Granular finger formation in a rotating cylinder

It is well known that the front of a fluid sheet flowing over an inclined surface is unstable to spanwise perturbations. This instability, which manifests itself in the formation of fingers of fairly constant wavelength, reflects a competition between viscous stresses and surface tension. We present the results of an experiment involving a thin granular layer flowing within a horizontal rotating cylinder and report an assortment of stationary and temporally varying spatial patterns. In particular, we observe a spanwise instability characterized by serrated frontal shapes remarkably similar to those encountered with Newtonian fluids. Because the materials used in these experiments are cohesionless and, thus, unable to sustain surface tension, this instability is surprising. As a step toward understanding these mechanisms, we develop a system of evolution equations that accounts for the steady motion of grains within the cylinder and for more complicated kinds of grain motions such as saltation and reptation. We find that the model is able to predict some of the qualitative features observed from our experiment.