Alluvial fans are ubiquitous sedimentary features in landscapes. They form at the outlets of relief, where rivers are no longer confine and can depose their sedimentary load.

We propose a model to quantitatively relate the sediment and water fluxes that fead a fan to its slope.

Considering that a fan is closed to its equilibrium slope of the system, we derive a set of equations predicting that:

1) the fan grows in a self-similar form

2) at the leading order, the growth velocity is controlled by the sediment flux only

3) the slope is closed to the threshold of motion but exhibits a deviation related to the sediment flux.

This model is successfully validated by one-dimension experiments performed with glass beads and diluted glycerine.

Therefore, in this simplified context, we are able to determine the slope according to the fluxes. This has great mplications in terms of reconstruction of paleo-fluxes in natural settings.

Related publication:

Laboratory alluvial fans in one dimension (pdf), L. Guerit, F. Métivier, O. Devauchelle, E. Lajeunesse, L. Barrier, Physical Review E 2014 - 90, 022203