  Aeolian sand beds exhibit regular patterns of ripples resulting from the
interaction between topography and sediment transport. Their characteristics
have been so far related to reptation transport caused by the impacts on the
ground of grains entrained by the wind into saltation. By means of direct
numerical simulations of grains interacting with a wind flow, we show that the
instability turns out to be driven by resonant grain trajectories, whose length
is close to a ripple wavelength and whose splash leads to a mass displacement
towards the ripple crests. The pattern selection results from a compromise
between this destabilizing mechanism and a diffusive downslope transport which
stabilizes small wavelengths. The initial wavelength is set by the ratio of the
sediment flux and the erosion/deposition rate, a ratio which increases linearly
with the wind velocity. We show that this scaling law, in agreement with
experiments, originates from an interfacial layer separating the saltation zone
from the static sand bed, where momentum transfers are dominated by mid-air
collisions. Finally, we provide quantitative support for the use the
propagation of these ripples as a proxy for remote measurements of sediment
transport.
