  Compared to barchan dunes, the morphodynamics of linear dunes that elongate
on a non-erodible bed is barely investigated by means of laboratory experiments
or numerical simulations. Using a cellular automaton model, we study the
elongation of a solitary linear dune from a sand source and show that it can
reach a steady state. This steady state is analyzed to understand the physical
processes at work along the dune. Crest reversals together with avalanche
processes control the shape of transverse sections. Dune width and height
decrease almost linearly with distance downstream until the minimum size for
dunes. This is associated with a constant sand loss along the dune, which
eventually compensates for the sediment influx and sets the dune length. This
sand budget is discussed to distinguish an elongating linear dune from a
barchan dune and to explain the complexity of linear dune fields in nature.
