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Granular column collapses down rough, inclined channels

Published online by Cambridge University Press:  04 April 2011

GERT LUBE ,
HERBERT E. HUPPERT ,
R. STEPHEN J. SPARKS  and
ARMIN FREUNDT
GERT LUBE
Affiliation:
Volcanic Risk Solutions, Massey University, Palmerston North, Private Bag 11222, New Zealand
HERBERT E. HUPPERT*
Affiliation:
Department of Applied Mathematics and Theoretical Physics, Institute of Theoretical Geophysics, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK
R. STEPHEN J. SPARKS
Affiliation:
Department of Earth Sciences, Centre of Environmental and Geophysical Flows, Bristol University, Bristol BS8 1RJ, UK
ARMIN FREUNDT
Affiliation:
Research Division ‘Dynamics of the Ocean Floor,’ IFM-GEOMAR, Leibniz Institute for Marine Sciences, Wischhofstrasse 1-3, D-24148 Kiel, Germany
*
†Email address for correspondence: heh1@esc.cam.ac.uk
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Abstract

We present experimental results for the collapse of rectangular columns of sand down rough, inclined, parallel-walled channels. Results for basal inclination θ varying between 4.2° and 25° are compared with previous results for horizontal channels. Shallow-water theory can be usefully combined with scaling relationships obtained by dimensional analysis to yield analytical functions of the maximum runout distance, the maximum deposit height and the time to reach the maximum runout. While the theory excellently predicts the maximum lengths of the deposit it generally overestimates the runout time. The inertial flows are characterized by a moving internal interface separating upper flowing and lower static regions of material. In an initial free-fall phase of collapse the deposited area (= volume per unit width) below the internal interface varies with the square-root of time, independent of the initial height of the column and channel inclination. In the subsequent, lateral spreading phase the deposition rate decreases with increasing basal inclination or with decreasing initial height. The local deposition rate at any fixed distance is a constant, dependent on the column aspect ratio, the channel inclination and the longitudinal position, but invariant with flow velocity and depth. In the lateral spreading phase, vertical velocity profile in the flowing layer take a universal form and are independent of flow depth and velocity. They can be characterized by a shear rate as a function of channel inclination and a length scale describing the fraction of the column involved in flow.

JFM classification

Granular media: Granular media
Type
Papers
Information
Journal of Fluid Mechanics , Volume 675 , 25 May 2011 , pp. 347 - 368
Copyright
Copyright © Cambridge University Press 2011

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References

REFERENCES

Balmforth, N. J. & Kerswell, R. R. 2005 Granular collapses in two dimensions. J. Fluid Mech. 538, 399–428.CrossRefGoogle Scholar
Dalziel, S. B. 2005 DigiFlow User Guide. Available at: http://www.damtp.cam.ac.uk/lab/digiflow/.Google Scholar
Doyle, E. E., Huppert, H. E., Lube, G., Mader, H. M. & Sparks, R. S. J. 2007 Static and flowing regions in granular column collapses down channels: insights from a sedimenting shallow water model. Phys. Fluids 19, 106601, 1–16.CrossRefGoogle Scholar
Midi, G.D.R. 2004 On dense granular flows. Eur. Phys. J. E 14, 341.CrossRefGoogle Scholar
Gauer, P., Rammer, L, Kern, M., Lied, K., Kristensen, K. & Schreiber, H. 2006 On pulsed Doppler radar measurements of avalanches and their implication to avalanche dynamics. Geophys. Res. Abstracts 8, 04683.Google Scholar
Huppert, H. E., Hallworth, M. A., Lube, G. & Sparks, R. S. J. 2003 Granular column collapses. Bull. Am. Phys. Soc. 48, 68.Google Scholar
Huppert, H. E., Lube, G., Sparks, R. S. J. & Hallworth, M. A. 2004 In Granular Column Collapse. ICTAM Proceedings. Kluwer.Google Scholar
Hutter, K., Koch, T., Pluss, C. & Savage, S. B. 1995 The dynamics of avalanches of granular materials from initiation to runout. Part II. Experiments. Acta Mech. 109, 127.CrossRefGoogle Scholar
Kerswell, R. R. 2005 Dam break with Coulomb friction: a model for granular slumping? Phys. Fluids 17, 057101, 1–16.CrossRefGoogle Scholar
Lajeunesse, E., Mangeney-Castelnau, A. & Vilotte, J. P. 2004 Spreading of a granular mass on a horizontal plane. Phys. Fluids 16, 2371–2381.CrossRefGoogle Scholar
Lajeunesse, E., Monnier, J. B. & Homsy, G. M. 2005 Granular slumping on a horizontal surface. Phys. Fluids 17, 103302.CrossRefGoogle Scholar
Larrieu, E., Staron, L. & Hinch, E. J. 2006 Raining into shallow water as a description of the collapse of a column of grains. J. Fluid Mech. 554, 259–270.CrossRefGoogle Scholar
Lube, G., Huppert, H. E., Sparks, R. S. J. & Freundt, A. 2005 Collapses of two-dimensional granular columns. Phys. Rev. E 72, 041301, 1–10.CrossRefGoogle ScholarPubMed
Lube, G., Huppert, H. E., Sparks, R. S. J. & Freundt, A. 2007 Static and flowing regions in granular column collapses down channels. Phys. Fluids 19, 043301, 1–9.CrossRefGoogle Scholar
Lube, G., Huppert, H. E., Sparks, R. S. J. & Hallworth, M. A. 2004 Axisymmetric collapses of granular columns. J. Fluid Mech. 508, 175–199.CrossRefGoogle Scholar
Mangeney, A., Heinrich, P. & Roche, R. 2000 Analytical solution for testing debris avalanche numerical models. Pure Appl. Geophys. 157, 1081–1096.CrossRefGoogle Scholar
Mangeney-Castelnau, A., Bouchut, B., Vilotte, J. P., Lajeunesse, E., Aubertin, A., & Pirulli, M. 2005 On the use of Saint–Venant equations for simulating the spreading of a granular mass. J. Geophys. Res. 110, B09103, 1–17.CrossRefGoogle Scholar
Pouliquen, O. 1999 Scaling laws in granular flows down rough inclined planes. Phys. Fluids 11, 542.CrossRefGoogle Scholar
Pouliquen, O. & Forterre, Y. 2002 Friction law for dense granular flows: application to the motion of a mass down a rough inclined plane. J. Fluid Mech. 453, 131.CrossRefGoogle Scholar
Savage, S.B. & Hutter, K. 1989 The motion of a finite mass of granular material down a rough incline. J. Fluid Mech. 199, 177.CrossRefGoogle Scholar
Siavoshi, S. & Kudrolli, A. 2005 Failure of a granular step. Phys. Rev. E 71, 051302, 1–6.Google ScholarPubMed
Staron, L. & Hinch, E. J. 2005 Study of the collapse of granular columns using 2D discrete grains simulation. J. Fluid Mech. 545, 1–27.CrossRefGoogle Scholar
Thompson, E. L. & Huppert, H. E. 2007 Granular column collapses: further experimental results. J. Fluid Mech. 575, 177–186.CrossRefGoogle Scholar
Zenit, R. 2005 Computer simulations of the collapse of a granular column. Phys. Fluids 17, 031703, 1–4.CrossRefGoogle Scholar