Abstract
We present in this paper a simplification of the dune model proposed
by Sauermann \textit{et al}. which keeps the basic
mechanisms but allows analytical and parametric studies. Two
kinds of purely propagative two dimensional solutions are exhibited: dunes
and domes, which, by contrast to the former, do not show avalanche
slip face. Their shape and velocity can be predicted as a function
of
their size. We recover in particular that dune profiles are not
scale invariant (small dunes are flatter than the large ones), and that
the
inverse of the velocity grows almost linearly with the dune size.
We furthermore get the existence of a critical mass below which no stable
dune exists. However, the linear stability analysis of a flat
sand sheet shows that it is unstable at large wavelengths and suggests
a
mechanism of dune initiation.
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