INSTABILITIES OF FULLY-DEVELOPED RAPID FLOW OF A GRANULAR MATERIAL INA CHANNEL

The equations of motion for 'rapid' flow of a granular material have f ully developed solutions representing flow driven by a body force, suc h as gravity, along a channel bounded by plane parallel walls. The sta bility of these solutions to small perturbations is investigated. For given properties of the particles and the channel walls it is found th at the condition of critical stability is a relation between the mean concentration of the particles and the width of the channel. When the base state is unstable the fastest growing modes are travelling waves propagating in the axial direction and these induce characteristic pat terns of variations in particle concentration, as well as velocity. Th ese instabilities are contrasted with those found for Couette shearing in an earlier publication.