Hostname: page-component-77c89778f8-sh8wx Total loading time: 0 Render date: 2024-07-17T04:56:49.276Z Has data issue: false hasContentIssue false
  • English
  • Français

Intense bed-load due to a sudden dam-break

Published online by Cambridge University Press:  23 August 2013

Benoit Spinewine  and
Hervé Capart
Benoit Spinewine
Affiliation:
Fonds National de la Recherche Scientifique and Institute of Mechanics, Materials and Civil Engineering, Université catholique de Louvain, Belgium
Hervé Capart*
Affiliation:
Department of Civil Engineering and Hydrotech Research Institute, National Taiwan University, Taiwan
*
†Email address for correspondence: hcapart@yahoo.com
Get access Rights & Permissions [Opens in a new window]

Abstract

Intense bed-load, or sheet flow, occurs when a free-surface flow of water drives a thick, rapidly sheared layer of water and grains over an erodible granular bed. We examine here the transient case where flow is induced by a sudden dam-break. Aiming for greater detail than achieved previously, we investigate this case using experiment and theory. The experiments combine particle tracking velocimetry (PTV) with a novel method of concentration measurement based on recording the penetration depth of a laser light sheet. The theory incorporates more vertical detail into the shallow water equations by using piecewise linear profiles of velocity and granular concentration, constrained by constitutive relations proposed recently for intense bed-load. These relations account for Coulomb yield at the bed, immersed granular collisions at the base, and equilibration of shear rate and density stratification across the bed-load layer. Using these approaches, both experiment and theory yield time- and depth-resolved profiles of velocity and granular concentration in addition to longitudinal wave profiles. Without any parameter adjustment, the theoretical predictions are in good agreement with the experimental measurements.

JFM classification

Geophysical and Geological Flows: Geophysical and Geological Flows Geophysical and Geological Flows: Sediment transport Geophysical and Geological Flows: Shallow water flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 731 , 25 September 2013 , pp. 579 - 614
Copyright
©2013 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.)

Footnotes

‡

Current affiliation: Fugro GeoConsulting, Brussels, Belgium.

References

Armanini, A., Capart, H., Fraccarollo, L. & Larcher, M. 2005 Rheological stratification in experimental free-surface flows of granular–liquid mixtures. J. Fluid Mech. 532, 269–319.Google Scholar
Asano, T. 1995 Sediment transport under sheet-flow conditions. J. Waterways Port Coast. Ocean Engng ASCE 121 (5), 239–246.Google Scholar
Bagnold, R. A. 1956 The flow of cohesionless grains in fluids. Trans. R. Soc. Lond. A 249, 235–297.Google Scholar
Batchelor, G. K. 1988 A new theory of the instability of a uniform fluidized bed. J. Fluid Mech. 193, 75–110.Google Scholar
Berzi, D. 2011 Analytical solution of collisional sheet flows. J. Hydraul. Engng ASCE 137 (10), 1200–1207.Google Scholar
Berzi, D. & Jenkins, J. T. 2008 Approximate analytical solutions in a model for highly concentrated granular–fluid flows. Phys. Rev. E 78, 011304.Google Scholar
Calantoni, J. & Puleo, J. A. 2006 Role of pressure gradients in sheet flow of coarse sediments under sawtooth waves. J. Geophys. Res. 111, C01010.Google Scholar
Cao, Z., Pender, G., Wallis, S. & Carling, P. 2004 Computational dam-break hydraulics over erodible sediment bed. J. Hydraul. Engng ASCE 130 (7), 689–703.Google Scholar
Capart, H. & Fraccarollo, L. 2011 Transport layer structure in intense bed-load. Geophys. Res. Lett. 38, L20402.CrossRefGoogle Scholar
Capart, H. & Young, D. L. 1998 Formation of a jump by the dam-break wave over a granular bed. J. Fluid Mech. 372, 165–187.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
Carrivick, J. L., Jones, R. & Keevil, G. 2011 Experimental insights on geomorphological processes within dam break outburst floods. J. Hydrol. 408, 151–163.Google Scholar
Du Boys, D. 1879 Le Rhône et les rivières à lit affouillable. Ann. Ponts Chaussées 5 (18), 141–195.Google Scholar
Einstein, H. A. 1950 The bed-load function for sediment transportation in open-channels. US Dept. of Agriculture Tech. Bull. 1026.Google Scholar
El Kadi Abderrezzak, K. & Paquier, A. 2011 Applicability of sediment transport capacity formulas to dam-break flows over movable beds. J. Hydraul. Engng ASCE 137 (2), 209–221.Google Scholar
Ellison, T. H. & Turner, J. S. 1959 Turbulent entrainment in stratified fluids. J. Fluid Mech. 6, 423–448.Google Scholar
Ferreira, R. M. L., Franca, M. J., Leal, J. G. A. B. & Cardoso, A. H. 2009 Mathematical modeling of shallow flows: closure models drawn from grain-scale mechanics of sediment transport and flow hydrodynamics. Can. J. Civ. Engng 36, 1605–1621.Google Scholar
Fraccarollo, L. & Capart, H. 2002 Riemann wave description of erosional dam-break flows. J. Fluid Mech. 461, 183–228.Google Scholar
Fraccarollo, L., Capart, H. & Zech, Y. 2003 A Godunov method for the computation of erosional shallow water transients. Intl J. Numer. Meth. Fluids 41, 951–976.CrossRefGoogle Scholar
Fraccarollo, L. & Marion, A. 1995 Statistical approach to bed-material surface sampling. J. Hydraul. Engng 121, 540–545.CrossRefGoogle Scholar
Frey, P. & Church, M. 2009 How river beds move. Science 325, 1509–1510.Google Scholar
Goutière, L., Soares-Frazão, S. & Zech, Y. 2011 Dam-break flow on mobile bed in abruptly widening channel: experimental data. J. Hydraul. Res. 49 (3), 367–371.CrossRefGoogle Scholar
Greco, M., Iervolino, M., Leopardi, A. & Vacca, A. 2012 A two-phase model for fast geomorphic shallow flows. Intl J. Sedim. Res. 27, 409–425.Google Scholar
Hanes, D. M. & Bowen, A. J. 1985 A granular–fluid model for steady intense bed-load transport. J. Geophys. Res. 90 (C5), 9149–9158.Google Scholar
Hsu, J. P. C. & Capart, H. 2008 Onset and growth of tributary-dammed lakes. Water Resour. Res. 44, W11201.CrossRefGoogle Scholar
Huang, M. Y. F., Huang, A. Y. L., Chen, R. H. & Capart, H. 2009 Automated tracking of liquid velocities in a refractive index matched porous medium. J. Chin. Inst. Engrs 32 (6), 877–882.CrossRefGoogle Scholar
Jenkins, J. T. & Hanes, D. M. 1998 Collisional sheet flows of sediment driven by a turbulent fluid. J. Fluid Mech. 370, 29–52.Google Scholar
Jop, P., Forterre, Y. & Pouliquen, O. 2006 A constitutive law for dense granular flows. Nature 441, 727–730.Google Scholar
Larcher, M., Fraccarollo, L., Armanini, A. & Capart, H. 2007 Set of measurement data from flume experiments on steady uniform debris flows. J. Hydraul. Res. 45 (Special Issue), 59–71.Google Scholar
Leal, J. G. A. B., Ferreira, R. M. L. & Cardoso, A. H. 2006 Dam-break wave-front celerity. J. Hydraul. Engng ASCE 132 (1), 69–76.Google Scholar
Leal, J. G. A. B., Ferreira, R. M. L. & Cardoso, A. H. 2009 Maximum level and time to peak of dam-break waves on mobile horizontal bed. J. Hydraul. Engng ASCE 135 (11), 995–999.CrossRefGoogle Scholar
Leal, J. G. A. B., Ferreira, R. M. L. & Cardoso, A. H. 2010 Geomorphic dam-break flows. Part II: numerical simulation. Proc. Inst. Civil Engrs – Water Mgmt 163 (6), 305–313.CrossRefGoogle Scholar
Li, S. C. & Duffy, C. J. 2011 Fully coupled approach to modeling shallow water flow, sediment transport, and bed evolution in rivers. Water Resour. Res. 47, W03508.Google Scholar
Liggett, J. A. 1994 Fluid Mechanics. McGraw-Hill.Google Scholar
Matoušek, V. 2009 Concentration profiles and solids transport above stationary deposit in enclosed conduit. J. Hydraul. Engng ASCE 135, 1101–1106.Google Scholar
Meyer-Peter, E. & Müller, R. 1948 Formulas for bedload transport. In Proceedings, 2nd Congress of the International Association for Hydraulic Research, Stockholm, pp. 39–64. International Association for Hydraulic Research.Google Scholar
Ni, W. J. & Capart, H. 2006 Groundwater drainage and recharge by networks of irregular channels. J. Geophys. Res.: Earth Surface 111, F02014.Google Scholar
Postacchini, M., Brocchini, M., Mancinelli, A. & Landon, A. 2012 A multi-purpose, intra-wave, shallow water hydro-morphodynamic solver. Adv. Water Resour. 38, 13–26.Google Scholar
Pugh, F. J. & Wilson, K. C. 1999 Velocity and concentration distributions in sheet flow above plane beds. J. Hydraul. Engng ASCE 125 (2), 117–125.CrossRefGoogle Scholar
Savage, S. B. & Jeffrey, D. J. 1981 The stress tensor in a granular flow at high shear rates. J. Fluid Mech. 110, 255–272.Google Scholar
Serrano-Pacheco, A., Murillo, J. & Garcia-Navarro, P. 2012 Finite volumes for 2D shallow water flow with bed-load transport on unstructured grids. J. Hydraul. Res. 50 (2), 154–163.CrossRefGoogle Scholar
Spinewine, B. 2005 Two-layer flow behaviour and the effects of granular dilatancy in dam-break induced sheet-flow. PhD thesis, Université catholique de Louvain, Belgium.Google Scholar
Spinewine, B., Capart, H., Fraccarollo, L. & Larcher, M. 2011 Laser stripe measurements of near-wall solid fraction in channel flows of liquid-granular mixtures. Exp. Fluids 50 (6), 1507–1525.CrossRefGoogle Scholar
Spinewine, B., Aleixo, R. & Capart, H. 2011a Velocity and concentration profiles within dam-break-induced intense bedload layers. Thesis 2011 Symposium on Two-Phase Modelling for Sediment Dynamics, Chatou, France, 26–28 April 2011.Google Scholar
Spinewine, B., Aleixo, R. & Capart, H. 2011b Intense bedload associated with unsteady dam-break surges. RCEM 2011 Conference on River Coastal and Estuarine Morphodynamics, Beijing, China, September 2011.Google Scholar
Spinewine, B. & Zech, Y. 2007 Small-scale laboratory dam-break waves on movable beds. J. Hydraul. Res. 45 (Extra Issue), 73–86.Google Scholar
Spinewine, B., Capart, H., Larcher, M. & Zech, Y. 2003 Three-dimensional Voronoï imaging methods for the measurement of near-wall particulate flows. Exp. Fluids 34, 227–241.Google Scholar
Sumer, B. M., Kozakiewicz, A., Fredsøe, J. & Deigaard, R. 1996 Velocity and concentration profiles in sheet-flow layer of movable bed. J. Hydraul. Engng ASCE 122 (10), 549–558.Google Scholar
Swartenbroekx, C., Zech, Y. & Soares-Frazão, S. 2013 Two-dimensional two-layer shallow water model for dam break flows with significant bed load transport. Intl J. Numer. Meth. Fluids doi:10.1002/fld.3809.Google Scholar
Turner, J. S. 1973 Buoyancy Effects in Fluids. Cambridge University Press.Google Scholar
Wilson, K. C. 1987 Analysis of bed-load motion at high shear stress. J. Hydraul. Engng ASCE 113 (1), 97–103.Google Scholar
Wilson, K. C. 2005 Rapid increase in suspended load at high bed shear. J. Hydraul. Engng ASCE 131 (1), 46–51.Google Scholar
Wu, W. & Wang, S. S. Y. 2007 One-dimensional modeling of dam-break flow over movable beds. J. Hydraul. Engng ASCE 133 (1), 48–58.CrossRefGoogle Scholar
Zhang, S. & Duan, J. G. 2011 1D finite volume model of unsteady flow over mobile bed. J. Hydrol. 405, 57–68.Google Scholar
Zhang, S., Duan, J. G. & Strelkoff, T. S. 2013 Grain-scale nonequilibrium sediment-transport model for unsteady flow. J. Hydraul. Engng ASCE 139 (1), 22–36.Google Scholar