Granular wave patterns in a horizontal rotating cylinder.

摘要

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, is thought to reflect a competition between bulk viscosity and surface tension.;Recent experiments have shown that the front of a granular layer flowing over an inclined surface may also develop fingers. Because the materials used in these experiments are cohesionless and, thus, unable to sustain surface tension, this instability is surprising. As an explanation, it has been suggested that frontal finger formation in granular materials is induced by the segregation of coarse, irregularly shaped grains.;We present the results of an experiment involving a thin granular layer flowing within a horizontal cylinder that is rotated about its axis. We uncover an assortment of stationary and temporally varying spatial patterns, patterns that bear close resemblance to aeolian ripples and sand dunes. In particular, we find that, even when the medium is well sieved and consists of nearly uniform spherical grains, its front may develop fingers, suggesting that, in general flow configurations, mechanisms other than grain segregation may drive the instability of a straight front.;As a step toward understanding these mechanisms, we develop a system of evolution equations that accounts for the steady motion of grains with the cylinder and for the motion of saltating and reptating grains. We develop a numerical algorithm for the solution of these equations and use this algorithm to determine a dispersion relation for the growth rate in terms of the wave number of frontal disturbances. We find that the model is able to predict some of the qualitative features observed from our rotating cylinder experiment.;Our long-term objective is to combine our experimental and computational results to determine the values of the critical constitutive parameters that appear in our theory.