Two-dimensional granular flow in a small-angle funnel

We have investigated a granular flow consisting of a single layer of uniform balls in a two dimensional funnel. The qualitative behavior of the flow depends in a sensitive way on the geometry. For a particular configuration in which only the funnel opening angle {β} is varied, we find three regimes. When {β}>2^∘{}, the flow is dense and steady, and the flow rate is determined by the geometry at the outlet. When 0.1^∘{}{}{β}{}1^∘{}, the flow is intermittent, consisting of quasiperiodic kinematic waves, probably shock waves, propagating against the flow. The flow rate reaches its maximum in this regime. When {β}0.05^∘{}, the waves become stationary, and the flow rate is now determined by the geometry at the inlet. We also measure the number density fluctuations of the flow and their power spectra. For all flows, the power spectra are white at low frequencies with structures at higher frequencies resulting from the kinematic waves and short-range correlations. {} 1996 The American Physical Society.