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Rapid granular chute flow - multiple steady flow solutions and their linear stability

Tuesday 6th January 2009 - 12:00 to 12:15
INI Seminar Room 1
The free-surface flow of highly agitated particles on an inclined chute is analysed using a continuum model that adopts the kinetic theory of rapid granular flows. Steady, fully developed profiles of the concentration of particle, the velocity of the flow down the slope and the granular temperature, which measures the agitation of the system, may be found as solutions to the governing equations. These are calculated using a Chebyshev pseudospectral method, which exploits the asymptotic form of the solutions at large heights to obtain highly accurate approximations. The character of the steady solutions is determined by a relatively small number of dimensionless parameters, which includes the slope inclination, coefficients of restitution, and roughness of the chute surface. An asymptotic analysis appropriate to high temperature flows has been developed to obtain the boundaries in parameter space where steady solutions exist. The pseudospectral approximation lends itself to parametric continuation, which allows us to efficiently track the form of the solutions as we vary the controlling parameters. In particular, we investigate the depth of steady flows, here defined as the centre of mass, as the volume flux of material is varied and find that, in some parameter regimes, three flow depths occur for a given volume flux of material. We consider the linear stability of the multiple solutions to small perturbations in both the cross-slope and downslope directions. We find regions in which flows are unstable to small perturbations, and show there is no correlation between the region of instability and the existence of density inversions in the steady flow profile.
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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons