Om boka This research is dedicated to studying longterm estuarine morphodynamic behavior under combined river and tidal forcing.
Morphodynamic sensitivities to river discharge magnitude and time variations, tidal strength and tidal constituents are then systematically explored. Analysis of river tides in the YRE reveals strong river-tide interactions and non-linear modulation of tides by river discharge.
Estuarine morphological modelling
River discharge alters tidal asymmetries and resultant tidal residual sediment transport. Analysis of morphodynamic modeling results exposes significant mechanisms inducing tidal residual sediment transport and controlling long-term morphodynamic development.
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Morphodynamic equilibria in 1D and 2D simulations can be defined by vanishing gradients of tidal residual sediment transports and meeting empirical morphodynamic relationships. This research indicates the value of numerical modeling in examining long-term morphodynamic development in millennia time scale. Physical models can be physical scale models or analogs. There is multitude of mathematical models , in one, two or three spatial dimensions.
Most of the hydrodynamic models in this category are process-based, i. The constituting equations, such as the Navier-Stokes equations for turbulent flow, are solved in various degrees of simplification. Analytical models seem to be regaining ground now that techniques become available to tackle systems of nonlinear equations e.
Schuttelaars and de Swart . Lumped or aggregated models basically involve a reduction of the number of spatial dimensions. Box models have no spatial dimension at all, i.
They are often used in ecology e. An example of such a model is ASMITA, which has been used extensively to describe the morphological behaviour of short tidal embayments such as those in the Wadden Sea Stive and Wang . Spatially integrated models reduce the number of dimensions by formally integrating the constituting equations over one or more spatial dimension. An example is ESTMORF, which describes the morphological evolution of a tidal channel and shoal system as a 1-D network with the shoals as storage areas for water and sediment Wang et al.
Grid-based models form a very large category of mathematical models. They exist in a variety of forms, to be distinguished by the type of grid and by the way the constituting equations are discretized and solved. In the case of morphological models, an important aspect is how the hydrodynamic, sediment transport and sediment balance components of the model are coupled, at time-step level like Delft3D; see Lesser et al.
A special category of grid models are cellular automata e. Dearing et al. Thus it is a mixed form of grid-based and particle-based models. Particle-based models are increasingly used now that computer power has sufficiently increased. Spectacular results have been obtained with Smooth Particle Hydrodynamics SPH , especially with highly non-linear water motion at small scales e. Random walk models were formerly used only at the analytical level, in order to come up with parameterisations of e.
Random-walk numerical simulation models seem to be coming within sight now. In sediment transport, grain-by-grain transport models are gaining ground, as they circumvent part of the empiricism of traditional sediment transport models. Especially in complex areas such as estuaries, this may become an important asset.
Swarm models describe the behaviour of large numbers of mutually interacting particles, such as emergent pattern formation. They may become of interest for cohesive sediment e. Tidal basins which are small as compared with the tidal wavelength allow for a special kind of modelling, based on the approximation that at every point in time the water surface elevation is in phase throughout the basin.
This simplifies the hydrodynamic computation significantly. Many tidal basins on barrier island coasts are of this type. It consists of a range of tidal basins, separated by more or less pronounced drainage divides. Wherever expedient in the model descriptions below, example applications from this system are shown, even though most models have been used for a variety of other systems, as well. Important morphological elements within each basin are channels, shoals and mudflats and marshlands in the back.
Typical channel networks in such basins are like the branches of an apple tree Van Veen  , i. There is a significant long-term interaction between the morphology of the basin, the ebb-tidal delta and the adjacent coastlines: they form a sediment-sharing system also see Cowell et al. A large amount of empirical evidence is available on certain aspects of the morphological equilibrium state of such systems.
The cross-sectional area of the inlet and the channels, for instance, is approximately proportional to the tidal prism, i. Also, the volume of the basin below mean sea level is approximately proportional to the tidal prism to a power between 1 and 1. Such empirical relationships are the basis of a number of conceptual models of the large-scale behaviour of this type of short tidal basins e. They also allow for a special kind of morphological models: closed-loop models which basically describe the deviation from the empirical equilibrium state. These models are complementary to open-loop ones, which start from a given state and integrate the constituting equations through time without prescribing the equilibrium state.
There is a whole family of aggregated models for this type of systems. Di Silvio  proposed a simple two-box model in which all channels and all shoals are lumped, respectively. The basic equations are the integrated water and sediment balances, combined with relationships between the sediment concentration and the state of the shoals and the channels, respectively.
They can be elaborated to a set of two coupled relaxation equations describing the long-term morphological evolution of the basin.
This type of model is only suitable to describe very long-term morphological changes, say at the scale of centuries, and only for systems with no strong interaction with the ebb-tidal delta. The model was applied successfully to the past evolution of Venice Lagoon Fig. As this model includes more of the dynamic interactions, it can be applied at somewhat shorter timescales, say decades to centuries. The model has been used in many applications, among which the long-term response of the Wadden Sea to accelerated sea level rise Van Goor et al.
It showed that at a certain rate of sea level rise the system is no longer able to keep pace with the rising sea level Fig 4. A more detailed model of the interaction between basin, ebb-tidal delta and adjacent coast is given by de Vriend et al.
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Going one step further in the description of the internal hydrodynamics in the basin, one may use a 1-D network model to describe flow and sediment transport in the channel network and combine that with a semi-empirical description of the water and sediment exchange with the shoals. This type of closed-loop model is primarily meant to be applied inside the basin, as it is difficult to include the interaction with the ebb-tidal delta. Such a model has been used, for instance, to analyse the response of the Frisian Inlet to the closure of one third of the basin area Fig.
Open-loop process-based grid models, such as 2-D depth-averaged morphological simulation models, have also been applied to these short basins e. De Vriend and Ribberink .
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Some of these applications focus on the morphological evolution of the channel pattern, others on larger-scale aspects like the response to sea level rise. Delft3D, for instance, has been used for various short-basin applications. Marciano et al. This type of results raises the question how to compare morphological model results with observations, so how to derive essential properties of the channel pattern from them.
A local statistical comparison like the Brier Skill Score  also see the section below is probably not good enough here. Dastgheib et al. He concludes that this type of process-based model system is suitable for long-term applications, and that the results seem to indicate a dependence of the large-scale equilibrium state on the initial conditions.
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Most of these models assume a sandy bed, often with uniform sediment. Usually, tidal basins contain a significant amount of mud, so modelling a combination of sand and fines may be useful. An important aspect to be properly modelled is the behaviour of fines in the water column flocculation, hindered settling, turbulence damping and their buffering in and pick-up from the top layer of the bottom.
Van Prooijen and Wang  present a spatially lumped model for fines under the influence of tides and waves. Van Ledden et al. New insights into mud erosion Winterwerp et al. Many estuaries do not allow for the assumption that the tidal wave is in phase throughout the system. In these longer estuaries other phenomena play a role, such as tidal propagation and deformation, residual currents and sediment transport, and estuarine circulation. Also, the pattern of channels and shoals tends to be different. The Western Scheldt Westerschelde is an example of such an estuary Figs.
It connects the river Scheldt with the North Sea, but the river discharge is small compared with the ebb and flood discharges. The estuary gives access to the harbour of Antwerp and is therefore an important fairway for commercial navigation.
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The functioning of the models described below are illustrated by applications to this estuary, even though most of them have also been applied to a range of other systems. Management objectives for this estuary aim to reconcile safety, accessibility and naturalness. Given the frequent human interventions, this explains why this system has been studied extensively, via field work as well as a wide range of models.
It is therefore a rich source of examples of estuarine morphological modelling.
Commercial interests constitute a drive to deepen the fairway, such that it requires more or less continuous maintenance.
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