Tidal inlet systems, which consist of back–barrier basins connected to the open sea by one or multiple inlets, are found at many places along sandy coasts. They are valuable for ecology (breeding and feeding areas), economy (gas–mining and sand–mining) and recreation, and are important for coastal safety. But they are also sensitive to external forcings like prevailing currents, tides, winds, sea level rise and human interferences. Therefore, it is important to investigate the morphodynamic behaviour of these tidal inlet systems, especially the formation of the channels and shoals. In this thesis, idealized models will be developed to study so–called double–inlet systems, which are tidal basins with two inlets connecting to the open sea. To assess the morphodynamic behaviour of double–inlet systems, a one–dimensional idealized model is developed. In this model, the water motion is governed by cross– sectionally averaged shallow water equations, forced by tides prescribed at the seaward boundaries. Sediment transport is governed by a width–averaged and depth–integrated advection diffusion equation,with sink and source terms. The bed evolution is described by the cross–sectionally averaged equation for the concentration of mass in a sediment layer. A system is said to be in morphodynamic equilibrium if the bed does not evolve on a long (morphodynamic) timescale anymore. The model is first analysed without the presence of externally prescribed overtides, so the water motion is only forced by theM2 tidal constituents. To systematically analyse the sensitivity of the resulting morphodynamic equilibria to the characteristics of theM2 forcing, a continuation approach is employed to obtain these equilibria in the parameter space spanned by the relative phase and amplitude of the M2 tidal constituent. In this parameter space, it was found that there are regions where no morphodynamic equilibrium, one equilibrium or multiple equilibria can exist. When there is no morphodynamic equilibrium, the double–inlet system is reduced to two single–inlet systems. For a certain parameter setting, four morphodynamic equilibria are found. The water depth of these four equilibria are further analysed, as well as the sediment transport contributions. The influence of the depth variations, the presence of externally generated overtides and width variations of this model are then further analysed for the stable morphodynamic equilibria. The model finally allows a qualitative comparison with observations in the Marsdiep–Vlie inlet system at the Dutch Wadden Sea. Using characteristic values of this system, one stable equilibria is obtained, suggesting that this double–inlet system can be stable on the long morphodynamic timescales. Next, the morphodynamic model is extended to include dynamics in the lateral direction. The model consists of depth–averaged shallow water equations neglecting the effects of earth rotation, a depth–integrated concentration equation and a tidally–averaged bottom evolution equation. Since the equations are still averaged over depth, a 2DHmodel is obtained. With this idealized model the initial formation of channel–shoal patterns in a double–inlet system with a rectangular geometry was systematically investigated. Utilizing infinitesimally small perturbations with a lateral structure, the initial formation of channels and shoals can be expected if the laterally uniform morphodynamic equilibria are linearly unstable with respect to these perturbations. When the water motion is only forced by an M2 tidal constituent, restricting only attention to that part of the parameter space spanned by the relative phase and amplitudes of M2 tidal forcing where laterally uniform morphodynamic equilibria exist, it is found that these equilibria can be either stable against two–dimensional perturbations, or linearly unstable. When linearly unstable, the instabilities can be either due to diffusive mechanisms, or due to advective mechanisms. When the morphodynamic equilibria become unstable due to diffusive processes, the classical diffusive mechanism has a destabilizing effect, while the topographically induced diffusive mechanism has a stabilizing effect. The associated eigenvalues are all real, implying an exponential growth/decay in time. When the advective mechanism results in linear instabilities, the eigenvalues are complex, implying that bedforms do not only grow/decay in time, but also migrate. When external overtides and a residual discharge are included, the laterally uniform morphodynamic equilibria can be unstable due to the convergences and divergences of both (interally and externally) advective and diffusive transport. Finally, we study channels and shoals in double–inlet systems, using a scaled depth– averaged model. Thismodel consists of scaled shallow water motion equations, a scaled depth–integrated concentration equation and a scaled bottom evolution equation. By focusing on a short rectangular tidal basin, laterally uniform morphodynamic equilibria can be found. These equilibria are either linearly stable or linearly unstable due to diffusive processes. When varying one or more parameters, such as the friction parameter and the width of the system, bifurcations can be found where the stabilities of morphodynamic equilibria change. Using associated eigenfunctions as a load vector, arclength method allows to switch branches. At different branches, morphodynamic equilibria are characterized by lateral variations with different mode numbers. When default parameters are used, the resulting bifurcation diagrams reveal thatmultiple morphodynamic equilibria exist. @en

The existence of morphodynamic equilibria of double-inlet systems is investigated using a cross-sectionally averaged morphodynamic model. The number of possible equilibria and their stability strongly depend on the forcing conditions and geometry considered. This is illustrated by considering a rectangular double-inlet system forced by M2 tidal constituents only. Depending on the M2 amplitudes and phases at both entrances, no equilibrium, one equilibrium or multiple morphodynamic equilibria may exist. In case no equilibrium is found, the minimum water depth becomes zero somewhere in the system, reducing the double-inlet system to two single-inlet systems. In the other cases, the location of the minimum water depth and the direction of the tidally-averaged sediment transport, as well as their actual values, depend strongly on the M2 tidal characteristics. Such parameter sensitivity is also observed when including the residual and M4 forcing contributions to the water motion, and when allowing for width variations. This suggests that, when considering a specific system, the number and stability of morphodynamic equilibria, as well as the characteristics of these quantities, can only be assessed by investigating that specific system in detail. As an example, the Marsdiep-Vlie inlet system in the Dutch Wadden Sea is considered. It is found that, by using parameter values and a geometry characteristic for this system, the water motion and bathymetry in morphodynamic equilibrium are qualitatively reproduced. Also the direction and order of magnitude of the tidally-averaged suspended sediment transport compare well with those obtained from a high-complexity numerical model.@en

Channel–shoal patterns are often observed in the back–barrier basins of inlet systems and are important from both an economical and ecological point of view. Focussing on double–inlet systems, the initial formation of these patterns is investigated using an idealized model. The model is governed by the depth–averaged shallow water equations, a depth–integrated concentration equation and a tidally–averaged bottom evolution equation. Focussing on rectangular basins and neglecting the effects of earth rotation, it is found that laterally uniform morphodynamic equilibria can become linearly unstable, resulting in initial patterns that resemble channels and shoals. When the water motion is only forced by an M2 tidal constituent, the existence of (laterally uniform) morphodynamic equilibria for which both inlets are connected strongly depends on the relative phase and amplitudes of the tidal forcing. If such equilibria exist, they can be either stable against small perturbations or linearly unstable. If these equilibria are linearly unstable, two instability mechanisms can be identified, the first related to the convergences and divergences of diffusive transports, the second mechanism related to a combination of advective and diffusive transports. In the former case, all eigenvalues are real and the bedforms grow exponentially in time. In the latter case, the eigenvalues are complex, resulting in bedforms that both migrate and grow in time. In case external overtides and a time–independent discharge are included, no diffusive instabilities are found anymore for the parameters considered in this paper. This implies that all instabilities are migrating in time. In all cases considered, the bed perturbations have only an appreciable amplitude at locations where the underlying laterally uniform equilibrium has a local minimum in water depth. This is consistent with observations from numerical models and laboratory experiments.@en