Eur. Phys. J. B 10, 543-548 (1999)
https://doi.org/10.1007/s100510050884

A nonlinear model for aeolian sand ripples

Groupe Matière Condensée et Matériaux (UMR 6626) , Université Rennes 1, 35042 Rennes Cedex, France

Corresponding author: ^a valance@truffaut.univ-rennes1.fr

Received: 5 January 1999
Published online: 15 August 1999

Abstract

Starting from the phenomenological model for sand ripple formation developed in [CITE], we proposed a new interpretation in the light of recent experiments. Furthermore, we derive, close to the threshold of ripple instability, a nonlinear equation for the spatio-temporal evolution of the sand bed profile, which to leading order has a quadratic nonlinearity. This equation is identical to that derived recently on the basis of geometry and conservation law [CITE]. Our derivation connects the coefficients of the nonlinear equation to the underlying physical mechanisms (reptation length...). This equation reveals ripple structures which then undergo a coarsening process, as observed in wind tunnel experiment. Small, fast moving ripples are absorbed by larger, slower forms resulting in a growth of the mean wavelength.