# 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

If a movie is not displayed, please use the links in the caption to
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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 *u*_{lens}
= 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 *S*_{r} = 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 *H*_{up}
= 0.9 and *H*_{down} = 0.1 that propagates downslope with
speed unity. The results are for linear shear and *S*_{r}
= 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.