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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., Comment: 29 pages, 20 figures, to be published in Journal of Fluid Mechanics

International audience; Long-surface-wave instability in dense granular flows down inclined planes is analysed using recently proposed three-dimensional constitutive equations. A full linear stability analysis of the local governing equations is performed and compared to previous experimental results obtained with glass beads. We show that the proposed rheology is able to capture all the features of the instability quantitatively. In particular, it predicts well the behaviour and scaling for the cutoff frequency of the instability observed in the experiments. This result gives strong support for the three-dimensional rheology proposed and suggests new terms in the Saint-Venant equations used to describe free-surface granular flows.