Density waves and coherent structures in granular Couette flows

Density inhomogeneities in granular flows can dramatically influence microscopic and macroscopic properties. Here, we numerically examine dilute rapid granular flows in the Couette geometry via large-scale particle-dynamic simulations, and characterize development of nonuniform particle distributions. For monodisperse grains we observe density waves in two- and three-dimensional computational domains of varying aspect ratios. Both fully developed and transient states are quantified using Fourier methods. For inelastic, planar (two-dimensional) flows exceeding a minimum solids fraction, one-dimensional, high-density clusters—well-known features of inelastic materials—align parallel to the walls. Above a critical streamwise length, these are destabilized by two-dimensional antisymmetric modes with wavelength ∼100 particle diameters. We relate oscillatory behavior to an underlying physical mechanism of the slow drift of clusters towards walls and their subsequent bursting. Further streamwise or spanwise expansions permit additional wave numbers to be expressed in these directions. In “shallow” three-dimensional flows, the planar wave types initially survive. As depth is increased above a critical value, cross-stream invariance experiences symmetry preserving instabilities to form coherent structures resembling steady and wavy Taylor–Couette fluid vortices. Their presence strongly impacts macroscopic behavior, as regions of sustained vorticity develop, and stresses and granular temperatures deviate by up to an order of magnitude from mean values. The influence of solids fraction, particle size, material elasticity, surface friction, polydispersity, and gravity are considered, and instabilities are found to intensify as collisional dissipation rises. For planar flows, transient and fully developed density distributions share many parametric responses with previous continuum results using kinetic theory. © 2004 American Institute of Physics.