This paper concerns the elliptical instability of a flow in a rotating deformed sphere. The aim of our work is to analyse the characteristics of this instability experimentally and to provide a theoretical model which accounts for the observations. For this purpose, an elastic and transparent hollow sphere has been moulded in a silicone gel block. The flow is visualized using Kalliroscope flakes illuminated with a laser sheet as the sphere is set into rotation and compressed by two rollers. The elliptical instability occurs by the appearance of the so-called 'spin-over' mode whose growth rate and saturation amplitude are measured by video image analysis at different Ekman numbers. Growth rates are predicted well by the linear stability analysis. A nonlinear model is developed and is shown to describe correctly the saturated regimes observed in the experiments. At low Ekman numbers, a secondary instability leading to an intermittent regime is also discovered.

A viscoplastic continuum theory has recently been proposed to model dense, cohesionless granular flows [P. Jop, Nature (London) 441, 727 (2006)10.1038/nature04801]. We confront this theory for the first time with a transient, three-dimensional flow situation--the simple collapse of a cylinder of granular matter onto a horizontal plane--by extracting stress and strain rate tensors directly from soft particle simulations. These simulations faithfully reproduce the different flow regimes and capture the observed scaling laws for the final deposit. Remarkably, the theoretical hypothesis that there is a simple stress-strain rate tensorial relationship does seem to hold across the whole flow even close to the rough boundary provided the flow is dense enough. These encouraging results suggest viscoplastic theory is more generally applicable to transient, multidirectional, dense flows and open the way for quantitative predictions in real applications.

The collapse of a granular column is an intriguingly simple table-top experiment which exhibits a host of interesting phenomena. Here, we introduce a planar version in which the collapsing column is only one particle deep perpendicular to the plane of motion to make observations of the internal motion possible. This configuration also particularly lends itself to comparison with discrete element simulations which are performed in tandem. Our experiments confirm that this planar system displays all the same features as collapsing cylinders and rectangular blocks. In particular, the dominant dependence on the initial parameters of the column runout is through a power law of the initial height-to-width aspect ratio. Discrete element simulations, which are found to reproduce the experimental behavior very well, are then used to analyze the velocity field of the collapse process. A predominantly linear velocity profile is found in a moving layer over an evolving static pile. The time-dependent strain rate in this moving layer is in reasonable correspondence with a strain rate prediction for flow down a fixed slope by Rajchenbach [Phys. Rev. Lett. 90, 144302 (2003)].