Scaling Behaviour of Velocity Fluctuations in Slow Granular Flows

  • Farhang Radjaï
  • Stéphane Roux
Conference paper
Part of the Advances in Mechanics and Mathematics book series (AMMA, volume 12)

Abstract

Steric exclusions among particles lead to strong velocity fluctuations in a granular flow. Modelling the effective behaviour of granular materials depends on the extent and scaling properties of these fluctuations. We consider here slow granular flows of rigid particles simulated by a discrete element method. Bi-periodic boundary conditions allow for macroscopically homogeneous shearing up to large strains. We obtain thus reliable statistics for an accurate analysis of particle velocity fluctuations. We find that the probability distribution function of velocity components, evaluated from particle displacements, crucially depends on time resolution. It varies from stretched exponential to gaussian as the integration time is increased. On the other hand, the spatial power spectrum of the fluctuating velocity field is a power law, reflecting long range correlations and the self-affine nature of the fluctuations. Finally, by considering individual particle displacements, we show that the particles have a superdiffusive motion with respect to the mean background flow. These scaling behaviours bear a close analogy with the known scaling properties of turbulent fluid flows although the underlying physics is drastically different.

Keywords

granular media discrete element method plastic deformation steric exclusions probability density function space correlations superdiffusion turbulence 
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Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  • Farhang Radjaï
    • 1
  • Stéphane Roux
    • 2
  1. 1.LMGC, CNRS-Université Montpellier IIMontpellier CedexFrance
  2. 2.Laboratoire Surface du Verre et InterfacesCNRS-Saint GobainAubervilliers CedexFrance

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