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The Spirals


The photographs on this page relate to our papers:

Thomas, P.J. 1994, Pattern Formation of Granules on the Bottom of a Differentially Rotating Tank, J. Fluid Mech. vol. 274 , pp.23-41.
Zoueshtiagh, F., Thomas, P.J. 2000, On the Wavelength Scaling of Spiral Patterns Formed by Granular Media Underneath a Rotating Fluid, Phys. Rev. E. 61 , pp. 5588-5592.
Zoueshtiagh, F., Thomas, P.J. 2003, Universal Scaling for Ripple Formation in Granular Media, Phys. Rev. E. 67 , 031301.

The following pictures E1 , E2 , E3 , E4 show spiral patterns formed by a granular media underneath a rotating fluid. Dark granules are viewed against a red background. The patterns were first described in Thomas (1994).

Prior to the experiment which initiated the spiral pattern formation the granules were distributed uniformly, in a thin layer across the bottom of a partially fluid-filled rotating tank (diameter 1m, the photographs E1-E4 show a view from vertically above the tank). The fluid above the granule layer was in a state of solid body rotation such that the fluid did not move relatively to the granule layer on the bottom of the tank. Spiral patterns are observed to form when the rotational velocity of the tank is suddenly increased by a sufficiently large increment. The fluid mass in the tank does not follow the instantaneous acceleration of the tank. Shear forces are established between the granule layer and the fluid above it. If these forces are large enough the granules are set in motion and slide across the bottom of the tank. As a results of this spiral patterns as shown in E1 , E2 , E3 , E4 are formed. We have recently developed a simple cellular-automaton model (Zoueshtiagh and Thomas, 1999) which succeeds in producing ripple patterns which look qualitatively similar to those observed in the experiment C1 , C2 . More importantly, however, the computational data show the same scaling behaviour for the number of spiral arms and the size of the inner patch as observed in the experiment. This corespondence enabled us to draw some conclusions concerning the origin of the patterns observed in the experiment.

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