Noise reduction and pattern formation in rapid granular flows

Spatial fluctuations in dissipative systems, such as rapid granular flows, behave very differently from those in elastic fluids. Fluctuations in the flow field drive the linear and nonlinear instability in the density field (clustering), while vortex structures appear and grow through the mechanism of noise reduction. The dynamics of the flow field on the largest space and time scales is described by diffusion equations with different diffusivities for the transverse and longitudinal flow fields. The results are obtained from analytic and simulation methods.