  Barchans are crescent-shaped sand dunes forming in aride regions with
unidirectional wind and limited sand supply. We report analytical and numerical
results for dune shapes under different environmental conditions as obtained
from the so-called `minimal model' of aeolian sand dunes. The profiles of
longitudinal vertical slices (i.e. along the wind direction) are analyzed as a
function of wind speed and sand supply. Shape transitions can be induced by
changes of mass, wind speed and sand supply. Within a minimal extension of the
model to the transverse direction the scale-invariant profile of transverse
vertical cuts can be derived analytically.
