Estuaries are often characterised by a complex network of branching channels, in which the water motion is primarily driven by tides and fresh water discharge. For both scientific reasons and management purposes, it is important to gain more fundamental knowledge about the hydrodynamics in such networks, as well as their implications for turbidity and ecological functioning. A generic 2DV estuarine network model is developed to study tides and river water transport and to understand the dependence of their along-channel and vertical structure on forcings, geometry characteristics and sea level changes. The model is subsequently applied to the Yangtze Estuary to investigate tides and the distribution of river water over channels during dry and wet season, spring tide, as well as prior to and after the formation of Hengsha Passage and the construction of the Deep Waterway Project and sea level rise. Increasing river discharge enhances the friction for tides by increasing both internal and bottom stresses. Changes in tidal forcing are correlated with the friction for both tide and river. A shortcut channel reduces the water level difference in adjacent channels, as well as tidal amplitudes difference. Sea level rise results in larger friction parameters and faster propagation of tides. The distribution of river water transport is hardly affected by above mentioned changes. Model results and current vertical structure are consistent with observations.

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 salinity structure in estuaries is classically described in terms of the salinity structure as well mixed, partially mixed, or salt wedge. The existing knowledge about the processes that result in such salinity structures comes from highly idealized models that are restricted to either well-mixed and partially mixed cases or subtidal salt wedge estuaries. Hence, there is still little knowledge about the processes driving transitions between these different salinity structures and the estuarine parameters at which such a transition is found. As an important step toward a unified description of the dominant processes driving well-mixed, partially mixed, and salt wedge estuaries, a subtidal width-averaged model applicable to all these salinity structures is developed and systematically analyzed. Using our model, we identify four salinity regimes, resulting from different balances of dominant processes. It is shown that each regime is uniquely determined by two dimensionless parameters: an estuarine Froude and Rayleigh number, representing freshwater discharge and tidal mixing, respectively, resulting in a classification of the regimes in terms of these two parameters. Furthermore, analytical expressions to approximate the salt intrusion length in each regime are developed. These expressions are used to illustrate that the salt intrusion length in different regimes responds in a highly different manner to changes in depth and freshwater discharge. As one of the key results, we show that there are only very weak relations between the process-based regime of an estuary and the salt intrusion length and top-bottom stratification. This implies that the salinity structure of an estuary cannot be uniquely matched to a regime.

Climate and human pressures can influence the evolution of estuarine sediment dynamics concurrently, but the understanding and quantification of their cause–effect relationships are still challenging due to the occurrence of complex hydro-morpho-sedimentary feedbacks. The Garonne Tidal River (GTR, upper Gironde Estuary, France) is a clear example of a system stressed by both anthropogenic and climate change, as it has been subject to decreasing river discharges, natural morphological changes, and gravel extraction. To understand the relative effect of each hydrological and geomorphological pressure on the turbidity maximum zone (TMZ), the sediment dynamics in the GTR over the last six decades was evaluated using the width-averaged idealized iFlow model. Model results show a gradual increase in tidal amplitude and currents over the decades that has led to the upstream shift of the landward sediment-transport capacity components (external M₄ tide, spatial settling lag, and tidal return flow). The upstream displacement of the TMZ between the 1950s and the 2010s was estimated to be at least 19 km, of which about three fourth was induced by geomorphological changes and one fourth by hydrological changes. Concerning the geomorphological changes, the natural evolution of the lower Gironde morphology was the main pressure inducing the displacement of the TMZ in the GTR. Anthropogenic and natural changes in morphology and bed roughness in the GTR itself also contributed to this evolution. The natural geomorphological changes were, in turn, probably promoted by the evolution of sediment dynamics, so this study reveals the closed circle that governs the intensification of the TMZ.

Sediment transport in estuaries and the formation of estuarine turbidity maxima (ETM) highly depend on the ability of suspended particulate matter (SPM) to flocculate into larger aggregates. While most literature focuses on the small-scale impact of biological flocculants on the formation of larger aggregates, the influence of the flocculation process on large-scale estuarine SPM profiles is still largely unknown. In this paper, we study the impact of flocculation of SPM on the formation of ETM. For this, a semianalytical width-integrated model called iFlow is utilized and extended by a flocculation model. Starting from a complex one-class flocculation model, we show that flocculation may be described as a linear relation between settling velocity and suspended sediment concentration to capture its leading-order effect on the ETM formation. The model is applied to a winter case in the Scheldt estuary (Belgium, Netherlands) and calibrated to a unique, long-term, two-dimensional set of turbidity (cf. SPM) observations. First, model results with and without the effect of flocculation are compared, showing that the spatial and temporal variations of the settling velocity due to flocculation are essential to reproduce the observed magnitude of the suspended sediment concentrations and its dependence on river discharge. Second, flocculation results in tidally averaged land-inward sediment transport. Third, we conduct a sensitivity analysis of the freshwater discharge and floc breakup parameter, which shows that flocculation can cause additional estuarine turbidity maxima and can prevent flushing of the ETM for high freshwater inflow.

Many estuaries are strongly deepened to improve navigation, with sometimes large and poorly understood consequences to suspended sediment dynamics. To improve understanding of such large changes, we study the Ems River Estuary, where a regime shift from low to high sediment concentrations was observed after deepening. The aim of this study is to improve understanding of the development of the sediment concentration regime over time and estimate the associated time scale. Using the idealized width-averaged iFlow model, we identify the coexistence of two distinct stable equilibrium regimes representing low and high sediment concentrations, qualitatively matching the regimes observed in the Ems. Depending on the river discharge, a critical depth profile is identified at which the regime shifts. By combining the model results and long-term observations of the tidal range, first indications of the regime shift are observed around 1989, taking approximately 6–7 years to develop.

Phytoplankton biomass in estuaries is controlled by complex biological and chemical processes that control growth and mortality, and physical processes that control transport and dilution. The effects of these processes on phytoplankton blooms were systematically analyzed, focusing on identifying the dominant controlling factors out of river-induced flushing, tidal dispersion, nutrient limitation, and light limitation. To capture the physical processes related to flow and sediment dynamics, we used the idealized width-averaged iFlow model. The model was extended with a nutrient-phytoplankton module to capture the essential biological-chemical processes. The model was applied to the Delaware River Estuary for the productive months of March to November. Model results were compared with field observations. It was found that phytoplankton blooms cannot form in the lower bay due to tidal dispersion, as water from the estuary and coastal ocean mix in early spring, and due to local effects of nitrogen limitation in summer. In the middle to upper bay, sediment-induced deterioration of the light climate limits the growth but allows for blooms in the mid bay, while no blooms can form in the turbidity maximum zone in the upper estuary. Further upstream in the tidal river, the effects of river-induced flushing dominate in early spring and prevent bloom formation. In the summer and fall, lower river discharges and higher growth rates at higher temperatures allow blooms to form and persist. Analysis of the connectivity between mid bay and tidal river blooms showed that coastal ocean phytoplankton may contribute to mid bay blooms, but do not penetrate beyond the turbidity maximum zone.

Many estuaries are strongly modified by human interventions, including substantive channel deepening. In the Ems River Estuary (Germany and Netherlands), channel deepening between the 1960s and early 2000s coincided with an increase in the maximum near-bed suspended sediment concentration from moderate (∼1 kg/m ³ ) to high (>10 kg/m ³ ). In this study the observed transition in the suspended sediment concentration in the Ems is qualitatively reproduced by using an idealized width-averaged iFlow model. The model is used to reproduce observations from 1965 and 2005 by only changing the channel depth between the years. Model results show an increase in sediment concentrations from approximately 1–2 kg/m ³ to 20–30 kg/m ³ near the bed between 1965 and 2005 if the river discharge is below 70 m ³ /s, which holds approximately 60% of the time. Thereby, this study for the first time provides strong evidence for earlier published hypotheses that channel deepening was the main driver of the increased sediment concentrations in the Ems. The results are explained using two aspects: sediment transport (longitudinal processes) and local resuspension (vertical processes). The magnitude of the sediment import increased, because a combination of channel deepening and sediment-induced damping of turbulence increased the M ₂ –M ₄ tidal asymmetry. This effect is particularly strong, because the M ₄ tide evolved to a state close to resonance. All imported sediment is kept in suspension when it is assumed that resuspension is sufficiently efficient, which depends on the value of the erosion parameter used and inclusion of hindered settling in the model.

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.

Over the last few decades, some estuaries have undergone a transition to a hyperturbid state, characterised by suspended sediment concentrations of several grammes per litre averaged over the water column. To improve our understanding of this transition and of naturally hyperturbid estuaries, we systematically identify the processes allowing for high suspended sediment concentrations using a water column (1DV) model. Under a range of realistic forcing conditions, the state of the water column can be characterised by one of two equilibrium states. The first is an erosion-limited state, in which there still is sediment available for erosion at the bed. We find that this state only occurs with relatively low concentrations. The second is a supply-limited state, in which all erodable sediment is in suspension. The concentration in this state depends entirely on the amount of sediment in the system and can potentially be very high. We identify the conditions under which the state of the water column can jump from a low to a high concentration and identify hysteresis in the transition between the two states. The mechanism responsible for this hysteresis is hindered settling. It thus follows that hyperturbidity is only possible in a supply-limited state. From this observation we derive a necessary condition for an estuarine system to make the transition from low turbidity to hyperturbidity in a 1DV context. This is an important step towards understanding why some estuaries are hyperturbid and assessing the risk that particular estuaries may become hyperturbid in the future.

Using an idealized width-averaged process-based model, the role of a mud pool on the bed and time-varying river discharge on the trapping of fine sediment is systematically investigated. For this purpose, a dynamically and physically motivated description of erodibility is presented, which relates the amount of sediment on the bed to the suspended sediment concentration (SSC). We can distinguish between two states: in the availability-limited state, the SSC is limited by the amount of erodible sediment at the bed. Over time, under constant forcing conditions, the estuary evolves to morphodynamic equilibrium. In the erosion-limited state, there is an abundant amount of sediment at the bed so that sediment pickup occurs at the maximum possible rate. The SSC is then limited by the local hydrodynamic conditions. In this state, the estuary keeps importing sediment, forming an erodible bottom pool that grows in time. These two states can be used to explain the response of an estuary to changing river discharge. Under availability-limited conditions, periods of high river discharge push estuarine turbidity maxima (ETMs) downstream, while drier periods allow ETMs to move upstream. However, when the estuary is in an erosion-limited state during low river discharge, a bottom pool is formed. When the discharge then increases, it takes time to deplete this pool, so that an ETM located over a bottom pool moves with a significant time lag relative to changes in the river discharge. Good qualitative agreement is found between model results and observations in the Scheldt Estuary of surface SSC using a representative year of discharge conditions.

The iFlow modelling framework is a width-averaged model for the systematic analysis of the water motion and sediment transport processes in estuaries and tidal rivers. The distinctive solution method, a mathematical perturbation method, used in the model allows for identification of the effect of individual physical processes on the water motion and sediment transport and study of the sensitivity of these processes to model parameters. This distinction between processes provides a unique tool for interpreting and explaining hydrodynamic interactions and sediment trapping. iFlow also includes a large number of options to configure the model geometry and multiple choices of turbulence and salinity models. Additionally, the model contains auxiliary components, including one that facilitates easy and fast sensitivity studies. iFlow has a modular structure, which makes it easy to include, exclude or change individual model components, called modules. Depending on the required functionality for the application at hand, modules can be selected to construct anything from very simple quasi-linear models to rather complex models involving multiple non-linear interactions. This way, the model complexity can be adjusted to the application. Once the modules containing the required functionality are selected, the underlying model structure automatically ensures modules are called in the correct order. The model inserts iteration loops over groups of modules that are mutually dependent. iFlow also ensures a smooth coupling of modules using analytical and numerical solution methods. This way the model combines the speed and accuracy of analytical solutions with the versatility of numerical solution methods. In this paper we present the modular structure, solution method and two examples of the use of iFlow. In the examples we present two case studies, of the Yangtze and Scheldt rivers, demonstrating how iFlow facilitates the analysis of model results, the understanding of the underlying physics and the testing of parameter sensitivity. A comparison of the model results to measurements shows a good qualitative agreement. iFlow is written in Python and is available as open source code under the LGPL license.

This study presents a detailed comparison between the k-. e(open) and k-. τ turbulence models. It is demonstrated that the numerical accuracy of the k-. e(open) turbulence model can be improved in geophysical and environmental high Reynolds number boundary layer flows. This is achieved by transforming the k-. e(open) model to the k-. τ model, so that both models use the same physical parametrisation. The models therefore only differ in numerical aspects. A comparison between the two models is carried out using four idealised one-dimensional vertical (1DV) test cases. The advantage of a 1DV model is that it is feasible to carry out convergence tests with grids containing 5 to several thousands of vertical layers. It is shown hat the k-. τ model is more accurate than the k-. e(open) model in stratified and non-stratified boundary layer flows for grid resolutions between 10 and 100 layers. The k-. τ model also shows a more monotonous convergence behaviour than the k-. e(open) model. The price for the improved accuracy is about 20% more computational time for the k-. τ model, which is due to additional terms in the model equations. The improved performance of the k-. τ model is explained by the linearity of τ in the boundary layer and the better defined boundary condition.