Eolian ripples as examples of self-organization in geomorphological systems

Abstract

Ripples arise spontaneoulsy from sandy beds subjected to winds sufficient to cause the saltation of surficial grains. While the initially fastest growing wavelengths are 4–6 times the mean hop length of grains impelled downwind by long-trajectory high-energy saltating grains, the ripple wavelengths developed over long periods can be several times this. Numerical simulations based upon techniques pioneered by P.K. Haff and coworkers reveal that a complex process of ripple coalescence is responsible for this evolution of the ripple field. Small, fast-moving ripples catch up with and are absorbed by larger, slower forms, each such merger resulting in a growth of the mean wavelength and a decline in the relative dispersion of the wavelengths. An heuristic argument is presented which accounts for the fast initial growth and subsequent slowing of growth of the mean wavelength as the ripple field evolves. Ripple cross-sectional shape appears to be controlled in large part by a distrianment function which represents the declining likelihood of a grain stopping on a surface as it slopes more steeply downwind. That the resulting asymptotic wavelength in the simulations depends strongly upon impact angle supports Sharp's (1963) suggestion that the length of the shadow zone plays an important role in controlling the final ripple wavelength.