| Summary: | At the scale of a river reach, the dynamics of the river bed is typically modelled by
Exner equation (conservation of the solid mass) with an empirical solid flux
of transported sediments, which is a simple deterministic algebraic formula
function of i) the sediment physical characteristics (size and mass) and of ii) the
averaged hydrodynamical description of the ambient water flow. This model has proved
useful, in particular through numerical simulations, for hydraulic engineering purposes
(like estimating the mass of sediments that is drained through an open dam). Though, the
model is also coarse. And its applicability at various space and time scales remains a
question of considerable interest for sedimentologists. In particular, physical
experiments from the grain scale to the laboratory scale reveal important fluctuations of
the solid flux in given hydrodynamical conditions.
This work is a preliminary study of the coupling of a stochastic Exner equation with a
hydrodynamical model for large scales. (Stochastic models with a probabilistic solid flux
are currently being investigated, but most often only from the viewpoint of theoretical
physics at the grain scale.) We introduce a new stochastic Exner model and discuss it
using numerical simulations in an appropriate test case.
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