A theoretical model for aeolian impact ripples

New insights into the grain-bed impact process arising from both numerical and physical experiments involving single grain impacts lead to a more complete conceptual model of the aeolian saltation process that in turn allows a simple model of aeolian impact ripples to be developed. The saltating population may be idealized as consisting of (1) long trajectory, high impact-energy, constant impact-angle ‘successive saltations’, and (2) short trajectory, low impact-energy ‘reptations’. It is argued that the spatial variations in mass flux due to the reptating population lead to the growth and translation of impact ripples. Using the sediment continuity equation, an expression for the spatial variation in the ejection rate of reptating grains from a sinusoidally perturbed bed, and a probability distribution for the reptation lengths, a simple stability analysis demonstrates that the flat bed is unstable to small amplitude perturbations. A fastest-growing wavelength emerges that is roughly six times the mean reptation length, and is only weakly dependent upon the detailed shape of the probability distribution of reptation lengths. The results match well with the observed initial wavelengths in wind tunnel experiments.