Raphaël Maurin, Philippe Frey, Julien Chauchat, Rémi Chassagne, John Gray, Centre National de la Recherche Scientifique - CNRS (FRANCE), Institut National Polytechnique de Toulouse - Toulouse INP (FRANCE), Institut polytechnique de Grenoble (FRANCE), Institut national de recherche pour l'agriculture, l'alimentation et l'environnement - INRAE (FRANCE), Institut national de Recherche en Sciences et Technologies pour l'Environnement et l'Agriculture - IRSTEA (FRANCE), Université Grenoble Alpes - UGA (FRANCE), Université Toulouse III - Paul Sabatier - UT3 (FRANCE), University of Manchester (UNITED KINGDOM), Erosion torrentielle neige et avalanches (UR ETGR (ETNA)), Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE), Institut de mécanique des fluides de Toulouse (IMFT), Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université Fédérale Toulouse Midi-Pyrénées, Laboratoire des Écoulements Géophysiques et Industriels [Grenoble] (LEGI), Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA), Department of Mathematics and Manchester Centre for Nonlinear Dynamics, University of Manchester [Manchester], UK Research & Innovation (UKRI) - Natural Environment Research Council (NERC) : NE/E003206/1, NE/K003011/1, UK Research & Innovation (UKRI) - Engineering & Physical Sciences Research Council (EPSRC) : EP/I019189/1, EP/K00428X/1, EP/M022447/1, INRAE, Royal Society of London : WM150058, Cambridge University Press, ANR-11-LABX-0030,TEC XXI,Ingénierie de la Complexité : la mécanique et ses interfaces au service des enjeux sociétaux du 21iè(2011), ANR-10-LABX-0056,OSUG@2020,Innovative strategies for observing and modelling natural systems(2010), and ANR-16-CE01-0005,SegSed,Tri granulométrique en Transport de Sédiments(2016)
Grain-scale discrete element simulations of bidisperse mixtures during bedload transport are used to understand, and model, bedload transport and particle-size segregation in granular media. For an initial distribution of fine particles on top of a coarse granular bed, this paper investigates the gravity driven percolation/segregation of the fine particles down into the quasi-static part of the bed. The segregation is observed to be driven by the inertial number at the bottom of the fine particle layer, and is independent of the number of fine particles. A novel travelling wave solution for the evolving concentration distribution is constructed using the continuum particle-size segregation model of Thornton, Gray & Hogg (J. Fluid Mech., vol. 550, 2006, pp. 1–25) and Gray & Chugunov (J. Fluid Mech., vol. 569, 2006, pp. 365–398). The observed behaviour is shown to be related to a local equilibrium between the influence of the concentration and of the inertial number. The existence of the exact solution relies on the segregation flux and the diffusion coefficient having the same dependency on the inertial number. This functional dependence allows the continuum model to quantitatively reproduce the discrete simulations. These results significantly improve on our understanding of the size segregation dynamics and represent a step forward in the up-scaling process to polydisperse granular flows in the context of turbulent bedload transport.