European Journal of Applied Mathematics

Fluvio-deltaic sedimentation: A generalized Stefan problem

J. B. SWENSON a1a2a4, V. R. VOLLER a1a3, C. PAOLA a1a2, G. PARKER a1a3 and J. G. MARR a1
a1 Saint Anthony Falls Laboratory, University of Minnesota, Minneapolis, MN 55414
a2 Department of Geology and Geophysics, University of Minnesota, Minneapolis, MN 55455
a3 Department of Civil Engineering, University of Minnesota, Minneapolis, MN 55455
a4 Department of Geological Sciences, University of Minnesota, Duluth, MN 55812


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.

(Received September 1 1999)
(Revised March 15 2000)