Barchan collision using multiple crest lines model

Crescent-shaped dunes called Barchans are found in areas with constant wind direction and little sand. They often cluster together, so we need to consider the interaction between each of the barchans. In previous research, two models represent the movement of barchan: one is the ABCDE model, which describes the collision of barchan by similar triangles in the cross-section, and the other is the single crest line model, which describes the movement of a single barchan by a single line. However, the single crest line model has the problems that the conservation of sand is not strictly considered and that the shape and height of the dune do not reach a steady state. Therefore, in this research, we take into account the conservation of sand and improve the single crest line model. As a result, we confirm that even near the boundary of the barchan, where the sand height is very small, the sand balance is kept and the shape of the barchan reaches a steady state. Numerical simulations of this single crest line show it could reproduce various phenomena that had been confirmed with the cellular model, such as the situation when sand was supplied to the barchan. In addition, to handle the behavior of multiple barchans in 3D space, a model that extends the single crest line model to multiple lines is effective. Hikosaka (master thesis, Hiroshima University, 2019) tried to derive a ”multiple crest lines model” by adding the idea of the ABCDE model to the single crest line model (Fig. 1). However, it is still in the process of completion. By using the sand balance matching method proposed in this research, we can handle the influence of sand at both ends of the barchan more accurately. Then we can make the model of dune collision phenomena with multiple crest lines. In our model, we also include a method for calculating the time evolution of a valley between two dunes created during their collisions. We compare the result of numerical simulation with the results of water tank experiments in previous research to analyze whether the collision patterns of recombination, breakup and coalescence appear or not. By using our proposal way, we can calculate the multiple dunes collision (Fig. 2). This means we get a step toward theoretical analysis of the dynamics of multiple dunes.