Multiple solutions for granular flow over a smooth two-dimensional bump

Abstract

Geophysical granular flows, such as avalanches, debris flows, lahars and pyroclastic flows, are always strongly influenced by the basal topography that they flow over. In particular, localised bumps or obstacles can generate rapid changes in the flow thickness and velocity, or shock waves, which dissipate significant amounts of energy. Understanding how a granular material is affected by the underlying topography is therefore crucial for hazard mitigation purposes, for example to improve the design of deflecting or catching dams for snow avalanches. Moreover, the interactions with solid boundaries can also have important applications in industrial processes. In this paper, small-scale experiments are performed to investigate the flow of a granular avalanche over a two-dimensional smooth symmetrical bump. The experiments show that, depending on the initial conditions, two different steady-state regimes can be observed: either the formation of a detached jet downstream of the bump, or a shock upstream of it. The transition between the two cases can be controlled by adding varying amounts of erodible particles in front of the obstacle. A depth-averaged terrain-following avalanche theory that is formulated in curvilinear coordinates is used to model the system. The results show good agreement with the experiments for both regimes. For the case of a shock, time-dependent numerical simulations of the full system show the evolution to the equilibrium state, as well as the deposition of particles upstream of the bump when the inflow ceases. The terrain-following theory is compared to a standard depth-averaged avalanche model in an aligned Cartesian coordinate system. For this very sensitive problem, it is shown that the steady-shock regime is captured significantly better by the terrain-following avalanche model, and that the standard theory is unable to predict the take-off point of the jet. To retain the practical simplicity of using Cartesian coordinates, but have the improved predictive power of the terrain-following model, a coordinate mapping is used to transform the terrain-following equations from curvilinear to Cartesian coordinates. The terrain-following model, in Cartesian coordinates, makes identical predictions to the original curvilinear formulation, but is much simpler to implement.

The kinematics of bidisperse granular roll waves

“…In this case one of the concentration characteristics (5.17) must travel into the shock and another travel out, because there are already three of the bulk characteristics travelling in and one travelling out (see e.g. Viroulet et al 2017). Choosingφ − =φ (1) andφ + =φ (2) at the end points satisfies this requirement, and, due to the two roots swapping over at the bifurcation point, is also consistent with the internal shock values.…”

A Free Interface Model for Static/Flowing Dynamics in Thin-Layer Flows of Granular Materials with Yield: Simple Shear Simulations and Comparison with Experiments

“…This would make it possible to study erosion in flows over complex topography in the laboratory (e.g., [45]) or at the natural scale (e.g., [46]). For the very simple case of flows over a constant slope and if the pressure is assumed to be hydrostatic (p = g cos θ(h − Z)), taking into account the X-variations is the same as (according to [41]) considering once again (3)-(6) with S including an additional term,…”

Les instabilités hydrodynamiques dans les écoulements granulaires géophysiques

“…Ces phénomènes peuvent être observés dans de nombreux endroits : près de piliers de ponts, dans les mascarets, ou plus simplement dans un évier lorsque le robi-net est ouvert. Il a récemment été montré que des chocs stationnaires peuvent également être créés en amont d'une irrégularité topographique du sol, modifiant considérablement les propriétés de l'écoulement [5]. En l'absence de particules devant l'obstacle, l'écoulement décolle au niveau du sommet de ce dernier pour former un jet granulaire.…”

“…Le système d'équations obtenu est plus complexe, mais permet de mieux tenir compte des termes d'accélération dus à la topographie. Il a été montré récemment qu'une bonne prise en compte de celle-ci permet d'améliorer de manière significative la description de la dynamique du glissement et, notamment, de prédire l'existence de chocs dans l'écoulement en amont du relief [5].…”