Abstract
A bed-load transport model has been derived in order to attain a better prediction of particle motion along river beds. Scientific studies have now moved towards a particle based approach in order to physically address the actual motion characteristics of the bed grains, such as the distance between entrainment and deposition, i.e. the step length. Step length clearly accounts for the heterogeneity faced by a grain along its path, such as bed roughness, flow intensity, river morphology. In this study, particles’ step lengths are regarded as a stochastic variable denoted by a lognormal distribution, whose statistics account for the effect of both bed arrangement and the near bed shearing flow. The 1D Exner equation is then reformulated to account for tracing particles by considering the deposition term as a function of the upstream entrainment events and the displacements computed by a particle before stopping. The implemented numerical method enables the computation of the concentration of bed-load tracers in time and space. As revealed by the model results, the step length distribution acts as a source of diffusion for particle motion along the river bed. The extent of advection and diffusion is not only controlled by the statistics of the step length, but it is also strongly influenced by the level of bed roughness. The thickness of the exchange layer also plays a role in the transport behaviour, as it delays particles temporarily stored in the active layer.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
Bradley DN, Tucker GE (2012) Measuring gravel transport and dispersion in a mountain river using passive radio tracers. Earth Surf Process. Landforms 37:1034–1045
Campagnol J, Radice A, Nokes R, Bulankina V, Lescova A, Ballio F (2013) Lagrangian analysis of bed-load sediment motion: database contribution. J Hydralics Res 51(5):589–596. doi:10.1080/00221686.2013.812152
Drake TG, Shreve RL, Dietrich WE, Whiting PJ, Leopold LB (1987) Bed load transport of fine gravel observed by motion-picture photography. J Fluid Mech 192:193–217
Einstein H A (1950) The bed-load function for sediment transportation in open channel flows. Technical bulletin number 1026, United States Department of Agriculture, Soil Conservation Service, Washington, DC 78 pp
Ferguson RI, Wathen SJ (1998) Tracer-pebble movement along a concave river profile: virtual velocity in relation to grain size and shear stress. Water Resour Res 34(8):2031–2038
Furbish DJ, Haff PK, Roseberry JC, Schmeeckle MW (2012) A probabilistic description of the bed load sediment flux: 1. Theory. J Geophys Res 117:F03031. doi:10.1029/2012JF002352
Ganti V, Meerschaert MM, Foufoula-Georgiou E, Viparelli E, Parker G (2010) Normal and anomalous diffusion of gravel tracer particles in rivers. J Geophys Res 115: F00A12. doi:10.1029/2008JF001222
Hassan MA, Church M, Ashworth PJ (1992) Virtual rate and mean distance of travel of individual clasts in gravel-bed channels. Earth Surf Proc Land 17:327–617
Hassan MA, Church M (2000) Experiments on surface structure and partial sediment transport on a gravel bed. Water Resour Res 36(7):1885–1895
Hassan MA, Voepel H, Schumer R, Parker G, Fraccarollo L (2013) Displacement characteristics of coarse fluvial bed sediment. J Geophys Res Earth Surf 118:155–165. doi:10.1029/2012JF002374
Hirano M (1971) On riverbed variation with armouring. Proc Jpn Soc Civ Eng 195:55–65
Lajeunesse E, Malverti L, Charru F(2010) Bed load transport in turbulent flow at the grain scale: experiments and modeling. J Geophys Res 115:F04001. doi:10.1029/2009JF001628
Liébault F, Bellot H, Chapuis M, Klotz S, Deschatres M (2011) Bedload tracing in a high-sediment-load mountain stream. Earth Surf Process Land. doi:10.1002/esp.2245
Marion A (1995) Analisi sperimentale della dinamica verticale dei sedimenti negli alvei fluviali, Ph.D. thesis, University of Padua, Padua, Italy
Marion A, Nikora V, Puijalon S, Bouma T, Koll K, Ballio F, Tait S, Zaramella M, Sukhodolov A, O’Hare M, Wharton G, Aberle J, Tregnaghi M, Davies P, Nepf H, Parker G, Statzner B (2014) Aquatic Interfaces: a hydrodynamic and ecological perspective. J Hydraul Eng doi:10.1080/00221686.2014.968887
McEwan I, Sorensen M, Heald J, Tait S, Cunningham G, Goring D, Willetts B (2004) Probabilistic modelling of bed-load composition. J Hydraul Eng. doi:10.1061/(ASCE)0733-9429(2004)130:2(129)
Meyer-Peter E, Muller R (1948) Formulas for bedload transport. International Association for Hydraulic Structures Research, Report of the second meeting, Stockholm, pp. 39–64
Nikora IV, Goring DG, Biggs BJF (1998) On gravel-bed roughness characterization. Water Resour Res 34(3):517–527
Nikora V, Goring D, McEwan I, Griffiths G (2001) Spatially averaged open-channel flow over rough bed. J Hydraul Eng 127(2)
Nikora V, Habersack H, Huber T, McEwan I (2002) On bed particle diffusion in gravel bed flows under weak bed load transport. Water Resour Res 38(6). doi:10.1029/2001WR000513
Parker G, Paola C, Leclair S (2000) Probabilistic Exner sediment continuity equation for mixtures with no active layer. J Hydraul Eng
Pelosi A, Parker G (2014) Morphodynamics of river bed variation with variable bedload step length. Earth Surf Dynam 2:243–253
Sayre W, Hubbell D (1965) Transport and dispersion of labeled bed material, North Loup River, Nebraska, US Geological Survey Professional Paper, 433-C, 48 pp
van Rijn LC (1984) Sediment pick-up function. J Hydraul Eng 110(10)
Viparelli E, Lauer JW, Belmont P, Parker G (2013) A numerical model to develop long-term sediment budgets using isotopic sediment fingerprints. Comput Geosci 53:114–122
Wilcock PR, Kenworthy ST (2002) A two-fraction model for the transport of sand/gravel mixtures. Water Resour Res 38(10):1194. doi:10.1029/2001WR000684
Wong M, Parker G, DeVries P, Brown TM, Burges SJ (2007) Experiments on dispersion of tracer stones under lower-regime plane-bed equilibrium bed load transport. Water Resour Res 43:W03440. doi:10.1029/2006WR005172
Yang C, Sayre W (1971) Stochastic model for sand dispersion. J Hydraul Div 97:265–288
Acknowledgments
This work was supported by the Research Executive Agency, through the 7th Framework Programme of the European Union, Support for Training and Career Development of Researchers (Marie Curie—FP7‐PEOPLE‐2012‐ITN), which funded the Initial Training Network (ITN) HYTECH ‘Hydrodynamic Transport in Ecologically Critical Heterogeneous Interfaces’, No. 316546.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Cecchetto, M., Tait, S., Marion, A. (2016). Step Length Influence in Modelling Advection and Diffusion of Bed-Load Particles. In: Rowiński, P., Marion, A. (eds) Hydrodynamic and Mass Transport at Freshwater Aquatic Interfaces. GeoPlanet: Earth and Planetary Sciences. Springer, Cham. https://doi.org/10.1007/978-3-319-27750-9_24
Download citation
DOI: https://doi.org/10.1007/978-3-319-27750-9_24
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-27749-3
Online ISBN: 978-3-319-27750-9
eBook Packages: Earth and Environmental ScienceEarth and Environmental Science (R0)