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Relaxation dynamics of water-immersed granular avalanches

Published online by Cambridge University Press:  19 April 2007

DELPHINE DOPPLER ,
PHILIPPE GONDRET ,
THOMAS LOISELEUX ,
SAM MEYER  and
MARC RABAUD
DELPHINE DOPPLER
Affiliation:
Lab FAST, UMR 7608, CNRS, Univ Paris-Sud, Université Pierre et Marie Curie-Paris 6, Bât. 502, F-91405 Orsay, France
PHILIPPE GONDRET
Affiliation:
Lab FAST, UMR 7608, CNRS, Univ Paris-Sud, Université Pierre et Marie Curie-Paris 6, Bât. 502, F-91405 Orsay, France
THOMAS LOISELEUX
Affiliation:
Lab FAST, UMR 7608, CNRS, Univ Paris-Sud, Université Pierre et Marie Curie-Paris 6, Bât. 502, F-91405 Orsay, France Unité de Mécanique, Ecole Nationale Supérieure de Techniques Avancées (ENSTA-ParisTech), 32 Bd Victor, F-75015 Paris, France
SAM MEYER
Affiliation:
Lab FAST, UMR 7608, CNRS, Univ Paris-Sud, Université Pierre et Marie Curie-Paris 6, Bât. 502, F-91405 Orsay, France
MARC RABAUD
Affiliation:
Lab FAST, UMR 7608, CNRS, Univ Paris-Sud, Université Pierre et Marie Curie-Paris 6, Bât. 502, F-91405 Orsay, France
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Abstract

We study water-immersed granular avalanches in a long rectangular cell of small thickness. By video means, both the angle of the granular pile and the velocity profiles of the grains across the depth are recorded as a function of time. These measurements give access to the instantaneous granular flux. By inclining the pile at initial angles larger than the maximum angle of stability, avalanches are triggered and last for a long time, up to several hours for small grains, during which both the slope angle and the granular flux relax slowly. We show that the relaxation is quasi-steady so that there is no inertia: the relaxation at a given time is controlled only by the slope angle at that time. This allows us to adapt a frictional model developed recently for dry or water-immersed grains flowing in stationary conditions. This model succeeds well in reproducing our unsteady avalanche flows, namely the flowing layer thickness, the granular flux and the temporal relaxation of the slope. When a water counter-flow is applied along the pile, the granular avalanches are slowed down and behave as if granular friction were increased by an amount proportional to the water flow. All these findings are also reproduced well with the same friction model by taking into account the additional fluid force.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 577 , 25 April 2007 , pp. 161 - 181
Copyright
Copyright © Cambridge University Press 2007

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References

REFERENCES

Allen, J. R. L. 1970 The avalanching of granular solids on dune and similar slopes. J. Geol. 78, 326–351.CrossRefGoogle Scholar
Andreotti, B. & Douady, S. 2001 Selection of velocity profile and flow depth in granular flows. Phys. Rev. E 63, 031305.Google ScholarPubMed
Armanini, A., Capart, H., Fraccarollo, L. & Larcherm, M. 2005 Rheological stratification in experimental free-surface flows of granular liquid mixtures. J. Fluid Mech. 532, 269–319.CrossRefGoogle Scholar
Beavers, G. S. & Joseph, D. D. 1967 Boundary conditions at a naturally permeable wall. J. Fluid Mech. 30, 197–207.CrossRefGoogle Scholar
Bonamy, D., Daviaud, F. & Laurent, L. 2002 Experimental study of granular flows via a fast camera: a continuous description. Phys. Fluids 14, 1666–1673.CrossRefGoogle Scholar
Carrigy, M. A. 1970 Experiments on the angles of repose of granular materials. Sedimentology 14, 147–158.CrossRefGoogle Scholar
Cassar, C. 2005 Etude expérimentale des écoulements granulaires immergés. PhD thesis, Université de Provence.Google Scholar
Cassar, C., Nicolas, M. & Pouliquen, O. 2005 Submarine granular flows down inclined planes. Phys. Fluids 17, 103301.CrossRefGoogle Scholar
Courrech, S., Fischer, R., Gondret, P., Perrin, B. & Rabaud, M. 2005 Instantaneous velocity profile during granular avalanches. Phys. Rev Lett. 94, 048003.CrossRefGoogle Scholar
Courrechdu Pont, S. du Pont, S., Gondret, P., Perrin, B. & Rabaud, M. 2003 a Granular avalanches in fluids. Phys. Rev. Lett. 90, 044301.CrossRefGoogle Scholar
Courrechdu Pont, S. du Pont, S., Gondret, P., Perrin, B. & Rabaud, M. 2003 b Wall effects on granular heap stability. Europhys. Lett. 61, 492–498.Google Scholar
daCruz, F. Cruz, F., Emam, S., Prochnow, M., Roux, J.-N. & Chevoir, F. 2005 Rheophysics of dense granular materials: Discrete simulation of plane shear flows. Phys. Rev. E 72, 021309.Google Scholar
Davis, R. H., Serayssol, J.-M. & Hinch, E. J. 1986 The elastohydrodynamic collision of two spheres. J. Fluid Mech. 163, 479–497.CrossRefGoogle Scholar
Doppler, D. 2005 Stabilité et dynamique de pentes granulaires sous-marines. PhD thesis, Université Paris Sud-11.Google Scholar
GDR MiDi 2004 On dense granular flows. Eur. Phys. J. E 14, 341–365.Google Scholar
Gondret, P., Lance, M. & Petit, L. 2002 Bouncing motion of spherical particles in fluids. Phys. Fluids 14, 643–652.CrossRefGoogle Scholar
Gondret, P., Rakotomalala, N., Rabaud, M., Salin, D. & Watzky, P. 1997 Viscous parallel flows in finite aspect ratio Hele-Shaw cell: analytical and numerical results. Phys. Fluids 9, 1841–1843.CrossRefGoogle Scholar
Hunter, R. E. 1985 Subaqueous sand flow cross-strata. J. Sedimentary Petrol. 55, 886–894.Google Scholar
Jain, N., Ottino, J. & Lueptow, R. M. 2004 Effect of interstitial fluid on a granular flowing layer. J. Fluid Mech. 508, 23–44.CrossRefGoogle Scholar
Jop, P., Forterre, Y. & Pouliquen, O. 2005 Crucial role of side walls for granular surface flows: consequences for the rheology. J. Fluid Mech. 541, 167–192.CrossRefGoogle Scholar
Joseph, G. G., Zenit, R., Hunt, M. L. & Rosenwinkel, A. M. 2001 Particle-wall collisons in a viscous fluid. J. Fluid Mech. 433, 329–346.CrossRefGoogle Scholar
Josserand, C., Lagree, P. & Lhuillier, D. 2004 Stationary shear flows of dense granular materials: a tentative continuum modelling. Eur. Phys. J. E 14, 127–135.Google ScholarPubMed
Loiseleux, T., Gondret, P., Rabaud, M. & Doppler, D. 2005 Onset of erosion and avalanche for an inclined granular bed sheared by a continuous laminar flow. Phys. Fluids 17, 103304.CrossRefGoogle Scholar
Lueptow, R. M., Akonur, A. & Shinbrot, T. 1999 PIV for granular flows. Exps. Fluids 28, 183–186.CrossRefGoogle Scholar
Mills, P., Loggia, D. & Texier, M. 1999 Model for stationary dense granular flow along an inclined wall. Europhys. Lett. 45, 733–738.CrossRefGoogle Scholar
Rajchenbach, J. 2003 Dense, rapid flows of inelastic grains under gravity. Phys. Rev. Lett. 90, 144302.CrossRefGoogle ScholarPubMed
Taberlet, N., Richard, P., Valance, A., Losert, W., Pasini, J. M., Jenkins, J. T. & Delannay, R. 2003 Superstable granular heap in a thin channel. Phys. Rev. Lett. 91, 264301.CrossRefGoogle Scholar