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)], 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.

Figure 1

Top views of an initially conical heap deformed by the water flow at different times (shown below each frame). The water flow is from left to right, $R$ is the radius of the initial pile, and black spots are the tracers. $\mathrm{Re}=1.82\times {10}^4$ and the heap initial mass was 6.2 g.

Figure 2

Trajectories of all marked grains during the growth of a barchan dune. The water flow is from top to bottom. $\mathrm{Re}=1.82\times {10}^4$ and the heap initial mass was equal to 6.2 g. The black dashed circle represents the initial pile of radius $R$.

Figure 3

Trajectories of marked grains that migrated to horns during the growth of a barchan dune. The water flow is from top to bottom. $\mathrm{Re}=1.82\times {10}^4$ and the heap initial mass was 6.2 g. The black dashed circle represents the initial pile of radius $R$.

Figure 4

PDF of the original position of the grains that migrated to horns during the growth of a barchan dune. A kernel smoothing function was used to plot the PDF [28]. The cases a, b, and c correspond to $\mathrm{Re}=1.21\times {10}^4$, $1.47\times {10}^4$ and $1.82\times {10}^4$, respectively, and initial mass equal to 6.2 g. The cases d, e, and f correspond to $\mathrm{Re}=1.21\times {10}^4$, $1.47\times {10}^4$ and $1.82\times {10}^4$, respectively, and initial mass equal to 10.3 g.

Figure 5

Frequency of occurrence of the initial position of grains migrating to the horns as a function of the angle with respect to the transverse direction (water flow direction is 270°). (a) Initial mass equal to 6.2 g and (b) initial mass equal to 10.3 g. The tips of appearing horns point to angles of approximately 240° and 300°.