Horns of subaqueous barchan dunes: A study at the grain scale

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.