Structure and intensity of estuarine exchange flow depend significantly on the eddy viscosity A_v profile which is dynamically linked to various forces (e.g., gravitational, tidal, wind-driven). The impact of winds on the exchange flow is complex due to its direct (local and remote changes in shear and density stratification) and indirect (modifications to A_v profiles) contributions. This study aims (i) to include wind entrainment effects in the tidally averaged A_v parameterization; (ii) to develop an analytical one-dimensional model for the wind driven exchange flow by using this novel parameterization and assess the tidally averaged dynamics over a relevant physical parameter-space, subdomains of which have not yet been explored numerically. This one-dimensional model is based on a balance between frictional forces and pressure gradient, calibrated with a tidally-resolving one-dimensional water-column model with second-moment closure. Structure and intensity of the resulting exchange flow profiles are analyzed with respect to three dimensionless parameters (the unsteadiness of boundary layer mixing U_n, scaled-directional wind stress W, and horizontal stratification S_i). While down-estuarine winds enhance the gravitational circulation, up-estuarine winds result in either a two-layer inverted circulation opposing the gravitational circulation, or a three-layer flow (favored by relatively strong S_i, weak W, and moderate U_n) that is up-estuarine at the surface with classical two-layer circulation underneath. Relative thickness of surface and bottom boundary layers affect both the intensity and the inflection depth of the exchange flow layers. Up-estuarine winds with W≳0.5 yield unstable stratification and reduce the exchange flow intensity with increasing W.

Many estuaries exhibit seasonality in the estuary-scale distribution of suspended particulate matter (SPM). This SPM distribution depends on various factors, including freshwater discharge, salinity intrusion, erodibility, and the ability of cohesive SPM to flocculate into larger aggregates. Various authors indicate that biotic factors, such as the presence of algae and their excretion of sticky transparent exopolymer particles (TEP), affect the flocculation and erosion processes. Consequently, seasonality in these biotic factors may play a role in the observed seasonality in SPM. Whereas the impact of abiotic factors on seasonality in SPM is well studied, the relative contribution of biotically induced seasonality is largely unknown. In this study, we employ two approaches to assess the aggregated importance of biotically induced seasonality in flocculation and erosion on seasonality in SPM in the Scheldt estuary. In the first approach, we focus on seasonality of in situ observations in the Scheldt estuary of turbidity, floc size, Chlorophyll-a, and TEP, showing that the abiotic parameters show seasonality, while seasonality in TEP is ambiguous. The second approach concerns a reverse engineering method to calibrate biotically affected parameters of a coupled sediment transport-flocculation model to turbidity observations, allowing us to compare the modeled SPM concentrations to the observations. Driven by seasonality in freshwater discharge, the model captures the observed seasonality in SPM without requiring biotically induced seasonality in flocculation and erosion, which is supported by the absence of seasonality in TEP.

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.

In finite element methods, the accuracy of the solution cannot increase indefinitely since the round-off error related to limited computer precision increases when the number of degrees of freedom (DoFs) is large enough. Because a priori information of the highest attainable accuracy is of great interest, we construct an innovative method to obtain the highest attainable accuracy given the order of the elements. In this method, the truncation error is extrapolated when it converges at the asymptotic rate, and the bound of the round-off error follows from a generically valid error estimate, obtained and validated through extensive numerical experiments. The highest attainable accuracy is obtained by minimizing the sum of these two types of errors. We validate this method using a one-dimensional Helmholtz equation in space. It shows that the highest attainable accuracy can be accurately predicted, and the CPU time required is much smaller compared with that using successive grid refinement.

A new parameterization for the estuarine turbulent eddy viscosity coefficient is developed considering the influence of wind forcing and feedback between stratification and shear. The emerging tidally averaged eddy viscosity profile A_v^T is parameterized as parabolic under well-mixed conditions, and is composed of a skewed-Gaussian-like form for the upper layer, and a parabolic form for the bottom layer under stratified conditions. The precise shape of the profiles depends parametrically on the bottom boundary layer thickness, the bulk Richardson number, and the Wedderburn number. The parameterized A_v^T profiles show excellent agreement with profiles obtained from numerical models. To explore the importance of vertically varying A_v^T with regard to exchange processes, an analytical model is designed. This one-dimensional model is based on a balance between frictional forces and pressure gradient. The resulting exchange flow is analyzed over the relevant parameter space that is associated with horizontal and vertical stratification through the bulk Richardson number, and the bi-directional wind stress via the Wedderburn number. Down-estuary wind enhances the up-estuary flow near the bottom and down-estuary flow near the surface driving an exchange flow pattern typically associated with gravitational circulation. Up-estuary wind results in either a two-layer inverted circulation opposing the gravitational circulation, or a three-layer flow that is up-estuarine at the surface with classical two-layer circulation underneath. Three-layer flow emerges with a weak wind. With increasing runoff velocity, three-layer flow transitions to a single layer flow under weak stratification conditions.

We investigate the hypothesis by Winterwerp and Wang (Ocean Dyn 63:1279–1292, 2013) that channel deepening in the Scheldt River Estuary could lead to a large increase in suspended sediment concentrations, with subsequent severe consequences to primary production and navigation. To this end, we use an idealised model to investigate the long-term development of the sediment concentration under the uncertainty of future changes in model parameter values and channel deepening. The water motion is calibrated to recent conditions after which the sediment concentration is validated against long-term observations and is subsequently tested for a wide range of parameter settings and deepening scenarios. We also investigate the effect of anthropogenic dumping of dredged sediments in the estuary on the sediment concentration. Deepening the channel, but keeping all other model parameters the same, we find lower long-term average sediment concentrations in most of the estuary. Thereby, our results suggest that deepening in the Scheldt alone cannot lead to high sediment concentrations, and we suggest to reject the investigated hypothesis. Further study of uncertain model parameters reveals that an increase of the erosion parameter by an order of magnitude allows for the development of high concentrations of several tens of grams per liter near the bed in narrow turbidity zones. It is unknown whether such an increase of the erosion parameter can happen in the future, which stresses the importance of further research into the factors that can lead to a change of this parameter.