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)] 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.

Figure 1

Top view of a subaqueous barchan dune with its horn length $L_h$ displayed. Flow is from left to right.

Figure 2

Experimental setup, definition of geometrical parameters, and particle detection. (a) Photograph of the experimental setup showing the test section, high-speed camera, traveling system, light-emitting diode lights, and grains placed on the bottom wall of the channel. (b) Top view of an initially conical heap of radius $R$ at time $t=0\mathrm{s}$, where $r_0$ is the initial position of the pile centroid and black spots are tracers. (c) Top-view image of a dune in gray scale showing the tracers. Flow is from top to bottom. (d) Example of a treated image showing the detected particles. Red circles are surrounding the tracers identified in (c), and the asterisk corresponds to the instantaneous position of the dune centroid. $\mathrm{Re}=1.82\times {10}^4$ and the heap initial mass was 6.2 g.

Figure 3

Pathlines of tracers over an evolving dune made of $0.15\mathrm{mm}\le d\le 0.25\mathrm{mm}$ glass beads. (a) All moving tracers during the growth of a barchan dune. (b) Tracers that migrated to horns during the growth of the barchan dune. The dashed black circle represents the initial pile of radius $R$, and the scaling bar shows the values of $r_c-r_0$ normalized by $R$. The water flow is from top to bottom, $\mathrm{Re}=1.82\times {10}^4, m_0=6.2\mathrm{g}$, and $R=2.6\mathrm{cm}$.

Figure 4

Pathlines of tracers over a developed dune made of $0.15\mathrm{mm}\le d\le 0.25\mathrm{mm}$ glass beads. (a) All moving tracers over the barchan dune. (b) Tracers that migrated to the barchan horns. The dashed black circle represents the initial pile of radius $R$, and the scaling bar shows the values of $r_c-r_0$ normalized by $R$. Water flow is from top to bottom, $\mathrm{Re}=1.82\times {10}^4, m_0=6.2\mathrm{g}$, and $R=2.6\mathrm{cm}$.

Figure 5

Pathlines of tracers over a developed dune made of $0.40\mathrm{mm}\le d\le 0.60\mathrm{mm}$ glass beads. (a) All moving tracers over the barchan dune. (b) Tracers that migrated to the barchan horns. The dashed black circle represents the initial pile of radius $R$, and the scaling bar shows the values of $r_c-r_0$ normalized by $R$. Water flow is from top to bottom, $\mathrm{Re}=1.47\times {10}^4, m_0=6.2\mathrm{g}$, and $R=2.6\mathrm{cm}$.

Figure 6

PDFs of the total (a) transverse and (b) longitudinal distances, ${\mathrm{\Delta }}_x$ and ${\mathrm{\Delta }}_y$, respectively, normalized by $L_{\mathrm{drag}}$ for case k in Table 1. Dashed blue lines correspond to grains that migrated to the horns and solid red lines to all other grains.

Figure 7

PDFs of the original position of the tracers that migrated to horns for both evolving and developed dunes. Cases listed in the key are presented in Table 1.

Figure 8

Frequencies of occurrence of the initial position of tracers migrating to the horns as a function of the angle with respect to the transverse direction. The water flow direction is ${270}^{\circ }$. All cases listed in Table 1 are shown.

Figure 9

PDFs of transverse velocities $V_x$ of tracers migrating to horns. Insets: Semilog plots of PDFs for $V_x>0$, where the solid line corresponds to a straight-line fit for this part of the distribution. (a) Case h and (b) case b from Table 1.

Figure 10

PDFs of streamwise velocities $V_y$ of tracers migrating to horns. Insets: Semilog plots of PDFs, where the solid line corresponds to a straight-line fit. (a) Case b and (b) case b from Table 1.

Figure 11

Traveled distance normalized by the grain diameter, $\delta /d$, as a function of the residence time of moving grains leaving the horns normalized by the settling time, $t/t^{*}$. A quasilinear relationship is verified for all tested cases. The cases listed in the key are presented in Table 1.

Figure 12

PDFs of (a) the traveled distance normalized by the grain diameter, $\delta /d$, and (b) the residence time of moving grains leaving the horns normalized by the settling time, $t/t^{*}$. Solid lines correspond to fittings using gamma functions. Cases d to l are included in these PDFs.