. La-forme-est-la-principale-différence-entre-les-billes-de-verre-et-le-sable-que-nous-utilisons, On constate ainsi, sans pouvoir l'expliquer quantitativement, que l'angle minimal d'´ ecoulement du sable est supérieur d'environ 10 ?à?`?à l'angle minimal

Y. Aihara, Formation of longitudinal vortices in the sublayer due to boundary-layer turbulence, Journal of Fluid Mechanics, vol.223, issue.-1, pp.111-129, 1990.
DOI : 10.1017/S0022112078002608

M. Alam and P. R. Nott, Stability of plane Couette flow of a granular material, Journal of Fluid Mechanics, vol.377, 1998.
DOI : 10.1017/S002211209800295X

V. Alavian, Behavior of Density Currents on an Incline, Journal of Hydraulic Engineering, vol.112, issue.1, pp.27-42, 1986.
DOI : 10.1061/(ASCE)0733-9429(1986)112:1(27)

. C. Ancey, Rhéologie desécoulementsdesécoulements granulaires en cisaillement simple : application aux laves torrentielles granulaires, Thèse de l'Ecole Centrale, 1997.

. C. Ancey, Dry granular flows down an inclined channel: Experimental investigations on the frictional-collisional regime, Physical Review E, vol.65, issue.1, p.11304, 2002.
DOI : 10.1103/PhysRevE.65.011304

K. G. Anderson and R. Jackson, 1992 A comparison of the solutions of some proposed equations of motion of granular materials for fully developed flow down inclined planes, J

B. Andreotti and S. Douady, Selection of velocity profile and flow depth in granular flows, Physical Review E, vol.63, issue.3, p.31305, 2001.
DOI : 10.1103/PhysRevE.63.031305

A. Aradian, E. Raphaël, and P. G. De-gennes, Surface flows of granular materials: a short introduction to some recent models, Comptes Rendus Physique, vol.3, issue.2, pp.187-196, 2002.
DOI : 10.1016/S1631-0705(02)01304-X

URL : https://hal.archives-ouvertes.fr/hal-00010087

I. S. Aranson and L. S. Tsimring, Continuum theory of partially fluidized granular flows. preprint cond-mat, 2001.

E. Azanza, granulaires bidimensionnels sur un plan incliné, Thèse de l'Ecole Nationale des Ponts et

E. Azanza, F. Chevoir, and P. Moucheront, Experimental study of collisional granular flows down an inclined plane, Journal of Fluid Mechanics, vol.400, pp.199-227, 1999.
DOI : 10.1017/S0022112099006461

H. Ahn, C. E. Brennen, and R. H. Sabersky, Analysis of the Fully Developed Chute Flow of Granular Materials, Journal of Applied Mechanics, vol.59, issue.1, pp.109-119, 1992.
DOI : 10.1115/1.2899415

R. A. Bagnold, 1954 Experiments on a gravity-free dispersion of large solid spheres in a Newtonian fluid under shear, Proc. R. Soc. Lond. A 225, pp.49-63

T. B. Benjamin, Wave formation in laminar flow down an inclined plane, Journal of Fluid Mechanics, vol.48, issue.06, pp.554-574, 1957.
DOI : 10.1021/ie50379a015

D. Bonamy, Phénomènes collectifs dans les matériaux granulaires. Ecoulements de surface et réarrangements internes dans des empilements modèles, Thèse de l'Université Paris 11, 2001.

J. J. Brey, J. W. Dufty, C. S. Kim, and A. Santos, Hydrodynamics for granular flow at low density, Physical Review E, vol.58, issue.4, pp.4638-4653, 1998.
DOI : 10.1103/PhysRevE.58.4638

C. S. Campbell and C. E. Brennen, Chute Flows of Granular Material: Some Computer Simulations, Journal of Applied Mechanics, vol.52, issue.1, pp.172-178, 1985.
DOI : 10.1115/1.3168990

C. S. Campbell, Rapid Granular Flows, Annual Review of Fluid Mechanics, vol.22, issue.1, pp.57-92, 1990.
DOI : 10.1146/annurev.fl.22.010190.000421

M. Caponeri, S. Douady, S. Fauve, and C. Laroche, Dynamics of Avalanches in a Rotating Cylinder, Mobile Particulate System, pp.331-366, 1995.
DOI : 10.1007/978-94-015-8518-7_20

H. Chang, Wave Evolution on a Falling Film, Annual Review of Fluid Mechanics, vol.26, issue.1, pp.103-136, 1994.
DOI : 10.1146/annurev.fl.26.010194.000535

V. Cornish, Ocean waves and kindred geophysical phenomena, 1934.

A. Daerr and S. Douady, Two types of avalanche behaviour in granular media, Nature, vol.399, issue.6733, pp.241-243, 1999.
DOI : 10.1038/20392

A. Daerr, Dynamical equilibrium of avalanches on a rough plane, Physics of Fluids, vol.13, issue.7, pp.2115-2125, 2001.
DOI : 10.1063/1.1377864

K. E. Daniels, B. P. Brendan, and E. Bodenschatz, Pattern Formation in Inclined Layer Convection, Physical Review Letters, vol.84, issue.23, pp.5320-5323, 2000.
DOI : 10.1103/PhysRevLett.84.5320

T. R. Davies, Deris flow surges-a laboratory investigation, 1988.

G. Debregas and C. Josserand, A self-similar model for shear flows in dense granular materials, Europhysics Letters (EPL), vol.52, issue.2, pp.137-143, 2000.
DOI : 10.1209/epl/i2000-00415-5

S. Douady, S. Fauve, and C. Laroche, Subharmonic Instabilities and Defects in a Granular Layer under Vertical Vibrations, Europhysics Letters (EPL), vol.8, issue.7, pp.621-627, 1989.
DOI : 10.1209/0295-5075/8/7/007

T. J. Drake, Structural features in granular flows, Journal of Geophysical Research, vol.7, issue.B6, pp.8681-8696, 1990.
DOI : 10.1029/JB095iB06p08681

R. F. Dressler, Mathematical solution of the problem of roll-waves in inclined open channels. Communs pure appl, pp.149-194, 1949.

P. Duru, M. Nicolas, J. Hinch, and E. Guazzelli, Constitutive laws in liquidfluidized beds, J. Fluid Mech, vol.452, pp.371-404, 2002.
URL : https://hal.archives-ouvertes.fr/hal-01440963

E. Falcon, S. Fauve, and C. Laroche, Cluster formation, pressure and density measurements in a granular medium fluidized by vibrations, The European Physical Journal B, vol.9, issue.2, pp.183-186, 1999.
DOI : 10.1007/s100510050755

Y. Forterre and O. Pouliquen, Stability analysis of rapid granular chute flows: formation of longitudinal vortices, Journal of Fluid Mechanics, vol.467, 2001.
DOI : 10.1017/S0022112002001581

URL : https://hal.archives-ouvertes.fr/hal-01432215

E. Fried, A. Q. Shen, and S. T. Thoroddsen, Wave patterns in a thin layer of sand within a rotating horizontal cylinder, Physics of Fluids, vol.10, issue.1, pp.10-13, 1998.
DOI : 10.1063/1.869539

I. Goldhirsch, Scales and kinetics of granular flows, Chaos: An Interdisciplinary Journal of Nonlinear Science, vol.9, issue.3, pp.659-672, 1999.
DOI : 10.1063/1.166440

H. Görtler, eine dreitridimensionale Instabilität laminarer Grenzschichten an konkaven Wänden, Nachr. Ges. Wiss

D. Gottlieb, M. Y. Hussaini, and S. A. Orszag, Theory and application of spectral methods, Spectral methods for partial differential equations Hussaini). Soc. Indus. & Appl. Math, 1984.

P. K. Haff, Grain flow as a fluid-mechanical phenomenon, Journal of Fluid Mechanics, vol.92, issue.-1, pp.401-430, 1983.
DOI : 10.1016/0009-2509(68)80016-8

X. He, B. Meerson, and G. Doolen, Hydrodynamics of thermal granular convection, Physical Review E, vol.65, issue.3, p.30301, 2002.
DOI : 10.1103/PhysRevE.65.030301

F. Heslot, T. Baumberger, B. Perrin, B. Caroli, and C. Caroli, Creep, stick-slip, and dry-friction dynamics: Experiments and a heuristic model, Physical Review E, vol.49, issue.6, pp.4973-4987, 1994.
DOI : 10.1103/PhysRevE.49.4973

K. M. Hill, A. Caprihan, and J. Kakalios, Axial segregation of granular media rotated in a drum mixer:???Pattern evolution, Physical Review E, vol.56, issue.4, pp.4386-4393, 1997.
DOI : 10.1103/PhysRevE.56.4386

E. J. Hinch, Introduction to mobile particulate systems. in Mobile particulate systems, pp.1-22, 1995.

E. J. Hopfinger, Snow Avalanche Motion and Related Phenomena, Annual Review of Fluid Mechanics, vol.15, issue.1, 1983.
DOI : 10.1146/annurev.fl.15.010183.000403

M. A. Hopkins and M. Y. Louge, Inelastic microstructure in rapid granular flows of smooth disks, Physics of Fluids A: Fluid Dynamics, vol.3, issue.1, pp.47-57, 1991.
DOI : 10.1063/1.857863

K. Hui, P. K. Haff, J. E. Ungar, and R. Jackson, Boundary conditions for high-shear grain flows, Journal of Fluid Mechanics, vol.108, issue.-1, pp.223-233, 1984.
DOI : 10.1007/BF01590859

O. Hungr and N. R. Morgenstern, Experiments on the flow behaviour of granular materials at high velocity in an open channel, G??otechnique, vol.34, issue.3, pp.405-413, 1984.
DOI : 10.1680/geot.1984.34.3.405

M. L. Hunt, R. Zenit, C. S. Valet, and C. E. Brennen, Revisiting the 1954 suspension experiments of R. A. Bagnold, Journal of Fluid Mechanics, vol.452, pp.1-24, 2002.
DOI : 10.1017/S0022112001006577

H. M. Jaeger, S. R. Nagel, and R. P. Behringer, Granular solids, liquids, and gases, Reviews of Modern Physics, vol.68, issue.4, pp.1259-1273, 1996.
DOI : 10.1103/RevModPhys.68.1259

H. Janssen, A 1895 Test on grains pressure in silos, Z. Vereins Deutsch Ing, vol.39, pp.1045-1049

J. T. Jenkins and S. B. Savage, A theory for the rapid flow of identical, smooth, nearly elastic, spherical particles, Journal of Fluid Mechanics, vol.157, issue.-1, pp.187-202
DOI : 10.1063/1.1672048

J. T. Jenkins and M. W. Richman, Grad's 13-moment system for dense gas of inelastic spheres, Arch. Rat. Mech. Anal, vol.87, pp.355-377, 1985.

J. T. Jenkins and M. W. Richman, Boundary conditions for plane flows of smooth, nearly elastic, circular disks, Journal of Fluid Mechanics, vol.164, issue.-1, pp.53-69, 1986.
DOI : 10.1017/S0022112083003419__S0022112083003419

J. T. Jenkins and F. Chevoir, Dense plane flows of frictional spheres down a bumby frictional incline, 2002.

P. Jeschke and H. Beer, Longitudinal vortices in a laminar natural convection boundary layer flow on an inclined flat plate and their influence on heat transfer, J. Fluid Mech, vol.432, pp.313-339, 2001.

P. C. Johnson, P. Nott, and R. Jackson, Frictional???collisional equations of motion for participate flows and their application to chutes, Journal of Fluid Mechanics, vol.20, issue.-1, pp.501-535, 1990.
DOI : 10.1017/S0022112079000525

Y. S. Kachanov, Physical Mechanisms of Laminar-Boundary-Layer Transition, Annual Review of Fluid Mechanics, vol.26, issue.1, 1994.
DOI : 10.1146/annurev.fl.26.010194.002211

P. L. Kapitza and S. P. Kapitza, Wave flow of thin layers of viscous fluid, 1949.

. Ekper and . Teor, Fiz. 19, 105. traduction anglaise dans Collected papers of, pp.690-709

D. V. Khakhar, J. J. Mccarthy, and J. M. Ottino, Radial segregation of granular mixtures in rotating cylinders, Physics of Fluids, vol.9, issue.12, pp.3600-3614, 1997.
DOI : 10.1063/1.869498

D. V. Khakhar, A. V. Orpe, P. Andredén, and J. M. Ottino, Surface flow of granular materials: model and experiments in heap formation, Journal of Fluid Mechanics, vol.441, pp.255-263, 2001.
DOI : 10.1017/S0022112001005201

P. S. Klebanoff, K. D. Tidstrom, and L. M. Sargent, The three-dimensional nature of boundary-layer instability, Journal of Fluid Mechanics, vol.28, issue.01, pp.1-34, 1962.
DOI : 10.1016/0016-0032(55)90094-6

C. Kranenburg, On the evolution of roll waves, Journal of Fluid Mechanics, vol.2, issue.-1, pp.249-261, 1992.
DOI : 10.1146/annurev.fl.11.010179.000303

A. Lemaitre, The origin of a respose angle: kinetic rearrangement for granular materials, 2002.

K. Liu and C. C. Mei, Roll waves on a layer of a muddy fluid flowing down a gentle slope???A Bingham model, Physics of Fluids, vol.6, issue.8, pp.2577-2590, 1994.
DOI : 10.1063/1.868148

J. Liu, J. D. Paul, and J. P. Gollub, Measurements of the primary instabilities of film flows, Journal of Fluid Mechanics, vol.1, issue.-1, pp.69-101, 1993.
DOI : 10.1063/1.857360

J. Liu, J. B. Schneider, and J. P. Gollub, Three???dimensional instabilities of film flows, Physics of Fluids, vol.7, issue.1, pp.55-67, 1995.
DOI : 10.1063/1.868782

W. Losert, L. Bocquet, T. C. Lubensky, and J. P. Gollub, Particle Dynamics in Sheared Granular Matter, Physical Review Letters, vol.85, issue.7, pp.1428-1431, 2000.
DOI : 10.1103/PhysRevLett.85.1428

C. K. Lun, S. B. Savage, D. J. Jeffrey, and N. Chepurniy, Kinetic theories for granular flow: inelastic particles in Couette flow and slightly inelastic particles in a general flowfield, Journal of Fluid Mechanics, vol.217, issue.-1, pp.223-256, 1984.
DOI : 10.1063/1.1672048

M. R. Malik, Numerical methods for hypersonic boundary layer stability, Journal of Computational Physics, vol.86, issue.2, pp.376-413, 1990.
DOI : 10.1016/0021-9991(90)90106-B

E. W. Mayer and K. G. Powel, Viscous and invicid instabilities of a trailing line vortex, J. Fluid Mech, vol.245, pp.191-114, 1992.

S. Mcnamara and W. R. Young, Inelastic collapse and clumping in a onedimensional granular medium, pp.496-504, 1992.

F. Melo, P. B. Umbanhowar, and H. L. Swinney, Hexagons, Kinks, and Disorder in Oscillated Granular Layers, Physical Review Letters, vol.75, issue.21, pp.3838-3841, 1995.
DOI : 10.1103/PhysRevLett.75.3838

P. Mills, M. Tixier, and D. Loggia, Influence of roughness and dilatancy for dense granular flow along an inclined wall, The European Physical Journal E - Soft Matter, vol.1, issue.1, pp.5-8, 2000.
DOI : 10.1007/s101890050002

URL : https://hal.archives-ouvertes.fr/hal-00693850

P. R. Nott, M. Alam, K. Agrawal, R. Jackson, and S. Sundaresan, The effect of boundaries on the plane Couette flow of granular materials: a bifurcation analysis, Journal of Fluid Mechanics, vol.397, 1999.
DOI : 10.1017/S0022112099006060

S. Ogawa, A. Umemura, and N. Oshima, On the equations of fully fluidized granular materials, Zeitschrift f??r angewandte Mathematik und Physik ZAMP, vol.384, issue.44, pp.483-493, 1980.
DOI : 10.1007/BF01590859

A. Oron, S. Davis, and S. G. Bankoff, Long-scale evolution of thin liquid films, Reviews of Modern Physics, vol.69, issue.3, 1997.
DOI : 10.1103/RevModPhys.69.931

P. Petitjeans, Etude expérimentale des instabilités de couches limites sur des parois concaves : instabilité de Görtler, Thèse de l, 1992.

O. Pouliquen and R. Gutfraind, Stress fluctuations and shear zones in quasistatic granular chute flows, Physical Review E, vol.53, issue.1, pp.552-561, 1996.
DOI : 10.1103/PhysRevE.53.552

O. Pouliquen and N. Renaut, Onset of granular flows on an onclined rough surface: dilatancy effect, J. Phys. II, vol.6, pp.923-935, 1996.

O. Pouliquen, J. Delour, and S. B. Savage, Fingering in granular flows, Nature, vol.386, issue.6627, pp.816-817, 1997.
DOI : 10.1038/386816a0

O. Pouliquen, Scaling laws in granular flows down rough inclined planes, Physics of Fluids, vol.11, issue.3, pp.542-548, 1999.
DOI : 10.1063/1.869928

O. Pouliquen, On the shape of granular fronts down rough inclined planes, Physics of Fluids, vol.11, issue.7, pp.1956-1958, 1999.
DOI : 10.1063/1.870057

O. Pouliquen, Y. Forterre, and S. Ledizes, SLOW DENSE GRANULAR FLOWS AS A SELF-INDUCED PROCESS, Advances in Complex Systems, vol.04, issue.04, pp.441-450, 2001.
DOI : 10.1142/S0219525901000358

URL : https://hal.archives-ouvertes.fr/hal-01432239

O. Pouliquen and Y. Forterre, Friction law for dense granular flows: application to the motion of a mass down a rough inclined plane, Journal of Fluid Mechanics, vol.453, pp.133-151, 2002.
DOI : 10.1017/S0022112001006796

URL : https://hal.archives-ouvertes.fr/hal-00135182

O. Pouliquen and F. Chevoir, Dense flows of dry granular material, Comptes Rendus Physique, vol.3, issue.2, pp.163-175, 2002.
DOI : 10.1016/S1631-0705(02)01309-9

S. N. Prasad, D. Pal, and M. J. Römkens, Wave formation on a shallow layer of flowing grains, Journal of Fluid Mechanics, vol.413, pp.89-110, 2000.
DOI : 10.1017/S0022112000008296

M. Prochnow, F. Chevoir, and M. Albertelli, Dense granular flows down a rough inclined plane, Proceedings, XIIIth Internationnal Congress on rheology, 2000.

F. Radjai, E. W. Dietrich, M. Jean, and J. Moreau, Bimodal Character of Stress Transmission in Granular Packings, Bimodal character of stress transmission in granular packings, pp.61-64, 1998.
DOI : 10.1103/PhysRevLett.80.61

URL : https://hal.archives-ouvertes.fr/hal-01407369

R. Ramírez, D. Risso, and P. Cordero, Thermal Convection in Fluidized Granular Systems, Physical Review Letters, vol.85, issue.6, pp.1230-1233, 2000.
DOI : 10.1103/PhysRevLett.85.1230

G. Reydellet, F. Rioul, and E. Clément, Granular hydrodynamics and density wave regimes in a vertical chute experiment, Europhysics Letters (EPL), vol.51, issue.1, pp.27-33, 2000.
DOI : 10.1209/epl/i2000-00333-0

F. Rouyer and N. Menon, Velocity Fluctuations in a Homogeneous 2D Granular Gas in Steady State, Physical Review Letters, vol.85, issue.17, pp.3676-3679, 2000.
DOI : 10.1103/PhysRevLett.85.3676

C. Ruyer-quil, Dynamique d'un film mince s'´ ecoulant le long d'un plan incliné, 1999.

C. Ruyer-quil and P. Manneville, Improved modeling of flows down inclined planes, The European Physical Journal B, vol.15, issue.2, pp.357-369, 2000.
DOI : 10.1007/s100510051137

URL : https://hal.archives-ouvertes.fr/hal-01025361

. De-saint and A. J. Venant, 1871 Théorie du mouvement non-permanent des eaux, avec application aux crues desrivì eres etàet`età l'introduction des marées dans leur lit, C. R. Acad

. Sci, Paris 73, pp.147-154

W. S. Saric, G??rtler Vortices, Görtler vortices, pp.379-409, 1994.
DOI : 10.1146/annurev.fl.26.010194.002115

S. B. Savage and D. J. Jeffrey, The stress tensor in a granular flow at high shear rates, Journal of Fluid Mechanics, vol.190, issue.-1, pp.255-272, 1981.
DOI : 10.1063/1.1734272

S. B. Savage, FLOW OF GRANULAR MATERIALS, Theoretical and Applied Mechanics, pp.241-266, 1989.
DOI : 10.1016/B978-0-444-87302-6.50022-3

S. B. Savage and K. Hutter, The motion of a finite mass of granular material down a rough incline, Journal of Fluid Mechanics, vol.196, issue.-1, pp.177-215, 0199.
DOI : 10.1007/BF01180101

S. B. Savage, Instability of unbounded uniform granular shear flow, Journal of Fluid Mechanics, vol.176, issue.-1, pp.109-123, 1992.
DOI : 10.1007/BF00250919

S. B. Savage, Analysis of slow high-concentration flows of granular materials, J, 1998.

N. Sela and I. Goldhirsch, Hydrodynamic equations for rapid flows of smooth inelastic spheres, to Burnett order, Journal of Fluid Mechanics, vol.361, pp.41-74, 1998.
DOI : 10.1017/S0022112098008660

A. Q. Shen, Granular fingering patterns in horizontal rotating cylinders, Physics of Fluids, vol.14, issue.2, pp.462-470, 2002.
DOI : 10.1063/1.1428748

L. E. Silbert, D. Ertas, G. S. Grest, T. C. Halsey, D. Levine et al., Granular flow down an inclined plane: Bagnold scaling and rheology, Physical Review E, vol.64, issue.5, p.12501, 2001.
DOI : 10.1103/PhysRevE.64.051302

URL : http://arxiv.org/abs/cond-mat/0105071

M. K. Smith, The mechanism for the long-wave instability in thin liquid films, Journal of Fluid Mechanics, vol.40, issue.-1, 1990.
DOI : 10.1063/1.857420

E. M. Sparrow and R. B. Husar, Longitudinal vortices in natural convection flow on inclined plates, Journal of Fluid Mechanics, vol.29, issue.02, pp.251-255
DOI : 10.1021/ja01871a511

A. Susuki and T. Tanaka, Measurement of Flow Properties of Powders along an Inclined Plane, Industrial & Engineering Chemistry Fundamentals, vol.10, issue.1, pp.84-91, 1971.
DOI : 10.1021/i160037a015

M. Tan and I. Goldhirsch, Rapid Granular Flows as Mesoscopic Systems, Physical Review Letters, vol.81, issue.14, 1999.
DOI : 10.1103/PhysRevLett.81.3022

P. B. Umbanhowar, F. Melo, and H. L. Swinney, Localized excitations in a vertically vibrated granular layer, Nature, vol.382, issue.6594, pp.793-796, 1996.
DOI : 10.1038/382793a0

J. W. Vallance, Experimental and field studies related to the behavior of granular mass flows and the characteristics of their deposits, 1994.

O. R. Walton, Numerical simulations of inelastic frictional particule-particule interactions . in Particulate Txo-phase Flow, Part I, pp.884-911, 1992.

C. Wang, R. Jackson, and S. Sundaresan, Stability of bounded rapid shear flows of a granular material, Journal of Fluid Mechanics, vol.171, issue.-1, pp.31-62, 1996.
DOI : 10.1063/1.857863

C. Wang, R. Jackson, and S. Sundaresan, Instabilities of fully developed rapid flow of a granular material in a channel, Journal of Fluid Mechanics, vol.342, pp.179-197, 1997.
DOI : 10.1017/S0022112097005648

S. Warr, J. M. Huntley, and G. T. Jacques, Fluidization of a two-dimensional granular system: Experimental study and scaling behavior, Physical Review E, vol.52, issue.5, pp.5583-5595, 1995.
DOI : 10.1103/PhysRevE.52.5583

H. A. Weaver and L. Danly, Formation and evolution of planetary systems Cambridge, 1989.

R. D. Wildman, J. M. Huntley, and D. J. Parker, Convection in Highly Fluidized Three-Dimensional Granular Beds, Physical Review Letters, vol.86, issue.15, pp.3304-3307, 2001.
DOI : 10.1103/PhysRevLett.86.3304

R. D. Wildman, J. M. Huntley, and D. J. Parker, Granular temperature profiles in three-dimensional vibrofluidized granular beds, Physical Review E, vol.63, issue.6, p.61311, 2001.
DOI : 10.1103/PhysRevE.63.061311