Abstract
The transport of sand by the wind results from the equilibrium between
the erosion
of grains dragged by the flow and the resulting slow down of the wind velocity.
The
dynamical mechanisms governing the saturation of the sand flux are investigated
theoretically.
We first demonstrate that previous models, based on the assumption that all
the grains have the same trajectory, are either not self-consistent or lead
to unstable
solutions. A model based on a discrete number of states is derived, which
solves these
problems. Two well defined species of grains appear, which correspond to
saltons (high
energy grains) and reptons (grains ejected from the sand bed by the impact
of saltons).
They play specific roles: the negative feedback of the transport on the wind
is limited to
the reptation layer while most of the transport is due to saltation. The
model is further
simplified, taking profit from the existence of these two species and the
dependencies of
the threshold velocity, the saturated flux, the aerodynamic roughness and
the saturation
length are derived and compared to experimental measurements.