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Fluvio-deltaic sedimentation: A generalized Stefan problem

Published online by Cambridge University Press:  23 November 2000

J. B. SWENSON ,
V. R. VOLLER ,
C. PAOLA ,
G. PARKER  and
J. G. MARR
J. B. SWENSON
Affiliation:
Saint Anthony Falls Laboratory, University of Minnesota, Minneapolis, MN 55414 Department of Geology and Geophysics, University of Minnesota, Minneapolis, MN 55455 Department of Geological Sciences, University of Minnesota, Duluth, MN 55812
V. R. VOLLER
Affiliation:
Saint Anthony Falls Laboratory, University of Minnesota, Minneapolis, MN 55414 Department of Civil Engineering, University of Minnesota, Minneapolis, MN 55455
C. PAOLA
Affiliation:
Saint Anthony Falls Laboratory, University of Minnesota, Minneapolis, MN 55414 Department of Geology and Geophysics, University of Minnesota, Minneapolis, MN 55455
G. PARKER
Affiliation:
Saint Anthony Falls Laboratory, University of Minnesota, Minneapolis, MN 55414 Department of Civil Engineering, University of Minnesota, Minneapolis, MN 55455
J. G. MARR
Affiliation:
Saint Anthony Falls Laboratory, University of Minnesota, Minneapolis, MN 55414
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Abstract

We present a model of sedimentation in a subsiding fluvio-deltaic basin with steady sediment supply and unsteady base level. We demonstrate that mass transfer in a fluvio-deltaic basin is analogous to heat transfer in a generalized Stefan problem, where the basin's shoreline represents the phase front. We obtain a numerical solution to the governing equations for sediment transport and deposition in this system via an extension of a deforming-grid technique from the phase-change literature. Through modification of the heat-balance integral method, we also develop a semi-analytical solution, which agrees well with the numerical solution. We construct a space of dimensionless groups for the basin and perform a systematic exploration of this space to illustrate the influence of each group on the shoreline trajectory. Our model results suggest that all subsiding fluvio-deltaic basins exhibit a standard autoretreat shoreline trajectory in which a brief period of shoreline advance is followed by an extended period of shoreline retreat. Base-level cycling produces a shoreline response that varies relative to the autoretreat signal. Contrary to previous studies, we fail to observe either a strong phase shift between shoreline and base level or a pronounced attenuation of the amplitude of shoreline response as the frequency of base-level cycling decreases. However, the amplitude of shoreline response to base-level cycling is a function of the basin's age.

Type
Research Article
Information
European Journal of Applied Mathematics , Volume 11 , Issue 5 , October 2000 , pp. 433 - 452
Copyright
2000 Cambridge University Press

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