Long surface wave instability in dense granular flows

In this paper we present an experimental study of the long surface wave instability that can develop when a granular material flows down a rough inclined plane. The threshold and the dispersion relation of the instability are precisely measured by imposing a controlled perturbation at the entrance of the flow and measuring its evolution along the slope. The results are compared with the prediction of a linear stability analysis conducted in the framework of the depth-averaged or Saint-Venant equations. We show that when the friction law proposed in Pouliquen (1999a) is introduced in the Saint-Venant equations, the theory is able to predict quantitatively the stability threshold and the phase velocity of the waves but fails in predicting the observed cutoff frequency. The instability is shown to be of the same nature as the long wave instability observed in classical fluids but with characteristics that can dramatically differ due to the specificity of the granular rheology.Comment: 29 pages, 20 figures, to be published in Journal of Fluid Mechanic

A constitutive law for dense granular flows

A continuum description of granular flows would be of considerable help in predicting natural geophysical hazards or in designing industrial processes. However, the constitutive equations for dry granular flows, which govern how the material moves under shear, are still a matter of debate. One difficulty is that grains can behave like a solid (in a sand pile), a liquid (when poured from a silo) or a gas (when strongly agitated). For the two extreme regimes, constitutive equations have been proposed based on kinetic theory for collisional rapid flows, and soil mechanics for slow plastic flows. However, the intermediate dense regime, where the granular material flows like a liquid, still lacks a unified view and has motivated many studies over the past decade. The main characteristics of granular liquids are: a yield criterion (a critical shear stress below which flow is not possible) and a complex dependence on shear rate when flowing. In this sense, granular matter shares similarities with classical visco-plastic fluids such as Bingham fluids. Here we propose a new constitutive relation for dense granular flows, inspired by this analogy and recent numerical and experimental work. We then test our three-dimensional (3D) model through experiments on granular flows on a pile between rough sidewalls, in which a complex 3D flow pattern develops. We show that, without any fitting parameter, the model gives quantitative predictions for the flow shape and velocity profiles. Our results support the idea that a simple visco-plastic approach can quantitatively capture granular flow properties, and could serve as a basic tool for modelling more complex flows in geophysical or industrial applications.Comment: http://www.nature.com/nature/journal/v441/n7094/abs/nature04801.htm

Stationary shear flows of dense granular materials : a tentative continuum modelling

We propose a simple continuum model to interpret the shearing motion of dense, dry and cohesion-less granular media. Compressibility, dilatancy and Coulomb-like friction are the three basic ingredients. The granular stress is split into a rate-dependent part representing the rebound-less impacts between grains and a rate-independent part associated with long-lived contacts. Because we consider stationary flows only, the grain compaction and the grain velocity are the two main variables. The predicted velocity and compaction profiles are in apparent agreement with the experimental or numerical results concerning free-surface shear flows as well as confined shear flow

The MESANGE model: re-estimation on National Accounts base 2000 / Part 2 Version with chained-linked volumes

Mesange is a medium-size quarterly macro-econometric model of the French economy (about 500 equations, three sectors). The model describes short-term Keynesian dynamics and its long-term equilibrium is driven by supply-side determinants. Its reestimation on data from the national accounts base 2000 with fixed-base volumes is presented in a recent working paper (Klein and Simon, 2010). This first version of the model has been optimized for simulation use. Other applications of the Mesange model (short-term forecasting, analyses of the past) required its adaptation to the published data from the quarterly accounts with chained-linked volumes, as well as the integration of the recent crisis episode. A second version of the Mesange model has, therefore, been developed for this purpose. This version is presented in this working paper. First, the problems raised for macroeconomic modelling by national accounts with chained-linked volumes are explained and the solutions chosen to adapt the model to these new conventions are discussed. The applications of the version of the model with chained-linked volumes are, then, explained and illustrated with examples. Last, the main reestimated equations are detailed. The differences with respect to the version of the model with fixed-base volumes are commented. They stem from estimations based on non-identical data, but also from the different uses made of the two versions of Mesange and the resulting various needs and constraints that have conditioned the methodological choices that have been made. As for the version of the model with chained-linked volumes, priority has been given to the quality of the adjustment to the data rather than to the underlying theoretical framework. Nonetheless, the philosophy and general structure of the two versions of the model remain very much alike.macroeconometric model, estimation, chained-linked volumes, short-term forecasting, contribution analysis

Dynamics and stress in gravity driven granular flow

We study, using simulations, the steady-state flow of dry sand driven by gravity in two-dimensions. An investigation of the microscopic grain dynamics reveals that grains remain separated but with a power-law distribution of distances and times between collisions. While there are large random grain velocities, many of these fluctuations are correlated across the system and local rearrangements are very slow. Stresses in the system are almost entirely transfered by collisions and the structure of the stress tensor comes almost entirely from a bias in the directions in which collisions occur.Comment: 4 pages, 3 eps figures, RevTe