Hostname: page-component-78c5997874-mlc7c Total loading time: 0 Render date: 2024-11-10T04:01:13.338Z Has data issue: false hasContentIssue false
  • English
  • Français

Revisiting slope influence in turbulent bedload transport: consequences for vertical flow structure and transport rate scaling

Published online by Cambridge University Press:  25 January 2018

Raphael Maurin Open the ORCID record for Raphael Maurin [Opens in a new window] ,
Julien Chauchat Open the ORCID record for Julien Chauchat [Opens in a new window]  and
Philippe Frey
Raphael Maurin*
Affiliation:
Institut de Mécanique des Fluides de Toulouse (IMFT), Université de Toulouse, CNRS, F-31400 Toulouse, France
Julien Chauchat
Affiliation:
CNRS, UMR 5519, LEGI, F-38000 Grenoble, France Univ. Grenoble Alpes, LEGI, F-38000 Grenoble, France
Philippe Frey
Affiliation:
Univ. Grenoble Alpes, Irstea, UR ETGR, 2 rue de la Papeterie-BP 76, F-38402 St-Martin-d’Hères, France
*
†Email address for correspondence: raphael.maurin@imft.fr
Get access Rights & Permissions [Opens in a new window]

Abstract

Gravity-driven turbulent bedload transport has been extensively studied over the past century in regard to its importance for Earth surface processes such as natural riverbed morphological evolution. In the present contribution, the influence of the longitudinal channel inclination angle on gravity-driven turbulent bedload transport is studied in an idealised framework considering steady and uniform flow conditions. From an analytical analysis based on the two-phase continuous equations, it is shown that: (i) the classical slope correction of the critical Shields number is based on an erroneous formulation of the buoyancy force, (ii) the influence of the slope is not restricted to the critical Shields number but affects the whole transport formula and (iii) pressure-driven and gravity-driven turbulent bedload transport are not equivalent from the slope influence standpoint. Analysing further the granular flow driving mechanisms, the longitudinal slope is shown to not only influence the fluid bed shear stress and the resistance of the granular bed, but also to affect the fluid flow inside the granular bed – responsible for the transition from bedload transport to debris flow. The relative influence of these coupled mechanisms allows us to understand the evolution of the vertical structure of the granular flow and to predict the transport rate scaling law as a function of a rescaled Shields number. The theoretical analysis is validated with coupled fluid–discrete element simulations of idealised gravity-driven turbulent bedload transport, performed over a wide range of Shields number values, density ratios and channel inclination angles. In particular, all the data are shown to collapse onto a master curve when considering the sediment transport rate as a function of the proposed rescaled Shields number.

JFM classification

Granular media: Granular media Multiphase and Particle-laden Flows: Particle/fluid flow Geophysical and Geological Flows: Sediment transport
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 839 , 25 March 2018 , pp. 135 - 156
Copyright
© 2018 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

Since original publication we have corrected the author affiliations by adding affiliation no. 4. See doi:10.1017/jfm.2018.121.

References

Anderson, T. B. & Jackson, R. 1967 Fluid mechanical description of fluidized beds. Equations of motion. Ind. Engng Chem. Fundam. 6 (4), 527–539.CrossRefGoogle Scholar
Andreotti, B., Forterre, Y. & Pouliquen, O. 2013 Granular Media: Between Fluid and Solid. Cambridge University Press.CrossRefGoogle Scholar
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
Armanini, A. & Gregoretti, C. 2005 Incipient sediment motion at high slopes in uniform flow condition. Water Resour. Res. 41 (12), w12431.CrossRefGoogle Scholar
Aussillous, P., Chauchat, J., Pailha, M., Médale, M. & Guazzelli, E. 2013 Investigation of the mobile granular layer in bedload transport by laminar shearing flows. J. Fluid Mech. 736, 594–615.CrossRefGoogle Scholar
Bagnold, R. A. 1956 The flow of cohesionless grains in fluids. Phil. Trans. R. Soc. Lond. A 249, 235–297.Google Scholar
Capart, H. & Fraccarollo, L. 2011 Transport layer structure in intense bed-load. Geophys. Res. Lett. 38 (20), L20402.CrossRefGoogle Scholar
Chauchat, J. 2017 A comprehensive two-phase flow model for unidirectional sheet-flows. J. Hydraul. Res. 0 (0), 1–14.Google Scholar
Cheng, N.-S. & Chen, X. 2014 Slope correction for calculation of bedload sediment transport rates in steep channels. J. Hydraul. Engng 140 (6), 04014018.Google Scholar
Chiew, Y.-M. & Parker, G. 1994 Incipient sediment motion on non-horizontal slopes. J. Hydraul. Res. 32 (5), 649–660.CrossRefGoogle Scholar
Christensen, B. A. 1995 Incipient sediment motion on non-horizontal slopes. J. Hydraul. Res. 33 (5), 725–730.CrossRefGoogle Scholar
Clark, A. H., Shattuck, M. D., Ouellette, N. T. & O’Hern, C. S. 2015 Onset and cessation of motion in hydrodynamically sheared granular beds. Phys. Rev. E 92, 042202.Google ScholarPubMed
DallaValle, J. M. 1948 Micrometrics: The Technology of Fine Particles, 2nd edn. Pitman.Google Scholar
Damgaard, J. S., Whitehouse, R. J. S. & Soulsby, R. L. 1997 Bed-load sediment transport on steep longitudinal slopes. J. Hydraul. Engng 123 (12), 1130–1138.CrossRefGoogle Scholar
Dey, S. 2003 Threshold of sediment motion on combined transverse and longitudinal sloping beds. J. Hydraul. Res. 41 (4), 405–415.CrossRefGoogle Scholar
Diplas, P., Dancey, C. L., Celik, A. O., Valyrakis, M., Greer, K. & Akar, T. 2008 The role of impulse on the initiation of particle movement under turbulent flow conditions. Science 322 (5902), 717–720.Google ScholarPubMed
Duran, O., Andreotti, B. & Claudin, P. 2012 Numerical simulation of turbulent sediment transport, from bed load to saltation. Phys. Fluids 24 (10), 103306.CrossRefGoogle Scholar
Einstein, H. A. 1942 Formulas for the transport of bed sediment. Trans. Amer. Soc. Civil Engrs 107, 561–574.CrossRefGoogle Scholar
Fernandez Luque, R. & Van Beek, R. 1976 Erosion and transport of bed-load sediment. J. Hydraul. Res. 14 (2), 127–144.CrossRefGoogle Scholar
Fredsøe, J. & Deigaard, R. 1992 Mechanics of Coastal Sediment Transport. World Scientific.CrossRefGoogle Scholar
Frey, P. 2014 Particle velocity and concentration profiles in bedload experiments on a steep slope. Earth Surf. Process. Landf. 39 (5), 646–655.CrossRefGoogle Scholar
Frey, P. & Church, M. 2011 Bedload: a granular phenomenon. Earth Surf. Process. Landf. 36, 58–69.CrossRefGoogle Scholar
Gilbert, G. K. 1914 The Transportation of Débris by Running Water. Government Printing Office.CrossRefGoogle Scholar
Hsu, T. J., Jenkins, J. T. & Liu, P. L. F. 2004 On two-phase sediment transport: sheet flow of massive particles. Proc. R. Soc. Lond. A 460 (2048), 2223–2250.CrossRefGoogle Scholar
Iversen, J. D. & Rasmussen, K. R. 1994 The effect of surface slope on saltation threshold. Sedimentology 41 (4), 721–728.CrossRefGoogle Scholar
Iversen, J. D. & Rasmussen, K. R. 1999 The effect of wind speed and bed slope on sand transport. Sedimentology 46 (4), 723–731.CrossRefGoogle Scholar
Jackson, R. 2000 The Dynamics of Fluidized Particles. Cambridge University Press.Google Scholar
Ji, C., Munjiza, A., Avital, E., Ma, J. & Williams, J. J. R. 2013 Direct numerical simulation of sediment entrainment in turbulent channel flow. Phys. Fluids 25 (5), 056601.CrossRefGoogle Scholar
Karmaker, T. & Dutta, S. 2016 Prediction of short-term morphological change in large braided river using 2D numerical model. J. Hydraul. Engng 142 (10), 04016039.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, 59–71.CrossRefGoogle Scholar
Li, F. & Cheng, L. 1999 Numerical model for local scour under offshore pipelines. J. Hydraul. Engng 125 (4), 400–406.CrossRefGoogle Scholar
Li, L. & Sawamoto, M. 1995 Multi-phase model on sediment transport in sheet-flow regime under oscillatory flow. Coast. Engng Japan 38, 157–178.CrossRefGoogle Scholar
Maurin, R.2015 Investigation of granular behavior in bedload transport using an Eulerian–Lagrangian model. PhD thesis, Université Grenoble Alpes.Google Scholar
Maurin, R., Chauchat, J., Chareyre, B. & Frey, P. 2015 A minimal coupled fluid-discrete element model for bedload transport. Phys. Fluids 27 (11), 113302.CrossRefGoogle Scholar
Maurin, R., Chauchat, J. & Frey, P. 2016 Dense granular flow rheology in turbulent bedload transport. J. Fluid Mech. 804, 490–512.CrossRefGoogle Scholar
Maxey, M. R. & Riley, J. J. 1983 Equation of motion for a small rigid sphere in a nonuniform flow. Phys. Fluids 26 (4), 883–889.CrossRefGoogle Scholar
Meyer-Peter, E. & Müller, R. 1948 Formulas for bed-load transport. In Proceedings of the 2nd Meeting of the IAHSR, pp. 39–64. IAHR.Google Scholar
Ni, W.-J. & Capart, H. 2015 Cross-sectional imaging of refractive-index-matched liquid-granular flows. Exp. Fluids 56 (8), 163.CrossRefGoogle Scholar
Niño, Y. & García, M. 1998 Using Lagrangian particle saltation observations for bedload sediment transport modelling. Hydrol. Process. 12 (8), 1197–1218.3.0.CO;2-U>CrossRefGoogle Scholar
Nino, Y. & Garcia, M. 1994 Gravel saltation: 2. Modeling. Water Resour. Res. 30 (6), 1915–1924.CrossRefGoogle Scholar
Ouriemi, M., Aussillous, P., Medale, M., Peysson, Y. & Guazzelli, É. 2007 Determination of the critical shields number for particle erosion in laminar flow. Phys. Fluids 19 (6), 061706.CrossRefGoogle Scholar
Prandtl, L. 1926 Bericht über neuere Turbulenzforschung. Hydraulische Probleme. Vorträge Hydrauliktagung Göttingen 5, 1–13.Google Scholar
Recking, A., Degoutte, G., Camenen, B. & Frey, P. 2013 Dynamique et aménagement des torrents et rivières de montagne, chap. Hydraulique et transport solide, pp. 133–199. Quae.Google Scholar
Revil-Baudard, T. & Chauchat, J. 2013 A two-phase model for sheet flow regime based on dense granular flow rheology. J. Geophys. Res. 118 (2), 619–634.CrossRefGoogle Scholar
Revil-Baudard, T., Chauchat, J., Hurther, D. & Barraud, P.-A. 2015 Investigation of sheet-flow processes based on novel acoustic high-resolution velocity and concentration measurements. J. Fluid Mech. 767, 1–30.CrossRefGoogle Scholar
Richardson, J. F. & Zaki, W. N. 1954 Sedimentation and fluidization: Part i. Trans. Inst. Chem. Engrs 32, 35–53.Google Scholar
Rickenmann, D. 1991 Hyperconcentrated flow and sediment transport at steep slopes. J. Hydraul. Engng 117 (11), 1419–1439.CrossRefGoogle Scholar
Rickenmann, D. 2001 Comparison of bed load transport in torrents and gravel bed streams. Water Resour. Res. 37 (12), 3295–3305.CrossRefGoogle Scholar
Saffman, P. G. 1965 The lift on a small sphere in a slow shear flow. J. Fluid Mech. 22 (2), 385–400.CrossRefGoogle Scholar
Schmeeckle, M. W., Nelson, J. M. & Shreve, R. L. 2007 Forces on stationary particles in near-bed turbulent flows. J. Geophys. Res. 112 (F2), F02003.CrossRefGoogle Scholar
Schwager, T. & Pöschel, T. 2007 Coefficient of restitution and linear spring-dashpot model revisited. Granul. Matt. 9, 465–469.CrossRefGoogle Scholar
Seminara, G., Solari, L. & Parker, G. 2002 Bed load at low shields stress on arbitrarily sloping beds: failure of the bagnold hypothesis. Water Resour. Res. 38 (11), 1249.CrossRefGoogle Scholar
Shields, A.1936 Anwendung der Aehnlichkeitsmechanik und der Turbulenzforschung auf die Geschiebebewegung. Doktor-Ingenieurs dissertation, Technischen Hochschule, Berlin.Google Scholar
Smart, G. M. 1984 Sediment transport formula for steep channels. J. Hydraul. Engng 110 (3), 267–276.CrossRefGoogle Scholar
Smart, G. M. & Jaeggi, M.1983 Sediment transport on steep slopes. Tech. Rep. 64. ETH Zurich.Google Scholar
Šmilauer, V. et al. 2015 Yade Documentation, 2nd edn. The Yade Project (http://yade-dem.org/doc/).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 122 (10), 549–558.CrossRefGoogle Scholar
Takahashi, T. 1978 Mechanical characteristics of debris flow. J. Hydraul. Div. 104 (8), 1153–1169.CrossRefGoogle Scholar
Takahashi, T. 2007 Debris Flow: Mechanics, Prediction and Countermeasures. Taylor & Francis.CrossRefGoogle Scholar
Valyrakis, M., Diplas, P., Dancey, C. L., Greer, K. & Celik, A. O. 2010 Role of instantaneous force magnitude and duration on particle entrainment. J. Geophys. Res. 115 (F2), F02006.CrossRefGoogle Scholar
Wiberg, P. L. & Smith, J. D. 1987 Calculations of the critical shear stress for motion of uniform and heterogeneous sediments. Water Resour. Res. 23 (8), 1471–1480.CrossRefGoogle Scholar
Wilcock, P. R. & Crowe, J. C. 2003 Surface-based transport model for mixed-size sediment. J. Hydraul. Engng 129 (2), 120–128.CrossRefGoogle Scholar