In the framework of the theory of partially fluidized granular flows we study the formation of longitudinal structures observed experimentally by Forterre and Pouliquen in a flow down a rough inclined plane. We show that the formation of longitudinal structures is related to the positive feedback between the fluidization rate and the lateral stress (side pressure), which leads to a convective instability. Our theory explains main experimental features, such as appearance and amplification of the structure at some distance from the outlet and non-stationary behavior of the structures.
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