Modeling equilibrium bed profiles of short tidal embayments |
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Authors: | Miriam C ter Brake Henk M Schuttelaars |
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Institution: | (1) Delft Institute of Applied Mathematics, Delft University of Technology, Mekelweg 4, Delft, 2628 CD, The Netherlands |
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Abstract: | 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. |
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