ABSTRACT
We study the steady free surface flow of granular material down an inclined bumpy chute. Our theoretical model adopts the kinetic theory of rapid granular flows, employing the constitutive equations of Lun et al. (1984), (see §§2.2), supplemented by the basal boundary conditions of (Richman 1988), (§§3.1). Fully developed steady flows then arise from the solution of a nonlinear system of odes which we integrate numerically using a pseudospectral Chebyshev collocation method (§4). The character of the solutions is determined by a relatively small number of dimensionless parameters which include the gradient of the slope. We find that solutions exist in only some regions of parameter space. From the solution we calculate the physically important variables of volume flux and center of mass, which can be measured experimentally (§5). In some parameter regimes we find three flow depths for a given volume flux (§6).
