  Barchans are crescentic dunes propagating on a solid ground. They form dune
fields in the shape of elongated corridors in which the size and spacing
between dunes are rather well selected. We show that even very realistic models
for solitary dunes do not reproduce these corridors. Instead, two instabilities
take place. First, barchans receive a sand flux at their back proportional to
their width while the sand escapes only from their horns. Large dunes
proportionally capture more than they loose sand, while the situation is
reversed for small ones: therefore, solitary dunes cannot remain in a steady
state. Second, the propagation speed of dunes decreases with the size of the
dune: this leads -- through the collision process -- to a coarsening of barchan
fields. We show that these phenomena are not specific to the model, but result
from general and robust mechanisms. The length scales needed for these
instabilities to develop are derived and discussed. They turn out to be much
smaller than the dune field length. As a conclusion, there should exist further
- yet unknown - mechanisms regulating and selecting the size of dunes.
