A nonlinear model for aeolian sand ripples
Résumé
Starting from the phenomenological model for sand ripple formation developed in [1], 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 [2]. 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.