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Abstract
Shallow granular avalanches on slopes close to repose exhibit hysteretic ζ behaviour. For instance, when a steady uniform granular flow is brought to rest it leaves a deposit of thickness hstop(ζ) on a rough slope inclined at an angle ζ to the horizontal. However, this layer will not spontaneously start to flow again until it is inclined to a higher angle ζ start, or the thickness is increased to hstart(ζ) > hstop(ζ). This simple phenomenology leads to a rich variety of flows with coexisting regions of solidlike and fluidlike granular behaviour that evolve in space and time. In particular, frictional hysteresis is directly responsible for the spontaneous formation of selfchannelized flows with static levees, retrogressive failures as well as erosiondeposition waves that travel through the material. This paper is motivated by the experimental observation that a travellingwave develops, when a steady uniform flow of carborundum particles on a bed of larger glass beads, runs out to leave a deposit that is approximately equal to hstop. Numerical simulations using the friction law originally proposed by Edwards et al. (2017) and modified here, demonstrate that there are in fact two travelling waves. One that marks the trailing edge of the steadyuniform flow and another that rapidly deposits the particles, directly connecting the point of minimum dynamic friction (at thickness h∗) with the deposited layer. The first wave moves slightly faster than the second wave, and so there is a slowly expanding region between them in which the flow thins and the particles slow down. An exact inviscid solution for the second travelling wave is derived and it is shown that for a steadyuniform flow of thickness h∗ it produces a deposit close to hstop for all inclination angles. Numerical simulations show that the twowave structure deposits layers that are approximately equal to hstop for all initial thicknesses. This insensitivity to the initial conditions implies that hstop is a universal quantity, at least for carborundum particles on a bed of larger glass beads. Numerical simulations are therefore able to capture the complete experimental staircase procedure, which is commonly used to determine the hstop and hstart curves by progressively increasing the inclination of the chute. In general, however, the deposit thickness may depend on the depth of the flowing layer that generated it, so the most robust way to determine hstop is to measure the deposit thickness from a flow that was moving at the minimum steady uniform velocity. Finally, some of the pathologies in earlier nonmonotonic friction laws are discussed and it is explicitly shown that with these models either steadilytravelling deposition waves do not form or they do not leave the correct deposit depth hstop.
Original language  English 

Journal  Journal of Fluid Mechanics 
DOIs  
Publication status  Published  30 Jul 2019 
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Dive into the research topics of 'Frictional hysteresis and particle deposition in granular freesurface flows'. Together they form a unique fingerprint.Projects
 1 Finished

GLOBAL Manchester Image Reconstruction and ANalysis (MIRAN): Step jumps in imaging by Global Exchange of user pull and method push
Lionheart, W., Cootes, T., Dorn, O., Gray, N., Grieve, B., Haigh, S., Harris, D., Hollis, C., Matthews, J., Mccann, H., Parker, G., Villegas Velasquez, R. & Withers, P.
1/04/12 → 31/03/13
Project: Research