Abstract
Abstract This chapter provides an overview of mechanisms and theoretical models of pattern formation in dense gravity-driven granular flows. A wide range of phenomena, from one- and two-dimensional avalanches flowing upon inclined planes, instabilities and fingering of avalanche fronts, flows in rotating drums to self-organized criticality and statistics of granular avalanches, are considered. In the majority of gravity-driven granular flows, the motion is confined at the surface of the granular system. Various approaches are used to describe surface flows, including depth-averaged hydrodynamic equations (the Saint-Venant model), two-phase models rolling and static fractions of erodible granular flows (Bouchaud, Cates, Ravi Prakash, and Edwards equations), and order parameter models for partially fluidized granular flows.
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