# Breaking size segregation waves and particle recirculation in granular avalanches

## Thornton, A. R. & Gray, J. M. N. T.

### Journal of Fluid Mechanics, vol. 596 (2008),   pp. 261-284

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Movie 1. Wave Breaking problem. Animation showing the evolution of a breaking size segregation wave in a frame (ξ,z) moving downstream at the same speed as the steady-state lens ulens = 1. A series of stills for this problem are illustrated in figure 6 and the final steady state is shown in figure 4(a). The initial condition consists of a linearly decreasing concentration shock that joins two constant height sections. In response to linear shear through the avalanche depth the shock steepens and breaks at t = 1 to form an oscillating lens. Computations are performed on a 300 x 300 grid and with Sr = 1. Contours of the small particle concentration are illustrated using the colour bar below, with red corresponding to pure fines and blue to pure large. For t > 20 the time-step is increased to speed up the convergence towards the steady-state solution. Download movie.

Movie 2. Lens interaction. Animation showing the development of the small particle concentration during the interaction of two breaking size segregation waves in a frame (ξ,z) moving downslope with speed unity. A series of stills for this problem are illustrated in figure 8 and the final steady state is shown in figure 4(a). At t = 0 the sharp downward steps in concentration break to form two lenses that propagate in opposite directions with speed 0.4. Just after t = 3 these begin to coalesce to form a single lens between Hup = 0.9 and Hdown = 0.1 that propagates downslope with speed unity. The results are for linear shear and Sr = 1. Computations are performed on a 300 x 300 grid and contours of the small particle concentration are illustrated using the colour bar above, with red corresponding to pure fines and blue to pure large. For t > 20 the time-step is increased to speed up the convergence towards the steady-state solution. Download movie.