Reproducing size distributions of swarms of barchan dunes on Mars and Earth using a mean-field model
We apply a mean-field model of interactions between migrating barchan dunes, the CAFE model, which includes spontaneous calving, aggregation, fragmentation, and mass-exchange, yielding a steady-state size distribution that can be resolved for different choices of interaction parameters. The CAFE model is applied to empirically measured distributions of dune sizes in two barchan swarms in the north circumpolar region of Mars, three swarms in Morocco, and one in Mauritania, each containing more than 1000 bedforms. When the sizes of bedforms are rescaled by the mean size in each zone two attractor states appear, with the Tarfaya zones all displaying a common distribution and the Martian and Mauritanian zones sharing a different distribution. Comparison of these attractor states with the outputs of the CAFE model reveals that the Tarfaya-type distribution results from a preference for aggregation and fragmentation interactions whereas the Mars-Mauritania distribution is more likely a result of exchange-dominated interactions. We observe that there appears to be a greater number of collisions happening in Tarfaya than in the other areas which is consistent with a greater rate of aggregation-fragmentation processes as suggested by our model. Our comparison with the CAFE model also predicts a universal rule for the outputs of the different types of interactions with exchange interactions favouring the production of two dunes roughly equal in size. Fragmentation interactions often result in three bedforms with volumes approximately in the ratio 1:1:2. Finally, we find that spontaneous calving of dunes does not play an important role in shaping the size distributions in barchan swarms.