Below are digital images of the sand in my experiment. These pictures are time-lapse digital photographs from a camera that is mounted to the apparatus (which shakes with the sand) and is a quasi 2-D slice through a sandpile that is shaking up and down. 200 pictures are taken over a 2 minute time-period, and the images are overlayed.
Above is an image that shows a nice ``4-roll state.'' There are 4 convection rolls visible in the picture, stacked in a 2x2 arrangement, circulating so that the sand in the lower left roll is moving clockwise, and the sand in the lower right cell is moving counter-clockwise. The sand in the exact middle of the cell is barely moving at all! The maximal acceleration of the shaker is only 20% greater than gravity.1 The sand in the cell is ``rough'', and has many facets and edges.
The above image is a false-colored streak photograph of Lake Ottawa sand, which is smooth and polished nearly into spheres from the action of the lake. The acceleration here is only 30% greater than gravity, but there is a completely different convection pattern.
And finally, the above is a streak photograph of the above ``rough sand'' shaken at 1/2 the amplitude, but at a much greater frequency so that the maximal acceleration is 50% greater than gravity. A nice ``vortex'' developed which moved around inside the sandpile.
1 - This means that if one measured the acceleration of the
bottom of the shaker, it would be accelerating towards the floor 20%
faster than a similar object in freefall. By extension, the sand is
briefly airborn for part of the shaking cycle, before smashing against the
bottom
again.
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