Role of Transverse Displacements in the Formation of Subaqueous Barchan Dunes.

Crescentic shape dunes, known as barchan dunes, are formed by the action of a fluid flow on a granular bed. These bedforms are common in many environments, existing under water or in air, and being formed from grains organized in different initial arrangements. Although they are frequently found in nature and industry, details about their development are still to be understood. In a recent paper [C. A. Alvarez and E. M. Franklin, Phys. Rev. E 96, 062906 (2017)PRESCM2470-004510.1103/PhysRevE.96.062906], we proposed a timescale for the development and equilibrium of single barchans based on the growth of their horns. In the present Letter, we report measurements of the growth of horns at the grain scale. In our experiments, conical heaps were placed in a closed conduit and individual grains were tracked as each heap, under the action of a water flow, evolved into a barchan dune. We identified the trajectories of the grains that migrated to the growing horns, and found that most of them came from upstream regions on the periphery of the initial heap, with an average displacement of the order of the heap size. In addition, we show that individual grains had transverse displacements by rolling and sliding that are not negligible, with many of them going around the heap. The mechanism of horns formation revealed by our experiments contrasts with the general picture that barchan horns form from the advance of the lateral dune flanks due to the scaling of migration velocity with the inverse of dune size. Our results change the way in which the growth of subaqueous barchan dunes is explained.

Dataset of turbulent flow over interacting barchan dunes.

Barchans are dunes commonly found in dune fields on Earth, Mars and other celestial bodies, where they can interact with each other. This article concerns experimental data for the flow over subaqueous barchans that are either isolated or interacting with each other. The experiments were carried out in a transparent channel of rectangular cross section in which turbulent water flows were imposed over either one single or a pair of barchans. The instantaneous flow fields were measured by using a low-frequency PIV (particle image velocimetry) and high-frequency PTV (particle tracking velocimetry). From the PIV and PTV data, the mean flow, trajectories, and second-order moments were computed, which are included in the datasets described in this paper, together with raw data (images), instantaneous fields, and scripts to process them. The datasets can be reused for benchmarking or for processing new images generated by other research groups.

Roles of packing fraction, microscopic friction, and projectile spin in cratering by impact.

From small seeds falling from trees to asteroids colliding with planets and moons, the impact of projectiles onto granular targets occurs in nature at different scales. In this paper, we investigate open questions in the mechanics of granular cratering, in particular, the forces acting on the projectile and the roles of granular packing, grain-grain friction, and projectile spin. For that, we carried out discrete element method computations of the impact of solid projectiles on a cohesionless granular medium, where we varied the projectile and grain properties (diameter, density, friction, and packing fraction) for different available energies (within relatively small values). We found that a denser region forms below the projectile, pushing it back and causing its rebound by the end of its motion, and that solid friction affects considerably the crater morphology. Besides, we show that the penetration length increases with the initial spin of the projectile, and that differences in initial packing fractions can engender the diversity of scaling laws found in the literature. Finally, we propose an ad hoc scaling that collapsed our data for the penetration length and can perhaps unify existing correlations. Our results provide new insights into the formation of craters in granular matter.

Impact craters formed by spinning granular projectiles.

Craters formed by the impact of agglomerated materials are commonly observed in nature, such as asteroids colliding with planets and moons. In this paper, we investigate how the projectile spin and cohesion lead to different crater shapes. For that, we carried out discrete element method computations of spinning granular projectiles impacting onto cohesionless grains for different bonding stresses, initial spins, and initial heights. We found that, as the bonding stresses decrease and the initial spin increases, the projectile's grains spread farther from the collision point, and in consequence, the crater shape becomes flatter, with peaks around the rim and in the center of the crater. Our results shed light on the dispersion of the projectile's material and the different shapes of craters found on Earth and other planetary environments.

Contacts, motion, and chain breaking in a two-dimensional granular system displaced by an intruder.

We investigate numerically how the motion of an intruder within a two-dimensional granular system affects its structure and produces drag on the intruder. We made use of discrete numerical simulations in which a larger disk (intruder) is driven at constant speed amid smaller disks confined in a rectangular cell. By varying the intruder's velocity and the basal friction, we obtained the resultant force on the intruder and the instantaneous network of contact forces, which we analyze at both the cell and grain scales. We found that there is a bearing network that percolates forces from the intruder toward the walls, being responsible for jammed regions and high values of the drag force, and a dissipative network that percolates small forces within the grains, in agreement with previous experiments on compressed granular systems. In addition, we found the anisotropy levels of the contact network for different force magnitudes and regions, that the force network can reach regions far downstream of the intruder by the end of the intruder's motion, that the extent of the force network decreases with decreasing the basal friction, and that the void region (cavity) that appears downstream of the intruder tends to disappear for lower values of the basal friction. Interestingly, our results show that grains within the bearing chains creep while the chains break, revealing the mechanism by which bearing chains collapse.

Shape evolution of numerically obtained subaqueous barchan dunes.

In the realm of granular bedforms, barchan dunes are strong attractors that can be found in rivers, terrestrial deserts, and other planetary environments. These bedforms are characterized by a crescentic shape, which, although robust, presents different scales according to the environment they are in, their length scale varying from the decimeter under water to the kilometer on Mars. In addition to the scales of bedforms, the transport of grains presents significant differences according to the nature of the entraining fluid, so that the growth of barchans is still not fully understood. Given the smaller length and time scales of the aquatic case, subaqueous barchans are the ideal object to study the growth of barchan dunes. In the present paper, we reproduce numerically the experiments of Alvarez and Franklin [Phys. Rev. E 96, 062906 (2017)2470-004510.1103/PhysRevE.96.062906; Phys. Rev. Lett. 121, 164503 (2018)PRLTAO0031-900710.1103/PhysRevLett.121.164503] on the shape evolution of barchans from their initiation until they have reached a stable shape. We computed the bed evolution by using the computational fluid dynamics-discrete element method, where we coupled the discrete element method with large eddy simulation for the same initial and boundary conditions of experiments, performed in a closed-conduit channel where initially conical heaps evolved to single barchans under the action of a water flow in a turbulent regime. Our simulations captured well the evolution of the initial pile toward a barchan dune in both the bedform and grain scales, with the same characteristic time and lengths observed in experiments. In addition, we obtained the local granular flux and the resultant force acting on each grain, the latter not yet previously measured nor computed. This shows that the present method is appropriate for numerical computations of bedforms, opening new possibilities for accessing data that are not available from current experiments.

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 [C. A. Alvarez and E. M. Franklin, Phys. Rev. Lett. 121, 164503 (2018)PRLTAO0031-900710.1103/PhysRevLett.121.164503] 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 turbulent water flow, from heaps of conical shape formed from glass beads poured on the bottom wall of a rectangular channel. Both for evolving and for 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 the strength of the 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 quasilinear relation. Our results provide new insights into the physical mechanisms underlying the shape of barchan dunes.

Birth of a subaqueous barchan dune.

Barchan dunes are crescentic shape dunes with horns pointing downstream. The present paper reports the formation of subaqueous barchan dunes from initially conical heaps in a rectangular channel. Because the most unique feature of a barchan dune is its horns, we associate the time scale for the appearance of horns to the formation of a barchan dune. A granular heap initially conical was placed on the bottom wall of a closed conduit and it was entrained by a water flow in turbulent regime. After a certain time, horns appear and grow, until an equilibrium length is reached. Our results show the existence of the time scales 0.5t_{c} and 2.5t_{c} for the appearance and equilibrium of horns, respectively, where t_{c} is a characteristic time that scales with the grains diameter, gravity acceleration, densities of the fluid and grains, and shear and threshold velocities.