Non-linear channel–shoal dynamics in long tidal embayments

The dynamics of finite-amplitude bed forms in a tidal channel is studied with the use of an idealized morphodynamic model. The latter is based on depth-averaged equations for the tidal flow over a sandy bottom. The model considers phenomena on spatial scales of the order of the tidal excursion length. Transport of sediment mainly takes place as suspended load. The reference state of this model is characterized by a spatially uniform M₂ tidal current over a fixed horizontal bed. The temporal evolution of deviations from this reference state is governed by amplitude equations: these are a set of non-linear equations that describe the temporal evolution of bed forms. These equations are used to obtain new morphodynamic equilibria which may be either static or time-periodic. Several of these bottom profiles show strong similarity with the tidal bars that are observed in natural estuaries. The dependence of the equilibrium solutions on the value of bottom friction and channel width is investigated systematically. For narrow channels (width small compared to the tidal excursion length) stable static equilibria exist if bottom friction is slightly larger than r_cr. For channel widths more comparable to the tidal excursion length, multiple stable steady states may exist for bottom friction parameter values below r_cr. Regardless of channel width, stable time-periodic equilibria seem to emerge as the bottom friction is increased.Responsible Editor: Jens Kappenberg     

The effect of a topographic high on the morphological stability of a two-inlet bay system

The cross-sectional stability of two tidal inlets connecting the same back-barrier lagoon to the ocean is investigated. The condition for equilibrium is the cross-sectional area tidal prism relationship. In an earlier study [Van de Kreeke, J., 1990. Can multiple inlets be stable? Estuarine, Coastal and Shelf Science 30: 261–273.], using the same equilibrium condition, it was concluded that where two inlets connect the same basin to the ocean ultimately one inlet will close. One of the major assumptions in that study was that the water level in the basin fluctuated uniformly. In hindsight this assumption might be too restrictive. For example, in the Wadden Sea the back barrier lagoon consists of a series of basins, rather than one single basin, separated by topographic highs. These topographic highs limit but do not exclude the exchange of water between the sub-basins. For this reason in the present study, a topographic high in the form of a weir was added, separating the back-barrier lagoon in two sub-basins. The water level in the sub-basins, rather than in the back-barrier as a whole, is assumed to fluctuate uniformly. For this schematization the hydrodynamic equations are solved using a finite difference method. The results, together with the equilibrium condition, yield the equilibrium flow curve for each of the inlets. The intersections of the two equilibrium flow curves represent combinations of cross-sectional areas for which both inlets are in equilibrium. The stability of the equilibriums was investigated using a non-linear stability analysis resulting in a flow diagram. Calculations were carried out for different inlet and weir characteristics. Sinussoidal tides were the same for both inlets. The results show that for relatively large wetted cross-sectional areas over the topographic high, approaching the situation of a single basin, there are no combinations of inlet cross-sectional areas for which both inlets are in a stable equilibrium. This supports the conclusion in the earlier study. For relatively small wetted cross-sectional areas over the topographic high there is one set of stable equilibriums. In that case the two-inlet bay system approaches that of two single-inlet bay systems.     

The effect of geometry and tidal forcing on hydrodynamics and net sediment transport in semi-enclosed tidal basins

A new depth-averaged exploratory model has been developed to investigate the hydrodynamics and the tidally averaged sediment transport in a semi-enclosed tidal basin. This model comprises the two-dimensional (2DH) dynamics in a tidal basin that consists of a channel of arbitrary length, flanked by tidal flats, in which the water motion is being driven by an asymmetric tidal forcing at the seaward side. The equations are discretized in space by means of the finite element method and solved in the frequency domain. In this study, the lateral variations of the tidal asymmetry and the tidally averaged sediment transport are analyzed, as well as their sensitivity to changes in basin geometry and external overtides. The Coriolis force is taken into account. It is found that the length of the tidal basin and, to a lesser extent, the tidal flat area and the convergence length determine the behaviour of the tidally averaged velocity and the overtides and consequently control the strength and the direction of the tidally averaged sediment transport. Furthermore, the externally prescribed overtides can have a major influence on tidal asymmetry in the basin, depending on their amplitude and phase. Finally, for sufficiently wide tidal basins, the Coriolis force generates significant lateral dynamics.     

Influence of geometrical variations on morphodynamic equilibria in short tidal basins

Ocean Dynamics - The existence of cross-sectionally averaged morphodynamic equilibria of tidal inlets is investigated, using a cross-sectionally averaged model, and their sensitivity to variations...     

Modeling equilibrium bed profiles of short tidal embayments

In many tidal embayments, bottom patterns, such as the channel-shoal systems of the Wadden Sea, are observed. To gain understanding of the mechanisms that result in these bottom patterns, an idealized model is developed and analyzed for short tidal embayments. In this model, the water motion is described by the depth- and width-averaged shallow water equations and forced by a prescribed sea surface elevation at the entrance of the embayment. The bed evolves due to the divergence and convergence of suspended sediment fluxes. To model this suspended-load sediment transport, the three-dimensional advection–diffusion equation is integrated over depth and averaged over the width. One of the sediment fluxes in the resulting one-dimensional advection–diffusion equation is proportional to the gradient of the local water depth. In most models, this topographically induced flux is not present. Using standard continuation techniques, morphodynamic equilibria are obtained for different parameter values and forcing conditions. The bathymetry of the resulting equilibrium bed profiles and their dependency on parameters, such as the phase difference between the externally prescribed M₂ and M₄ tide and the sediment fall velocity, are explained physically. With this model, it is then shown that for embayments that are dominated by a net import of sediment, morphodynamic equilibria only exist up to a maximum embayment length. Furthermore, the sensitivity of the model to different morphological boundary conditions at the entrance of the embayment is investigated and it is demonstrated how this strongly influences the shape and number of possible equilibrium bottom profiles. This paper ends with a comparison between the developed model and field data for the Wadden Sea’s Ameland and Frisian inlets. When the model is forced with the observed M₂ and M₄ tidal constituents, morphodynamic equilibria can be found with embayment lengths similar to those observed in these inlets. However, this is only possible when the topographically induced suspended sediment flux is included. Without this flux, the maximum embayment length for which morphodynamic equilibria can be found is approximately a third of the observed length. The sensitivity of the model to the topographically induced sediment flux is discussed in detail.     

Subsurface Characterization Using a Cellular Automaton Approach

In this paper, a random Cellular Automaton model is developed to characterise heterogeneity of geological formations. The CA-model is multilateral and can be easily applied in both two and three dimensions. We demonstrate that conditioning on well data is possible and the method is numerically efficient. To construct the model, the subsurface is subdivided into N cells, with an initial lithology assigned to each cell. Rules to update the current cell states are chosen from a set of rules, independently for each cell. The model converges typically in less than 50 iterations to a steady state or periodic solution. Within one period the realisations exhibit similar statistical properties. The final fraction of the various lithologies can be tuned by choosing the proper initial fractions. In this way, geological knowledge of those fractions can be satisfied.     

Oblique sand ridges in confined tidal channels due to Coriolis and frictional torques

Ocean Dynamics - The role of the Coriolis effect in the initial formation of bottom patterns in a tidal channel is studied by means of a linear stability analysis. The key finding is that the...     

Can the Scheldt River Estuary become hyperturbid?

Ocean Dynamics - 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...