Abstract
Barchan dunes emerge as a collective phenomena involving the generation
of thousands of them in so called barchan dune fields. By measuring the
size and position of dunes in Moroccan barchan dune fields, we find that
these dunes tend to distribute uniformly in space and follow an unique
size distribution function. We introduce an analytical mean-field
approach to show that this empirical size distribution emerges from the
interplay of dune collisions and sand flux balance, the two simplest
mechanisms for size selection. The analytical model also predicts a
scaling relation between the fundamental macroscopic properties
characterizing a dune field, namely the inter-dune spacing and the first
and second moments of the dune size distribution.
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