Sand influx effect on barchan dynamics using crest line model

Barchans are crescent-shaped sand dunes found in desert areas with little sand and a consistent seasonal wind direction. The characteristic parts at the tips of the leeward side of the barchan is called horns, from which sand flows out. Since barchans exist in groups, the expelled sand is supplied to the barchans located on the leeward side. Therefore, when considering the movement of barchans, it is important to consider the interaction between barchans due to such sand flow. In spite of this importance, there has been little research on the indirect interaction of sand between barchans. A previous research on the indirect interaction has used a cell model to calculate the movement of sand on each grid. According to the study, when the same amount of sand that flows out from a barchan is supplied to a point on the windward side away from the central axis, the apex of the barchan moves smoothly in a direction perpendicular to the wind direction while maintaining its shape and volume, at the same time as moving downwind. And it finally reaches the sand supply source [1]. However, the cell model just simulates the dynamics of barchans and further theoretical analysis of the mechanism of barchan movement is beyond the scope of the model. Therefore, in order to mathematically analyze the movement of barchans due to sand supply, the crest line model has been proposed[2]. The crest line model focuses on the cross section of the barchan and is a differential equation-based mathematical approach to dune dynamics using only two variables, the height h of the apex of the triangle of the cross section and the position x of it (Figure1). In the sense, the crest line model is a minimal model which enables us mathematical treatment of the dynamics of dune. This model has mainly been applied to analyze the shape stability of transverse dunes. As the first new aspect of this study, we have extended this model to the barchans with influx (Figure2). The research results can provide new insights into the mathematical solution of barchan migration due to sand supply and further understandings the dynamics of barchan collisions.

             

[1] A. Kastuki, et al., Simulation of barchan dynamics with inter-dune sand streams, New Journal of Physics (2011) 
[2] L. Guignier, et al., Sand dunes as migrating strings, Physical Review E (2013)