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.

Figure 1

Top view of a barchan dune and its characteristic lengths: length $L$, width $W$, and horn length $L_h$.

Figure 2

Top views of initially conical heaps deformed by the water flow at different times; the water flow is from left to right. (a) Re = $1.47\times {10}^4, {\rho }_s$ = $2500\mathrm{kg}/{\mathrm{m}}^3$, and $0.40\mathrm{mm}\le d\le 0.60$ mm. (b) Re = $1.67\times {10}^4, {\rho }_s$ = $4100\mathrm{kg}/{\mathrm{m}}^3$, and $0.40\mathrm{mm}\le d\le 0.60$ mm. (c) Re = $1.47\times {10}^4, {\rho }_s$ = $4100\mathrm{kg}/{\mathrm{m}}^3$, and $0.40\mathrm{mm}\le d\le 0.60$ mm.

Figure 3

$W/L$ versus $t/t_c$ for different flow conditions and solid particles. The cases listed in the key are presented in Table 1. This figure shows every $n$ measurements for each experimental condition, where 5 $\le n\le$ 15.

Figure 4

(a) $L$ versus $t/t_c$ and (b) $W$ versus $t/t_c$ for different flow conditions and solid particles. The cases listed in the key are presented in Table 1. This figure shows every $n$ measurements for each experimental condition, where 5 $\le n\le$ 15.

Figure 5

$L_h/L_{\mathrm{drag}}$ versus $t/t_c$ for glass beads under different flow conditions over the entire duration of test runs. This figure shows every $n$ measurements for each experimental condition, where 5 $\le n\le$ 15. The cases (a) to (i) are summarized in Table 1, and each different symbol in each graphic corresponds to a different test run.

Figure 6

Detail for 0 $\le t/t_c\le$ 1.5 of $L_h/L_{\mathrm{drag}}$ versus $t/t_c$ for glass beads under different flow conditions. This figure shows every measurement points within this time interval. The cases (a) to (i) are summarized in Table 1, and each different symbol in each graphic corresponds to a different test run.

Figure 7

$L_h/L_{\mathrm{drag}}$ versus $t/t_c$ for zirconium beads under different flow conditions over the entire duration of test runs. This figure shows every $n$ measurements for each experimental condition, where 5 $\le n\le$ 15. The cases (j) to (m) are summarized in Table 1, and each different symbol in each graphic corresponds to a different test run.

Figure 8

Detail for 0 $\le t/t_c\le$ 1.5 of $L_h/L_{\mathrm{drag}}$ versus $t/t_c$ for zirconium beads under different flow conditions. This figure shows every measurement points within this time interval. The cases (j) to (m) are summarized in Table 1, and each different symbol in each graphic corresponds to a different test run.