## References

Allen, M. P. & Tildesley, D. J.
1989
Computer Simulation of Liquids. Oxford University Press.

Babic, M.
1997
Average balance equations for granular materials. Intl J. Engng Sci.
35 (5), 523–548.

Baker, J. L., Johnson, C. G. & Gray, J. M. N. T.
2016
Segregation-induced finger formation in granular free-surface flows. J. Fluid Mech.
809, 168–212.

Berzi, D. & Jenkins, J. T.
2009
Steady inclined flows of granular-fluid mixtures. J. Fluid Mech.
641, 359–387.

Bokhove, O. & Thornton, A. R.
2012
Shallow granular flows. In Handbook of Environmental Fluid Dynamics (ed. Fernando, H. J.). CRC Press.

Bridgwater, J., Foo, W. S. & Stephens, D. J.
1985
Particle mixing and segregation in failure zones – theory and experiment. Powder Technol.
41 (2), 147–158.

Bristeau, M. O. & Coussin, B.2001 Boundary conditions for the shallow water equations solved by kinetic schemes. PhD thesis, INRIA.

Brodu, N., Richard, P. & Delannay, R.
2013
Shallow granular flows down flat frictional channels: steady flows and longitudinal vortices. Phys. Rev. E
87 (2), 022202.

Bunya, S., Kubatko, E. J., Westerink, J. J. & Dawson, C.
2009
A wetting and drying treatment for the Runge–Kutta discontinuous Galerkin solution to the shallow water equations. Comput. Meth. Appl. Mech. Engng
198 (17), 1548–1562.

Campbell, C. S., Cleary, P. W. & Hopkins, M.
1995
Large-scale landslide simulations: global deformation, velocities and basal friction. J. Geophys. Res.
100 (B5), 8267–8283.

Cockburn, B. & Shu, C. W.
1989
TVB Runge–Kutta local projection discontinuous Galerkin finite element method for conservation laws. II. General framework. Math. Comput.
52 (186), 411–435.

Cundall, P. A. & Strack, O. D. L.
1979
A discrete numerical model for granular assemblies. Geotechnique
29 (1), 47–65.

Dalbey, K., Patra, A. K., Pitman, E. B., Bursik, M. I. & Sheridan, M. F.
2008
Input uncertainty propagation methods and hazard mapping of geophysical mass flows. J. Geophys. Res.
113 (B5), B05203.

Davies, T. R. H.
1990
Debris-flow surges – experimental simulation. J. Hydrol. (New Zealand)
29, 18–46.

Delannay, R., Valance, A., Mangeney, A., Roche, O. & Richard, P.
2017
Granular and particle-laden flows: from laboratory experiments to field observations. J. Phys. D
50 (5), 053001.

Dippel, S. & Luding, S.
1995
Simulations on size segregation: geometrical effects in the absence of convection. J. Phys. I France
5, 1527–1537.

Dunning, S. A. & Armitage, P. J.
2011
The grain-size distribution of rock-avalanche deposits: implications for natural dam stability. In Natural and Artificial Rockslide Dams, pp. 479–498. Springer.

Edwards, A. N. & Vriend, N. M.
2016
Size segregation in a granular bore. Phys. Rev. Fluids
1 (6), 064201.

Fan, Y. & Hill, K. M.
2011
Theory for shear-induced segregation of dense granular mixtures. New J. Phys.
13 (9), 095009.

Faug, T., Childs, P., Wyburn, E. & Einav, I.
2015
Standing jumps in shallow granular flows down smooth inclines. Phys. Fluids
27 (7), 073304.

Forterre, Y. & Pouliquen, O.
2003
Long-surface-wave instability in dense granular flows. J. Fluid Mech.
486, 21–50.

Gajjar, P., van der Vaart, K., Thornton, A. R., Johnson, C. G., Ancey, C. & Gray, J. M. N. T.
2016
Asymmetric breaking size-segregation waves in dense granular free-surface flows. J. Fluid Mech.
794, 460–505.

GDR-MiDi
2004
On dense granular flows. Eur. Phys. J. E
14 (4), 341–365.

Gillemot, K. A, Somfai, E. & Börzsönyi, T.
2017
Shear-driven segregation of dry granular materials with different friction coefficients. Soft Matt.
13 (2), 415–420.

Goldhirsch, I.
2010
Stress, stress asymmetry and couple stress: from discrete particles to continuous fields. Granul. Matt.
12 (3), 239–252.

González, S., Windows-Yule, C. R. K., Luding, S., Parker, D. J. & Thornton, A. R.
2015
Forced axial segregation in axially inhomogeneous rotating systems. Phys. Rev. E
92, 022202.

Goujon, C., Dalloz-Dubrujeaud, B. & Thomas, N.
2007
Bidisperse granular avalanches on inclined planes: a rich variety of behaviors. Eur. Phys. J. E
23 (2), 199–215.

Gray, J. M. N. T . & Chugunov, V. A.
2006
Particle-size segregation and diffusive remixing in shallow granular avalanches. J. Fluid Mech.
569, 365–398.

Gray, J. M. N. T. & Ancey, C.
2009
Segregation, recirculation and deposition of coarse particles near two-dimensional avalanche fronts. J. Fluid Mech.
629, 387–423.

Gray, J. M. N. T. & Ancey, C.
2011
Multi-component particle-size segregation in shallow granular avalanches. J. Fluid Mech.
678, 535–588.

Gray, J. M. N. T. & Edwards, A. N.
2014
A depth-averaged-rheology for shallow granular free-surface flows. J. Fluid Mech.
755, 503–534.

Gray, J. M. N. T. & Kokelaar, B. P.
2010a
Large particle segregation, transport and accumulation in granular free-surface flows. J. Fluid Mech.
652, 105–137.

Gray, J. M. N. T. & Kokelaar, B. P.
2010b
Large particle segregation, transport and accumulation in granular free-surface flows – erratum. J. Fluid Mech.
657, 539–539.

Gray, J. M. N. T., Tai, Y.-C. & Noelle, S.
2003
Shock waves, dead zones and particle-free regions in rapid granular free-surface flows. J. Fluid Mech.
491, 161–181.

Gray, J. M. N. T. & Thornton, A. R.
2005
A theory for particle size segregation in shallow granular free-surface flows. Proc. R. Soc. Lond. A
461 (2057), 1447–1473.

Haas, T., Braat, L., Leuven, J. R. F. W., Lokhorst, I. R. & Kleinhans, M. G.
2015
Effects of debris flow composition on runout, depositional mechanisms, and deposit morphology in laboratory experiments. J. Geophys. Res.
120 (9), 1949–1972.

Harten, A., Lax, P. D. & van Leer, B.
1983
On upstream differencing and Godunov-type schemes for hyperbolic conservation laws. SIAM Rev.
25 (1), 35–61.

Hill, K. M. & Fan, Y.
2016
Granular temperature and segregation in dense sheared particulate mixtures. KONA Powder Particle J.
33 (0), 150–168.

Hogg, A. J. & Pritchard, D.
2004
The effects of hydraulic resistance on dam-break and other shallow inertial flows. J. Fluid Mech.
501, 179–212.

Hong, D. C., Quinn, P. V. & Luding, S.
2001
Reverse brazil nut problem: competition between percolation and condensation. Phys. Rev. Lett.
86 (15), 3423–3426.

Iverson, R. M.
1997
The physics of debris flows. Rev. Geophys.
35 (3), 245–296.

Iverson, R. M.
2003
The debris-flow rheology myth. In Debris flow Mechanics and Mitigation Conference, Mills Press, Davos, pp. 303–314.

Iverson, R. M. & Lahusen, R. G.
1993
Friction in debris flows: Inferences from large-scale flume experiments. In Hydraulic Engineering (ed. American Society of Civil Engineers), vol. 93. ASCE.

Iverson, R. M., Logan, M., Lahusen, R. G. & Berti, M.
2010
The perfect debris flow? Aggregated results from 28 large-scale experiments. J. Geophys. Res.
115, F03005.

Jenkins, J. T.
1998
Particle segregation in collisional flows of inelastic spheres. In Physics of Dry Granular Media (ed. Herrmann, Hovi & Luding), NATO ASI Series, vol. 350, pp. 645–658. Kluwer.

Jenkins, J. T. & Yoon, D. K.
2002
Segregation in binary mixtures under gravity. Phys. Rev. Lett.
88 (19), 1.

Johnson, C. G., Kokelaar, B. P., Iverson, R. M., Logan, M., Lahusen, R. G. & Gray, J. M. N. T.
2012
Grain-size segregation and levee formation in geophysical mass flows. J. Geophys. Res.
117 (F1), F01032.

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.

Kesserwani, G., Ghostine, R., Vazquez, J., Ghenaim, A. & Mosé, R.
2008
Application of a second-order Runge–Kutta discontinuous Galerkin scheme for the shallow water equations with source terms. Intl J. Numer. Meth. Fluids
56 (7), 805–821.

Khakhar, D. V., McCarthy, J. J. & Ottino, J. M.
1999
Mixing and segregation of granular materials in chute flows. Chaos: An Interdisciplinary J. Nonlin. Sci.
9 (3), 594–610.

Kokelaar, B. P., Bahia, R. S., Joy, K. H., Viroulet, S. & Gray, J. M. N. T.
2018
Granular avalanches on the moon: mass-wasting conditions, processes and features. J. Geophys. Res. Planets
122, 1893–1925.

Kokelaar, B. P., Graham, R. L., Gray, J. M. N. T. & Vallance, J. W.
2014
Fine-grained linings of leveed channels facilitate runout of granular flows. Earth Planet. Sci. Lett.
385, 172–180.

Kowalski, J. & McElwaine, J. N.
2013
Shallow two-component gravity-driven flows with vertical variation. J. Fluid Mech.
714, 434–462.

Larcher, M. & Jenkins, J. T.
2013
Segregation and mixture profiles in dense, inclined flows of two types of spheres. Phys. Fluids
25 (11), 113301.

Larcher, M. & Jenkins, J. T.
2015
The evolution of segregation in dense inclined flows of binary mixtures of spheres. J. Fluid Mech.
782, 405–429.

Leveque, R. J.
2002
Finite Volume Methods for Hyperbolic Problems, vol. 31. Cambridge University Press.

Logan, M. & Iverson, R. M.2013 Video documentation of experiments at the usgs debris-flow flume 2008. *US Geological Survey Open-File Rep.* 2007–1315 v. 1.3.

Luding, S.
2008
Cohesive, frictional powders: contact models for tension. Granul. Matt.
10 (4), 235–246.

Luding, S., Clément, E., Rajchenbach, J. & Duran, J.
1996
Simulations of pattern formation in vibrated granular media. Europhys. Lett.
36 (4), 247.

Marks, B., Rognon, P. & Einav, I.
2012
Grainsize dynamics of polydisperse granular segregation down inclined planes. J. Fluid Mech.
690, 499–511.

Middleton, G. V.
1970
Experimental Studies Related to Problems of Flysch Sedimentation, vol. 7. The Geological Association of Canada.

Mobius, M. E., Lauderdale, B. E., Nageland, S. R. & Jaeger, H. M.
2001
Size separation of granular particles. Nature
414, 270.

Mullin, T.
2000
Coarsening of self-organised clusters in binary particle mixtures. Phys. Rev. Lett.
84, 4741.

Nurijanyan, S.2013 Discrete and continuous hamiltonian systems for wave modelling. PhD thesis, University of Twente, Enschede.

Pesch, L., Bell, A., Sollie, W. E. H., Ambati, V. R., Bokhove, O. & van der Vegt, J. J. W.
2007
hpGEM – a software framework for discontinuous Galerkin finite element methods. ACM Trans. Math. Softw.
33 (4), 23.

Pouliquen, O.
1999a
On the shape of granular fronts down rough inclined planes. Phys. Fluids
11 (7), 1956–1958.

Pouliquen, O.
1999b
Scaling laws in granular flows down rough inclined planes. Phys. Fluids
11 (3), 542–548.

Pouliquen, O. & Vallance, J. W.
1999
Segregation induced instabilities of granular fronts. Chaos
9 (3), 621–630.

Press, W. H.
2007
Numerical Recipes: The Art of Scientific Computing, 3rd edn. Cambridge University Press.

Reed, W. H. & Hill, T. R.1973 Triangular mesh methods for the neutron transport equation. *Tech. Rep.* Los Alamos Scientific Laboratory.

Rognon, P. G., Chevoir, F., Bellot, H., Ousset, F., Naaïm, M. & Coussot, P.
2008
Rheology of dense snow flows: inferences from steady state chute-flow experiments. J. Rheol.
52 (3), 729–748.

Saingier, G., Deboeuf, S. & Lagrée, P.-Y.
2016
On the front shape of an inertial granular flow down a rough incline. Phys. Fluids
28 (5), 053302.

Savage, S. B. & Hutter, K.
1989
The motion of a finite mass of granular material down a rough incline. J. Fluid Mech.
199, 177–215.

Savage, S. B. & Lun, C. K. K.
1988
Particle size segregation in inclined chute flow of dry cohesionless granular solids. J. Fluid Mech.
189, 311–335.

Schlick, C. P., Isner, A. B., Freireich, B. J, Fan, Y., Umbanhowar, P. B., Ottino, J. M. & Lueptow, R. M.
2016
A continuum approach for predicting segregation in flowing polydisperse granular materials. J. Fluid Mech.
797, 95–109.

Shu, C. W.
2013
A brief survey on discontinuous Galerkin methods in computational fluid dynamics. Adv. Mech.
v43, 541–554.

Silbert, L. E., Ertaş, D., Grest, G. S., Halsey, T. C., Levine, D. & Plimpton, S. J.
2001
Granular flow down an inclined plane: Bagnold scaling and rheology. Phys. Rev. E
64 (5), 051302.

Silbert, L. E., Landry, J. W. & Grest, G. S.
2003
Granular flow down a rough inclined plane: transition between thin and thick piles. Phys. Fluids
15 (1), 1–10.

Staron, L. & Phillips, J. C.
2015a
How large grains increase bulk friction in bi-disperse granular chute flows. Comput. Particle Mech.
3, 367–372.

Staron, L. & Phillips, J. C.
2015b
Stress partition and microstructure in size-segregating granular flows. Phys. Rev. E
92, 022210.

Takahashi, T.
2014
Debris Flow: Mechanics, Prediction and Countermeasures, 2nd edn. CRC Press.

Takahashi, T., Nakagawa, H., Harada, T. & Yamashiki, Y.
1992
Routing debris flows with particle segregation. ASCE J. Hydraul. Engng
118 (11), 1490–1507.

Thornton, A. R. & Gray, J. M. N. T.
2008
Breaking size segregation waves and particle recirculation in granular avalanches. J. Fluid Mech.
596, 261.

Thornton, A. R., Gray, J. M. N. T. & Hogg, A. J.
2006
A three-phase mixture theory for particle size segregation in shallow granular free-surface flows. J. Fluid Mech.
550, 1–25.

Thornton, A. R., Krijgsman, D., Te Voortwis, A., Ogarko, V., Luding, S., Fransen, R., Gonzalez, S., Bokhove, O., Imole, O. & Weinhart, T.
2013a
A review of recent work on the discrete particle method at the University of Twente: An introduction to the open-source package MercuryDPM. In Proceedings of the 6th International Conference on Discrete Element Methods and Related Techniques, pp. 50–56. Colorado School of Mines.

Thornton, A. R., Krijsgman, D., Fransen, R., Gonzalez, S., Tunuguntla, D. R., te Voortwis, A., Luding, S., Bokhove, O. & Weinhart, T.
2013b
MercuryDPM: fast particle simulations in complex geometries. News. Enginsoft
10, 48–53.

Thornton, A. R., Weinhart, T., Luding, S. & Bokhove, O.
2012a
Frictional dependence of shallow-granular flows from discrete particle simulations. Eur. Phys. J. E
35 (12), 1–8.

Thornton, A. R., Weinhart, T., Luding, S. & Bokhove, O.
2012b
Modeling of particle size segregation: calibration using the discrete particle method. Intl J. Modern Phys. C
23 (08), 1240014.

Toro, E. F.
2013
Riemann Solvers and Numerical Methods for Fluid Dynamics: A Practical Introduction. Springer Science & Business Media.

Tripathi, A. & Khakhar, D. V.
2011
Rheology of binary granular mixtures in the dense flow regime. Phys. Fluids
23 (11), 113302.

Tunuguntla, D. R., Bokhove, O. & Thornton, A. R.
2014
A mixture theory for size and density segregation in shallow granular free-surface flows. J. Fluid Mech.
749, 99–112.

Tunuguntla, D. R., Thornton, A. R. & Weinhart, T.
2016a
From discrete elements to continuum fields: extension to bidisperse systems. Comput. Particle Mech.
3 (3), 349–365.

Tunuguntla, D. R., Weinhart, T. & Thornton, A. R.
2016b
Comparing and contrasting size-based particle segregation models. Comput. Particle Mech.
4, 1–19.

van der Vaart, K., van Schrojenstein Lantman, M. P., Weinhart, T., Luding, S., Ancey, C. & Thornton, A. R.2017 Segregation of large particles in dense granular flows: a granular Saffman effect? Preprint, arXiv:1705.06803.
van der Vaart, K., Thornton, A. R., Johnson, C. G., Weinhart, T., Jing, L., Gajjar, P., Gray, J. M. N. T. & Ancey, C.
2018
Breaking size-segregation waves and mobility feedback in dense granular avalanches. Granul. Matt.
20 (3), 46.

Vallance, J. W. & Savage, S. B.
2000
Particle segregation in granular flows down chutes. In IUTAM Symposium on Segregation in Granular Flows, pp. 31–51. Springer.

Voortwis, A. Te2013 Closure laws for granular, shallow-layer, bi-disperse flows down an inclined chute. Master’s thesis, MSM Group, Univ. Twente, the Netherlands.

Weinhart, T., Hartkamp, R., Thornton, A. R. & Luding, S.
2013
Coarse-grained local and objective continuum description of three-dimensional granular flows down an inclined surface. Phys. Fluids
25 (7), 070605.

Weinhart, T., Thornton, A. R., Luding, S. & Bokhove, O.
2012
Closure relations for shallow granular flows from particle simulations. Granul. Matt.
14 (4), 531–552.

Weinhart, T., Tunuguntla, D. R., van Schrojenstein-Lantman, M. P., van der Horn, A. J., Denissen, I. F. C., Windows-Yule, C. R., de Jong, A. C. & Thornton, A. R.
2017
MercuryDPM: A Fast and Flexible Particle Solver Part A: Technical Advances. pp. 1353–1360. Springer.

Wiederseiner, S., Andreini, N., Épely-Chauvin, G., Moser, G., Monnereau, M., Gray, J. M. N. T. & Ancey, C.
2011
Experimental investigation into segregating granular flows down chutes. Phys. Fluids
23 (1), 013301.

Windows-Yule, C. R. K., Scheper, B. J., van der Horn, A. J., Hainsworth, N., Saunders, J., Parker, D. J. & Thornton, A. R.
2016
Understanding and exploiting competing segregation mechanisms in horizontally rotated granular media. New J. Phys.
18 (2), 023013.

Woodhouse, M. J., Thornton, A. R., Johnson, C. G., Kokelaar, B. P. & Gray, J. M. N. T.
2012
Segregation-induced fingering instabilities in granular free-surface flows. J. Fluid Mech.
709, 543–580.