In times of rapid urbanization, engineering interventions in coastal systems have become more common. It is important to understand the interplay of these engineered solutions with their natural environment to minimize hazardous side effects to our ecology, economy and coastal safety. In a numerical study by Rijnsburger (2021), a flow recirculation with a diameter of 10 to 20 km - similar to an eddy - was identified in the North Sea. It remained unclear what causes the recirculation, but its location in the Rhine region of freshwater influence and near the artificial Maasvlakte headland, suggest that the recirculation could both be baroclinic or barotropic. This numerical model study is set out to understand what processes drive the recirculation. Identifying these processes is important to understand what is required to properly model the hydrodynamics along the Dutch coast, and accordingly, the spreading of sediment, pollutants and phytoplankton. A realistic 3D hydrodynamic model was used to assess the recirculation during a validated spring-neap cycle. Our analysis shows that the recirculation has a maximum diameter of roughly 15 km during neap tide and 5 km during spring tide. The recirculation occurs in the buoyant top layer of the water column and grows offshore from its onset north of the Maasmond around HW+3 until it is overtaken by ebb tidal velocities around HW+5. This study shows that the onshore advection of negative (clockwise) vorticity water results in most water flowing back to the river mouth into an expanding clockwise recirculation, the vorticity and strength of which are strongly influenced by buoyant river outflow. Our analysis shows that the headland is not a prerequisite for its onset. Nevertheless, two mechanisms are identified of how the headland influences the recirculation. First, during spring tide, the headland is found to ‘shelter’ the recirculation from strong ambient currents in the midfield which would otherwise hamper the recirculation. Secondly, the geometry of the river mouth influences the vorticity input in the North Sea associated with the buoyant river outflow. To further investigate what processes influenced by the river outflow could contribute to the recirculation, a scale analysis and particle tracking study were deployed. Although, the study is not yet conclusive on what drives the onshore advection of the spinning water that flows into the recirculation, several potential processes have been identified. For future studies that want to model the spreading of freshwater, pollutants or suspended sediment near the river mouth of the Rhine-Meuse system, this study underlines the importance of using a three-dimensional numerical model that accounts for density differences and the influence of the studied recirculation. The latter is especially important when the boundaries of the numerical domain are located close to the river mouth, due to which the influence of the recirculation is not resolved unless explicitly accounted for in the boundary conditions. This study therefore contributes to the improvement of future modelling studies of the Rhine ROFI and to our understanding of the processes that govern the hydrodynamics along the Dutch coast.

This thesis introduces a new algorithm for optimising shipping routes within a dredging project. Highly dynamic and time-dependent hydrodynamic features influence shipping routes. Due to the complex interactions between the horizontal tide, vertical tide, stratifying forces, wind-driven forces, and limited water-depth, shipping routes were previously only optimised for large scale routes (order of 1000 km). This study presents an algorithm that can optimise shipping routes that are influenced by these small scales (order of 10 km) hydrodynamic features. This algorithm uses graph theory to solve for the time-dependent fastest path between start and destination. Graph theory searches for the optimal path through a set of nodes that are connected with edges. This study uses the time-dependent shortest path algorithm which accounts for the FIFO-criteria (Waiting criteria) and can solve the non-convex nature of the problem The input of this algorithm is a hydrodynamic model. These models are Computational Fluid Dynamic (CFD) models that calculate currents and water levels in a specific domain. The domain is discretised into cells and nodes to calculate these hydrodynamic features. This study uses the nodes of this hydrodynamic model as the vertices of the graph. However, for some cases, the hydrodynamic model has too many nodes for the shortest path algorithm. This study presents a method for reducing the number of nodes without reducing the spatial resolution. The nodes are reduced based on a combination of the vorticity and the magnitude of the flow. This algorithm is implemented in a python software package named Hydrodynamic Algorithm for Logistic enhancement Module (HALEM). HALEM can determine the optimal shipping route for a given hydrodynamic model. Defining different cost functions results in different optimisation purposes. This thesis presents cost functions for the fastest route, shortest route, cheapest route and least polluting route. This software is then implemented in the OpenCLSim software so that this combination of software can optimise routes of entire projects. A case study simulates a beach-nourishment at Schouwen Westkop Noord to demonstrate the practical use of HALEM and OpenCLSim. For this project, 425,500 m3 sand should be dredged offshore and pumped onto the beach. Due to the narrow gullies and tidal changes in hydrodynamic features, the routes were hard to predict. The simulation with HALEM and OpenCLSim shows an increase in the production with 21 % compared to the simulation with just OpenCLSim.

In the ocean resides a large amount of plastic. This has severe environmental consequences for the oceans. To be able to clean up all this plastic the location of the plastic is needed. A lot of times plastic is cleaned up at the source, but to clean up here this location needs to be known. However, what if the start location is not known and only the end location is known. This thesis looks at the following research question: Can the method of particle filtering be used to find the start location of a plastic particle of which the end location is known?. The method of particle filtering compares the end locations of the released particles and the end location of the end particle. (The end particle is the particle of which the end location is known and we want to know the start location.) The method calculates weights on the basis of this comparison for each of the released particles. Then the weights are used to calculate a probability density function that gives the likelihood of possible start locations being the right start location of the end particle. The method is applied to the MSC Zoe case, which is a container accident, and a simplification of this case. The MSC Zoe lost in this accident hundreds of containers above the Wadden Islands in the Netherlands, in these containers were bags of plastic particles. A lot of these particles washed ashore on the Wadden Islands. However, it is not known exactly where all the containers fell overboard. So the start location of the plastic particles that washed ashore is not known. The method of particle filtering applied to the simplification showed that it can indeed be used to find the likelihood of possible start locations. However, it also showed that for some values of the variables it was possible to get multiple peaks with weights that are zero in between. This is not a desired outcome for a probability density function (pdf). So a kernel estimation is used to smooth out the pdf's. It uses the weights calculated in the method of particle filtering to estimate the pdf. This gives results that also in this way the likelihood of possible start locations can be found and now without multiple peaks. The kernel estimation was also applied to the MSC Zoe case and the results were calculated for multiple end particles. The locations that came out of this were very close to a few of the possible main locations were containers fell overboard. These possible main locations came from the international investigation into the MSC Zoe accident. A simplification of this research is that the start location is found for one specific plastic particle. For future research it could be interesting to look if the method can be adapted to find the start location of concentrations of plastic particles.

Globally, at each river mouth freshwater is discharged to coastal waters. At each river mouth a freshwater plume is formed. These fresh water plumes are also known as the regions of freshwater influence (or ROFI’s). Furthermore, the freshwater plume will affect local coastal water levels. In order to improve global flood forecasting, research on this topic has been conducted. Through a combination of numerical (DFlow-fm) and probabilistic (vine copula) models predictions can be made for the size- and hydraulic effect of these river plumes.

Even though negative effects on the use of crude oil have surfaced over the past years, our energy matrix still largely relies on this energy source. The production of oil, therefore, plays an important role in our society. Unfortunately, the process of oil production is highly uncertain. There are uncertainties associated on the production strategy, e.g. where and how many wells should be drilled and how these wells should operate because of the uncertainties associated with the limited knowledge about the subsurface. In this thesis we are dealing with the uncertainty of the rock permeability distribution. Typically, rock permeabilities in the rock vary, but from the outside this can’t be perceived. If these rock permeabilities are estimated inaccurately, they will result in inaccurate pressure solutions. Then, this can lead to faulty decisions regarding the oil exploitation. To resolve this issue, a data assimilation technique may be applied to correct these model parameters based on mismatch of simulated data and observations. For this optimization technique, often gradient information is required. Since in reservoir simulation the number of parameters generally is extremely high, computation of this information is computationally expensive. Therefore, a multiscale framework is employed to improve the computational efficiency of the forward simulation. Multiscale methods are able to solve the model equations at a computationally efficient coarse scale and can easily interpolate this solution to the fine scale resolution. Next, we use a Lagrangian set-up together with a multiscale framework to re-derive an efficient formulation for the derivative computation. However, as the multiscale method is prone to errors, this derivative computation formulation is recast in an iterative fashion, using a residual based iterative multiscale method to provide control of these errors. In this thesis we show that this method generates accurate gradients. In contract to the high accuracy of the method, this method comprises a computationally heavy smoothing step. This issue can be resolved by making smart use of the Lagrange multipliers, to re-derive an efficient iterative multiscale solution strategy. The multipliers are used to identify important domains of the region for which smoothing is required and for which regions we may neglect the smoothing. We show that the newly proposed iterative multiscale goal oriented method is computationally more efficient and we show that method is promising for efficient derivative computation, but that more work is required to fully demonstrate the benefit of this method.

Subsea Rock Installation vessels cover pipelines, which transport oil from oil and gas fields. This is done by means of a flexible fallpipe until depths of 1000 meters. Around the Shetland Islands, the workability of the vessels at two specific project locations is compromised by the conditions in the ocean. In this research, data from a 3D hydrodynamic model and logged information from the vessels has been analysed and combined to find an explanation for these problems. At the second location, for tidal flow to the east or east-northeast in the bottom and middle part of the water column, it is highly likely that the working activities have to be interrupted. Moreover, if the value of the turbulent vertical eddy viscosity exceeds 0.028 m²/s, the chance on non-working conditions increases with 70%. For the other project location, these kind of correlations have not been observed.

Due to climate change and human interventions, saltwater intrusion is becoming a topic of increasing concern worldwide. Salt water intrudes into the Rotterdam Waterway (RWW) by an exchange flow, where the denser sea water propagates landwards at the bottom. The main competing mechanism for this stratified exchange flow is vertical mixing, which can be realised by internal wave induced shear instabilities or wave breaking. The goal of this study is to investigate whether internal waves generated over undular bottom topography in the RWW can generate additional vertical mixing. The underlying assumption is that a decrease in stratification decreases salt intrusion.   The approach to answer the main research question is a combination of an analytical and a numerical analysis. The analytical study is based on frictionless linear theory. Internal wave behaviour is further analysed with FinLab, a finite element model which includes the non-hydrostatic processes and effects of density differences. FinLab is evaluated for the application of this study by means of a validation case.  In the analytical study, linear theory is applied to obtain a relation between the bed wave parameters and average internal wave energy density E for internal waves generated over sinusoidal bottom topography in a linearly stratified fluid. The derived expression describes that the bottom topography amplitude h0 and bed wave number kT both have a positive quadratic relation with the energy. Additionally, kTkinfluences the resonance conditions.  To validate FinLab for internal wave breaking and mixing an experiment in a wave tank, according to an example from literature, is simulated. The validation case reveals a shortcoming in the turbulent mixing parameterization. However, on scales relevant for the RWW the effect of this will not have the same significance. The validation case offers a suggestion for a subgrid closure of diffusion, where density effects are taken into account.  Numerical simulations of a 2D channel stretch with sinusoidal bottom topography, a linearly stratified fluid and a linearly varying background velocity, show generation of resonant trapped internal waves for the first two resonant modes. These occurrences correspond to the highest values of kinetic energy as function of vertical velocity averaged over the bed wave domain. The vertical buoyancy flux b is downward directed during occurrences of internal waves and becomes upward directed for increasing background flow. Vertical mixing is associated with an increase in average potential energy Ep, which is 17% higher for the base case (containing bed waves) than for a similar case without bed waves. This increase is larger when bottom shear stress increases. Richardson numbers below 0.25, associated with shear instabilities and mixing, are only observed near the bed, mainly when internal waves are present. The effect of variations in bottom topography wavelength LT and amplitude h0 on internal wave energy can be explained by the analytical formulation. The effect of bed wave parameter changes on b and relative increase in Ep can be related to the effect of the changed amount of bed friction rather than the difference in wave energy.   The first resonant mode is the most energetic, however, the average energy density found for these waves is only 0.4% to 6.7% of the potential energy anomaly (PEA); the energy required to fully mix a stratified water column. In the simulations the only mechanism that could transfer internal wave energy to turbulent kinetic energy are shear instabilities near the bed. Over the full simulation, the net vertical buoyancy transport is of negligible magnitude, where Ep shows significant increases between 6% and 99% compared to similar cases without bed waves and is enhanced during the presence of internal waves.  The main discussion point is that the quantification of vertical mixing requires improvement, particularly to determine the importance of mixing by internal wave-induced shear instabilities and by bed shear. Mixing by local shear instabilities (of which the relevant scales cannot be resolved with the current grid resolution) does not have an adequate parameterization, because density effects are not included in the turbulence closure. The bed friction parameter, which greatly influences the behaviour of the system, has to be validated. Furthermore, cases where internal waves might break in practice (e.g. at banks) were not considered. Finally, the observed internal wave energy is of small magnitude, however field measurements by Pietrzak(1991) shows that turbulence production by internal waves was significant.   

Establishing an accurate global unified vertical reference frame (VRF) is a long-standing objective of geodesy. However, that objective has still not been achieved. One particular application where the lack of such a VRF is evident, is the improvement of hydrodynamic models by assimilating total water levels acquired by tide gauges. Indeed, to facilitate a straightforward assimilation requires that both the observed and modeled water levels refer to the same vertical datum. The required accuracy is high; it is expected to be in the order of 1centimeter. The best alternative VRF for the area of interest, the northwest European continental shelf, is the European Vertical Reference Frame 2019 (EVRF2019). The EVRF2019, however, still lacks complete coverage and the required accuracy. The key reason is that it is solely based on geopotential differences from spirit leveling/gravimetry, which are not available between benchmarks separated by large water bodies. This thesis exploits model-based hydrodynamic leveling to provide these differences. The specific objective is to assess the potential of including these data in realizing of European Vertical Reference System (EVRS).@en

Plastic pollution is a big problem all over the world. Every year more plastic is produced, a lot of plastic litter is mismanaged and enters the ocean. It’s important to know where these plastics accumulate. With this information the problem can be quantified and the plastic litter can be cleaned up. In this project, the transport of micro plastics will be studied. These are plastic particles with a diameter smaller than 5 mm. To model micro plastics in an accurate way, it is important to include the physical properties of plastics in a transport model. Plastic particles have an extra upwards buoyancy force in the vertical direction, this force has to be taken into account in the model. Therefore, the two-dimensional vertical behavior of plastic particles is studied in this project. Two common transport models are explored: the advection-diffusion equation and a stochastic random walk model. The properties of plastics are discussed and how the transport models can be adapted to be adequate to model micro plastics. Micro plastics are assumed as spheres in fluid. With this assumption, the flow regime around a plastic particle is estimated with the Reynolds number. These assumptions make it possible to calculate a terminal buoyancy velocity, due to the floating character of plastic. This velocity is added in the vertical direction to both transport models. To model the turbulence in the ocean, the eddy diffusivity coefficient is defined. This is a variable that states how turbulent the flow is, it can be described as an enhanced diffusion coefficient. The eddy diffusivity coefficient can be estimated with the model Prandlt defined. Here we used a simplified turbulence model for the tests described. In combination with Delft3D-FM the eddy diffusivity from the turbulence model in there can be used. Both models are implemented in Matlab. The characteristics of the model match with the expected behavior of floating plastics. Plastic particles will perfectly follow the velocity field, except for the extra vertical velocity. When this term is non-zero, the particles will float. Both models have some limitations in efficiency for modeling plastic particles. The advection-diffusion equation is not suitable for high concentration gradients. The random walk model is not suitable for big areas or long timescales. The choice between both models is depending on the sort of case that someone wants to model. This project has been carried out at Deltares, an independent water research institute. At Deltares there is a two-dimensional horizontal model available to model particles in the ocean. In the future the existing model of Deltares and the model in this project could be combined. This combined model can be tested for real-life situations in the ocean. With this combined model, the physical properties of plastics are included in a three-dimensional particle model.

Polder areas as typical in the Netherlands require real time control on the water levels. Efficient pumping is a subject with increasing interest due to a required use of 20% green energy by 2020 set by the government. In 2010, the energy requirements already exceeded 175 GWh per year. For optimal control, water level predictions are important. However, they are uncertain due to errors in model structure, parameter estimation, initial states and observed forcing data. Especially the rainfall was found to contribute to water level prediction uncertainty. The uncorrected radar rainfall forcing data available in real time underestimate the corrected radar rainfall measurement over 100%, worsening with increasing rainfall intensities. The aim of the research was to asses whether data assimilation can reduce the uncertainty on the water level predictions in a Delfland polder. The polder is modelled with a conceptual rainfall-runoff model in Sobek RR, while the data assimilation is implemented as an ensemble Kalman filter in OpenDA. In order to manipulate the states in Sobek RR for data assimilation, the model was extended by a black-box wrapper that was newly created in Java for this research. To asses the theoretical applicability of data assimilation in a polder area, four twin experiments were carried out, which differed only in the model components to which noise was applied. The four set-ups included the use of a rainfall multiplier, additive noise on the model states, additive noise on the groundwater state and a single multiplier for all states. The results were compared visually and objectively through the probabilistic Nash Sutcliffe, a model efficiency coefficient. All set ups for the twin experiment generated good results for the assimilated water level, mimicking the observed water levels closely with probabilistic Nash Sutcliffe values ranging between 0.92 to 0.97. However, only the set up with the rainfall multiplier exhibited good score measures for the hidden states, with an average of 0.6, showing a significant improvement over the case without assimilation. The other twin experiments failed to represent the hidden states, with average score measures below zero. The data assimilation set-up with the rainfall multiplier was then applied using water level observations from Tedingerbroek polder. The pump pattern and magnitude of water levels of the modelled and observed water level differed significantly. The influence of the different model components on the modelled water level was assessed, from which was concluded that these could not account for the difference in modelled and observed values. Possible explanations are due to a non-representative measurement point in the polder or additional unknown water fluxes coming into the polder. Recommended further research should focus on creating a larger observation network; implementing multiple water level observation locations, collecting pump discharges and taking measurements of the storage in greenhouse basins. The last could give a method to validate the assimilation of the hidden states, whereas the pump discharges should be used as additional observation in the data assimilation.

Dit onderzoek bestudeert het energieverlies van het barotroop getij aan de opwekking van intern getij. Dit energieverlies vindt plaats bij stroming van de gestratificeerde oceaan over steile topografieën, zoals ruggen in de oceaan en bij de randen van continentale platen. Zo'n 25-30% van de totale getij-energie, die wordt opgewekt door de zon en de maan gaat zo verloren. In een wereldwijd getijmodel wordt alleen het dieptegemiddelde gedrag van de getijstroming beschouwd, waardoor de opwekking van intern getij niet expliciet gemodelleerd kan worden. Om het effect daar wel in mee te nemen, wordt het verlies van barotroop getij aan de opwekking van intern getij geparametriseerd aan de hand van variabelen, die in dat model wel meegenomen zijn. Het onderzoek is numeriek uitgevoerd met het hydrostatisch oceaanmodel Delft3D-Flexible Mesh. In het 3D model is expliciet de opwekking van intern getij gesimuleerd en vergeleken met analytische resultaten voor de opwekking van intern getij. Daarnaast zijn deze resultaten gebruikt om de huidige geïmplementeerde parametrisering, van de opwekking van intern getij, in het 2D model te toetsen. De expliciete simulering van de opwekking van intern getij in Delft3D-FM is succesvol gedaan. Het energieverlies van barotroop getij aan de opwekking van intern getij was in overeenstemming de literatuur. Voor smalle topografieën hoger dan (ongeveer) een halve oceaandiepte lijkt de hydrostatische aanname in het model te worden overschreden waardoor numerieke dissipatie van intern getij optreedt. De huidige geïmplementeerde parametrisering van het verlies van barotroop getij aan de opwekking van intern getij is voor een beperkte verzameling topografieën en stratificaties getest. De resultaten geven indicaties, dat de huidige parametrisering niet in staat is om de conversie over een breder scala van topografieën in de oceanen goed te benaderen. Het voorspelbare gedrag van de conversie voor steile, superkritische topografieën wijst erop dat zo'n parametrisering wel mogelijk is. Aanbevelingen voor verder onderzoek zijn het uitbreiden van het gebruikte model met stromingen in x- en y-richting en het effect van de Coriolis parameter. Om de parametrisering beter te testen kan het bestaande model op meer verschillende typische topografieën en stratificaties in de oceaan worden toegepast.

Waves in coastal waters play a role in forecasting storm conditions, as boundary conditions for the assessment of coastal risk and in coastal structure design. Assessment of their impact can be made through numerical modeling. In a forecasting context, the CPU time of the wave model is decisive in its suitability. Recent years wave model approaches have been to describe both linear and non-linear generation, dissipation and transfer processes in the wave spectrum explicitly. This resulted in computationally demanding tools. Such models are very suitable for research purposes or for design and assessment if time is available, but are rather heavy tools for forecasting applications on larger scales. Parametric models describe the wave spectrum through characteristics in a smaller solution space compared to spectral models, which makes them potentially faster solvers. In this thesis the suitability for forecasting of a spectrally integrated approach to the wave action balance is investigated. The stationary wave drivers from the storm impact assessment model XBeach were taken as a starting point. A second balance equation was identified to model the evolution of the mean period. In estuaries and behind shoals, locally generated waves can be dominant over offshore wave conditions. As part of the project, a wave generation mechanism is developed for the modified wave drivers based on prediction relations for growth of wind-waves under fetch-limited conditions. The two-equation approach was discretized and tested in a 1D Matlab model and the solution was proven to converge towards the literature prescribed growth curves for total wave energy and mean wave period. This approach was then implemented in the unstructured Frequency Integrated wave drivers in D-Flow FM. The implementation has been verified through semi-1D test cases and showed convergence behavior equal to the Matlab model. A hindcast of a 1982 storm in the Haringvliet was performed to compare the model skill of the unstructured frequency integrated model (FIM-FM) to the spectral wave model SWAN. In this hindcast the model skill of FIM-FM is comparable to SWAN for significant wave height and mean wave period for all locations apart from directly behind a shoal. Depth and wave height dependence of bottom friction coefficients should be studied in more validation cases to improve the prediction of wave steepening over shoals. Further research should also look into the iterative method in the solver for stationary solutions of the model equations to realize faster CPU time of a stationary problem. Although not established in this thesis, faster CPU time compared to a spectral model like SWAN should be possible based on the reduction of the solution space.

Vector-based graphics are not directly compatible with the raster-based structure of dedicated graphics hardware. They suffer from a locality problem where, in order to check if a specific display pixel lies inside or outside the shape, the entire shape needs to be taken into account. This negates the advantage that the graphics pipeline’s parallel rendering structure offers. Current solutions rasterize vector graphics into a discrete raster-based texture in an extra render pass, every time the required texture resolution changes. This work presents an approach to store vector-based shapes into discrete raster-based textures, optimized for parallel rendering. This is done by encoding the shape as piece-wise cubic Bézier curves, structured in a quad-tree. Additional data is added to remove aliasing effects in case of minification. These textures are then rendered by a custom fragment shader. This work discusses the implementation of both the serialization and deserialization steps, as well as rendering regular vector shapes with a comparable quality.