  Many complex aspects are involved in the morphodynamics of crescent-shaped
dunes, known as barchans. One of them concerns the trajectories of individual
grains over the dune, and how they affect its shape. In the case of subaqueous
barchans, we proposed in Alvarez and Franklin [Phys. Rev. Lett. 121, 164503
(2018)] that their extremities, called horns, are formed mainly by grains
migrating from upstream regions of the initial pile, and that they exhibit
significant transverse displacements. Here, we extend our previous work to
address the dynamics of grains migrating to horns after the dune has reached
its crescentic shape, and present new aspects of the problem. In our
experiments, single barchans evolve, under the action of a water turbulent
flow, from heaps of conical shape formed from glass beads poured on the bottom
wall of a rectangular channel. Both for evolving and developed barchans, the
horns are fed up with grains coming from upstream regions of the bedform and
traveling with significant transverse components, differently from the dynamics
usually described for the aeolian case. For these grains, irrespective of their
size and strength of water flow, the distributions of transverse and streamwise
components of velocities are well described by exponential functions, with the
probability density functions of their magnitudes being similar to results
obtained from previous studies on flat beds. Focusing on moving grains whose
initial positions were on the horns, we show that their residence time and
traveled distance are related following a quasi-linear relation. Our results
provide new insights into the physical mechanisms underlying the shape of
barchan dunes.
