Rapid granular shear flows driven by identical, bumpy, frictionless boundaries

Motivated by flows of granular materials down inclines that involve a relatively passive mass of material supported upon a narrow region of intensely sheared, colliding grains, we consider the steady, rapid shearing of identical frictionless spheres driven by the relative motion of identical, bumpy, frictionless boundaries. We relate the ratio of shear to normal stress supported by the flow to a nondimesional measure of the relative velocity of the boundaries over a range of boundary geometries and material properties. The stress ratio may be an increasing or decreasing function of velocity, depending on whether the boundaries provide energy to or remove energy from the velocity fluctuations in the flow.