Eur. Phys. J. B 5, 245-249 (1998)
https://doi.org/10.1007/s100510050441

A model for ripple instabilities in granular media

Service de Physique de l'État Condensé, C.E. Saclay, Orme des Merisiers, 91191 Gif-sur-Yvette Cedex, France

Corresponding author: ^a terzidis@spec.saclay.cea.fr

Received: 30 January 1998
Revised: 12 May 1998
Accepted: 8 June 1998
Published online: 15 September 1998

Abstract

We extend the model of surface granular flow proposed in [CITE] to account for the effect of an external `wind', which acts as to dislodge particles from the static bed, such that a stationary state of flowing grains is reached. We discuss in detail how this mechanism can be described in a phenomenological way, and show that a flat bed is linearly unstable against ripple formation in a certain region of parameter space. We focus in particular on the (realistic) case where the migration velocity of the instability is much smaller than the grains' velocity. In this limit, the full dispersion relation can be established. We relate the critical wave vector to the mean hopping length and to the ratio of the flight time to the `stick' time. We provide an intuitive interpretation of the instability.