper than 1: 10, has not yet been researched very extensively. Applications of mild slopes in practice are for example landfalls of oil pipelines and outfalls of sewage systems. The objective of this study is to improve the theoretical knowledge of the stability of stones on mild slopes in the surf zone by researching the flow in breaking waves. The stability relations for stones on mild slopes established so far, followed the trend of experimental results quite well in a qualitative way, but the difference in stability for spilling breakers and plunging breakers was predicted too small by the relations. Probably the main reason of this imperfection is the influence of the plunging jet in a plunging breaker. Therefore, the processes which take place in plunging breakers are studied. From a study by Basco (1985) it was concluded that processes in spilling and plunging breakers are similar, albeit that the vortex systems in plunging breakers are of a much larger scale. Experiments were carried out in the large wave flume of the Laboratory of Fluid Mechanics for a better understanding of the stability of stones on a slope subjected to wave attack. The model structure consisted of a 1: 10 impermeable slope, on which a layer of stones (Dnso =1.21 cm) was laid. Only regular waves were used, because these wave are more suitable for researching the flow in a particular wave. For three waves with different wave steepnesses, incipient motion of the stones was determined. SUbsequently, in the breaking regions of these waves, velocity measurements were carried out by means of LDV and video recordings. From the damage experiments it was concluded that maximum damage was located at about h/Ho =0.6 and that the direction of displacement of the stones depends on the breaker parameter. Furthermore, the stone displacement in upslope direction seemed to be caused by the plunging jets of the breaking waves. The velocities in the plunging jet were equivalent for the three different waves, which is in line with the fact that these waves cause incipient motion. The plunging jets of the breaking waves cause incipient motion of the stones. Up to now no theories were available for the stone stability in plunging jets. Therefore, an attempt was made to model the stone stability in a plunging jet. Two different models were considered, which both schematize the plunging jet on a stone as static forces on a single cubical stone. From the modelling it was concluded that the results deviate from experimental results. The missing of the turbulent fluctuations of the jet and to a less extent the dynamic characteristics of the stone stability were probably the main reasons of this deviation. Nevertheless, the modelling can improve the theoretical understanding of the stone stability in plunging jets. The numerical results of the stability relation by Izbash for uniform flow are close to the experimental results. Therefore, it seems that stone stability in a plunging jet is not as unfavourable as expected, compared to stone stability in uniform flow. The resulting stability equations for the stone stability in plunging breakers is in conformance with existing relations.

In this report we describe the development and calibration of a model which predicts the vertical distribution of the horizontal velocities induced by waves, the so-called undertow. Location of interest is the nearshore region where the flow is induced by both breaking and non-breaking waves. The model consists out of three modules. The first module computes the properties of the incoming (breaking) waves, a second module converts the resulting dat from the first module so that it can be used as input for the third module which is a 2DY model. The 2DY model is a 2DY version of DELFT HYDRAULICS' TRISULA which is a 3D hydrostatic tidal model. The waves influence the flow in three ways. A first effect is a shear stress at the water surface which originates from the breaking of waves. Also is shown in this thesis that the waves induce a mass flux which has as a result that there is a nett flow directed off-shore. The third effect is the influence of the orbital motion on the viscosity distribution. All these effects are included in the model described in this thesis. The model has been tested against measured data in the Delta flume to see how accurate the model predicts the undertow. Also published as Delft Hydraulics report H 1684

The present wave transformation models for random waves make use of an explicit formulation of the energy dissipation. A time-averaged model has been studied in which the dissipation rate per breaking wave is estimated from that in a bore of corresponding height. The probability of occurrence of breaking is derived from a wave height distribution in which all breaking waves have been assumed to have the same height. This probability can be interpreted as the fraction of waves that are breaking at a certain location. Comparisons with measurements show that with the calibrated values for the parameters the wave height decay is predicted well, The fraction of breaking waves however is underpredicted, especially for high steepness waves. A second drawback is an inaccurate prediction of the mean water level. The positive gradient in the mean water level is predicted too early compared to measurements. The prediction of the mean water level has been improved by taking the transition zone into account. In this zone shoreward of the breaker point the just broken wave develops its turbulence. It is characterised by a rapid wave height decay and roughly constant mean water level. The organised wave energy is not dissipated immediately, but transferred into kinetic energy of the so-called roller, a body of water at the front face of the wave. A recently developed model has been used for the contribution of the roller in which the fraction of breaking waves plays an important role. A sensitivity analysis of the model with respect to its parameter values has lead to two improvements in the model. The first improvement consists of a new choice of the two free parameters in the model. With the new parameter setting both wave height decay and fraction of breaking waves can be predicted well. The second improvement consists of a small change in the formulation of the dissipation rate. In this formulation the energy dissipation rate in a breaking wave more closely resembles the dissipation in a bore. The optimal parameter values yield similar predictions of wave height and fraction of breaking waves, but the parameters have a clearer physical meaning. For the parameters qualitative relations have been found with wave and bottom parameters. On non-monotonic profiles the predictions of the fraction of breaking waves are less satisfactory. The maximum fraction of breaking waves is not found at the bar-crest, as predicted, but some di stance beyond it. Also the model is not able to reproduce the breaking persistenee of the waves. In the analysis existing laboratory measurements have been used on both plane slopes and non-monotonic profiles. Video records of large scale experiments have been analysed for the fraction of breaking waves. The study has taken place at the Universitat Politècnica de Catalunya in Barcelona as part of the ERASMUS exchange program.

This new land will be exposed to a North Sea wave climate and tidal currents. Severe erosion of the dunes and a large draw back of the coastline has to be avoided. One of the possibilities to influence the wave climate and thus the sediment transport nearshore is by using a perched beach with a submerged breakwater (see Figures A2 and A3). The influence of this structure on the dynamic equilibrium profile behind the submerged breakwater has to be determined since this alternative saves large quantities of sand and therefore the construction costs are decreased. This will be investigated in this research project and the following research questions will be answered (see Figure A2): What is the effect of a submerged breakwater on the dynamic equilibrium profile of the perched beach for Maasvlakte II? What is the difference in the required quantity (m3) of sand to construct the required dynamic equilibrium profile in comparison with the situation without a perched beach with a submerged breakwater and what is the difference in costs? The objective of this research project is dual and has to give answer to the two research questions for this research project: Determine the effect of a perched beach with a submerged breakwater on the dynamic equilibrium profile of the perched beach for Maasvlakte II; Determine the required quantity of sand required for the dynamic equilibrium profile for the situation with and without a perched beach with a submerged breakwater. In an economical analysis the costs will be compared. Since the cross-shore sediment transport is mainly responsible for fluctuations in the coastal profile, the study of the development of the bottom profile landward of the submerged breakwater is mainly a two dimensional problem, perpendicular to the coastline and depth contour lines. After an inventory of the theoretical knowledge and available tools to answer the research questions, the crosssediment transport module of the Unibest Coastal Softwane Package, Unibest-TC (TC: Iimed dependent .Cross-shore) was chosen to provide insight in the development of the dynamic equilibrium profile landward of the submerged breakwater under the combined action of waves, longshore tidal currents and wind. The submerged breakwater will be positioned on different cross-shore positions of the shoreline.

We present a new method to break symmetry in graph coloring problems, which can be applied in many classes of combinatorial problems. While most alternative techniques add symmetry breaking predicates in a pre-processing step, we developed a learning scheme that translates each encountered conflict into one conflict clause which covers equivalent conflicts arising from any permutation of the colors. Our technique combines Extended Resolution with domain specific knowledge. Although the Extended Resolution proof system is powerful in theory, it is rarely used in practice because it is hard to determine which variables to introduce defining useful predicates. In case of graph coloring, the reason for each conflicting coloring can be expressed as a node in the Zykov-tree, that stems from merging some vertices and adding some edges. So, we focus on variables that represent the Boolean expression that two vertices can be merged (if set to true), or that an edge can be placed between them (if set to false). Further, our algorithm reduces the number of introduced variables by reusing them as much as possible. We implemented our technique in the state-of-the-art solver MiniSat2. It is competitive with alternative SAT based techniques for graph coloring problems. Moreover, our technique can be used on top of other symmetry breaking techniques. In fact, combined with adding symmetry breaking predicates, huge performance gains are realized.

The nearshore zone is an active zone that can be quite inhospitable to humans due to violent wave breaking and strong rip currents. Rip currents are shore normal jet-like currents that typically extend from near the shoreline out past the line of breaking waves. Observations have concluded that a rip current system generally consists of 4 parts. Part 1 is the shoreward mass transport due to the waves carrying water through the breaker zone in the direction of wave propagation. Part 2 is the movement of this water mass parallel to the coast known as a longshore current. Part 3 is the rip current itself, a seaward flow of water through a narrow rip channel. And part 4 is an alongshore movement outside the breaker zone of the expanding rip head. With the use of the numerical model XBeach, in which a non-hydrostatic model based upon the numerical scheme as developed by Stelling and Zijlema (2003)was implemented, the fluid motions in the nearshore zone are simulated. The method of Stelling and Zijlema utilizes an edge based compact difference scheme for the approximation of the vertical gradient of the non-hydrostatic pressure. This ensures accurate wave breaking and dispersion characteristics, which is important for an accurate simulation of the nearshore hydrodynamics. Two test cases are used to verify the model for replication of the hydrodynamics in the nearshore zone. The first case consists of irregular wave breaking in a laboratory barred surf zone. The second case is a wave induced and bathymetry driven rip current in a directional wave basin. The numerical model is further developed with the addition of an eddy viscosity model and a non-reflecting boundary condition. With these additions the depth averaged model gave very satisfactorily results for both cases. The XBeach model is an accurate and efficient simulation package for the dynamics in the nearshore zone. This study shows that application to real world situations should give realistic and accurate results. Therefore the model could be applied in coastal engineering applications and in the research for energy extraction methods from wave induced currents.

A description is given of a model developed for the prediction of the dissipation of energy in random waves breaking on a beach. The dissipation rate per breaking wave is estimated from that in a bore of corresponding height, while the probability of occurrence of breaking waves is estimated on the basis of a wave height distribution with an upper cut-off which in shallow water is determined mainly by the local depth. A comparison with measurements of wave height decay and set-up, on a plane beach and on a beach with a bar-trough profile, indicates that the model is capable of predicting qualitatively and quantitatively all the main features of the data. A summary of this thesis is published as: Battjes, J.A., Janssen, J.P.F.M. (1978) Energy loss and set-up due to breaking random waves, proc. ICCE Hamburg

Looking at a surfzone, one immediately notices the short breaking waves. Looking more carefully, will show in most cases that the wave height of the breaking waves is not constant, but varies in time. Often one may observe that groups of relatively high waves are followed by groups of lower waves. This short wave groupiness may cause low frequency fluctuations in the nearshore zone by generating so called long waves. These are less noticeable, because of their longer time scale. This study was made to see whether it is possible to predict the generation of long waves in the nearshore zone due to the groupiness of obliquely incident short waves, and if so, extend an existing numerical model, SURFBEÀT [Roelvink, 1991] to the case of obliquely incident waves.

A description is given of a model developed for the prediction of the dissipation of energy in random waves breaking on a beach. The dissipation rate per breaking wave is estimated from that in a bore of corresponding height, while the probability of occurrence of breaking waves is estimated on the basis of a wave height distribution with an upper cut-off which in shallow water is determined mainly by the local depth. A comparison with measurements of wave height decay and set-up, on a plane beach and on a beach with a bar-trough profile, indicates that the model is capable of predicting qualitatively and quantitatively all the main features of the data.

Nonlinear aspects of breaking and non-breaking waves propagating over a submerged trapezoidal bar have been investigated by laboratory experiments, with special emphasis on the generation of high-frequency energy. Data collected from the measurements are used for computing spectral and bispectral estimates in order to assess the contribution of wave breaking to the spectral evolution, as distinguished from that of the conservative nonlinear interactions. It is found that wave breaking itself, even in the case of plunging breakers, does not play a decisive role in the evolution of the spectral sahm, but contributes by simply extracting energy in almost averaged manner. An approach is described to utilize this observation by using a semi-empirical formulation for dissipation due to breaking in conjunction with a weakly nonlinear numerical model.

The effect of short wave breaking on low frequency waves is investigated using two breaker formulations implemented in a time-dependent numerical model (XBeach): (1) an advective-deterministic approach (ADA) and (2) the probabilistic breaker formulation of Roelvink (1993). Previous research has shown that the ADA breaker model gives different results for the cross-shore pattern of the fraction of breaking waves, which is now shown to affect not only the short wave height but also the short wave groupiness. While RMS short wave heights are comparable to measurements using both breaker models, the ADA breaker model allows higher levels of short wave groupiness into the surf zone. It is shown that this acts as an additional forcing mechanism for low frequency waves in the shoaling and nearshore zone, which, in addition to greater levels of breaking, leads to higher values of wave set-up. These findings are dependent on the complexity of the local bathymetry. For a plane slope, the differences in the low frequency wave heights and set-up predicted by both breaker models are negligible. Where arbitrary breakpoints are present in the field of wave propagation, such as nearshore bars or reefs, the ADA model predicts higher localized set-up, indicative of greater flow over such features. Differences are even more pronounced when the incident wave regime is highly energetic.

It has been found by many researchers that low frequency (LF) waves dominate the wave energy spectrum in very shallow water. Given that many longshore and cross-shore morphological processes are located within this zone, LF waves play an important role in determining morphological change, especially dune erosion and overwash during storm events. The numerical model, XBeach [Roelvink et al. (2008)], has been developed to simulate such morphological processes which are influenced by LF waves. For hydrodynamics, it utilizes the wave forcing determined from a second generation wave module to drive linearized shallow water equations within a flow module. The objective of this thesis focuses on validating the hydrodynamics of XBeach with particular attention paid to the estimated LF waves. This is particularly important to correctly estimate morphological changes, as it is highly dependent on the accurate representation of waves and currents. In the validation study, XBeach is used to replicate the flume experiment of van Noorloos [2003] in which bichromatic and irregular wave conditions are imposed on a plane sloping beach. The advantage of using this experiment is that measurements have a high spatial resolution, allowing for decomposition into incoming and outgoing wave components. Group-varying time-averaged short wave parameters are used to investigate the accuracy of the short wave module in XBeach, while at the same time the relationship between the short waves and LF waves are determined by looking at the energy transfer to and from the LF components. The results confirm many previous findings, such as the plus 180 degree phase difference between the short wave envelope and the bound LF wave, the dominance of LF wave energy in shallow water and the ability of LF waves to extend their reach to the uppermost parts on a beach. Given the limitations of the assumptions based on linear wave theory, the short wave results from XBeach are quite good, especially when using a newly modified breaker parameterization of Battjes and Janssen [1978] by Roelvink [Pers. Com. 2009]. The main shortfall of the model is that it tends to overestimate the bound LF wave heights in shallow water for irregular waves. This is believed to be partly due to the overestimation of the energy and radiation stresses contained in the short waves in this region. In reality, as waves approach breaking, the non-linearities present in the waves increase, which, during breaking, effectively redistributes energy within the wave spectrum. Since frequency dependent shoaling of short waves is not currently enabled in XBeach, the energy within the HF band may tend to encourage continued shoaling of the LF waves in the surf zone. As such, it is recommended that the current wave action conservation scheme be improved to allow for either reduction or redistribution of the short wave energy during shoaling. Wave run-up as modelled with the linearized shallow water equations is shown to over-steepen the front of the LF wave in the swash zone. This effect is a likely result of the numerical scheme used, which tends to limit the maximum run-up height based on a minimum depth for which a computational grid cell is determined to be wet. In general, XBeach has shown that it is capable of modelling both quantitatively and qualitatively the short wave energy flux and LF wave shoaling and reflection quite will without inducing serious errors from the linear simplifications in the wave module. Wave-current interaction, which was not considered in the modelling, can most likely give even better results if it is successfully incorporated in the model.

Against the background of enhanced hydraulic loads due to climate change there will be a need for improvement of the flood defence system in the Netherlands in the future. These days there is a growing interest in grass as a dike cover because it is a cheap and a sustainable dike protection. Yet at the moment there is a hiatus in the knowledge on the erosion resistance of grass covers on especially the outer slope. For this reason large scale tests have been performed in the Große WellenKanal (Large Wave Flume) in Hannover in 2008 for both EroGRASS and FLOODsite. With the help of the EroGRASS data the MSc-study presented here aimed to develop a model that describes the initiation of erosion of a grass cover layer on the outer slope by wave attack. The erosion process was investigated first to gain some insight in the failure mechanisms on the outer slope. For wave-induced erosion of grass cover layers on the outer slope two failure mechanisms can be distinguished which can occur independently of each other. Aggregate erosion occurs when the soil is cracked and saturated with water. Uplift pressures can then develop underneath the aggregates shortly after a wave impact and on the surface small aggregates may be lifted and washed away. This eventually results in an erosion hole. Block erosion may occur when impact pressures can penetrate into the soil due to the presence of a large crack or irregularity. The balloon mechanism may then be triggered; at the location of minimum fracture strength a horizontal crack is formed. This crack gradually extends until it reaches a critical size. From this point a large block can instantly erode from the grass cover. For these erosion mechanisms the Wave Impact Pressure Erosion model has been developed, which describes the initiation of erosion of grass covers on the outer slope by wave impact pressures. The basic equation of the WIPE model can be adapted to obtain limit states for aggregate erosion block erosion. The WIPE model was calibrated and verified with the data of the EroGRASS experiments. For aggregate erosion the model behavior resembled the observed progression of aggregate erosion during the experiments after calibration. The WIPE model is considered suitable for the prediction of aggregate erosion of a good quality grass cover. Yet because the grass cover strength is dominated by the grass reinforcement, which decays with depth, the model will require adaptations to make it suitable for grass covers of lower quality. For block erosion the model was calibrated using a parameter that determines the moment of block erosion and a crack growth parameter, which determines the size of the eroded block. As the model was calibrated on merely two characteristic block erosion events, universal calibration factors for block erosion could unfortunately not be found. To obtain more reliable and uniform results for block erosion more data is required.