Erosion waves: When a model experiment meets a theory

We present recent results on two laboratory scale avalanches experiments taking place both in the air and under-water. In both cases, a family of solitary erosion/deposition waves are triggered. At higher inclination angles, we show the existence of a linear long wavelength transverse instability followed by a coarsening dynamics and finally, the onset of a fingering pattern. Both experiments strongly differ by the spatial and time scales involved, nevertheless, the quantitative agreement between the stability diagram, the wavelengths selection and the avalanche morphology suggest a common erosion /deposition scenario. These experiments are studied theoretically in the framework of the "partial fluidization" model that was developed earlier to describe dense granular flows. This model identifies a family of propagating solitary waves displaying a behavior similar to the experimental observation. A primary cause for the transverse instability is directly related to the dependence of the solitary wave velocity on the granular mass trapped in the avalanche, a results recovered experimentally.