Self-stabilization of barchan dune chasing

Barchan dunes migrate in swarms, with rich but not fully revealed self-stabilization mechanisms. The interaction between dunes is considered as 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-mentioned 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.