Ripple and kink dynamics

We propose a relevant modification of the Nishimori-Ouchi model [{\em Phys. Rev. Lett.} {\bf 71}, 197 (1993)] for granular landscape erosion. We explicitly introduce a new parameter: the angle of repose $\theta_r$, and a new process: avalanches. We show that the $\theta_r$ parameter leads to an asymmetry of the ripples, as observed in natural patterns. The temporal evolution of the maximum ripple height $h_{max}$ is limited and not linear, according to recent observations. The ripple symmetry and the kink dynamics are studied and discussed.