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); Phys. Rev. Lett. 121, 164503 (2018)] 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 experiments1011CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICO - CNPQFUNDAÇÃO DE AMPARO À PESQUISA DO ESTADO DE SÃO PAULO - FAPESP400284/2016-2; 140773/2016-92018/14981-7C.A.A. is grateful to SENESCYT (Grant No. 2013-AR2Q2850) and to CNPq (Grant No. 140773/2016-9). E.M.F. is grateful to FAPESP (Grant No. 2018/14981-7), to CNPq (Grant No. 400284/2016-2), and to FAEPEX/UNICAMP (Grant No. 2112/19) for the financial support provided. Part of the work was completed while C.A.A. was a visiting graduate student at Western University, Canada, supported through the Emerging Leaders in the Americas Program, Global Affairs Canada. The authors would like to thank J. M. Floryan from Western University, Canada, for helpful discussions. SHARCNET (www.sharcnet.ca) provided part of computational resources used in the projec