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Channel and shoal development in a short tidal embayment: an idealized model study

Published online by Cambridge University Press:  03 May 2011

MIRIAM C. ter BRAKE  and
HENK M. SCHUTTELAARS
MIRIAM C. ter BRAKE*
Affiliation:
Delft Institute of Applied Mathematics, TU Delft, Mekelweg 4, Delft 2628CD, The Netherlands
HENK M. SCHUTTELAARS
Affiliation:
Delft Institute of Applied Mathematics, TU Delft, Mekelweg 4, Delft 2628CD, The Netherlands
*
†Email address for correspondence: [email protected]
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Abstract

In many tidal embayments, complex patterns of channels and shoals are observed. To gain a better understanding of these features, an idealized model, that describes the interaction of water motion, sediment transport and bed evolution in a semi-enclosed, rectangular basin, is developed and analysed. To explain the initial formation of channels and shoals, two-dimensional perturbations superposed on a laterally uniform equilibrium bottom are studied. These perturbations evolve due to convergences of various residual suspended sediment fluxes: a diffusive flux, a flux related to the bed topography, an advective flux resulting from internally generated overtides and an advective flux due to externally prescribed overtides. For most combinations of these fluxes, perturbations start to grow if the bottom friction is strong enough. Their growth is mainly a result of convergences of diffusive and topographically induced sediment fluxes. Advective contributions due to internally generated overtides enhance this growth. If only diffusive sediment fluxes are considered, the underlying equilibrium is always unstable. This can be traced back to the depth dependence of the deposition parameter. Contrary to the results of previous idealized models, the channels and shoals always initiate in the shallow, landward areas. This is explained by the enhanced generation (compared to that in previous models) of frictional torques in shallow regions. The resulting initial channel–shoal formation compares well with results found in complex numerical model studies. The instability mechanism and the location of the initial formation of bottom patterns do not change qualitatively when varying parameters. Changes are mainly related to differences in the underlying equilibrium profile due to parameter variations.

JFM classification

Geophysical and Geological Flows: Coastal engineering Phase change: Morphological instability Nonlinear Dynamical Systems: Pattern formation
Type
Papers
Information
Journal of Fluid Mechanics , Volume 677 , 25 June 2011 , pp. 503 - 529
Copyright
Copyright © Cambridge University Press 2011

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