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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Allen, M. P. and Tildesley, D. J. (1987). Computer Simulation of Liquids. Oxford University Press, Oxford.
de Gennes, P.-G. (1999). Granular matter: a tentative review. Reviews of Modern Physics, 71:S374–S382.
Feder, J. (1988). Fractals. Plenum press, NewYork.
Frisch, U. (1995). Turbulence, the Legacy of A. N. Kolmogorov. Cambridge University Press, Cambridge, England.
Hicher, P.-Y. (2000). Experimental behaviour of granular materials. In Cambou, B., editor, Behaviour of Granular Materials, pages 1–98, Wien. Springer.
Jaeger, H. M., Nagel, S. R., and Behringer, R. P. (1996). Granular solids, liquids, and gases. Reviews of Modern Physics, 68(4):1259–1273.
Kuhn, M. (1999). Mechanics of Materials, 31:407.
Miller, B., O’Hern, C., and Behringer, R. P. (1996). Stress fluctuations for continously sheared granular materials. Phys. Rev. Lett., 77:3110–3113.
Misra, A. and Jiang, H. (1997). Measured kinematic fields in the biaxial shear of granular materials. Computers and Geotechnics, 20(3/4):267–285.
Moreau, J. J. (1988). Unilateral contact and dry friction in finite freedom dynamics, pages 1–82. Number 302.
Moreau, J. J. (1993). New computation methods in granular dynamics. In Powders & Grains 93, page 227, Rotterdam. A. A. Balkema.
Moreau, J. J. (1994a). Some numerical methods in multibody dynamics: Application to granular materials. European Journal of Mechanics A/Solids, supp.(4):93–114.
Moreau, J. J. (1994b). Some numerical methods in multibody dynamics: application to granular materials. Eur. J. Mech. A, 13:93.
Moreau, J. J. (1997). Numerical investigation of shear zones in granular materials. In Wolf, D. E. and Grassberger, P., editors, Friction, Arching and Contact Dynamics, Singapore. World Scientific.
Parrinello, M. and Rahman, A. (1980). Phys. Rev. Lett., 45:1196.
Radjai, F., Jean, M., Moreau, J. J., and Roux, S. (1996). Force distribution in dense two-dimensional granular systems. Phys. Rev. Lett., 77(2):274.
Radjai, F. and Roux, S. (2002). Turbulentlike fluctuations in quasistatic flow of granular media. Phys. Rev. Lett., 89:064302.
Rothenburg, L. and Bathurst, R. J. (1989). Analytical study of induced anisotropy in idealized granular materials. Geotechnique, 39:601–614.
Roux, S. and Radjai, F. (2001). Statistical approach to the mechanical behavior of granular media. In Aref, H. and Philips, J., editors, Mechanics for a New Millennium, pages 181–196, Netherlands. Kluwer Acad. Pub.
Troadec, H., Radjai, F., Roux, S., and Charmet, J.-C. (2002). Model for granular texture with steric exclusions. Phys. Rev. E, 66:041305.
Wood, D. (1990). Soil behaviour and critical state soil mechanics. Cambridge University Press, Cambridge, England.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer Science+Business Media, Inc.
About this paper
Cite this paper
Radjaï, F., Roux, S. (2006). Scaling Behaviour of Velocity Fluctuations in Slow Granular Flows. In: Alart, P., Maisonneuve, O., Rockafellar, R.T. (eds) Nonsmooth Mechanics and Analysis. Advances in Mechanics and Mathematics, vol 12. Springer, Boston, MA. https://doi.org/10.1007/0-387-29195-4_20
Download citation
DOI: https://doi.org/10.1007/0-387-29195-4_20
Publisher Name: Springer, Boston, MA
Print ISBN: 978-0-387-29196-3
Online ISBN: 978-0-387-29195-6
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)