Alluvial fans formed by channelized fluvial and sheet flow. I: theory

Alluvial fans and fan-deltas are of three basic types: those built up primarily by the action of constantly avulsing river and stream channels, those constructed by sheet flows, and those resulting from the successive deposit of debris flows. The present analysis is directed toward the first two types. A mechanistic formulation of flow and sediment transport through river channels is combined with a simple quantification of the overall effect of frequent avulsion to derive relations describing the temporal and spatial evolution of mean (ie averaged over many avulsions) bed slope and elevation in an axially symmetric fan. An example of a fan formed predominantly by the deposition of sand is compared to a similar one formed predominantly by the deposition of gravel. In each example the case of channelized flow is compared to the case of sheet flow. The model is applied to the tailings basin of a mine in the companion paper.