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.

中文翻译：

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空中碰撞控制风沙波纹的波长

风沙波纹的波长随着风速的增加而增加，但这种增加的原因至今仍不清楚。通过数值模拟，我们发现，在没有空中碰撞的情况下，风强度和初始波长之间的关系消失，这意味着空中碰撞对波纹的初始波长有至关重要的贡献。随着风强度的增加，非碰撞粒子的平均跳跃长度减小。受床表面地形和沿波状表面不均匀的空中碰撞概率的影响，非碰撞颗粒引起表面调制的侵蚀/沉积通量。通量波动的一阶贡献使原始床表面变得不稳定，并且相对于表面轮廓具有依赖于风的相移。这种相移导致初始波长随风速增加。基于这些发现，我们推导了风沙波纹初始波长的标度律，这与实验结果非常吻合。已经发现波纹波长和风速之间存在弱非线性关系，特别是对于大风强度。