Hostname: page-component-78c5997874-s2hrs Total loading time: 0 Render date: 2024-11-11T08:16:28.819Z Has data issue: false hasContentIssue false
  • English
  • Français

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: miriam.terbrake@bmtargoss.com
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Boyd, J. P. 2001 Chebyshev and Fourier Spectral Methods. Mineola.Google Scholar
ter Brake, M. C. & Schuttelaars, H. M. 2009 Influence of bottom friction formulation on the initial formation of channels in a short tidal embayment. In River, Coastal and Estuarine Morphodynamics 2009 (ed. Vionnet, C., Garcia, M., Latrubesse, A. & Perillo, G.), pp. 153–159. Taylor & Francis.Google Scholar
ter Brake, M. C. & Schuttelaars, H. M. 2010 Modeling equilibrium bed profiles of short tidal. On the effect of the vertical distribution of suspended sediment and the influence of the boundary conditions. Ocean Dyn. 60, 183–204.Google Scholar
Cleveringa, J. & Oost, A. P. 1999 The fractal geometry of tidal channel systems in the Dutch Wadden Sea. Geol. Mijnb. 78, 21–30.CrossRefGoogle Scholar
D'Alpaos, A., Lanzoni, S., Marani, M. & Rinaldo, A. 2007 Landscape evolution in tidal embayments: modeling the interplay of erosion, sedimentation, and vegetation dynamics. J. Geophys. Res. 112, F01008.Google Scholar
Davis, R. A. J. 1996 Coasts. Prentice Hall.Google Scholar
de Swart, H. E. & Zimmerman, J. T. F. 2009 Morphodynamics of tidal inlet systems. Annu. Rev. Fluid Mech. 41, 203–229.CrossRefGoogle Scholar
Dissanayake, D. M. P. K., Roelvink, J. A. & van der Wegen, M. 2009 Modelled channel patterns in a schematized tidal inlet. Coast. Engng 56, 1069–1083.CrossRefGoogle Scholar
Ehlers, J. 1988 The Morphodynamics of the Wadden Sea. Balkema.Google Scholar
Hibma, A., Schuttelaars, H. M. & de Vriend, H. 2004 Initial formation and evolution of channel–shoal patterns in estuaries. Cont. Shelf Res. 24, 1637–1650.Google Scholar
Hibma, A., de Vriend, H. J. & Stive, M. J. F. 2003 Numerical modelling of shoal pattern formation in well-mixed elongated estuaries. Estuar. Coast. Shelf Sci. 57, 981–991.Google Scholar
van Leeuwen, S. M. 2002 Tidal inlet systems: bottom pattern formation and outer delta development. PhD thesis, Utrecht University.Google Scholar
van Leeuwen, S. M., Schuttelaars, H. M. & de Swart, H. E. 2000 Tidal and morphologic properties of embayments: effects of sediment deposition processes and length variation. Phys. Chem. Earth B 25, 365–368.Google Scholar
van Leeuwen, S. M. & de Swart, H. E. 2001 The effect of advective processes on the morphodynamic stability of short tidal embayments. Phys. Chem. Earth B 26, 735–740.CrossRefGoogle Scholar
van Leeuwen, S. M. & de Swart, H. E. 2004 Effect of advective and diffusive sediment transport on the formation of local and global bottom patterns in tidal embayments. Ocean Dyn. 54, 441–451.Google Scholar
Marani, M., Belluco, E., D'Alpaos, A., Defina, A., Lanzoni, S. & Rinaldo, A. 2003 On the drainage density of tidal networks. Water Resour. Res. 39, 10–40.Google Scholar
Marciano, R., Wang, Z. B., Hibma, A. & de Vriend, H. J. 2005 Modeling of channel patterns in short tidal basins. J. Geophys. Res. 110, F01001.Google Scholar
Roelvink, J. A. 2006 Coastal morphodynamic evolution techniques. Coast. Engng 53, 277–287.CrossRefGoogle Scholar
Schramkowski, G. P., Schuttelaars, H. M. & de Swart, H. E. 2002 The effect of geometry and bottom friction on local bed forms in a tidal embayment. Cont. Shelf Res. 22, 1821–1834.Google Scholar
Schuttelaars, H. M., Schramkowski, G. P. & de Swart, H. E. 2001 Initial formation of estuarine sections. In River, Coastal and Estuarine Morphodynamics, pp. 443–452. IAHR.Google Scholar
Schuttelaars, H. M. & de Swart, H. E. 1996 An idealized long-term morphodynamic model of a tidal embayment. Eur. J. Mech. B/Fluids 15 (1), 55–80.Google Scholar
Schuttelaars, H. M. & de Swart, H. E. 1999 Initial formation of channels and shoals in a short tidal embayment. J. Fluid Mech. 386, 15–42.Google Scholar
Schuttelaars, H. M. & de Swart, H. E. 2000 Multiple morphodynamic equilibria in tidal embayments. J. Geophys. Res. 105, 24105–24118.Google Scholar
Sha, L. P. 1989 Cyclic morphological changes of the ebb tidal delta off Texel inlet, The Netherlands. Geol. Mijnb. 35–48.Google Scholar
Vreugdenhil, C. B. 1994 Numerical Methods for Shallow Water Flow (Water Sci. & Techn. Libr.). Kluwer.CrossRefGoogle Scholar
van der Wegen, M. & Roelvink, J. A. 2008 Long-term morphodynamic evolution of a tidal embayment using a two-dimensional process-based model. J. Geophys. Res. 7, C03016.Google Scholar
Zimmerman, J. T. F. 1982 On the Lorentz linearization of a quadratically damped forced oscillator. Phys. Lett. 89A, 123–124.Google Scholar