Mid‐Air Collisions Control the Wavelength of Aeolian Sand Ripples

Abstract

The wavelength of aeolian sand ripples increases with wind velocity, but the cause for this increase remained unclear until now. Using numerical simulations, we find that the relationship between the wind strength and the initial wavelength disappears without mid‐air collisions, which means that mid‐air collisions crucially contribute to the initial wavelength of ripples. As wind strength increases, the average hop length of non‐colliding particles decreases. Affected by the bed surface topography and the non‐uniform mid‐air colliding probability along the wavy surface, non‐colliding particles cause a surface modulated erosion/deposition flux. The first order contribution of the flux fluctuation destabilizes the original bed surface and has a wind‐dependent phase shift with respect to the surface profile. This phase shift leads to an initial wavelength that increases with wind velocity. Based on these findings we derive the scaling law for the initial wavelength of aeolian sand ripples, which agrees well with experimental results. A weak non‐linear relationship between ripple wavelength and wind velocity has been found, especially for large wind strengths.