Hostname: page-component-78c5997874-ndw9j Total loading time: 0 Render date: 2024-11-14T17:38:39.198Z Has data issue: false hasContentIssue false
  • English
  • Français

Depth-integrated equations for entraining granular flows in narrow channels

Published online by Cambridge University Press:  30 January 2015

H. Capart ,
C.-Y. Hung  and
C. P. Stark
H. Capart*
Affiliation:
Department of Civil Engineering and Hydrotech Research Institute, National Taiwan University, Taipei 106, Taiwan
C.-Y. Hung
Affiliation:
Department of Civil Engineering and Hydrotech Research Institute, National Taiwan University, Taipei 106, Taiwan Lamont-Doherty Earth Observatory of Columbia University, Palisades, New York, USA
C. P. Stark
Affiliation:
Lamont-Doherty Earth Observatory of Columbia University, Palisades, New York, USA
*
†Email address for correspondence: hcapart@yahoo.com
Get access Rights & Permissions [Opens in a new window]

Abstract

Flowing over erodible beds, channelized granular avalanches can alter their volume by entraining or detraining basal grains. In detail, entrainment results from a gradual adjustment of stress and velocity profiles over depth, bringing bed material past yield (and vice versa for detrainment). To capture this process, we propose new depth-integrated equations that balance kinetic energy in addition to mass and momentum. The equations require a local granular rheology, assumed viscoplastic, but no extra erosion law. Entrainment rates are instead deduced from the depth-integrated layer dynamics. To check the approach, we obtain solutions for non-equilibrium heap flows, and compare them with experiments conducted in a seesaw channel.

JFM classification

Waves/Free-surface Flows: Channel flow Granular media: Granular media
Type
Rapids
Information
Journal of Fluid Mechanics , Volume 765 , 25 February 2015 , R4
Check for updates
Copyright
© 2015 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Berzi, D. & Jenkins, J. T. 2008 A theoretical analysis of free-surface flows of saturated granular–liquid mixtures. J. Fluid Mech. 608, 393–410.CrossRefGoogle Scholar
Capart, H., Young, D. L. & Zech, Y. 2002 Voronoï imaging methods for the measurement of granular flows. Exp. Fluids 32, 121–135.CrossRefGoogle Scholar
Chen, H., Crosta, G. B. & Lee, C. F. 2006 Erosion effects on runout of fast landslides, debris flows and avalanches: a numerical investigation. Géotechnique 56, 305–322.CrossRefGoogle Scholar
Chou, H. T., Lee, C. F., Chung, Y. C. & Hsiau, S. S. 2012 Discrete element modelling and experimental validation for the falling process of dry granular steps. Powder Technol. 231, 122–134.Google Scholar
da 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 ScholarPubMed
Gray, J. M. N. T. 2001 Granular flow in partially filled slowly rotating drums. J. Fluid Mech. 441, 1–29.CrossRefGoogle Scholar
Gray, J. M. N. T. & Edwards, A. N. 2014 A depth-averaged ${\it\mu}(I)$ -rheology for shallow granular free-surface flows. J. Fluid Mech. 755, 503–534.CrossRefGoogle Scholar
Henann, D. L. & Kamrin, K. 2013 A predictive, size-dependent continuum model for dense granular flows. Proc. Natl Acad. Sci. USA 110, 6730–6735.CrossRefGoogle ScholarPubMed
Ionescu, I., Mangeney, A., Bouchut, F. & Roche, O.2014 Viscoplastic modelling of granular column collapse with pressure dependent rheology. Available at: https://tel.archives-ouvertes.fr/hal-01080456/document.CrossRefGoogle Scholar
Iverson, R. M. 2012 Elementary theory of bed-sediment entrainment by debris flows and avalanches. J. Geophys. Res. 117, F03006.Google Scholar
Jop, P., Forterre, Y. & Pouliquen, O. 2005 Crucial role of sidewalls in granular surface flows: consequences for the rheology. J. Fluid Mech. 541, 167–192.CrossRefGoogle Scholar
Jop, P., Forterre, Y. & Pouliquen, O. 2007 Initiation of granular surface flows in a narrow channel. Phys. Fluids 19, 088102.CrossRefGoogle Scholar
Kamrin, K. 2010 Nonlinear elasto-plastic model for dense granular flow. Int. J. Plast. 26, 167–188.CrossRefGoogle Scholar
Komatsu, T. S., Inagaki, S., Nakagawa, N. & Nasuno, S. 2001 Creep motion in a granular pile exhibiting steady surface flow. Phys. Rev. Lett. 86, 1757–1760.CrossRefGoogle Scholar
Lagrée, P.-Y., Staron, L. & Popinet, S. 2011 The granular column collapse as a continuum: validity of a two-dimensional Navier–Stokes model with a ${\it\mu}(I)$ -rheology. J. Fluid Mech. 686, 378–408.CrossRefGoogle Scholar
Lê, L. & Pitman, E. B. 2010 A model for granular flows over an erodible surface. SIAM J. Appl. Maths 70, 1407–1427.CrossRefGoogle Scholar
Liggett, J. A. 1994 Fluid Mechanics. McGraw-Hill.Google Scholar
Lube, G., Huppert, H. E., Sparks, R. S. & Freundt, A. 2007 Static and flowing regions in granular collapses down channels. Phys. Fluids 19, 043301.CrossRefGoogle Scholar
Mangeney, A., Roche, O., Hungr, O., Mangold, N., Faccanoni, G. & Lucas, A. 2010 Erosion and mobility in granular collapse over sloping beds. J. Geophys. Res. 115, F03040.Google Scholar
Richard, G. L. & Gavrilyuk, S. L. 2013 The classical hydraulic jump in a model of shear shallow-water flows. J. Fluid Mech. 725, 492–521.CrossRefGoogle Scholar
Savage, S. B. & Hutter, K. 1991 The dynamics of avalanches of granular materials from initiation to run-out. Acta Mechanica 86, 201–223.CrossRefGoogle Scholar
Steffler, P. M. & Jin, Y.-C. 1993 Depth averaged and moment equations for moderately shallow free surface flow. J. Hydraul. Res. 31, 5–17.CrossRefGoogle Scholar
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
Tai, Y. C. & Kuo, C. Y. 2008 A new model of granular flows over general topography with erosion and deposition. Acta Mechanica 199, 71–96.CrossRefGoogle Scholar
Takahashi, T. 1991 Debris Flow. IAHR/Balkema.Google Scholar
Tsubaki, T., Hashimoto, H. & Suetsugi, T. 1982 Grain stresses and flow properties of debris flow. Proc. Japan. Soc. Civ. Engrs 317, 79–91.CrossRefGoogle Scholar