The salinity profile in a coastal sea-river system is the result of balancing of salt transport due to mixing of the water by tides and the freshwater discharge from the river. When for example during times of drought freshwater discharge suddenly declines, the salinity in the river may increase significantly and threaten drinking water supplies and agriculture. The time it takes for the salinity to reach the new equilibrium may be considerable. Thorough understanding of the adaptation process is essential for taking appropriate prevention measures. However, much about this adjustment process is still unknown, in particular regarding the interaction between the river and the adjacent sea. In this study, a simplified linear model is developed to describe a well-mixed river and the adjacent sea where the water flows radially away from the mouth of the river. The unique assumptions, most notably a time-independent intrusion length, allow for a unique analytical approach using the method of eigenfunction expansion. The smallest eigenvalues are found to define a time scale of the adjustment process. The eigenfunctions provide insight about how the salinity adjustment time varies within the system. The adjustment time does not only depend on the parameters that describe the new equilibrium, but also on the initial salinity. The eigenvalue time scales corresponding to the sea and to the river can then be used to determine the time scale of the coupled system. It is found that when the sea adjusts much faster than the river, the time scale of the river is leading the adjustment. When the eigenvalue time scale of the sea is similar to or larger than the eigenvalue time scale of the river, the adjustment time is significantly increased by the sea. When salinity is increasing, the sea restricts the inflow of salt in the river, while for decreasing salinity, the sea keeps transporting salt to the river by mixing which delays the adjustment. The model is applied to analyse a sudden decrease in freshwater discharge in the Rotterdam Waterway, which is part of the Dutch Rhine-Meuse delta. Results show that the salinity response is delayed compared to freshwater discharge, indicating that the adjustment time of the river indeed plays an important role. Further research should consider a more general dispersion relation or an extra vertical dimension to better describe estuaries that are not well-mixed. Using numerical methods there are many other possibilities to extend the model. The effect of tides on the presence and dynamics of the fresh water bulge in the sea is of specific interest.

The principle of competitive exclusion states that, in equilibrium, the amount of coexisting species is limited by the amount of limiting resource types in an ecosystem. However, in phytoplankton communities the paradox of plankton appears, amounts of plankton species can coexist that far exceed this
upper limit. A resource competition model is formulated and it is shown that the paradox arises for several systems, which indicates that the bloom in biodiversity is a result of the resource competition and not of any external factors. A proof is given that the principle of competitive exclusion only holds in equilibrium solutions. Therefore, as long as a system does not intersect with an equilibrium solution the biodiversity is not restricted by the amount of limiting resource types. It is concluded that intersecting with an equilibrium solution is avoided when there are only unstable equilibrium solutions present in the system. When a plankton species allows an asymptotically stable equilibrium solution, with a region of convergence equal to the domain of the system, to appear it will be called dominant. It is proven that an asymptotically stable equilibrium solution always exists in a simplified system with less than three limiting resource types. Furthermore, an algorithm is constructed that determines all the new equilibrium solutions, and their respective stabilities, when a new plankton species is introduced to a system.
By applying this algorithm it can be determined whether a species is suitable for an ecosystem, when the goal is to maintain biodiversity. The resource competition model is expanded to include light as an additional resource for all plankton species. It is observed that the coexistence of the plankton species and the total biomass is limited
if there is too little light for the plankton species to consume, or if one plankton species becomes dominant due to it being significantly better at consuming light than the other species.
Additionally, the physical context of a flowing river is introduced, with dispersive and advective mass transfer and finite length. It is observed that while the spatial distribution of the plankton species along the river is strongly influenced by the spatial parameters, the biodiversity of the ecosystem is still primarily determined by the original parameters from the resource competition model, as long as the dispersive mass transfer is the dominant type of mass transfer not too large in comparison to the length of the river.

River estuaries are strongly modified by human interventions, such as dredging. For example the Ems river (Germany and Netherlands) has been deepened between in 1965 and 2005. As a result the sediment (sand and dirt) concentration has increased enormously \cite{Ems_data}. The muddiness of this sediment blocks sunlight and decreases the friction of the water with the bed level. The transport of sediment into the river is mainly caused by non-linearity in tidal waves. As a result of the elevation of the bed level and the friction change of the Ems river, the amplitude of the M2 and M4 tide has changed, which was concluded in previous research. In this study the M2 and M4 tide are studied individually, subjected to deepening, widening and friction change. The main research question in this study is '\textit{How does the propagation of the M2 and M4 tide change, subjected to deepening, change in width and change in friction?}' The result to this question can be applied to tidal rivers. To illustrate this, the results are compared to historical data of the Ems river. The sub question in this study is; '\textit{Can historical observations of the amplitude of the M2 and M4 tides in the Ems river over the years be explained with the change in propagation of the M2 and M4 tides, subjected to deepening and friction change?}'.

The questions are answered with help of a model. The model is constructed with the one dimensional water equations, where boundary conditions are used. Next the equations can be used in two cases. In the first case, which is used to answer the main question, the variables width, depth and friction of the river basin are taken to be length independent variables. In the second case, the width, depth and friction of the river basin are taken to be length dependent variables. This second case is used to model the propagation of the M2 and M4 tide for the Ems river. For the first case an analytical and numerical solution exist. From the error, the optimal grid size for the numerical model is obtained, which is taken as $N=100$. For the second case only a numerical solution exists.

With the model it is concluded that widening and an increasing friction cause a damping effect on the propagation of the M2 and M4 tide. Deepening, however, has a different effect on the M2 and M4 tide. It was seen that for certain value change in depth the M2 tide shows an amplification in amplitude, while the M4 tide shows an damping in amplitude for the same value change. The plots obtained in this part of the study can be used to see what is expected to happen to the amplitude of the M2 and M4 tide when a variable is varied in a tidal river basin. The latter is done for the Ems river.


An important observation made with the $x$-dependent model is that the amplification in amplitude from 1965 to 2005 can be explained by the decreased friction, due to increasing muddiness in the Ems river. Secondly, relatively, it was seen that the amplitude of the M4 tide shows a much greater amplification in amplitude at the beginning of the river than the amplitude of the M2 tide. This could be explained by the different change in amplitude of the M2 and M4 tide subjected to deepening, which was concluded from the $x$-independent model as well. However, the difference in M2 and M4 tide between 1965 and 2005 is not due to deepening on its own. Namely, the change in amplitude due to deepening highly depends on the value of the friction, which is different for the years 1965 and 2005. It is concluded that the exact amplitude of the M2 and M4 tide cannot be predicted with the $x$-independent model. However, it is concluded that the results from the $x$-independent model can be used to predict how the M2 and M4 tide will change due to deepening relatively to each other.


The results of this study are strongly influenced by the assumptions made to derive the model. Before the one dimensional, $x$-independent model was compared to the observations for the Ems river between 1965 and 2005 a few decisions had to be made regarding $x$-dependent to $x$-independent variables. This process needs to be further researched, before applying the x-independent model to other tidal rivers, which is left for further research.

Due to climate change, the sea temperature is rising. This temperature change has an effect on the phytoplankton population. Phytoplankton is responsible for more than 50 percent of the oxygen production on earth, and is therefore crucial for life on earth. In this report, the research question is: is the temperature increase of the water important for the development in space and time of the plankton population in a 2D model of a coastal area of an ocean?

To investigate this, first a 2D model for a coastal area of an ocean is formed. As a basis for this model the 0D model of Steele and Henderson is used to describe the predator-prey model for zooplankton and phytoplankton. Due to this model a repeating pattern in time arises, which is called a limit cycle. This predator-prey
model is expanded to a 2D model by applying convection (v) and diffusion (D) to it, representing the current and dispersion in the water. The chosen parameters and boundary conditions are inspired by the coastal area of the west coast of Portugal.

To evaluate the effect of the water temperature rising, first, the effect of diffusion and convection are studied by answering the following questions: is the convection important for the development in space and time of the plankton population in a 2D model of a coastal area of an ocean? And: is the diffusion important for the development in space and time of the plankton population in a 2D model of a coastal area of an ocean?

The diffusion is dominant in the direction perpendicular to the coast. Due to the diffusion the limit cycle of the predator-prey model is suppressed. Its range gets smaller until the plankton population is completely constant for D > 2.5 m^2/s. This critical value is included in the realistic value of D, which varies from 1 to 2000 m^2/s.

Due to convection, the limit cycle corresponding to the boundary condition occurs in the direction parallel to the coast, making every point in the domain steady state. The higher the velocity v corresponding to the convection is, the less oscillations in phytoplankton density there are in the domain, thus the larger the wavelength of the oscillation is. For v > 0.06 m/s the current is so fast that the predator-prey model has little time to develop before it reaches the right boundary, making the left boundary value more important. This critical value is included in the realistic value of v, which varies from 0.03 to 0.28 m/s.

The model experiences both diffusion and convection more or less equally when the Péclet number vH^2/DL≈1, resulting in D/v≈50 m. If this number is significantly larger than 50 m, diffusion dominates the solution. If the number is significantly smaller than 50 m, convection dominates the solution.

Now the main research question can be answered. By increasing the temperature of the water the growth rate of phytoplankton increases. Due to this increase, the timescale of the predator-prey (τpp ) decreases. The value of D and v for which the predator-prey model and diffusion and convection all influence the solution
equally depends on the timescale with the factor 1/τpp . A smaller time scale means that the predator-prey model contributes more to the model. However, this change is very small in comparison to the scale of the realistic values. In conclusion, in the formed 2D model the temperature increase of the water is not important for the development of the plankton population in space and time.

The results of this report are influenced by the assumptions and approximations made. In this study, several processes, both physical and biological, are described with constants and simplifications. Improving the models of these processes is left for further research.

Because the demand for green energy increases rapidly, it is expected that solar and wind energy will dominate future power generation. New in this field is the development of offshore floating solar systems, consisting of multiple interconnected platforms that are covered with PV panels. Besides satisfying the demand for electricity, these floating solar systems may have a beneficial impact on their wave environment. If waves are attenuated, down-wave shadow zones could be useful for other marine activities such as aquaculture or for the protection of a harbour, creating opportunities for offshore multi-use. The overall research objective of this study is to research the effect of an interconnected multi-body floating solar structure on the transmission of wave height. This was done using a scale model test and a numerical model, in a two-dimensional setting.

From the scale model tests, wave transmission showed to be highly dependent on the wave frequency, and thus the wavelength, of the incident waves. The floating solar system acts as a low pass filter: it lets the low-frequency waves pass through, whereas the waves with higher frequency are attenuated by the structure. This dependence is governed by the ratio between the incident wavelength and the length of the rigid platforms that the solar structure consists of, measured in parallel to the wave propagation direction. When the wavelengths were smaller than twice the length of a platform, waves were almost fully attenuated. Apart from the dependence on frequency, the basin test results also showed that the amount of wave attenuation increases linearly with the total length of the system, but only with a small slope. Furthermore, analysis of the reflected wave signal indicated that higher-order dissipative effects are likely needed to describe the decrease in transmission accurately, because the amount of wave energy that was reflected by the structure was limited.

A proof-of-concept for applying a linear numerical boundary element diffraction model to a fixed shallow solar structure was carried out. The wave surface elevation could be obtained, and these solutions were in accordance with the physical expectations. The results showed similar trends to the basin test results, but did not match quantitatively. This difference could lie in the model approach, where a two-dimensional transmission coefficient is determined from three-dimensional simulations. It could also be that the scattering effects alone cannot approximate the transmission behaviour of the system, because linear radiation effects or higher-order dissipation effects might be of similar importance and are therefore required for an accurate simulation. Radiation could be included in a linear diffraction model, but dissipation requires higher-order wave theory.

Regarding the multi-use context, a down-wave shadow zone can form if the incident waves are short enough. For the North Sea location considered, waves are typically longer than twice the length of the rigid platforms, thus the floating solar structure might not have the breakwater performance that is desired to protect other offshore activities.

Er wordt geschat dat 80% van al het zuurstof op aarde geproduceerd wordt door fytoplankton. Dit is een soort eencellige plant die voorkomen in wateren over de hele wereld. Deze kleine planten worden voornamelijk gegeten door zoöplankton, kleine organismen bestaand uit meestal enkele cellen. Afsterving of overbevolking van fytoplankton heeft ook verregaande gevolgen voor de rest van het maritieme ecosysteem. Fyto- en zoöplankton hebben populaties die een oscillerend patroon kunnen volgen. De groei van de ene beïnvloed het voorkomen van de ander en zo ontstaat een interessante wisselwerking. Er zijn vele modellen die dit gedrag proberen te simuleren om zo inzicht te krijgen in de verschillende patronen die zichtbaar zijn in planktonpopulaties. Een van deze modellen is het model van Steele en Henderson uit 1992. Dat model is echter gemaakt voor wateren zonder ruimtelijke structuren. Om het model van Steele en Henderson ook toe te passen op stromend water in een rivier wordt in dit onderzoek een model beschreven voor planktonpopulaties in rivieren, waarbij de volgende onderzoeksvragen zijn gesteld:
- Welke patronen zijn er te vinden in het model van Steele en Henderson zonder convectie en diffusie?
- Wat is het effect van convectie in een rivier op de uitkomsten van het plankton model van Steele en Henderson?
- Wat is het effect van diffusie in een rivier op de uitkomsten van het plankton model van Steele en Henderson?
- Wat is het effect van convectie én diffusie

The goal of this thesis is to create a theoreticalmodel that captures the influence of wind on the horizontal and vertical salinity distribution in an estuary, as well as the dynamics that arise within the estuary. A secondary, numerical model, that uses fewer assumptions, will be developed and analysed. This serves to determine whether the implications from the theoretical model hold only because of all the assumptions that are made, or whether the results are equally valid when some of these assumptions are relaxed. The focus of this thesis is on gaining conceptual insight in estuaries subject to wind, rather than on obtaining a high accuracy in describing a specific estuary. This thesis is focused on steady-state solution in partially orwell mixed estuaries. Moreover, the dynamics and salinity averaged over the width of the estuary are considered, such that only dynamics in the vertical and along channel direction are modelled. Estuaries are subject to periodical variations forced by tides. The variation within a tidal period is not studied in this thesis, but the dynamics and salinity averaged over a tidal period are considered. The effects of tides or variation along the width of the estuary are not neglected from this model, but are incorporated in the parametrisation of the model instead.

A study of five European estuaries by Winterwerp and Wang (2013) showed that tidal ranges increased significantly along with the ongoing narrowing and deepening of these estuaries. In addition to an increase in tidal range, a dramatic increase in suspended sediment concentrations has been observed in the Ems (Germany) and Loire (France) estuaries, often referred to as a regime shift towards hyperturbid state. While it is generally accepted that the increase in tidal range is a consequence of deepening and narrowing, it is not generally true that deepening and narrowing leads to a dramatic increase in sediment concentrations. Whether deepening is a potential cause for the high sediment concentrations observed in the Loire, is still unclear. Although very little observations have been reported over the 20th century, literature clearly shows that sediment concentrations increased drastically over the years. The scarcity of data not only applied for the sediment concentrations over the years but also for bathymetry and hydrodynamics, resulting in uncertainty about the historical states of the estuary. To cope with the large range of uncertainty and variability in the reported observations and model parameters, an idealised model called iFlow has been used. The strength of the iFlow model for this research was twofold. Firstly, iFlow allowed to identify the essential physical processes driving the estuarine sediment dynamics. Secondly, iFlow is computationally efficient, allowing to perform extensive sensitivity studies. In this way, we could determine which processes play a role in the current state of the Loire estuary and how they are affected by deepening. Furthermore, by mapping the effects of the uncertainty on the different physical processes, robust conclusions could be drawn about the effects of deepening despite the given uncertainty. The effects of deepening on the physical processes has been assessed by only varying the depth in the model. Deepening generally resulted in enhanced sediment import or decreased sediment export. Hence, the transport capacity in the Loire became much more favourable for the import of sediment. In order to determine the robustness of these findings, an extensive sensitivity study was performed of 14.157 simulations (1287 conditions for 11 bottom profiles over time) to capture the influence of uncertainties in multiple input parameters. For the bottom profile representing the bathymetry in the year 1900, none of the conditions resulted in a hyperturbid state, whereas independent of the conditions, the likelihood to find a hyperturbid state always increased for increasing depth. From this we can conclude, that the observed regime shift towards high sediment concentrations would not have happened without the deepening of the Loire estuary.