Comment on “Minimal size of a barchan dune”

Abstract

It is now an accepted fact that the size at which dunes form from a flat sand bed as well as their "minimal size" scales on the flux saturation length. This length is by definition the relaxation length of the slowest mode toward equilibrium transport. The model presented by Parteli, Durán, and Herrmann [Phys. Rev. E 75, 011301 (2007)] predicts that the saturation length decreases to zero as the inverse of the wind shear stress far from the threshold. We first show that their model is not self-consistent: even under large wind, the relaxation rate is limited by grain inertia and thus cannot decrease to zero. A key argument presented by these authors comes from the discussion of the typical dune wavelength on Mars (650 m) on the basis of which they refute the scaling of the dune size with the drag length evidenced by Claudin and Andreotti [Earth Planet. Sci. Lett. 252, 30 (2006)]. They instead propose that Martian dunes, composed of large grains (500 microm), were formed in the past under very strong winds. We emphasize that this saltating grain size, estimated from thermal diffusion measurements, is far from straightforward. Moreover, the microscopic photographs taken by the rovers on Martian Aeolian bedforms show a grain size of 87+/-25 microm together with hematite spherules at millimeter scale. As those so-called "blueberries" cannot be entrained more frequently than a few hours per century, we conclude that the saltating grains on Mars are the small ones, which gives a second strong argument against the model of Parteli.