  In this paper we present an experimental study of the long surface wave
instability that can develop when a granular material flows down a rough
inclined plane. The threshold and the dispersion relation of the instability
are precisely measured by imposing a controlled perturbation at the entrance of
the flow and measuring its evolution along the slope. The results are compared
with the prediction of a linear stability analysis conducted in the framework
of the depth-averaged or Saint-Venant equations. We show that when the friction
law proposed in Pouliquen (1999a) is introduced in the Saint-Venant equations,
the theory is able to predict quantitatively the stability threshold and the
phase velocity of the waves but fails in predicting the observed cutoff
frequency. The instability is shown to be of the same nature as the long wave
instability observed in classical fluids but with characteristics that can
dramatically differ due to the specificity of the granular rheology.

Materials Science