Blown by wind: nonlinear dynamics of aeolian sand ripples

A nonlinear continuum model is considered that describes the dynamics of two-dimensional aeolian sand ripples. This integro-differential model is based on a phenomenological approach due to Anderson. Linear stability analysis using this model shows that a flat sand bed exposed to the action of wind is linearly unstable to long-wavelength perturbations. As the ripples grow, nonlinear effects become important, ripples become asymmetric and the wavelength increases due to merging events. A long-wavelength approximation to the full integral model is then derived. The ripple field produced by the long-wave theory undergoes coarsening, drifts downwind and displays bifurcations and defects which move from one ripple to another, similar to what is observed for sand ripples in the desert. (C) 2004 Published by Elsevier B.V.