Fluvio-deltaic sedimentation: A generalized Stefan problem

We present a model of sedimentation in a subsiding fluvio-deltaic basin wit h steady sediment supply and unsteady base level. We demonstrate that mass transfer in a fluvio-deltaic basin is analogous to heat transfer in a gener alized Stefan problem, where the basin's shoreline represents the phase fro nt. We obtain a numerical solution to the governing equations for sediment transport and deposition in this system via an extension of a deforming-gri d technique from the phase-change literature. Through modification of the h eat-balance integral method, we also develop a semi-analytical solution, wh ich agrees well with the numerical solution, We construct a space of dimens ionless groups for the basin and perform a systematic exploration of this s pace 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 sho reline advance is followed by an extended period of shoreline retreat. Base -level cycling produces a shoreline response that varies relative to the au toretreat signal. Contrary to previous studies, we fail to observe either a strong phase shift between shoreline and base level or a pronounced attenu ation of the amplitude of shoreline response as the frequency of base-level cycling decreases. However, the amplitude of shoreline response to base-le vel cycling is a function of the basin's age.