A nonlinear model for aeolian sand ripples
Groupe Matière Condensée et Matériaux (UMR 6626) ,
Université Rennes 1, 35042 Rennes Cedex, France
Corresponding author: a email@example.com
Published online: 15 August 1999
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.
PACS: 83.70.Fn – Granular solids / 81.05.Rm – Porous materials; granular materials / 47.20.-k – Hydrodynamic stability
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 1999