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Dynamics of granular avalanches caused by local perturbations

Thorsten Emig·Philippe Claudin·Jean-Philippe Bouchaud
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Abstract

Surface flow of granular material is investigated within a continuum approach in two dimensions. The dynamics is described by a non-linear coupling between the two `states' of the granular material: a mobile layer and a static bed. Following previous studies, we use mass and momentum conservation to derive St-Venant like equations for the evolution of the thickness R of the mobile layer and the profile Z of the static bed. This approach allows the rheology in the flowing layer to be specified independently, and we consider in details the two following models: a constant plug flow and a linear velocity profile. We study and compare these models for non-stationary avalanches triggered by a localized amount of mobile grains on a static bed of constant slope. We solve analytically the non-linear dynamical equations by the method of characteristics. This enables us to investigate the temporal evolution of the avalanche size, amplitude and shape as a function of model parameters and initial conditions. In particular, we can compute their large time behavior as well as the condition for the formation of shocks.

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Thorsten Emig, Philippe Claudin, Jean-Philippe Bouchaud. 2004-07-13. Dynamics of granular avalanches caused by local perturbations. https://doi.org/10.1103/physreve.71.031305

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