  Crescent shaped barchan dunes are highly mobile dunes that are usually
presented as a prototypical model of sand dunes. Although they have been
theoretically shown to be unstable when considered separately, it is well known
that they form large assemblies in desert. Collisions of dunes have been
proposed as a mechanism to redistribute sand between dunes and prevent the
formation of heavily large dunes, resulting in a stabilizing effect in the
context of a dense barchan field. Yet, no models are able to explain the
spatial structures of dunes observed in deserts. Here, we use an agent-based
model with elementary rules of sand redistribution during collisions to access
the full dynamics of very large barchan dune fields. Consequently, stationnary,
out of equilibrium states emerge. Trigging the dune field density by a sand
load/lost ratio, we show that large dune fields exhibit two assymtotic regimes:
a dilute regime, where sand dune nucleation is needed to maintain a dune field,
and a dense regime, where dune collisions allow to stabilize the whole dune
field. In this dense regime, spatial structures form: the dune field is
structured in narrow corridors of dunes extending in the wind direction, as
observed in dense barchan deserts.
