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Large particle segregation, transport and accumulation in granular free-surface flows

Gray, J. M. N. T. & Kokelaar, B. P.

Journal of Fluid Mechanics, vol. 652 (2010),   pp. 105-137

If a movie is not displayed, please use the links in the caption to download it to your computer.


Movie 1. An animation of the wave steepening problem shown in figure 5. In each panel a vertical slice through the avalanche is shown with the x axis along the horizontal and the z axis along the vertical. The white region corresponds to large particles, the dark grey region contains small particles and intermediate shades of grey represent the particle concentration in mixed regions. In the top panel an exact solution for the position of the inversely graded interface is shown for the one-dimensional depth averaged transport theory, while in the lower panel a shock capturing numerical solution is shown for the full two-dimensional hyperbolic theory with Sr=0 α=0. Both solutions are identical prior to the interface breaking at t=1. At subsequent times the breaking size segregation wave in the full solution is represented by a shock in the depth-averaged theory. Download movie.


Movie 2. An animation of the wave merging problem shown in figure 7. In each panel a vertical slice through the avalanche is shown with the x axis along the horizontal and the z axis along the vertical. The white region corresponds to large particles, the dark grey region contains small particles and intermediate shades of grey represent the particle concentration in mixed regions. In the top panel an exact solution for the position of the inversely graded interface is shown for the one-dimensional depth averaged transport theory, while in the lower panel a shock capturing numerical solution is shown for the full two-dimensional hyperbolic theory with Sr=0 α=0. Two breaking size segregation waves form at the outset and propagate downslope. The upper one moves faster than the lower one and they merge at t=3.25 to form a single breaking size segregation wave. In the exact depth averaged solution in the top panel the breaking waves are represented as shocks in the interface height that move at the same speed as the breaking waves. Download movie.


Movie 3. An animation showing how the stratification pattern in figure 9 is built up by the passage of two avalanches that are brought to rest by a combination of deposition and the upslope propagation of a granular bore (Gray & Ancey 2009). Each avalanche has a coarse rich flow front and is strongly inversely graded behind, with large white sugar crystals on top of smaller more mobile iron spheres. Once the entire avalanche has come to rest, the stationary free-surface forms the new slope for the next avalanche to flow down. By placing a ruler along the initial slope of the pile it is possible to visualize the deposition of large particles as the coarse rich front flows past. Download movie.


Movie 4. An animation of the large particle transport and accumulation problem shown in figure 14. A vertical slice through the avalanche front is shown in a frame moving with speed uF. The ξ axis lies along the horizontal and the z axis is along the vertical coordinate. In the moving frame the front is fixed at ξ=0 and the free-surface of the avalanche lies along the solid line. The white region below the free-surface contains large particles and the dark grey region contains fines. Initially the avalanche front is composed of all small particles, and at subsequent times large particles are advected towards the flow front, reaching it at τ=10. The inversely graded interface (dot dash line) then becomes multiple valued and a shock fitting procedure is used to locate the position of the discontinuity that divides the bouldery flow front from the inversely graded avalanche behind. This exact solution for the depth-averaged transport model is for parameters α=0 and β=0.3. Note that large particles are sheared towards the flow front and then accumulate there to create a bouldery margin. Download movie.


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