Discrete Element Method simulations of the saturation of aeolian sand transport

The saturation length of aeolian sand transport ($L_s$), characterizing the distance needed by wind-blown sand to adapt to changes in the wind shear, is essential for accurate modeling of the morphodynamics of Earth's sandy landscapes and for explaining the formation and shape of sand dunes. In the last decade, it has become a widely-accepted hypothesis that $L_s$ is proportional to the characteristic distance needed by transported particles to reach the wind speed (the ``drag length''). Here we challenge this hypothesis. From extensive numerical Discrete Element Method simulations, we find that, for medium and strong winds, $L_s\propto V_s^2/g$, where $V_s$ is the saturated value of the average speed of sand particles traveling above the surface and $g$ the gravitational constant. We show that this proportionality is consistent with a recent analytical model, in which the drag length is just one of four similarly important length scales relevant for sand transport saturation.