Mid-Air Collisions Control the Wavelength of Aeolian Sand Ripples

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. Sand ripples are a commonly observed geomorphological feature, yet the theoretical explanation for the relationship between their wavelength and wind strength has remained elusive until now. In the present paper we explore this issue from a novel perspective. By a combination of stability analysis and detailed simulations, we discover that inter-particle collisions in the air are the crucial mechanism linking ripple topology to the wind strength. According to this recognition, a nonlinear relation is derived, which fits the experimental and numerical results of aeolian sand ripples. Without mid-air collisions of sand particles, the wavelength of aeolian sand ripples will not increase with the wind strength Colliding particles and non-colliding particles contribute differently to the ripple formation process A wind-dependent flux of non-colliding particles relates the initial wavelength of sand ripples to the wind strength