这是一场有关两个颗粒堆积体互相追逐、达至平衡的故事~

He Nan, Lin Yuanwei, Zhang Yang*, Yang Bin*, Gao Xin. Self-stabilization of barchan dune chasing. Physics of Fluids, 2023, 35(10): 106609.

Barchan dunes migrate in swarms, with rich but not fully revealed self-stabilization mechanisms. The interaction between dunes is considered one of the key reasons for these mechanisms. Contact-type interactions, known as collisions, have been widely studied, while non-contact-type interactions have received less attention. In this paper, a water tunnel experiment was performed to study the non-contact dune chasing. With the aid of numerical simulations, a general model was proposed to interpret the convergence of distance between two dunes chasing each other. The model consists of three factors: inter-dune repulsive vortex, embracing vortex downstream, and difference in dune mass. Then, we reported a scaling law, expressed as the relation between the normalized dune spacing and time, to describe the convergence of dune spacing, and develop a governing equation in the form of area summation to explain the violation of convergence by combining the above three factors, both of which were verified experimentally. Our findings could help advance the understanding of the self-stabilization characteristics of dune swarms in nature.

Figure. Variation in dune spacing with time and the corresponding vortex structure. (a) Dune chasing process, where the red and blue hollow circles represent the centroids of the upstream and downstream dune projections, respectively. (b) Snapshots of the relative position of the two dunes. Left: e_m = 0.70, where e_m is the red-to-blue mass ratio; right: e_m = 1.50. The bright dashed lines represent the traces of the centroid. The vortex structure is shown at (c) e_m = 0.38, t = 240 s, (d) e_m = 1.00, t = 240 s, and (e) e_m = 1.50, t = 140 s. The upstream dune is fixed to highlight the variation in dune spacing. The vortex area and the upstream and downstream dunes are marked in bright yellow, red, and blue, respectively. The thin bold-headed arrow denotes the flow direction, and the hollow arrow denotes the pushing of the vortex on the dune body.